lectures/CH-3-Graphical-Causal-Models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 3: Graphical Causal Models\n",
    "\n",
    "## Key Points Learned in this Chapter:\n",
    "\n",
    "### 1. Graphical Causal Models: \n",
    "* DAGs represent and visualize causal relationships between variables.\n",
    "### 2. d-Separation: \n",
    "* A graphical criterion to determine conditional independence in a DAG.\n",
    "### 3. Markov Properties: \n",
    "* Describe how conditional independence is inferred from DAGs for probabilistic reasoning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "6c5bf2a9-480b-448f-bc9f-84ff3ed37c21",
    "deepnote_cell_height": 729.421875,
    "deepnote_cell_type": "markdown"
   },
   "source": [
    "---\n",
    "\n",
    "## Section 3.1. Introduction to Graphical Models\n",
    "\n",
    "### Overview of Graphical Models\n",
    "\n",
    "Graphical models provide a powerful framework for representing and reasoning about complex dependencies between variables. In causal inference, they help us visualize and formalize assumptions about causal relationships, using nodes to represent variables and edges to depict the causal influences between them.\n",
    "\n",
    "The most commonly used graphical models for causal inference are **Directed Acyclic Graphs (DAGs)**. These graphs offer a structured approach to understanding the flow of causality and are particularly useful in determining the influence of interventions, highlighting pathways for potential confounding, and uncovering mediating variables.\n",
    "\n",
    "### Types of Graphical Models\n",
    "There are various types of graphical models, each serving different purposes based on the context:\n",
    "\n",
    "* **A. Undirected Graphical Models**: Also called Markov Random Fields (MRFs), these graphs capture the dependency structure between variables but lack directionality. \n",
    "\n",
    "* **b. Directed Graphical Models**: This category includes Bayesian Networks and DAGs. These graphs capture the direction of influence, which aligns with the nature of cause and effect.\n",
    "  \n",
    "* **Partially Directed Acyclic Graphs (PDAGs) and Complete Partially Directed Acyclic Graphs (CPDAGs)**: These graphs are used when the direction of some relationships is uncertain. They are valuable in exploratory analyses where the causal structure is not fully established.\n",
    "\n",
    "While each type of graphical model has its strengths, **DAGs** are the primary focus in causal inference because they provide explicit modeling of causal directions, so we focus on them in this chapter.\n",
    "\n",
    "### Why DAGs are Essential for Causal Inference?\n",
    "\n",
    "DAGs serve as a bridge between causal assumptions and statistical data. They are crucial in several key aspects of causal inference:\n",
    "\n",
    "* **Clarity in Causal Assumptions**: DAGs allow researchers to explicitly state assumptions about which variables influence others, making the model easier to interpret and critique.\n",
    "\n",
    "* **Understanding Confounding and Bias**: One of the most powerful features of DAGs is their ability to identify potential confounders—variables that influence both the treatment and the outcome, thereby creating bias in causal estimation. DAGs help visualize and control for these confounders.\n",
    "  \n",
    "* **Testable Implications**: While some causal relationships cannot be tested directly, DAGs can identify conditional independencies that are testable using statistical methods. This makes it possible to empirically assess whether the data are consistent with the proposed causal model.\n",
    "\n",
    "\n",
    "Causal DAGs are **acyclic** because:\n",
    "    - One cannot trace a sequence of arcs in the direction of the arrows and arrive where one started.\n",
    "    - We impose acyclicness since a variable can’t cause itself.\n",
    "    - The future cannot directly or indirectly cause the past.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Section 3.2. Types of Graph Structures and their Role in Causality\n",
    "\n",
    "In causal inference, different types of Directed Acyclic Graph (DAG) structures play an essential role in representing and understanding causal relationships. Three primary types of DAG structures are commonly observed: **Fork (Confounder), Chain (Mediator), and V-Structure (Collider)**. Understanding these structures is crucial for identifying the appropriate causal pathways and dealing with potential biases like confounding or collider bias. But, we review some basic termonology or graphs that you may know from the past.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00003-5eed9118-789c-4e7e-a339-28ea8453019c",
    "deepnote_cell_height": 234.34375,
    "deepnote_cell_type": "markdown"
   },
   "source": [
    "### 3.2.1. Basic Terminologies for Graphs\n",
    "\n",
    "For our purpose, it is (very) important that we understand what kind of independence and conditional independence assumptions a graphical model entails. To understand this, let's explain some common graphical definition and structures. They will be quite simple, but they are the sufficient building blocks to understand everything about graphical models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "1d93add9-278d-4503-a633-2c0b39c78686",
    "deepnote_cell_height": 74.78125,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "**Graph:** A graph $G = (V, E)$ is a set V of vertices (nodes) and a set E of edges, which can be graphically illustrated, for example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "cell_id": "700e0795-16b7-4991-9c8d-33feb26b930e",
    "deepnote_cell_height": 381,
    "deepnote_cell_type": "code",
    "deepnote_output_heights": [
     122
    ],
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 27,
    "execution_start": 1647607230350,
    "source_hash": "ec6e9c07",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 12.1.1 (20240910.0053)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"332pt\" height=\"92pt\"\n",
       " viewBox=\"0.00 0.00 332.00 91.50\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 87.5)\">\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-87.5 328,-87.5 328,4 -4,4\"/>\n",
       "<text text-anchor=\"middle\" x=\"162\" y=\"-7.2\" font-family=\"Times,serif\" font-size=\"14.00\">A graph with nodes L, U, A, and Y</text>\n",
       "<!-- L -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>L</title>\n",
       "<ellipse fill=\"lightgrey\" stroke=\"blue\" cx=\"27\" cy=\"-42.5\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-36.7\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"blue\">L</text>\n",
       "</g>\n",
       "<!-- U -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>U</title>\n",
       "<ellipse fill=\"lightgrey\" stroke=\"blue\" cx=\"117\" cy=\"-65.5\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"117\" y=\"-59.7\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"blue\">U</text>\n",
       "</g>\n",
       "<!-- L&#45;&gt;U -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>L&#45;&gt;U</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M52.51,-48.91C64.62,-52.07 79.19,-55.88 91.31,-59.05\"/>\n",
       "</g>\n",
       "<!-- A -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>A</title>\n",
       "<ellipse fill=\"lightgrey\" stroke=\"blue\" cx=\"207\" cy=\"-42.5\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"207\" y=\"-36.7\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"blue\">A</text>\n",
       "</g>\n",
       "<!-- L&#45;&gt;A -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>L&#45;&gt;A</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M54.23,-40.43C65.26,-39.66 78.25,-38.88 90,-38.5 113.99,-37.73 120.01,-37.73 144,-38.5 151.99,-38.76 160.54,-39.2 168.67,-39.7\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"178.56,-40.35 168.28,-44.19 174.78,-40.1 168.58,-39.69 168.58,-39.69 168.58,-39.69 174.78,-40.1 168.87,-35.2 178.56,-40.35\"/>\n",
       "</g>\n",
       "<!-- U&#45;&gt;A -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>U&#45;&gt;A</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M142.51,-59.09C151.21,-56.82 161.19,-54.21 170.61,-51.75\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"180.13,-49.26 171.6,-56.14 176.48,-50.22 170.46,-51.79 170.46,-51.79 170.46,-51.79 176.48,-50.22 169.32,-47.44 180.13,-49.26\"/>\n",
       "</g>\n",
       "<!-- Y -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>Y</title>\n",
       "<ellipse fill=\"lightgrey\" stroke=\"blue\" cx=\"297\" cy=\"-42.5\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"297\" y=\"-36.7\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"blue\">Y</text>\n",
       "</g>\n",
       "<!-- A&#45;&gt;Y -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>A&#45;&gt;Y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M234.4,-42.5C241.97,-42.5 250.38,-42.5 258.48,-42.5\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"268.4,-42.5 258.4,-47 264.62,-42.5 258.4,-42.5 258.4,-42.5 258.4,-42.5 264.62,-42.5 258.4,-38 268.4,-42.5\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x146b892a0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Import the graphviz library\n",
    "import graphviz as gr\n",
    "\n",
    "# Create the graph with consistent styling\n",
    "g = gr.Digraph(graph_attr={'rankdir': 'LR', 'label': \"A graph with nodes L, U, A, and Y\"}, \n",
    "               edge_attr={'arrowhead': 'vee', 'arrowsize': '1'})\n",
    "\n",
    "# Add nodes with consistent style: blue color, bold, and font\n",
    "g.node(\"L\", \"L\", color=\"blue\", fontcolor=\"blue\", style=\"filled\", fillcolor=\"lightgrey\", fontname=\"Helvetica\")\n",
    "g.node(\"U\", \"U\", color=\"blue\", fontcolor=\"blue\", style=\"filled\", fillcolor=\"lightgrey\", fontname=\"Helvetica\")\n",
    "g.node(\"A\", \"A\", color=\"blue\", fontcolor=\"blue\", style=\"filled\", fillcolor=\"lightgrey\", fontname=\"Helvetica\")\n",
    "g.node(\"Y\", \"Y\", color=\"blue\", fontcolor=\"blue\", style=\"filled\", fillcolor=\"lightgrey\", fontname=\"Helvetica\")\n",
    "\n",
    "# Add edges with consistent edge attributes\n",
    "g.edge(\"L\", \"U\", dir=\"none\")\n",
    "g.edge(\"L\", \"A\")\n",
    "g.edge(\"U\", \"A\")\n",
    "g.edge(\"A\", \"Y\")\n",
    "\n",
    "# Render the graph\n",
    "g\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "b8d1e253-e1dc-46bf-b48c-c126e0f2b6ca",
    "deepnote_cell_height": 382.6875,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "**Nodes:** typically represent random variables.\n",
    "\n",
    "**Edges (arrows):** can be undirected, directed or bi-directed and typically indicate a certain relationship between nodes or possible direct causal effects.\n",
    "\n",
    "**Path:** A trail of edges going from one node to another, not necessarily following the direction of arrows. a path cannot cross a node more than once.\n",
    "\n",
    "**Cyclic Graph:** A cyclic graph has at least one path that can be followed through directed edges back to the original node​\n",
    "\n",
    "**Acyclic Graph:** An acyclic graph is a graph that contains no such cycles.\n",
    "\n",
    "<br/>\n",
    "\n",
    "### Example: Paths in a Graph\n",
    "\n",
    "What are paths from $X$ to $C$ in the following graph?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 351,
   "metadata": {
    "cell_id": "6043cb7b-c4fd-4bd0-b069-35b9bc3aff93",
    "deepnote_cell_height": 518,
    "deepnote_cell_type": "code",
    "deepnote_output_heights": [
     187
    ],
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 42,
    "execution_start": 1647607230380,
    "source_hash": "1abe9b0d",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 12.1.1 (20240910.0053)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"422pt\" height=\"139pt\"\n",
       " viewBox=\"0.00 0.00 422.00 138.95\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 134.95)\">\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-134.95 418,-134.95 418,4 -4,4\"/>\n",
       "<!-- X -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>X</title>\n",
       "<ellipse fill=\"none\" stroke=\"blue\" cx=\"117\" cy=\"-76.95\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"117\" y=\"-71.9\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"blue\">X</text>\n",
       "</g>\n",
       "<!-- C -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>C</title>\n",
       "<ellipse fill=\"none\" stroke=\"blue\" cx=\"297\" cy=\"-68.95\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"297\" y=\"-63.9\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"blue\">C</text>\n",
       "</g>\n",
       "<!-- X&#45;&gt;C -->\n",
       "<g id=\"edge8\" class=\"edge\">\n",
       "<title>X&#45;&gt;C</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M144.26,-75.77C174.5,-74.41 224.39,-72.16 258.66,-70.62\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"268.41,-70.19 258.62,-75.13 264.63,-70.36 258.42,-70.64 258.42,-70.64 258.42,-70.64 264.63,-70.36 258.22,-66.14 268.41,-70.19\"/>\n",
       "</g>\n",
       "<!-- Y -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>Y</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"387\" cy=\"-91.95\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"387\" y=\"-86.9\" font-family=\"Times,serif\" font-size=\"14.00\">Y</text>\n",
       "</g>\n",
       "<!-- X&#45;&gt;Y -->\n",
       "<g id=\"edge9\" class=\"edge\">\n",
       "<title>X&#45;&gt;Y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M143.59,-81.43C154.75,-83.29 168,-85.38 180,-86.95 243.59,-95.25 259.91,-98.01 324,-95.95 331.99,-95.69 340.54,-95.25 348.67,-94.75\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"358.56,-94.09 348.87,-99.24 354.78,-94.34 348.58,-94.75 348.58,-94.75 348.58,-94.75 354.78,-94.34 348.28,-90.26 358.56,-94.09\"/>\n",
       "</g>\n",
       "<!-- T -->\n",
       "<g id=\"node6\" class=\"node\">\n",
       "<title>T</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"207\" cy=\"-30.95\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"207\" y=\"-25.9\" font-family=\"Times,serif\" font-size=\"14.00\">T</text>\n",
       "</g>\n",
       "<!-- X&#45;&gt;T -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>X&#45;&gt;T</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M138.85,-66.04C149.73,-60.36 163.25,-53.29 175.3,-46.99\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"183.91,-42.49 177.13,-51.11 180.56,-44.25 175.05,-47.13 175.05,-47.13 175.05,-47.13 180.56,-44.25 172.96,-43.14 183.91,-42.49\"/>\n",
       "</g>\n",
       "<!-- C&#45;&gt;Y -->\n",
       "<g id=\"edge7\" class=\"edge\">\n",
       "<title>C&#45;&gt;Y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M322.51,-75.35C331.21,-77.63 341.19,-80.23 350.61,-82.7\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"360.13,-85.19 349.32,-87.01 356.48,-84.23 350.46,-82.66 350.46,-82.66 350.46,-82.66 356.48,-84.23 351.6,-78.3 360.13,-85.19\"/>\n",
       "</g>\n",
       "<!-- U1 -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>U1</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-112.95\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-107.9\" font-family=\"Times,serif\" font-size=\"14.00\">U1</text>\n",
       "</g>\n",
       "<!-- U1&#45;&gt;X -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>U1&#45;&gt;X</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M50.66,-103.68C60.52,-99.64 72.25,-94.84 83.04,-90.43\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"92.29,-86.65 84.74,-94.6 88.79,-88.08 83.03,-90.43 83.03,-90.43 83.03,-90.43 88.79,-88.08 81.33,-86.27 92.29,-86.65\"/>\n",
       "</g>\n",
       "<!-- U1&#45;&gt;Y -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>U1&#45;&gt;Y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M53.92,-115.03C105.62,-118.68 225.11,-124.52 324,-109.95 333.3,-108.58 343.17,-106.17 352.22,-103.56\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"361.62,-100.67 353.38,-107.91 358,-101.78 352.06,-103.61 352.06,-103.61 352.06,-103.61 358,-101.78 350.74,-99.3 361.62,-100.67\"/>\n",
       "</g>\n",
       "<!-- U2 -->\n",
       "<g id=\"node5\" class=\"node\">\n",
       "<title>U2</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-39.95\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-34.9\" font-family=\"Times,serif\" font-size=\"14.00\">U2</text>\n",
       "</g>\n",
       "<!-- U2&#45;&gt;X -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>U2&#45;&gt;X</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M50.21,-49.28C60.24,-53.5 72.29,-58.57 83.33,-63.21\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"92.37,-67.01 81.41,-67.28 88.89,-65.55 83.15,-63.14 83.15,-63.14 83.15,-63.14 88.89,-65.55 84.9,-58.99 92.37,-67.01\"/>\n",
       "</g>\n",
       "<!-- U2&#45;&gt;Y -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>U2&#45;&gt;Y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M50.33,-30.57C88.21,-15.89 167.46,9.53 234,-3.95 276.56,-12.56 286.74,-19.66 324,-41.95 337.39,-49.96 351.02,-60.62 362.08,-70.04\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"369.43,-76.45 358.93,-73.27 366.58,-73.97 361.89,-69.88 361.89,-69.88 361.89,-69.88 366.58,-73.97 364.85,-66.49 369.43,-76.45\"/>\n",
       "</g>\n",
       "<!-- T&#45;&gt;C -->\n",
       "<g id=\"edge6\" class=\"edge\">\n",
       "<title>T&#45;&gt;C</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M230.21,-40.54C240.32,-44.9 252.48,-50.15 263.58,-54.95\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"272.68,-58.88 261.72,-59.04 269.21,-57.38 263.5,-54.91 263.5,-54.91 263.5,-54.91 269.21,-57.38 265.29,-50.78 272.68,-58.88\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x2abf16b00>"
      ]
     },
     "execution_count": 351,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = gr.Digraph(graph_attr={'rankdir':'LR'}, \n",
    "               edge_attr={'arrowhead':'vee', 'arrowsize':'1'})\n",
    "g.node(\"X\", \"X\", color=\"blue\", fontcolor=\"blue\")\n",
    "g.node(\"C\", \"C\", color=\"blue\", fontcolor=\"blue\")\n",
    "g.edge(\"U1\", \"Y\")\n",
    "g.edge(\"U1\", \"X\")\n",
    "g.edge(\"U2\", \"X\")\n",
    "g.edge(\"U2\", \"Y\")\n",
    "g.edge(\"X\", \"T\")\n",
    "g.edge(\"T\", \"C\")\n",
    "g.edge(\"C\", \"Y\")\n",
    "g.edge(\"X\", \"C\")\n",
    "g.edge(\"X\", \"Y\")\n",
    "g"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "54c7d2fe-eaf9-400c-bedb-8e7dcf68b30c",
    "deepnote_cell_height": 153.5625,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "Paths from $X$ to $C$ are:\n",
    "\n",
    "- $ X \\rightarrow C$\n",
    "- $ X \\rightarrow T \\rightarrow C$\n",
    "- $ X \\rightarrow U_2 \\rightarrow Y \\rightarrow C$\n",
    "- $ X \\rightarrow U_1 \\rightarrow Y \\rightarrow C$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "c2281eb1-f83b-4845-8672-1a0b63f181f0",
    "deepnote_cell_height": 242.734375,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "### More Terminologies:\n",
    "\n",
    "**Children and Parents:** Nodes directly affected by and affecting other nodes respectively.​\n",
    "\n",
    "**Ancestors and Descendants:** Nodes directly or indirectly affected by and affecting other nodes\n",
    "\n",
    "**Exogenous and Endogenous Nodes:** Nodes without and with parents respectively​\n",
    "\n",
    "\n",
    "### Example: Parentship in a Graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 354,
   "metadata": {
    "cell_id": "5fb1a843-4c68-4d0b-82a2-ff6b019f20c0",
    "deepnote_cell_height": 496,
    "deepnote_cell_type": "code",
    "deepnote_output_heights": [
     183
    ],
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 31,
    "execution_start": 1647607230430,
    "source_hash": "4a339dca",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 12.1.1 (20240910.0053)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"422pt\" height=\"136pt\"\n",
       " viewBox=\"0.00 0.00 422.00 135.72\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 131.72)\">\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-131.72 418,-131.72 418,4 -4,4\"/>\n",
       "<!-- T -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>T</title>\n",
       "<ellipse fill=\"none\" stroke=\"blue\" cx=\"207\" cy=\"-97\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"207\" y=\"-91.95\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"blue\">T</text>\n",
       "</g>\n",
       "<!-- C -->\n",
       "<g id=\"node6\" class=\"node\">\n",
       "<title>C</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"297\" cy=\"-59\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"297\" y=\"-53.95\" font-family=\"Times,serif\" font-size=\"14.00\">C</text>\n",
       "</g>\n",
       "<!-- T&#45;&gt;C -->\n",
       "<g id=\"edge6\" class=\"edge\">\n",
       "<title>T&#45;&gt;C</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M230.21,-87.41C240.32,-83.05 252.48,-77.79 263.58,-73\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"272.68,-69.07 265.29,-77.16 269.21,-70.57 263.5,-73.03 263.5,-73.03 263.5,-73.03 269.21,-70.57 261.72,-68.9 272.68,-69.07\"/>\n",
       "</g>\n",
       "<!-- U1 -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>U1</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-83\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-77.95\" font-family=\"Times,serif\" font-size=\"14.00\">U1</text>\n",
       "</g>\n",
       "<!-- Y -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>Y</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"387\" cy=\"-36\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"387\" y=\"-30.95\" font-family=\"Times,serif\" font-size=\"14.00\">Y</text>\n",
       "</g>\n",
       "<!-- U1&#45;&gt;Y -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>U1&#45;&gt;Y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M49.96,-93.15C87.63,-109.27 166.99,-137.57 234,-124 276.56,-115.38 286.74,-108.29 324,-86 337.39,-77.99 351.02,-67.33 362.08,-57.91\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"369.43,-51.49 364.85,-61.46 366.58,-53.98 361.89,-58.07 361.89,-58.07 361.89,-58.07 366.58,-53.98 358.93,-54.68 369.43,-51.49\"/>\n",
       "</g>\n",
       "<!-- X -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>X</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"117\" cy=\"-51\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"117\" y=\"-45.95\" font-family=\"Times,serif\" font-size=\"14.00\">X</text>\n",
       "</g>\n",
       "<!-- U1&#45;&gt;X -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>U1&#45;&gt;X</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M51.12,-74.59C60.65,-71.13 71.87,-67.05 82.28,-63.26\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"91.58,-59.88 83.72,-67.53 88.03,-61.17 82.18,-63.3 82.18,-63.3 82.18,-63.3 88.03,-61.17 80.65,-59.07 91.58,-59.88\"/>\n",
       "</g>\n",
       "<!-- X&#45;&gt;T -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>X&#45;&gt;T</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M138.85,-61.9C149.73,-67.59 163.25,-74.66 175.3,-80.95\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"183.91,-85.45 172.96,-84.81 180.56,-83.7 175.05,-80.82 175.05,-80.82 175.05,-80.82 180.56,-83.7 177.13,-76.83 183.91,-85.45\"/>\n",
       "</g>\n",
       "<!-- X&#45;&gt;Y -->\n",
       "<g id=\"edge9\" class=\"edge\">\n",
       "<title>X&#45;&gt;Y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M143.73,-46.79C173.88,-42.09 225.41,-34.78 270,-32 293.95,-30.51 300.01,-31.23 324,-32 331.99,-32.26 340.54,-32.7 348.67,-33.2\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"358.56,-33.85 348.28,-37.69 354.78,-33.6 348.58,-33.19 348.58,-33.19 348.58,-33.19 354.78,-33.6 348.87,-28.7 358.56,-33.85\"/>\n",
       "</g>\n",
       "<!-- X&#45;&gt;C -->\n",
       "<g id=\"edge8\" class=\"edge\">\n",
       "<title>X&#45;&gt;C</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M144.26,-52.18C174.5,-53.54 224.39,-55.78 258.66,-57.32\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"268.41,-57.76 258.22,-61.81 264.63,-57.59 258.42,-57.31 258.42,-57.31 258.42,-57.31 264.63,-57.59 258.62,-52.82 268.41,-57.76\"/>\n",
       "</g>\n",
       "<!-- U2 -->\n",
       "<g id=\"node5\" class=\"node\">\n",
       "<title>U2</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\">U2</text>\n",
       "</g>\n",
       "<!-- U2&#45;&gt;Y -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>U2&#45;&gt;Y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M54.19,-17.8C105.89,-17.62 224.64,-18.31 324,-27 332.27,-27.72 341.12,-28.82 349.46,-29.99\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"359.23,-31.44 348.68,-34.42 355.49,-30.89 349.34,-29.97 349.34,-29.97 349.34,-29.97 355.49,-30.89 350,-25.52 359.23,-31.44\"/>\n",
       "</g>\n",
       "<!-- U2&#45;&gt;X -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>U2&#45;&gt;X</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M51.12,-26.67C60.82,-30.31 72.29,-34.61 82.86,-38.57\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"91.89,-41.96 80.95,-42.66 88.35,-40.63 82.53,-38.45 82.53,-38.45 82.53,-38.45 88.35,-40.63 84.11,-34.23 91.89,-41.96\"/>\n",
       "</g>\n",
       "<!-- C&#45;&gt;Y -->\n",
       "<g id=\"edge7\" class=\"edge\">\n",
       "<title>C&#45;&gt;Y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M322.51,-52.59C331.21,-50.32 341.19,-47.71 350.61,-45.25\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"360.13,-42.76 351.6,-49.64 356.48,-43.72 350.46,-45.29 350.46,-45.29 350.46,-45.29 356.48,-43.72 349.32,-40.94 360.13,-42.76\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x2abf17cd0>"
      ]
     },
     "execution_count": 354,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = gr.Digraph(graph_attr={'rankdir':'LR'}, \n",
    "               edge_attr={'arrowhead':'vee', 'arrowsize':'1'})\n",
    "g.node(\"T\", \"T\", color=\"blue\", fontcolor=\"blue\")\n",
    "g.edge(\"U1\", \"Y\")\n",
    "g.edge(\"U1\", \"X\")\n",
    "g.edge(\"U2\", \"X\")\n",
    "g.edge(\"U2\", \"Y\")\n",
    "g.edge(\"X\", \"T\")\n",
    "g.edge(\"T\", \"C\")\n",
    "g.edge(\"C\", \"Y\")\n",
    "g.edge(\"X\", \"C\")\n",
    "g.edge(\"X\", \"Y\")\n",
    "g"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "7d209a97-7341-41a3-b9c6-7120508fa8a4",
    "deepnote_cell_height": 220.34375,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "Here are parental relations in the graph:\n",
    "\n",
    "**Parents:** $pa(T) = \\{ X \\}$​\n",
    "\n",
    "**Children:** $ch(T) = \\{ C \\}$​\n",
    "\n",
    "**Ancestors:** $anc(T) = \\{ X, U_1, U_2 \\}$​\n",
    "\n",
    "**Descendants:** $desc(T) = \\{ C, Y \\}$​\n",
    "\n",
    "<br/><br/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### 3.2.2. Major DAG Structures\n",
    "\n",
    "Three primary types of DAG structures are commonly observed: **Fork (Confounder), Chain (Mediator), and V-Structure (Collider)**. Understanding these structures is crucial for identifying the appropriate causal pathways and dealing with potential biases like confounding or collider bias.\n",
    "\n",
    "\n",
    "### Major DAG Structure 1: Fork (Confounder)\n",
    "\n",
    "A **fork structure** occurs when a common cause (or confounder) affects both the treatment and the outcome. This type of structure is represented as:\n",
    "\n",
    "- $A ← C → B$, where:\n",
    "  - $C$ is the confounder.\n",
    "  - $C$ is a common cause of $A$ and $B$. \n",
    "  - $A$ and $B$ are both influenced by $C$.\n",
    "  - $A$ and $B$ have a common cause (direct or indirect). \n",
    "  - $A$ and $B$ are often referred to as \"children\" or \"descendants\" of the common cause."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 357,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 12.1.1 (20240910.0053)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"134pt\" height=\"116pt\"\n",
       " viewBox=\"0.00 0.00 134.00 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-112 130,-112 130,4 -4,4\"/>\n",
       "<!-- C -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>C</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"63\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"63\" y=\"-84.95\" font-family=\"Times,serif\" font-size=\"14.00\">C</text>\n",
       "</g>\n",
       "<!-- A -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>A</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\">A</text>\n",
       "</g>\n",
       "<!-- C&#45;&gt;A -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>C&#45;&gt;A</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M54.65,-72.76C50.42,-64.55 45.19,-54.37 40.42,-45.09\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"43.68,-43.79 36,-36.49 37.46,-46.99 43.68,-43.79\"/>\n",
       "</g>\n",
       "<!-- B -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>B</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"99\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\">B</text>\n",
       "</g>\n",
       "<!-- C&#45;&gt;B -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>C&#45;&gt;B</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M71.35,-72.76C75.58,-64.55 80.81,-54.37 85.58,-45.09\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"88.54,-46.99 90,-36.49 82.32,-43.79 88.54,-46.99\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x2abf166e0>"
      ]
     },
     "execution_count": 357,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "import graphviz as gr\n",
    "\n",
    "# Create a fork structure (confounder)\n",
    "fork_dag = gr.Digraph()\n",
    "\n",
    "# Add edges\n",
    "fork_dag.edge(\"C\", \"A\")\n",
    "fork_dag.edge(\"C\", \"B\")\n",
    "\n",
    "# Render the graph\n",
    "fork_dag\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Since Fork $C$ is a common cause of $A$ and $B$, $A$ and $B$ are not independent in general.\n",
    "\n",
    "    $A \\not\\!\\perp\\!\\!\\!\\perp B$ \n",
    "\n",
    "- In fork structure, the dependence flows backward through the arrows and we have what is called a **backdoor path**. \n",
    "\n",
    "- We can close the backdoor path and shut down dependence by conditioning on the common cause.\n",
    "\n",
    "    $A \\!\\perp\\!\\!\\!\\perp B | C$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 359,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 12.1.1 (20240910.0053)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"134pt\" height=\"116pt\"\n",
       " viewBox=\"0.00 0.00 134.00 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-112 130,-112 130,4 -4,4\"/>\n",
       "<!-- C -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>C</title>\n",
       "<ellipse fill=\"none\" stroke=\"red\" cx=\"63\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"63\" y=\"-84.95\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"red\">C</text>\n",
       "</g>\n",
       "<!-- A -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>A</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\">A</text>\n",
       "</g>\n",
       "<!-- C&#45;&gt;A -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>C&#45;&gt;A</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M54.65,-72.76C50.42,-64.55 45.19,-54.37 40.42,-45.09\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"43.68,-43.79 36,-36.49 37.46,-46.99 43.68,-43.79\"/>\n",
       "</g>\n",
       "<!-- B -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>B</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"99\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\">B</text>\n",
       "</g>\n",
       "<!-- C&#45;&gt;B -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>C&#45;&gt;B</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M71.35,-72.76C75.58,-64.55 80.81,-54.37 85.58,-45.09\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"88.54,-46.99 90,-36.49 82.32,-43.79 88.54,-46.99\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x2abf2cb50>"
      ]
     },
     "execution_count": 359,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz as gr\n",
    "\n",
    "# Create a fork structure (confounder)\n",
    "fork_dag = gr.Digraph()\n",
    "\n",
    "# Add node C with red border and label\n",
    "fork_dag.node(\"C\", color=\"red\", fontcolor=\"red\")\n",
    "\n",
    "# Add edges\n",
    "fork_dag.edge(\"C\", \"A\")\n",
    "fork_dag.edge(\"C\", \"B\")\n",
    "\n",
    "# Render the graph\n",
    "fork_dag\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fork Bias\n",
    "- Forks represent situations where two variables appear to be associated or correlated, but the association is not due to a direct causal relationship between them. Instead, the association is induced by the shared influence of the common cause.\n",
    "\n",
    "- Failure to address a fork confounder can lead to biased estimates of the causal effect between the treatment and outcome. Neglecting the confounder can result in mistakenly attributing the observed association to a direct causal effect, when it is actually due, at least in part, to the unmeasured confounder.\n",
    "  \n",
    "- This bias is also called **[confounding bias](https://catalogofbias.org/biases/confounding/)**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Confounder Structure Example: Ice Cream Consumption, Sunburns, and Hot Temperature\n",
    "\n",
    "In hot summer months, people tend to consume more ice cream and are also more likely to get sunburns. While it might seem that **Ice Cream Consumption** and **Number of Sunburns** are related, this relationship is actually driven by a third variable, **Hot Temperature**. \n",
    "\n",
    "<img src=\"img/ch3/IceCream-Sunburn.png\" alt=\"img\" width=\"500\"/>\n",
    "\n",
    "This is an example of a **fork structure** where **Hot Temperature (T)** is the common cause (confounder) that influences both **Ice Cream Consumption (I)** and **Number of Sunburns (S)**. Understanding this structure helps to avoid drawing spurious conclusions about the relationship between **I** and **S**.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 362,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 12.1.1 (20240910.0053)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"410pt\" height=\"116pt\"\n",
       " viewBox=\"0.00 0.00 409.76 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-112 405.76,-112 405.76,4 -4,4\"/>\n",
       "<!-- T -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>T</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"207.53\" cy=\"-90\" rx=\"74.38\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"207.53\" y=\"-84.95\" font-family=\"Times,serif\" font-size=\"14.00\">Hot Temperature</text>\n",
       "</g>\n",
       "<!-- I -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>I</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"102.53\" cy=\"-18\" rx=\"102.53\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"102.53\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\">Ice Cream Consumption</text>\n",
       "</g>\n",
       "<!-- T&#45;&gt;I -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>T&#45;&gt;I</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M182.91,-72.59C169.29,-63.51 152.14,-52.07 137.18,-42.1\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"139.25,-39.27 128.98,-36.63 135.36,-45.09 139.25,-39.27\"/>\n",
       "</g>\n",
       "<!-- S -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>S</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"312.53\" cy=\"-18\" rx=\"89.23\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"312.53\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\">Number of Sunburns</text>\n",
       "</g>\n",
       "<!-- T&#45;&gt;S -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>T&#45;&gt;S</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M232.15,-72.59C245.87,-63.44 263.18,-51.9 278.21,-41.88\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"280.07,-44.85 286.45,-36.39 276.18,-39.03 280.07,-44.85\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x2abf2e8c0>"
      ]
     },
     "execution_count": 362,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### 1. Visualize the DAG (Fork Structure)\n",
    "import graphviz as gr\n",
    "\n",
    "# Create a fork structure for Ice Cream and Sunburns example\n",
    "fork_dag = gr.Digraph()\n",
    "\n",
    "# Add nodes\n",
    "fork_dag.node(\"T\", label=\"Hot Temperature\", color=\"black\", fontcolor=\"black\")\n",
    "fork_dag.node(\"I\", label=\"Ice Cream Consumption\", color=\"black\", fontcolor=\"black\")\n",
    "fork_dag.node(\"S\", label=\"Number of Sunburns\", color=\"black\", fontcolor=\"black\")\n",
    "\n",
    "# Add edges representing the fork structure\n",
    "fork_dag.edge(\"T\", \"I\")  # Hot Temperature influences Ice Cream Consumption\n",
    "fork_dag.edge(\"T\", \"S\")  # Hot Temperature influences Number of Sunburns\n",
    "\n",
    "# Render the graph\n",
    "fork_dag"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulate Data:\n",
    "Let's generate synthetic data for the three variables:\n",
    "- **Hot Temperature (T)** drives both **Ice Cream Consumption (I)** and **Number of Sunburns (S)**.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 364,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Hot Temperature</th>\n",
       "      <th>Ice Cream Consumption</th>\n",
       "      <th>Number of Sunburns</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>32.483571</td>\n",
       "      <td>57.890288</td>\n",
       "      <td>49.798718</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>29.308678</td>\n",
       "      <td>56.514130</td>\n",
       "      <td>45.645371</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>33.238443</td>\n",
       "      <td>64.763313</td>\n",
       "      <td>53.106818</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>37.615149</td>\n",
       "      <td>71.218912</td>\n",
       "      <td>59.584130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>28.829233</td>\n",
       "      <td>56.852038</td>\n",
       "      <td>39.110842</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Hot Temperature  Ice Cream Consumption  Number of Sunburns\n",
       "0        32.483571              57.890288           49.798718\n",
       "1        29.308678              56.514130           45.645371\n",
       "2        33.238443              64.763313           53.106818\n",
       "3        37.615149              71.218912           59.584130\n",
       "4        28.829233              56.852038           39.110842"
      ]
     },
     "execution_count": 364,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "# Set seed for reproducibility\n",
    "np.random.seed(42)\n",
    "\n",
    "# Simulating Hot Temperature (T)\n",
    "hot_temperature = np.random.normal(loc=30, scale=5, size=100)  # Average temperature of 30 degrees with some variation\n",
    "\n",
    "# Simulating Ice Cream Consumption (I) based on Temperature (T)\n",
    "ice_cream_consumption = 2 * hot_temperature + np.random.normal(loc=0, scale=5, size=100)  # Higher temperature, more ice cream\n",
    "\n",
    "# Simulating Number of Sunburns (S) based on Temperature (T)\n",
    "number_of_sunburns = 1.5 * hot_temperature + np.random.normal(loc=0, scale=3, size=100)  # Higher temperature, more sunburns\n",
    "\n",
    "# Creating a DataFrame for the data\n",
    "data = pd.DataFrame({\n",
    "    'Hot Temperature': hot_temperature,\n",
    "    'Ice Cream Consumption': ice_cream_consumption,\n",
    "    'Number of Sunburns': number_of_sunburns\n",
    "})\n",
    "\n",
    "# Display the first few rows of the dataset\n",
    "data.head()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Explore Relationships\n",
    "We now use a scatter plot matrix to visualize the pairwise relationships between **Hot Temperature**, **Ice Cream Consumption**, and **Number of Sunburns**.\n",
    "\n",
    "${Ice\\ Cream\\ Consumption} \\not\\!\\perp\\!\\!\\!\\perp {Number\\ of\\ Sunburns} $ \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 366,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 750x750 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualizing the scatter plot matrix\n",
    "sns.pairplot(data)\n",
    "plt.suptitle(\"Scatter Plot Matrix: Ice Cream Consumption, Sunburns, and Hot Temperature\", y=1.02)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Observations\n",
    "\n",
    "From the **scatter plot matrix**, you can observe:\n",
    "- **Hot Temperature** has a positive correlation with both **Ice Cream Consumption** and **Number of Sunburns**. This makes sense because hotter days lead to more ice cream consumption and an increased likelihood of sunburns.\n",
    "- There may also appear to be a correlation between **Ice Cream Consumption** and **Number of Sunburns**. However, this is a spurious correlation driven by the confounding effect of **Hot Temperature**. \n",
    "\n",
    "Without accounting for **Hot Temperature**, we might mistakenly conclude that eating more ice cream causes sunburns, but the true underlying cause is the hotter weather.\n",
    "\n",
    "### Conditioning on the confunder (Hot Temperature)\n",
    "\n",
    "Now, let condition on the confunder, **Hot Temperature**:\n",
    "\n",
    "${Ice\\ Cream\\ Consumption} \\!\\perp\\!\\!\\!\\perp {Number\\ of\\ Sunburns} | {Hot\\ Temperature}$ \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 368,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x500 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation between Ice Cream Consumption and Sunburns after conditioning on Temperature:\n",
      "                                   Ice Cream Residuals (Conditioned)  \\\n",
      "Ice Cream Residuals (Conditioned)                            1.00000   \n",
      "Sunburns Residuals (Conditioned)                            -0.10736   \n",
      "\n",
      "                                   Sunburns Residuals (Conditioned)  \n",
      "Ice Cream Residuals (Conditioned)                          -0.10736  \n",
      "Sunburns Residuals (Conditioned)                            1.00000  \n"
     ]
    }
   ],
   "source": [
    "# Import required libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# Re-define variables from the first part\n",
    "\n",
    "# Simulating Hot Temperature (T)\n",
    "hot_temperature = np.random.normal(loc=30, scale=5, size=100)  # Average temperature of 30 degrees with some variation\n",
    "\n",
    "# Simulating Ice Cream Consumption (I) based on Temperature (T)\n",
    "ice_cream_consumption = 2 * hot_temperature + np.random.normal(loc=0, scale=5, size=100)  # Higher temperature, more ice cream\n",
    "\n",
    "# Simulating Number of Sunburns (S) based on Temperature (T)\n",
    "number_of_sunburns = 1.5 * hot_temperature + np.random.normal(loc=0, scale=3, size=100)  # Higher temperature, more sunburns\n",
    "\n",
    "# Conditioning on the confounder (Temperature)\n",
    "\n",
    "# Regress Ice Cream Consumption on Temperature\n",
    "ice_cream_residuals = ice_cream_consumption - LinearRegression().fit(hot_temperature.reshape(-1, 1), ice_cream_consumption).predict(hot_temperature.reshape(-1, 1))\n",
    "\n",
    "# Regress Number of Sunburns on Temperature\n",
    "sunburns_residuals = number_of_sunburns - LinearRegression().fit(hot_temperature.reshape(-1, 1), number_of_sunburns).predict(hot_temperature.reshape(-1, 1))\n",
    "\n",
    "# Create a DataFrame of the residuals\n",
    "residuals_data = pd.DataFrame({\n",
    "    'Ice Cream Residuals (Conditioned)': ice_cream_residuals,\n",
    "    'Sunburns Residuals (Conditioned)': sunburns_residuals\n",
    "})\n",
    "\n",
    "# Visualize residuals (relationship after conditioning)\n",
    "sns.pairplot(residuals_data)\n",
    "plt.suptitle(\"Residuals (Conditioned on Temperature)\", y=1.02)\n",
    "plt.show()\n",
    "\n",
    "# Correlation matrix after conditioning\n",
    "correlation_after = residuals_data.corr()\n",
    "print(\"Correlation between Ice Cream Consumption and Sunburns after conditioning on Temperature:\")\n",
    "print(correlation_after)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Independence After Conditioning**: The scatter plot and correlation matrix show that the correlation between Ice Cream Consumption and Sunburns is near zero (-0.003), indicating that after removing the effect of Temperature, the two variables are effectively independent. This confirms that the initial observed correlation was due to the common influence of Temperature.\n",
    "\n",
    "**Residuals Visualization**: The residuals' scatter plot is a cloud of points with no clear pattern, which visually confirms that Ice Cream Consumption and Sunburns have no direct relationship after adjusting for Temperature. This supports the concept that conditioning on a confounder (in this case, Temperature) can remove spurious correlations between two otherwise unrelated variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### Major DAG Structure 2: Chain (Mediator)\n",
    "\n",
    "A **chain structure** represents a causal pathway where one variable transmits the effect of the cause to the outcome. This structure is represented as:\n",
    "\n",
    "- $A → C → B$, where:\n",
    "  - $A$ is the cause.\n",
    "  - $C$ is the mediator.\n",
    "  - $B$ is the outcome.\n",
    "  - A node $C$ is a mediator if it lies on a directed path from $A$ to $B$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 371,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 12.1.1 (20240910.0053)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"62pt\" height=\"188pt\"\n",
       " viewBox=\"0.00 0.00 62.00 188.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 184)\">\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-184 58,-184 58,4 -4,4\"/>\n",
       "<!-- A -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>A</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-156.95\" font-family=\"Times,serif\" font-size=\"14.00\">A</text>\n",
       "</g>\n",
       "<!-- C -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>C</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-84.95\" font-family=\"Times,serif\" font-size=\"14.00\">C</text>\n",
       "</g>\n",
       "<!-- A&#45;&gt;C -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>A&#45;&gt;C</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M27,-143.7C27,-136.41 27,-127.73 27,-119.54\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"30.5,-119.62 27,-109.62 23.5,-119.62 30.5,-119.62\"/>\n",
       "</g>\n",
       "<!-- B -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>B</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\">B</text>\n",
       "</g>\n",
       "<!-- C&#45;&gt;B -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>C&#45;&gt;B</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M27,-71.7C27,-64.41 27,-55.73 27,-47.54\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"30.5,-47.62 27,-37.62 23.5,-47.62 30.5,-47.62\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x2a9a64df0>"
      ]
     },
     "execution_count": 371,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a chain structure (mediator)\n",
    "chain_dag = gr.Digraph()\n",
    "\n",
    "# Add edges\n",
    "chain_dag.edge(\"A\", \"C\")\n",
    "chain_dag.edge(\"C\", \"B\")\n",
    "\n",
    "# Render the graph\n",
    "chain_dag\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a general rule, the dependence flow in the direct path from $A$ to $B$ is blocked when we condition on an intermediary variable $C$.\n",
    "\n",
    "  - $A \\not\\!\\perp\\!\\!\\!\\perp B$   \n",
    "\n",
    "  - $A \\!\\perp\\!\\!\\!\\perp B | C$ \n",
    "\n",
    "In this case, $C$ mediates the relationship between $A$ and $B$. It is important to distinguish this indirect path from a direct causal effect between $A$ and $B$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 373,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 12.1.1 (20240910.0053)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"62pt\" height=\"188pt\"\n",
       " viewBox=\"0.00 0.00 62.00 188.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 184)\">\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-184 58,-184 58,4 -4,4\"/>\n",
       "<!-- C -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>C</title>\n",
       "<ellipse fill=\"none\" stroke=\"red\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-84.95\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"red\">C</text>\n",
       "</g>\n",
       "<!-- B -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>B</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\">B</text>\n",
       "</g>\n",
       "<!-- C&#45;&gt;B -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>C&#45;&gt;B</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M27,-71.7C27,-64.41 27,-55.73 27,-47.54\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"30.5,-47.62 27,-37.62 23.5,-47.62 30.5,-47.62\"/>\n",
       "</g>\n",
       "<!-- A -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>A</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-156.95\" font-family=\"Times,serif\" font-size=\"14.00\">A</text>\n",
       "</g>\n",
       "<!-- A&#45;&gt;C -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>A&#45;&gt;C</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M27,-143.7C27,-136.41 27,-127.73 27,-119.54\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"30.5,-119.62 27,-109.62 23.5,-119.62 30.5,-119.62\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x2aa2b46d0>"
      ]
     },
     "execution_count": 373,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz as gr\n",
    "\n",
    "# Create a chain structure (mediator)\n",
    "chain_dag = gr.Digraph()\n",
    "\n",
    "# Add node C with red border and red font\n",
    "chain_dag.node(\"C\", color=\"red\", fontcolor=\"red\")\n",
    "\n",
    "# Add edges representing the chain structure\n",
    "chain_dag.edge(\"A\", \"C\")\n",
    "chain_dag.edge(\"C\", \"B\")\n",
    "\n",
    "# Render the graph\n",
    "chain_dag"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Chain Structure Example: Exercise, Weight Loss, and Heart Health\n",
    "\n",
    "### Background:\n",
    "In this example, we explore how **Exercise** leads to **Weight Loss**, which in turn improves **Heart Health**. This represents a **chain structure**, where **Exercise (X)** influences **Weight Loss (M)**, and **Weight Loss** mediates the effect of **Exercise** on **Heart Health (Y)**.\n",
    "\n",
    "This scenario helps illustrate mediation, where the effect of Exercise on Heart Health is both direct and indirect, through the intermediate variable of Weight Loss.\n",
    "\n",
    "- **Exercise (X)** → leads to → **Weight Loss (M)** → leads to → **Improved Heart Health (Y)**.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 375,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 12.1.1 (20240910.0053)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"125pt\" height=\"188pt\"\n",
       " viewBox=\"0.00 0.00 125.03 188.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 184)\">\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-184 121.03,-184 121.03,4 -4,4\"/>\n",
       "<!-- X -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>X</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"58.52\" cy=\"-162\" rx=\"42.65\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"58.52\" y=\"-156.95\" font-family=\"Times,serif\" font-size=\"14.00\">Exercise</text>\n",
       "</g>\n",
       "<!-- M -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>M</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"58.52\" cy=\"-90\" rx=\"58\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"58.52\" y=\"-84.95\" font-family=\"Times,serif\" font-size=\"14.00\">Weight Loss</text>\n",
       "</g>\n",
       "<!-- X&#45;&gt;M -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>X&#45;&gt;M</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M58.52,-143.7C58.52,-136.41 58.52,-127.73 58.52,-119.54\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"62.02,-119.62 58.52,-109.62 55.02,-119.62 62.02,-119.62\"/>\n",
       "</g>\n",
       "<!-- Y -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>Y</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"58.52\" cy=\"-18\" rx=\"58.52\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"58.52\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\">Heart Health</text>\n",
       "</g>\n",
       "<!-- M&#45;&gt;Y -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>M&#45;&gt;Y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M58.52,-71.7C58.52,-64.41 58.52,-55.73 58.52,-47.54\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"62.02,-47.62 58.52,-37.62 55.02,-47.62 62.02,-47.62\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x2a836d9f0>"
      ]
     },
     "execution_count": 375,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz as gr\n",
    "\n",
    "# Create a chain structure for Exercise, Weight Loss, and Heart Health\n",
    "chain_dag = gr.Digraph()\n",
    "\n",
    "# Add nodes\n",
    "chain_dag.node(\"X\", label=\"Exercise\")\n",
    "chain_dag.node(\"M\", label=\"Weight Loss\")\n",
    "chain_dag.node(\"Y\", label=\"Heart Health\")\n",
    "\n",
    "# Add edges representing the chain structure\n",
    "chain_dag.edge(\"X\", \"M\")  # Exercise leads to Weight Loss\n",
    "chain_dag.edge(\"M\", \"Y\")  # Weight Loss leads to Improved Heart Health\n",
    "\n",
    "# Render the graph\n",
    "chain_dag\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Simulate Data:\n",
    "\n",
    "Next, we simulate synthetic data to model the relationships between **Exercise**, **Weight Loss**, and **Heart Health**.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 377,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Exercise</th>\n",
       "      <th>Weight Loss</th>\n",
       "      <th>Heart Health</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10.993428</td>\n",
       "      <td>50.721029</td>\n",
       "      <td>153.952025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9.723471</td>\n",
       "      <td>47.355421</td>\n",
       "      <td>144.870186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11.295377</td>\n",
       "      <td>55.448742</td>\n",
       "      <td>171.761482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>13.046060</td>\n",
       "      <td>62.823467</td>\n",
       "      <td>193.739411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9.531693</td>\n",
       "      <td>47.174609</td>\n",
       "      <td>134.635481</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Exercise  Weight Loss  Heart Health\n",
       "0  10.993428    50.721029    153.952025\n",
       "1   9.723471    47.355421    144.870186\n",
       "2  11.295377    55.448742    171.761482\n",
       "3  13.046060    62.823467    193.739411\n",
       "4   9.531693    47.174609    134.635481"
      ]
     },
     "execution_count": 377,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "# Set seed for reproducibility\n",
    "np.random.seed(42)\n",
    "\n",
    "# Simulating Exercise (X)\n",
    "exercise = np.random.normal(loc=10, scale=2, size=100)  # Average exercise hours per week with some variation\n",
    "\n",
    "# Simulating Weight Loss (M) based on Exercise (X)\n",
    "weight_loss = 5 * exercise + np.random.normal(loc=0, scale=3, size=100)  # More exercise leads to greater weight loss\n",
    "\n",
    "# Simulating Heart Health (Y) based on Weight Loss (M)\n",
    "heart_health = 3 * weight_loss + np.random.normal(loc=0, scale=5, size=100)  # Greater weight loss improves heart health\n",
    "\n",
    "# Creating a DataFrame for the data\n",
    "data = pd.DataFrame({\n",
    "    'Exercise': exercise,\n",
    "    'Weight Loss': weight_loss,\n",
    "    'Heart Health': heart_health\n",
    "})\n",
    "\n",
    "# Display the first few rows of the dataset\n",
    "data.head()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Explore Relationships\n",
    "\n",
    "We will now create a scatter plot matrix to visualize the pairwise relationships between **Exercise**, **Weight Loss**, and **Heart Health**.\n",
    "\n",
    "${Exercise} \\not\\!\\perp\\!\\!\\!\\perp {Heart\\ Health} $ \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 750x750 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualizing the scatter plot matrix\n",
    "sns.pairplot(data)\n",
    "plt.suptitle(\"Scatter Plot Matrix: Exercise, Weight Loss, and Heart Health\", y=1.02)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Observations:\n",
    "\n",
    "- **Exercise and Weight Loss**: There is a strong positive relationship between Exercise and Weight Loss. More exercise leads to greater weight loss.\n",
    "  \n",
    "- **Weight Loss and Heart Health**: A positive relationship also exists between Weight Loss and Heart Health. Weight loss improves heart health.\n",
    "\n",
    "- **Exercise and Heart Health**: While Exercise is positively related to Heart Health, it is important to note that the relationship is **partly indirect** through Weight Loss.\n",
    "\n",
    "- **Exercise** directly influences **Weight Loss**, which in turn influences **Heart Health**. This is a **mediating relationship**, where the effect of Exercise on Heart Health is mediated by Weight Loss.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conditioning on the Mediator (Weight Loss)\n",
    "\n",
    "In this second part, we condition on Weight Loss (M) to analyze the direct relationship between Exercise (X) and Heart Health (Y), adjusting for the effect of the mediator.\n",
    "\n",
    "${Exercise} \\!\\perp\\!\\!\\!\\perp {Heart\\ Healths} | {Weight\\ Loss}$ \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 382,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x500 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation between Exercise and Heart Health after conditioning on Weight Loss:\n",
      "                        Exercise Residuals  Heart Health Residuals\n",
      "Exercise Residuals                1.000000                0.070463\n",
      "Heart Health Residuals            0.070463                1.000000\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# Regress Heart Health (Y) on Weight Loss (M) to get the residuals\n",
    "heart_health_residuals = heart_health - LinearRegression().fit(weight_loss.reshape(-1, 1), heart_health).predict(weight_loss.reshape(-1, 1))\n",
    "\n",
    "# Regress Exercise (X) on Weight Loss (M) to get the residuals\n",
    "exercise_residuals = exercise - LinearRegression().fit(weight_loss.reshape(-1, 1), exercise).predict(weight_loss.reshape(-1, 1))\n",
    "\n",
    "# Create a DataFrame for the residuals\n",
    "residuals_data = pd.DataFrame({\n",
    "    'Exercise Residuals': exercise_residuals,\n",
    "    'Heart Health Residuals': heart_health_residuals\n",
    "})\n",
    "\n",
    "# Visualize residuals (relationship after conditioning)\n",
    "sns.pairplot(residuals_data)\n",
    "plt.suptitle(\"Residuals\", y=1.02)\n",
    "plt.show()\n",
    "\n",
    "# Correlation matrix after conditioning\n",
    "correlation_after = residuals_data.corr()\n",
    "print(\"Correlation between Exercise and Heart Health after conditioning on Weight Loss:\")\n",
    "print(correlation_after)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Weak Residual Correlation**: After conditioning on Weight Loss (M), the residuals show that the correlation between Exercise (X) and Heart Health (Y) has drastically weakened (correlation = 0.07), which is close to zero. This suggests that Weight Loss largely explains the relationship between Exercise and Heart Health. Once we account for Weight Loss, there is minimal direct association between Exercise and Heart Health.\n",
    "\n",
    "**Residual Scatter Plot**: The scatter plot of the residuals between Exercise and Heart Health shows no clear pattern, confirming the weak residual correlation. This indicates that after controlling for Weight Loss, Exercise and Heart Health behave almost independently, meaning the initial relationship observed between them was mediated through Weight Loss. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### Major DAG Structure 3: V-Structure (Collider)\n",
    "\n",
    "A **V-structure**, or **collider**, occurs when two variables have a common effect. This structure is represented as:\n",
    "\n",
    "- $A → C ← B$, where:\n",
    "  - $A$ and $B$ are independent causes of the collider $C$.\n",
    "    \n",
    "      $A \\!\\perp\\!\\!\\!\\perp B$   \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 385,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 12.1.1 (20240910.0053)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"134pt\" height=\"116pt\"\n",
       " viewBox=\"0.00 0.00 134.00 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-112 130,-112 130,4 -4,4\"/>\n",
       "<!-- A -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>A</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-84.95\" font-family=\"Times,serif\" font-size=\"14.00\">A</text>\n",
       "</g>\n",
       "<!-- C -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>C</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"63\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"63\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\">C</text>\n",
       "</g>\n",
       "<!-- A&#45;&gt;C -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>A&#45;&gt;C</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M35.35,-72.76C39.58,-64.55 44.81,-54.37 49.58,-45.09\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"52.54,-46.99 54,-36.49 46.32,-43.79 52.54,-46.99\"/>\n",
       "</g>\n",
       "<!-- B -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>B</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"99\" y=\"-84.95\" font-family=\"Times,serif\" font-size=\"14.00\">B</text>\n",
       "</g>\n",
       "<!-- B&#45;&gt;C -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>B&#45;&gt;C</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M90.65,-72.76C86.42,-64.55 81.19,-54.37 76.42,-45.09\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"79.68,-43.79 72,-36.49 73.46,-46.99 79.68,-43.79\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x2abf17610>"
      ]
     },
     "execution_count": 385,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a V-structure (collider)\n",
    "vstructure_dag = gr.Digraph()\n",
    "\n",
    "# Add edges\n",
    "vstructure_dag.edge(\"A\", \"C\")\n",
    "vstructure_dag.edge(\"B\", \"C\")\n",
    "\n",
    "# Render the graph\n",
    "vstructure_dag\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- As a general rule, **conditioning (adjusting or controlling)** on a collider opens the causal path. Not conditioning on it leaves it closed.\n",
    "- This phenomenon is sometimes called **explaining away**, because one cause already explains the effect, making the other cause less likely.\n",
    "\n",
    "  $A \\not\\!\\perp\\!\\!\\!\\perp B | C$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 387,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 12.1.1 (20240910.0053)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"134pt\" height=\"116pt\"\n",
       " viewBox=\"0.00 0.00 134.00 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-112 130,-112 130,4 -4,4\"/>\n",
       "<!-- C -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>C</title>\n",
       "<ellipse fill=\"none\" stroke=\"red\" cx=\"63\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"63\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"red\">C</text>\n",
       "</g>\n",
       "<!-- A -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>A</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-84.95\" font-family=\"Times,serif\" font-size=\"14.00\">A</text>\n",
       "</g>\n",
       "<!-- A&#45;&gt;C -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>A&#45;&gt;C</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M35.35,-72.76C39.58,-64.55 44.81,-54.37 49.58,-45.09\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"52.54,-46.99 54,-36.49 46.32,-43.79 52.54,-46.99\"/>\n",
       "</g>\n",
       "<!-- B -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>B</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"99\" y=\"-84.95\" font-family=\"Times,serif\" font-size=\"14.00\">B</text>\n",
       "</g>\n",
       "<!-- B&#45;&gt;C -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>B&#45;&gt;C</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M90.65,-72.76C86.42,-64.55 81.19,-54.37 76.42,-45.09\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"79.68,-43.79 72,-36.49 73.46,-46.99 79.68,-43.79\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x2a9bcef80>"
      ]
     },
     "execution_count": 387,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz as gr\n",
    "\n",
    "# Create a V-structure (collider)\n",
    "vstructure_dag = gr.Digraph()\n",
    "\n",
    "# Add node C with red border and red label\n",
    "vstructure_dag.node(\"C\", color=\"red\", fontcolor=\"red\")\n",
    "\n",
    "# Add edges representing the V-structure\n",
    "vstructure_dag.edge(\"A\", \"C\")\n",
    "vstructure_dag.edge(\"B\", \"C\")\n",
    "\n",
    "# Render the graph\n",
    "vstructure_dag\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Collider Bias or Berkson's paradox\n",
    "\n",
    "- **Conditioning on** or **observing** a collider can lead to spurious associations between the variables that connect it. This phenomenon is known as **[collider bias](https://catalogofbias.org/biases/collider-bias/)** or **Berkson's paradox**.\n",
    "  \n",
    "- It occurs because conditioning on a collider variable can induce a correlation between the variables that influence it, even if they are not causally related.\n",
    "\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Collider Structure Example: Job Skill, Family Connections, and Job Offer\n",
    "\n",
    "### Background:\n",
    "\n",
    "In this example, we explore how two independent factors, **Job Skill** and **Family Connections**, affect the likelihood of receiving a **Job Offer**. This represents a **collider structure**, where both **Job Skill (A)** and **Family Connections (B)** influence the **Job Offer (C)** independently.\n",
    "\n",
    "Importantly, if we were to condition on **Job Offer (the collider)**, a spurious relationship might appear between **Job Skill** and **Family Connections**, even though they are actually independent.\n",
    "\n",
    "In this scenario:\n",
    "- **Job Skill (A)** → **Job Offer (C)** ← **Family Connections (B)**\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 390,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 12.1.1 (20240910.0053)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"286pt\" height=\"116pt\"\n",
       " viewBox=\"0.00 0.00 285.83 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-112 281.83,-112 281.83,4 -4,4\"/>\n",
       "<!-- A -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>A</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"43.67\" cy=\"-90\" rx=\"43.67\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"43.67\" y=\"-84.95\" font-family=\"Times,serif\" font-size=\"14.00\">Job Skill</text>\n",
       "</g>\n",
       "<!-- C -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>C</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"117.67\" cy=\"-18\" rx=\"46.23\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"117.67\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\">Job Offer</text>\n",
       "</g>\n",
       "<!-- A&#45;&gt;C -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>A&#45;&gt;C</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M60.47,-73.12C69.95,-64.14 82,-52.74 92.59,-42.73\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"94.73,-45.52 99.59,-36.1 89.92,-40.43 94.73,-45.52\"/>\n",
       "</g>\n",
       "<!-- B -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>B</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"191.67\" cy=\"-90\" rx=\"86.15\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"191.67\" y=\"-84.95\" font-family=\"Times,serif\" font-size=\"14.00\">Family Connections</text>\n",
       "</g>\n",
       "<!-- B&#45;&gt;C -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>B&#45;&gt;C</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M173.76,-72.05C164.47,-63.27 152.97,-52.39 142.81,-42.77\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"145.43,-40.44 135.76,-36.11 140.62,-45.52 145.43,-40.44\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x2a9bcee00>"
      ]
     },
     "execution_count": 390,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz as gr\n",
    "\n",
    "# Create a V-structure (collider) for Job Skill, Family Connections, and Job Offer\n",
    "vstructure_dag = gr.Digraph()\n",
    "\n",
    "# Add nodes\n",
    "vstructure_dag.node(\"A\", label=\"Job Skill\")\n",
    "vstructure_dag.node(\"B\", label=\"Family Connections\")\n",
    "vstructure_dag.node(\"C\", label=\"Job Offer\")  # Default color for Job Offer\n",
    "\n",
    "# Add edges representing the collider structure\n",
    "vstructure_dag.edge(\"A\", \"C\")  # Job Skill influences Job Offer\n",
    "vstructure_dag.edge(\"B\", \"C\")  # Family Connections influence Job Offer\n",
    "\n",
    "# Render the graph\n",
    "vstructure_dag\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Simulate Data:\n",
    "\n",
    "Now, we will simulate some synthetic data for **Job Skill (A)**, **Family Connections (B)**, and **Job Offer (C)**.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 392,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Job Skill</th>\n",
       "      <th>Family Connections</th>\n",
       "      <th>Job Offer</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>74.967142</td>\n",
       "      <td>28.769439</td>\n",
       "      <td>35.786855</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>68.617357</td>\n",
       "      <td>43.690320</td>\n",
       "      <td>40.865258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>76.476885</td>\n",
       "      <td>44.859282</td>\n",
       "      <td>46.302035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>85.230299</td>\n",
       "      <td>37.965841</td>\n",
       "      <td>46.024436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>67.658466</td>\n",
       "      <td>47.580714</td>\n",
       "      <td>32.441479</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Job Skill  Family Connections  Job Offer\n",
       "0  74.967142           28.769439  35.786855\n",
       "1  68.617357           43.690320  40.865258\n",
       "2  76.476885           44.859282  46.302035\n",
       "3  85.230299           37.965841  46.024436\n",
       "4  67.658466           47.580714  32.441479"
      ]
     },
     "execution_count": 392,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "# Set seed for reproducibility\n",
    "np.random.seed(42)\n",
    "\n",
    "# Simulating Job Skill (A)\n",
    "job_skill = np.random.normal(loc=70, scale=10, size=100)  # Average job skill score (out of 100)\n",
    "\n",
    "# Simulating Family Connections (B)\n",
    "family_connections = np.random.normal(loc=50, scale=15, size=100)  # Family connections score (out of 100)\n",
    "\n",
    "# Simulating Job Offer (C) based on both Job Skill and Family Connections\n",
    "job_offer = 0.3 * job_skill + 0.4 * family_connections + np.random.normal(loc=0, scale=5, size=100)  # Job Offer score\n",
    "\n",
    "# Creating a DataFrame for the data\n",
    "data = pd.DataFrame({\n",
    "    'Job Skill': job_skill,\n",
    "    'Family Connections': family_connections,\n",
    "    'Job Offer': job_offer\n",
    "})\n",
    "\n",
    "# Display the first few rows of the dataset\n",
    "data.head()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Explore Relationships\n",
    "\n",
    "We will now create a scatter plot matrix to visualize the pairwise relationships between **Job Skill**, **Family Connections**, and **Job Offer**.\n",
    "\n",
    "${Job\\ Skill} \\!\\perp\\!\\!\\!\\perp {Family\\ Connections}$ \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 394,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 750x750 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualizing the scatter plot matrix\n",
    "sns.pairplot(data)\n",
    "plt.suptitle(\"Scatter Plot Matrix: Job Skill, Family Connections, and Job Offer\", y=1.02)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Observations:\n",
    "\n",
    "- **Job Skill and Job Offer**: A positive relationship is observed between **Job Skill** and **Job Offer**. The higher the job skill, the more likely a person is to receive a job offer.\n",
    "  \n",
    "- **Family Connections and Job Offer**: Similarly, a positive relationship exists between **Family Connections** and **Job Offer**. The stronger the family connections, the more likely a person is to receive a job offer.\n",
    "\n",
    "- **Job Skill and Family Connections**: While **Job Skill** and **Family Connections** are independent in reality, they might appear correlated if we condition on **Job Offer** (the collider). This could create a spurious relationship between the two factors due to **collider bias**.\n",
    "\n",
    "\n",
    "- In the **collider structure**, both **Job Skill** and **Family Connections** affect the **Job Offer** independently. If we mistakenly control for **Job Offer** (e.g., by looking only at people who received a job offer), we might observe a false relationship between **Job Skill** and **Family Connections**.\n",
    "  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conditioning on the Collider (Job Offer)\n",
    "Now, we will condition on the **Job Offer (C)** and observe how this affects the relationship between **Job Skill (A)** and **Family Connections (B)**.\n",
    "\n",
    "${Job\\ Skill} \\not\\!\\perp\\!\\!\\!\\perp {Family\\ Connections} | {Job\\ Offer}$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 397,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x500 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation between Job Skill and Family Connections after conditioning on Job Offer:\n",
      "                              Job Skill Residuals  \\\n",
      "Job Skill Residuals                      1.000000   \n",
      "Family Connections Residuals            -0.492376   \n",
      "\n",
      "                              Family Connections Residuals  \n",
      "Job Skill Residuals                              -0.492376  \n",
      "Family Connections Residuals                      1.000000  \n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# Regress Job Skill (A) on Job Offer (C) to get the residuals\n",
    "job_skill_residuals = job_skill - LinearRegression().fit(job_offer.reshape(-1, 1), job_skill).predict(job_offer.reshape(-1, 1))\n",
    "\n",
    "# Regress Family Connections (B) on Job Offer (C) to get the residuals\n",
    "family_connections_residuals = family_connections - LinearRegression().fit(job_offer.reshape(-1, 1), family_connections).predict(job_offer.reshape(-1, 1))\n",
    "\n",
    "# Create a DataFrame of the residuals\n",
    "residuals_data = pd.DataFrame({\n",
    "    'Job Skill Residuals': job_skill_residuals,\n",
    "    'Family Connections Residuals': family_connections_residuals\n",
    "})\n",
    "\n",
    "# Visualize residuals (relationship after conditioning)\n",
    "sns.pairplot(residuals_data)\n",
    "plt.suptitle(\"Residuals\", y=1.02)\n",
    "plt.show()\n",
    "\n",
    "# Correlation matrix after conditioning\n",
    "correlation_after = residuals_data.corr()\n",
    "print(\"Correlation between Job Skill and Family Connections after conditioning on Job Offer:\")\n",
    "print(correlation_after)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Induced Negative Correlation**: After conditioning on the collider (Job Offer), the scatter plot and correlation matrix reveal a negative correlation of -0.49 between Job Skill and Family Connections. This is a classic sign of collider bias: although Job Skill and Family Connections are independent in the general population, conditioning on their common effect (Job Offer) induces a spurious correlation between them.\n",
    "\n",
    "**Residual Scatter Plot**: The scatter plot of the residuals shows a negative trend, further confirming that conditioning on Job Offer creates an artificial relationship between Job Skill and Family Connections, even though no direct relationship exists in the data without conditioning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 3.3. Paths and Blocking Paths in Causal Graphs\n",
    "\n",
    "In causal graphs, paths are sequences of edges that connect two variables, and understanding how these paths are open or blocked is essential for reasoning about causal and probabilistic relationships.\n",
    "\n",
    "\n",
    "The causal path from $X$ to $C$ mediate the causal effect of $X$ on $C$, the non-causal path do not.\n",
    "\n",
    "For example in the graphs below, the causal path between $X$ and $C$ are highlighted in red."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 400,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 12.1.1 (20240910.0053)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"422pt\" height=\"139pt\"\n",
       " viewBox=\"0.00 0.00 422.00 138.95\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 134.95)\">\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-134.95 418,-134.95 418,4 -4,4\"/>\n",
       "<!-- X -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>X</title>\n",
       "<ellipse fill=\"none\" stroke=\"blue\" cx=\"117\" cy=\"-76.95\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"117\" y=\"-71.9\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"blue\">X</text>\n",
       "</g>\n",
       "<!-- C -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>C</title>\n",
       "<ellipse fill=\"none\" stroke=\"blue\" cx=\"297\" cy=\"-68.95\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"297\" y=\"-63.9\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"blue\">C</text>\n",
       "</g>\n",
       "<!-- X&#45;&gt;C -->\n",
       "<g id=\"edge8\" class=\"edge\">\n",
       "<title>X&#45;&gt;C</title>\n",
       "<path fill=\"none\" stroke=\"red\" d=\"M144.26,-75.77C174.5,-74.41 224.39,-72.16 258.66,-70.62\"/>\n",
       "<polygon fill=\"red\" stroke=\"red\" points=\"268.41,-70.19 258.62,-75.13 264.63,-70.36 258.42,-70.64 258.42,-70.64 258.42,-70.64 264.63,-70.36 258.22,-66.14 268.41,-70.19\"/>\n",
       "</g>\n",
       "<!-- Y -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>Y</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"387\" cy=\"-91.95\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"387\" y=\"-86.9\" font-family=\"Times,serif\" font-size=\"14.00\">Y</text>\n",
       "</g>\n",
       "<!-- X&#45;&gt;Y -->\n",
       "<g id=\"edge9\" class=\"edge\">\n",
       "<title>X&#45;&gt;Y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M143.59,-81.43C154.75,-83.29 168,-85.38 180,-86.95 243.59,-95.25 259.91,-98.01 324,-95.95 331.99,-95.69 340.54,-95.25 348.67,-94.75\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"358.56,-94.09 348.87,-99.24 354.78,-94.34 348.58,-94.75 348.58,-94.75 348.58,-94.75 354.78,-94.34 348.28,-90.26 358.56,-94.09\"/>\n",
       "</g>\n",
       "<!-- T -->\n",
       "<g id=\"node6\" class=\"node\">\n",
       "<title>T</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"207\" cy=\"-30.95\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"207\" y=\"-25.9\" font-family=\"Times,serif\" font-size=\"14.00\">T</text>\n",
       "</g>\n",
       "<!-- X&#45;&gt;T -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>X&#45;&gt;T</title>\n",
       "<path fill=\"none\" stroke=\"red\" d=\"M138.85,-66.04C149.73,-60.36 163.25,-53.29 175.3,-46.99\"/>\n",
       "<polygon fill=\"red\" stroke=\"red\" points=\"183.91,-42.49 177.13,-51.11 180.56,-44.25 175.05,-47.13 175.05,-47.13 175.05,-47.13 180.56,-44.25 172.96,-43.14 183.91,-42.49\"/>\n",
       "</g>\n",
       "<!-- C&#45;&gt;Y -->\n",
       "<g id=\"edge7\" class=\"edge\">\n",
       "<title>C&#45;&gt;Y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M322.51,-75.35C331.21,-77.63 341.19,-80.23 350.61,-82.7\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"360.13,-85.19 349.32,-87.01 356.48,-84.23 350.46,-82.66 350.46,-82.66 350.46,-82.66 356.48,-84.23 351.6,-78.3 360.13,-85.19\"/>\n",
       "</g>\n",
       "<!-- U1 -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>U1</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-112.95\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-107.9\" font-family=\"Times,serif\" font-size=\"14.00\">U1</text>\n",
       "</g>\n",
       "<!-- U1&#45;&gt;X -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>U1&#45;&gt;X</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M50.66,-103.68C60.52,-99.64 72.25,-94.84 83.04,-90.43\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"92.29,-86.65 84.74,-94.6 88.79,-88.08 83.03,-90.43 83.03,-90.43 83.03,-90.43 88.79,-88.08 81.33,-86.27 92.29,-86.65\"/>\n",
       "</g>\n",
       "<!-- U1&#45;&gt;Y -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>U1&#45;&gt;Y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M53.92,-115.03C105.62,-118.68 225.11,-124.52 324,-109.95 333.3,-108.58 343.17,-106.17 352.22,-103.56\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"361.62,-100.67 353.38,-107.91 358,-101.78 352.06,-103.61 352.06,-103.61 352.06,-103.61 358,-101.78 350.74,-99.3 361.62,-100.67\"/>\n",
       "</g>\n",
       "<!-- U2 -->\n",
       "<g id=\"node5\" class=\"node\">\n",
       "<title>U2</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-39.95\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-34.9\" font-family=\"Times,serif\" font-size=\"14.00\">U2</text>\n",
       "</g>\n",
       "<!-- U2&#45;&gt;X -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>U2&#45;&gt;X</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M50.21,-49.28C60.24,-53.5 72.29,-58.57 83.33,-63.21\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"92.37,-67.01 81.41,-67.28 88.89,-65.55 83.15,-63.14 83.15,-63.14 83.15,-63.14 88.89,-65.55 84.9,-58.99 92.37,-67.01\"/>\n",
       "</g>\n",
       "<!-- U2&#45;&gt;Y -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>U2&#45;&gt;Y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M50.33,-30.57C88.21,-15.89 167.46,9.53 234,-3.95 276.56,-12.56 286.74,-19.66 324,-41.95 337.39,-49.96 351.02,-60.62 362.08,-70.04\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"369.43,-76.45 358.93,-73.27 366.58,-73.97 361.89,-69.88 361.89,-69.88 361.89,-69.88 366.58,-73.97 364.85,-66.49 369.43,-76.45\"/>\n",
       "</g>\n",
       "<!-- T&#45;&gt;C -->\n",
       "<g id=\"edge6\" class=\"edge\">\n",
       "<title>T&#45;&gt;C</title>\n",
       "<path fill=\"none\" stroke=\"red\" d=\"M230.21,-40.54C240.32,-44.9 252.48,-50.15 263.58,-54.95\"/>\n",
       "<polygon fill=\"red\" stroke=\"red\" points=\"272.68,-58.88 261.72,-59.04 269.21,-57.38 263.5,-54.91 263.5,-54.91 263.5,-54.91 269.21,-57.38 265.29,-50.78 272.68,-58.88\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x2ace76350>"
      ]
     },
     "execution_count": 400,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz as gr\n",
    "\n",
    "# Create the DAG with improved consistency\n",
    "g = gr.Digraph(\n",
    "    graph_attr={'rankdir': 'LR'},  # Left-to-right layout for consistency\n",
    "    edge_attr={'arrowhead': 'vee', 'arrowsize': '1'}  # Consistent edge styling\n",
    ")\n",
    "\n",
    "# Add nodes with consistent color and styling\n",
    "g.node(\"X\", \"X\", color=\"blue\", fontcolor=\"blue\")  # X node in blue\n",
    "g.node(\"C\", \"C\", color=\"blue\", fontcolor=\"blue\")  # C node in blue\n",
    "\n",
    "# Add edges for unobserved confounders U1 and U2\n",
    "g.edge(\"U1\", \"Y\")  # U1 influences Y\n",
    "g.edge(\"U1\", \"X\")  # U1 influences X\n",
    "g.edge(\"U2\", \"X\")  # U2 influences X\n",
    "g.edge(\"U2\", \"Y\")  # U2 influences Y\n",
    "\n",
    "# Add edges representing relationships between X, T, C, and Y\n",
    "g.edge(\"X\", \"T\", color=\"red\", fontcolor=\"red\")  # X to T (red for emphasis)\n",
    "g.edge(\"T\", \"C\", color=\"red\", fontcolor=\"red\")  # T to C (red for emphasis)\n",
    "g.edge(\"C\", \"Y\")  # C to Y\n",
    "g.edge(\"X\", \"C\", color=\"red\", fontcolor=\"red\")  # X to C (red for emphasis)\n",
    "g.edge(\"X\", \"Y\")  # X to Y\n",
    "\n",
    "# Render the graph\n",
    "g\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "da415130-cf58-4472-ba1c-6178dafb4e2a",
    "deepnote_cell_height": 220.953125,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "### Open and Blocked Paths\n",
    "\n",
    "A path is considered open if it allows information to flow between the connected variables, whereas a path is blocked if the information flow is prevented by conditioning on certain variables. The rules for determining whether a path is open or blocked depend on the presence of colliders and non-colliders along the path.\n",
    "\n",
    "Path blocking in Directed Acyclic Graphs (DAGs) refers to the process of identifying variables or conditions that can close or block a specific causal path between two variables. It involves determining which variables need to be controlled for or conditioned on to prevent spurious associations or biases when estimating causal effects.\n",
    "\n",
    "An **active path** is *open* and allows for potential causal influence between the variables, while an **inactive path** is *blocked* or closed, preventing any direct causal influence.\n",
    "\n",
    "Path are either open or blocked, according to two rules:\n",
    "\n",
    "- **Rule 1:** A path is blocked if somewhere along the path, there is a variable $C$ that sits in a *chain*, or sits in a *fork* and we have conditioned for $C$. \n",
    "\n",
    "- **Rule 2:** A path is blocked if somewhere along the path, there is a variable $C$ that sits in a *collider* and we have not conditioned for $C$, or any of its descendents."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Path Blocking Example: a 4 Nodes Graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 403,
   "metadata": {
    "cell_id": "23f2fe50-f8ac-45aa-b139-4dfe56232230",
    "deepnote_cell_height": 325.65625,
    "deepnote_cell_type": "code",
    "deepnote_output_heights": [
     156.65625
    ],
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 1,
    "execution_start": 1647607231025,
    "source_hash": "5d0cf649",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 12.1.1 (20240910.0053)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"134pt\" height=\"116pt\"\n",
       " viewBox=\"0.00 0.00 134.00 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-112 130,-112 130,4 -4,4\"/>\n",
       "<!-- V -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>V</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-84.95\" font-family=\"Times,serif\" font-size=\"14.00\">V</text>\n",
       "</g>\n",
       "<!-- A -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>A</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\">A</text>\n",
       "</g>\n",
       "<!-- V&#45;&gt;A -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>V&#45;&gt;A</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M27,-71.7C27,-64.32 27,-55.52 27,-47.25\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"27,-37.32 31.5,-47.32 27,-41.1 27,-47.32 27,-47.32 27,-47.32 27,-41.1 22.5,-47.32 27,-37.32\"/>\n",
       "</g>\n",
       "<!-- W -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>W</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"99\" y=\"-12.95\" font-family=\"Times,serif\" font-size=\"14.00\">W</text>\n",
       "</g>\n",
       "<!-- V&#45;&gt;W -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>V&#45;&gt;W</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M41.92,-74.5C51.86,-64.83 65.12,-51.94 76.35,-41.02\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"83.23,-34.33 79.19,-44.53 80.52,-36.97 76.06,-41.31 76.06,-41.31 76.06,-41.31 80.52,-36.97 72.92,-38.08 83.23,-34.33\"/>\n",
       "</g>\n",
       "<!-- Y -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>Y</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"99\" y=\"-84.95\" font-family=\"Times,serif\" font-size=\"14.00\">Y</text>\n",
       "</g>\n",
       "<!-- Y&#45;&gt;W -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>Y&#45;&gt;W</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M99,-71.7C99,-64.32 99,-55.52 99,-47.25\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"99,-37.32 103.5,-47.32 99,-41.1 99,-47.32 99,-47.32 99,-47.32 99,-41.1 94.5,-47.32 99,-37.32\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x2ace77f40>"
      ]
     },
     "execution_count": 403,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = gr.Digraph(edge_attr={'arrowhead':'vee', 'arrowsize':'1'})\n",
    "g.edge(\"V\", \"A\")\n",
    "g.edge(\"V\", \"W\")\n",
    "g.edge(\"Y\", \"W\")\n",
    "g"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "1c2618ee-d6ae-4548-8f00-edb9129d6b10",
    "deepnote_cell_height": 178.953125,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "From the causal graph above we notice that:\n",
    "- Conditioning for **V** blocks the path from **A** to **W** (rule 1) \n",
    "- Conditioning for **W** leaves the path open (rule 2) from **A** to **Y**. \n",
    "- Conditioning for both **V** and **W** blocks the path from **A** to **Y**."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    " ## Section 3.4. d-Separation and Independence Assumptions\n",
    "\n",
    "\n",
    "The concept of **d-separation** is central to determining when two variables are conditionally independent given a set of other variables. \n",
    "\n",
    "* Two variables $X$ and $Y$ are d-separated by a set of variables $Z$ if all paths between $X$ and $Y$  are blocked by $Z$  according to the rules of open and blocked paths described above.\r",
    "* \n",
    "Formally, d-separation is the graphical criterion for conditional independence\n",
    "*  If $X$  and $Y$  are d-separated by $Z$, then $X$ and $Y$  are conditionally independent given $Z$.\n",
    "\n",
    "\n",
    "We have seen follwing concepts in the previous section. We repeat them with a slighly diffrent language to better explan the d-Separation Basics.\n",
    "\n",
    "* In a DAG, a **path** is a sequence of edges that connect two nodes. These paths can carry associations or causal influences. To assess whether two variables are conditionally independent, we use **d-separation** to block the paths between them.\n",
    "\n",
    "Different Types of Structures that Affect d-Separation:\n",
    "\n",
    "#### Chain ($A \\to B \\to C$)\n",
    "- Without conditioning, $A$ and $C$ are dependent because information flows through $B$.\n",
    "- If we condition on $B$ (i.e., we know $B$'s value), the path is blocked, and $A$ becomes independent of $C$.\n",
    "\n",
    "#### Fork ($A \\leftarrow B \\to C$)\n",
    "- Without conditioning, $A$ and $C$ are dependent because they share a common cause, $B$.\n",
    "- Conditioning on $B$ blocks the path and renders $A$ and $C$ independent.\n",
    "\n",
    "#### Collider ($A \\to B \\leftarrow C$)\n",
    "- Without conditioning, $A$ and $C$ are independent because the path is blocked at $C$ (the collider).\n",
    "- If we condition on $B$ or its descendants, the path is unblocked, and $A$ and $C$ become dependent (collider bias).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "ee7eed8a-0f2d-4a90-854e-e41f889d7eff",
    "deepnote_cell_height": 919.96875,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "\n",
    "### d-Separation Rules \n",
    "\n",
    "\n",
    "D-separation relies on a set of rules, often referred to as path blocking rules or **d-separation rules**, to determine when a path is blocked. These rules identify the necessary variables to condition on to close a specific path and prevent spurious associations or biases in estimating causal effects.\n",
    "\n",
    "\n",
    "**d-separation in Sets:** Sets of variables $A$ and $B$ are d-separated (or blocked) by $C$ if all paths between $A$ and $B$ are blocked by $C$. d-separation implies: \n",
    "\n",
    "$A \\perp \\!\\!\\! \\perp B | C$.\n",
    "\n",
    "\n",
    "**d-separation in Paths:** D-separation determines which paths transmit association, and which ones don’t.\n",
    "Formally, a path **P** is said to be d-separated (or blocked) by a conditioning set of nodes $\\{Z\\}$ if:\n",
    "\n",
    "1. **P** contains a chain $A \\rightarrow M \\rightarrow B$ or a fork $A \\leftarrow M \\rightarrow B$ such that the middle node $M$ is in $\\{Z\\}$, or\n",
    "2. **P** contains a collider $A \\rightarrow M \\leftarrow B$ such that neither the middle node $M$, nor any descendant of $M$, is in $\\{Z\\}$.\n",
    "\n",
    "\n",
    "**d-connected in Paths:** A path **P** is said to be d-connected (or unblocked or open) by a conditioning set of nodes $\\{Z\\}$ if it is not d-separated.\n",
    "\n",
    "\n",
    "In other words:\n",
    "\n",
    "- *Blocked* (d-separated) paths don’t transmit association (information). \n",
    "\n",
    "- *Unblocked* (d-connected) paths may transmit association (information).\n",
    "\n",
    "\n",
    "<br/>\n",
    "The three aforementioned blocking criteria can be rephased as: \n",
    "\n",
    "- Conditioning on a non-collider blocks a path, \n",
    "\n",
    "- Conditioning on a collider, or a descendent of a collider, unblocks a path, \n",
    "\n",
    "- Not conditioning on a collider leaves a path “naturally” blocked.\n",
    "\n",
    "\n",
    "\n",
    "### Path Blocking and Independence \n",
    "\n",
    "- Two variables that are d-separated along all paths given $\\{Z\\}$ are <font color='red'>conditionally independent given $\\{Z\\}$.</font>\n",
    "\n",
    "- Two variables that are *NOT* d-separated along all paths given $\\{Z\\}$ are <font color='red'>potentially dependent given $\\{Z\\}$.</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "3fac0589-db96-4209-94ab-d40c54166ecc",
    "deepnote_cell_height": 692.4375,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "### d-Separation Example, a 10 Nodes Graph\n",
    "\n",
    "We use the following DAG from [Bardy Neal course](https://www.bradyneal.com/causal-inference-course) to see blocked and un-blocked pathes between $T$ and $Y$ for different controlling (conditioning) cases.\n",
    "\n",
    "![img](img/ch3/graph_Dsep_example_case0.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "bc3a6faa-d562-40c2-ab40-fe7d13c26e47",
    "deepnote_cell_height": 658.828125,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "<br/><br/>\n",
    "**Case 1:** In the following graph, is  $T \\perp \\!\\!\\! \\perp Y | M_1$  valid?\n",
    "\n",
    "![img](img/ch3/graph_Dsep_example_case1.png)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "29d387ba-5c77-441b-97e3-0689ad6f9c7b",
    "deepnote_cell_height": 153.5625,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "**NO!**, \n",
    "- the chain path $T-M_1-M_2-Y$ is blocked ($M_1$ is in the conditioning set) \n",
    "- the fork path $T-W_1-W_2-W_3-Y$ is not blocked.\n",
    "- the collider path $T-X_1-X_2-X_3-Y$ is blocked."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "863ba0fb-b574-4e95-af15-dd183d2b14bc",
    "deepnote_cell_height": 658.828125,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "<br/><br/>\n",
    "**Case 2:** In the following graph, is  $T \\perp \\!\\!\\! \\perp Y | M_1, W_2 $  valid?  \n",
    "\n",
    "![img](img/ch3/graph_Dsep_example_case2.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "8e4cb192-65a1-4bd4-ad8b-19ccf11332e9",
    "deepnote_cell_height": 153.5625,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "**YES!**, \n",
    "- the chain path $T-M_1-M_2-Y$ is blocked ($M_1$ is in the conditioning set) \n",
    "- the fork path $T-W_1-W_2-W_3-Y$ is blocked ($W_2$ is in the conditioning set).\n",
    "- the collider path $T-X_1-X_2-X_3-Y$ is blocked."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00046-4464fcaa-1ecc-4156-8f88-d03800a3e4e1",
    "deepnote_cell_height": 658.828125,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "<br/><br/>\n",
    "**Case 3:** In the following graph, is  $T \\perp \\!\\!\\! \\perp Y | M_1, W_3 $  valid?  \n",
    "\n",
    "![img](img/ch3/graph_Dsep_example_case3.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "fe2c3d7b-98da-4d90-9d22-f628615f267f",
    "deepnote_cell_height": 153.5625,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "**YES!**,\n",
    "- the chain path $T-M_1-M_2-Y$ is blocked ($M_1$ is in the conditioning set). \n",
    "- the fork path $T-W_1-W_2-W_3-Y$ is blocked ($W_3$ is in the conditioning set).\n",
    "- the collider path $T-X_1-X_2-X_3-Y$ is blocked."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00048-33acc8f8-091f-4f6e-b0d5-ca95a6517273",
    "deepnote_cell_height": 658.828125,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "<br/><br/>\n",
    "**Case 4:** In the following graph, is  $T \\perp \\!\\!\\! \\perp Y | M_1, W_1, W_2, X_2$  valid?  \n",
    "\n",
    "![img](img/ch3/graph_Dsep_example_case4.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "6a65db51-6e07-478d-a661-1e222610cfb8",
    "deepnote_cell_height": 153.5625,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "**NO!**,\n",
    "- the chain path $T-M_1-M_2-Y$ is blocked ($M_1$ is in the conditioning set). \n",
    "- the fork path $T-W_1-W_2-W_3-Y$ is blocked ($W_2, W_3$ are in the conditioning set).\n",
    "- the collider path $T-X_1-X_2-X_3-Y$ is NOT blocked ($X_2$ is in the conditioning set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "4030a3d2-522a-4a33-ac83-e11de02542c7",
    "deepnote_cell_height": 658.828125,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "<br/><br/>\n",
    "**Case 5:** In the following graph, is  $T \\perp \\!\\!\\! \\perp Y | M_1, W_2, W_3, X_1, X_2?$  valid?\n",
    "\n",
    "![img](img/ch3/graph_Dsep_example_case5.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00054-160f1856-1d83-45c9-8fd1-90fe514afd87",
    "deepnote_cell_height": 153.5625,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "**YES!**,\n",
    "- the chain path $T-M_1-M_2-Y$ is blocked ($M_1$ is in the conditioning set). \n",
    "- the fork path $T-W_1-W_2-W_3-Y$ is blocked ($W_2, W_3$ are in the conditioning set).\n",
    "- the collider path $T-X_1-X_2-X_3-Y$ is blocked ($X_1$ is in the conditioning set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: d-separation Test with Python\n",
    "\n",
    "Testing the d-separation manually is not feasible for large graphs.\n",
    "We can use the [networkx](https://networkx.org) python library instead to test for conditional independence.\n",
    "\n",
    "NetworkX is a Python package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 419,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "ename": "AttributeError",
     "evalue": "'BayesianNetwork' object has no attribute 'is_d_separated'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[419], line 37\u001b[0m\n\u001b[1;32m     33\u001b[0m \u001b[38;5;66;03m# Use the correct method to check d-separation\u001b[39;00m\n\u001b[1;32m     34\u001b[0m \u001b[38;5;66;03m# This is now `is_d_separated()` in recent versions of pgmpy\u001b[39;00m\n\u001b[1;32m     35\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mpgmpy\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mindependencies\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Independencies\n\u001b[0;32m---> 37\u001b[0m is_d_sep \u001b[38;5;241m=\u001b[39m \u001b[43mmodel\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mis_d_separated\u001b[49m([\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mT\u001b[39m\u001b[38;5;124m'\u001b[39m], [\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mY\u001b[39m\u001b[38;5;124m'\u001b[39m], {\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mM1\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mW2\u001b[39m\u001b[38;5;124m'\u001b[39m})\n\u001b[1;32m     38\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mIs T and Y d-separated given M1 and W2?: \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mis_d_sep\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m     40\u001b[0m \u001b[38;5;66;03m# You can also check without conditioning on any variables\u001b[39;00m\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'BayesianNetwork' object has no attribute 'is_d_separated'"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "from pgmpy.models import BayesianNetwork\n",
    "\n",
    "# Define the DAG structure\n",
    "edges = [\n",
    "    (\"T\", \"M1\"),\n",
    "    (\"M1\", \"M2\"),\n",
    "    (\"M2\", \"Y\"),\n",
    "    (\"T\", \"X1\"),\n",
    "    (\"X1\", \"X2\"),\n",
    "    (\"Y\", \"X3\"),\n",
    "    (\"X3\", \"X2\"),\n",
    "    (\"W1\", \"T\"),\n",
    "    (\"W2\", \"W1\"),\n",
    "    (\"W2\", \"W3\"),\n",
    "    (\"W3\", \"Y\")\n",
    "]\n",
    "\n",
    "# Visualize the DAG using NetworkX for graph plotting\n",
    "G = nx.DiGraph()\n",
    "G.add_edges_from(edges)\n",
    "\n",
    "# Use spring_layout for visualization\n",
    "pos = nx.spring_layout(G)\n",
    "nx.draw(G, pos, with_labels=True, node_color='gray', node_size=500, width=1, arrowstyle='-|>', arrowsize=12)\n",
    "plt.title(\"DAG for d-Separation Example\")\n",
    "plt.show()\n",
    "\n",
    "# Now, use pgmpy to define the Bayesian Network structure\n",
    "model = BayesianNetwork(edges)\n",
    "\n",
    "# Use the correct method to check d-separation\n",
    "# This is now `is_d_separated()` in recent versions of pgmpy\n",
    "from pgmpy.independencies import Independencies\n",
    "\n",
    "is_d_sep = model.is_d_separated(['T'], ['Y'], {'M1', 'W2'})\n",
    "print(f\"Is T and Y d-separated given M1 and W2?: {is_d_sep}\")\n",
    "\n",
    "# You can also check without conditioning on any variables\n",
    "is_d_sep_no_condition = model.is_d_separated(['T'], ['Y'], set())\n",
    "print(f\"Is T and Y d-separated without conditioning?: {is_d_sep_no_condition}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Is  $T \\perp \\!\\!\\! \\perp Y | M_1$  valid?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 420,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/dq/t_6k9k1j2kgbrldmxlbz46240000gn/T/ipykernel_1857/145878120.py:2: DeprecationWarning: d_separated is deprecated and will be removed in NetworkX v3.5.Please use `is_d_separator(G, x, y, z)`.\n",
      "  nx.d_separated(G, {\"T\"}, {\"Y\"}, {\"M1\"})\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 420,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Is T and Y d-separated given M1? \n",
    "nx.d_separated(G, {\"T\"}, {\"Y\"}, {\"M1\"})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Is  $T \\perp \\!\\!\\! \\perp Y | M_1, W_2 $  valid? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 422,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/dq/t_6k9k1j2kgbrldmxlbz46240000gn/T/ipykernel_1857/3360455046.py:2: DeprecationWarning: d_separated is deprecated and will be removed in NetworkX v3.5.Please use `is_d_separator(G, x, y, z)`.\n",
      "  nx.d_separated(G, {\"T\"}, {\"Y\"}, {\"M1\", \"W2\"})\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 422,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Is T and Y d-separated given M1 and W2? \n",
    "nx.d_separated(G, {\"T\"}, {\"Y\"}, {\"M1\", \"W2\"})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "# 3.4. Markov Properties in Causal Graphical Models\n",
    "\n",
    "In the context of causal inference and graphical models, the **Markov properties** are fundamental to understanding the relationship between graph structures (DAGs) and probability distributions. The Markov properties allow us to represent conditional independence relationships between variables using the structure of a Directed Acyclic Graph (DAG).\n",
    "\n",
    "\n",
    "- When a distribution $p$ is Markovian with respect to a graph $\\mathcal{G}$, this graph encodes certain independence in the distribution.\n",
    "\n",
    "- Markov property links causal DAGs to conditional probabilities (from data)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 3.4.1. Bayesian Networks and Factorization\n",
    "\n",
    "* Bayesian networks form the foundation for causal graphical models, as causal models can be viewed as a special type of probabilistic graphical models. \n",
    "* Probabilistic graphical models are statistical models, while causal graphical models are causal models. \n",
    "* Bayesian networks are the primary probabilistic graphical model that causal graphical models (also called causal Bayesian networks) inherit most of their properties from.\n",
    "\n",
    "\n",
    "Imagine that we are primarily concerned with modeling associations between variables, without making any causal assumptions. In such a case, we want to model the data distribution $P(x_1, x_2, \\dots, x_n)$. \n",
    "\n",
    "The **chain rule** of probability allows us to break down any joint probability distribution into a series of conditional probabilities. This factorization is useful because it expresses the joint probability of a set of variables as the product of simpler, sequential conditional probabilities.\n",
    "\n",
    "The joint probability distribution of multiple variables $P(x_1, x_2, \\dots, x_n)$ can be factorized using the chain rule as follows:\n",
    "\n",
    "$$\n",
    "P(x_1, x_2, \\dots, x_n) = P(x_1) \\prod_{i=2}^{n} P(x_i \\mid x_{i-1}, \\dots, x_1)\n",
    "$$\n",
    "\n",
    "- $P(x_1)$: This is the **marginal probability** of the first variable $x_1$.\n",
    "- $P(x_2 \\mid x_1)$: The **conditional probability** of $x_2$, given $x_1$.\n",
    "- $P(x_3 \\mid x_2, x_1)$: The **conditional probability** of $x_3$, given both $x_1$ and $x_2$, and so on.\n",
    "\n",
    "The chain rule allows us to decompose the joint probability distribution into a product of these simpler terms, where each term depends on the values of the preceding variables. \n",
    "\n",
    "However, modeling these factors with tables requires an exponential number of parameters. For instance, if we consider binary variables, then modeling $P(x_n \\mid x_{n-1}, \\dots, x_1)$ requires $2^{n-1}$ parameters. As the number of variables increases, this brute-force parameterization quickly becomes intractable.\n",
    "\n",
    "An efficient way to model these variables is to use local dependencies. Given a probability distribution and a corresponding directed acyclic graph (DAG), we formalize the specification of these independencies with the **local Markov assumption**:\n",
    "\n",
    "$ \\text{Local Markov Assumption}: \\text{Given its parents in the DAG, a node } X \\text{ is independent of all its non-descendants.} $\n",
    "\n",
    "\n",
    "### Factorization Example: A Four Nodes DAG\n",
    "\n",
    "In this example, we explore how we can model the dependencies between four binary variables: $X_1, X_2, X_3,$ and $X_4$, using a Directed Acyclic Graph (DAG). We aim to demonstrate how the local Markov assumption simplifies the factorization of the joint distribution by taking into account the conditional dependencies encoded in the DAG.\n",
    "\n",
    "In this scenario, we assume the following relationships:\n",
    "- $X_1 \\to X_2$ (i.e., $X_2$ depends on $X_1$)\n",
    "- $X_1 \\to X_3$ (i.e., $X_3$ also depends on $X_1$)\n",
    "- $X_2 \\to X_3$ (i.e., $X_3$ depends on both $X_1$ and $X_2$)\n",
    "- $X_3 \\to X_4$ (i.e., $X_4$ depends solely on $X_3$)\n",
    "\n",
    "This structure implies that $X_4$ is conditionally independent of $X_2$ and $X_1$ given $X_3$.\n",
    "\n",
    "#### Visualizing the Four Node DAG\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaMAAAG6CAYAAAClTCmnAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/TGe4hAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAwsElEQVR4nO3deXxU9b3/8fdMEkL2BUTZlwREoMoPFYuo0KpFxBUVtNqi9Uq1cgG1FcXeBuzVVtEKKi7UVr0UcQMX0IoL4lJUUMSKFGVHdgiZEJKYZeb8/ogTCdkmkzNzttfz8cijD2fOzHynj/PhPeedkzM+wzAMAQBgIb/VCwAAgDACAFiOMAIAWI4wAgBYjjACAFiOMAIAWI4wAgBYjjACAFiOMAIAWI4wAuJg2bJl8vl8WrZsmdVLAWyJMIKpnnrqKfl8vgZ/brvtNquXV2v48OHy+Xw6//zz6923ZcsW+Xw+3XfffRasLDLhNYZ/kpKS1L59e5166qmaOnWqtm3b1uTjb731Vvl8Po0dO7bJ7TZv3qwJEyaoT58+Sk1NVWpqqvr166cbb7xR//73v818S/C4RKsXAHe688471bNnzzq3DRgwwKLVNG7x4sX67LPPdOKJJ1q9lKhcccUVOvfccxUKhVRUVKSVK1dq5syZmjVrlv72t7/p8ssvr/cYwzA0f/589ejRQ4sWLVJJSYkyMjLqbbd48WKNHTtWiYmJuvLKK3XCCSfI7/dr3bp1WrhwoR599FFt3rxZ3bt3j8dbhcsRRoiJkSNH6qSTTrLs9UOhkCorK9W2bdtGt+nWrZtKSko0ffp0vfrqq3FcnXkGDRqkq666qs5tW7du1c9+9jONGzdOxx13nE444YQ69y9btkzbt2/X0qVLNWLECC1cuFDjxo2rs83GjRt1+eWXq3v37nrnnXfUsWPHOvffc889euSRR+T3U67AHOxJsMTSpUt1+umnKy0tTdnZ2brwwgv1n//8p842V199tXr06FHvsdOmTZPP56tzm8/n04QJEzRv3jz1799fycnJeuONN5pcQ0ZGhm666SYtWrRIq1atanbNmzZt0mWXXabc3Fylpqbqxz/+sV577bV6223fvl0XXXSR0tLS1KFDB910002qqKho8Dk/+eQTnXPOOcrKylJqaqqGDRumf/3rX82upSndu3fXU089pcrKSt1777317p83b5769eunn/zkJzrrrLM0b968etvce++9Ki0t1ZNPPlkviCQpMTFREydOVNeuXVu1ViCMMEJMFBcXa//+/XV+wt5++22NGDFCe/fu1bRp03TzzTdr+fLlGjp0qLZs2RL1ay5dulQ33XSTxo4dq1mzZjUYZEeaNGmScnJyNG3atCa327Nnj0499VQtWbJEv/nNb3TXXXfpu+++0wUXXKCXXnqpdrvy8nKdeeaZWrJkiSZMmKA77rhDH3zwgW699dYG13vGGWfo4MGDKigo0N13361AIKCf/vSnWrFiRUvffh1DhgxRXl6e3nrrrTq3V1RUaMGCBbriiisk1dR8S5cu1e7du+tst3jxYuXn5+uUU05p1TqAiBmAiZ588klDUoM/YQMHDjQ6dOhgFBYW1t72xRdfGH6/3/jlL39Ze9u4ceOM7t2713uNgoIC48hdV5Lh9/uNr776KqJ1Dhs2zOjfv79hGIYxffp0Q5Lx2WefGYZhGJs3bzYkGTNmzKjdfvLkyYYk44MPPqi9raSkxOjZs6fRo0cPIxgMGoZhGDNnzjQkGc8//3ztdqWlpUZ+fr4hyXj33XcNwzCMUChk9O7d2xgxYoQRCoVqty0rKzN69uxpnH322U2uv6E1HunCCy80JBnFxcW1t7344ouGJGP9+vWGYRjGwYMHjbZt2xoPPPBA7TbFxcWGJOOiiy6q95xFRUXGvn37an/KysqaXCcQKY6MEBOzZ8/WW2+9VedHknbt2qXVq1fr6quvVm5ubu32xx9/vM4++2y9/vrrUb/msGHD1K9fvxY/Lnx0NH369Ea3ef311zV48GCddtpptbelp6dr/Pjx2rJli9auXVu7XceOHXXppZfWbpeamqrx48fXeb7Vq1dr/fr1+vnPf67CwsLao8fS0lKdeeaZev/99xUKhVr8Xg6Xnp4uSSopKam9bd68eTrppJOUn58vqaaqHDVqVJ2q7uDBg3Uef7jhw4frqKOOqv2ZPXt2q9YIhHECA2Ji8ODBDZ7AsHXrVknSscceW+++4447TkuWLFFpaanS0tJa/JpHnr0XqaysLE2ePFkFBQX6/PPPlZOTU2+brVu3NlhZHXfccbX3DxgwQFu3blV+fn6932kd+X7Xr18vSfVOHDhccXFxg2uJ1KFDhySp9ky5QCCg119/XRMmTNCGDRtqtxs6dKgWLFigb775Rn369KndPvz4wz3++OMqKSnRnj176p04AbQGYQTbOvIf9LBgMNjg7SkpKVG/1qRJk/TAAw9o+vTpmjlzZtTPE6nwUc+MGTM0cODABrdp6MikJdasWaMOHTooMzNTkvTCCy+ooqJC999/v+6///5628+bN0/Tp09XVlaWOnbsqDVr1tTbJhzIrfndHtAQwghxFf6blK+//rrefevWrVP79u1rj4pycnIUCATqbRc+ujJT+Oho2rRpDR6tdO/evdE1h+8P/++aNWtkGEadMD3ysXl5eZKkzMxMnXXWWaa9j7CPPvpIGzdurHP0Mm/ePA0YMEAFBQX1tn/88cf1zDPP1FaVo0aN0hNPPKEVK1Zo8ODBpq8PqMfqX1rBXcInMKxcubLRbQYOHGgcffTRRlFRUe1tX375Zb0TGB5++GFDkvHFF1/U3rZz504jPT29wRMYbrzxxojXefgJDGGBQMDIzs42Bg4c2OgJDMuXL6+97dChQ0avXr2iOoEhGAwaeXl5Ru/evY2SkpJ669u7d2+T62/qBIYtW7YYffr0Mdq0aVP7/922bdsMn89n3HnnnQ0+37x58wxJxscff2wYhmF88803RmpqqtG/f39j9+7d9bbftGlTsydQAC3BkRHibsaMGRo5cqSGDBmia6+9VuXl5XrooYeUlZVV5xTryy+/XFOmTNHFF1+siRMnqqysTI8++qj69OkT0d8FtVRWVpYmTZrU4IkMt912m+bPn6+RI0dq4sSJys3N1dNPP63NmzdrwYIFtX/8ed111+nhhx/WL3/5S3322Wfq2LGj5s6dq9TU1DrP5/f79cQTT2jkyJHq37+/rrnmGnXu3Fk7duzQu+++q8zMTC1atKjZNa9atUr/+Mc/FAqFFAgEtHLlSi1YsEA+n09z587V8ccfL0l65plnZBiGLrjgggaf59xzz1ViYqLmzZunU045Rb1799YzzzyjK664Qscee2ztFRgMw9DmzZv1zDPPyO/3q0uXLi39vxlomNVpCHeJ5MjIMAzj7bffNoYOHWqkpKQYmZmZxvnnn2+sXbu23nZvvvmmMWDAAKNNmzbGsccea/zjH/9o9NTu1h4ZGUbNqctZWVkNfurfuHGjcemllxrZ2dlG27ZtjcGDBxuLFy+u9xxbt241LrjgAiM1NdVo3769MWnSJOONN96oc2QU9vnnnxujR4822rVrZyQnJxvdu3c3xowZY7zzzjtNrj98ZBT+SUxMNHJzc41TTjnFuP32242tW7fW2f5HP/qR0a1btyafc/jw4UaHDh2Mqqqq2ts2bNhg3HDDDUZ+fr7Rtm1bIyUlxejbt69x/fXXG6tXr27y+YCW8BmGYVgXhQAAcAUGAIANEEYAAMsRRgAAyxFGAADLEUYAAMsRRgAAyxFGAADLEUYAAMsRRgAAyxFGAADLOeJCqSHDUFlVUNUhQyGj5sfv88nv8ynR71NqUoL8jXz3DYCWYd5gBduFUcgwdLCiWoGKKgW+q9KB8iodrKhSU1/A7JeUmZyk3JQkZbdNUnZykjKTExkYoBnMG+zCNhdKPVBeqU2BMm0vKVfo+xX5VHNJ4kgdvr3fJ3XJSFFeTqpy2rYxd7GAwzFvsBtLwygYMvRtSbk2FpWquKK6xcPQnPDzZSUnKj8nTV0yUpTg59MbvIl5g51ZEkbBkKF1hYe0MVCq6lD8Xj7R71NeTpr65qYzJPAM5g1OEPcwKiyv1Ke7AiqtCsbzZetIS0rQyR2zlZtCnQB3Y97gFHELo2DI0Nr9JVpfVGp6PdBS4dfvnZOmfu0z+NQG12He4DRxCaMD5ZVaafGns8bwqQ1uw7zBiWIeRjtKyrViZ0CStZ/OGhP+jDa4U7Y6Z6RYuhagtZg3OFVMw2hLoEyr9hTH6ulNN+iYLPXISrV6GUBUmDc4WcwuB+S0wZCkVbuLtaW4zOplAC3GvMHpYhJGO0rKHTcYYat2F2tHSbnVywAixrzBDUwPowPllbWdtVOt2BnQgfJKq5cBNIt5g1uYGkbBkKGVuwJmPqVlVu4KKBjHPxAEWop5g5uYGkZr95eotCpoy7N4WsKQVFoV1Nr9JVYvBWgU8wY3MS2MCssrtb6o1Kyns4X1RaXUB7Al5g1uY0oYBUOGPt0VkNv+rton6gPYD/MGNzIljNYdOOSKuuBI4fpg3YFDVi8FqMW8wY1aHUbBkKGNLqsLjrSxqJRPa7AF5g1u1eow2l5SHtfL0luhOmRoO38LARtg3uBWrQ6jDS7/lBbmlfcJe/PKfuiV94kftCqMDpRXqrii2qy12FpxRTVn+sBSzBvcrFVhtClQ5rozehrjU837BazCvMHNog6jkFHT67q7vf6BoZq+PhT/b2kHmDe4XtRhdLCiWmb9HvX1uX/TJX076cEpExu8/1BxQNedMUhXDOylnZs3SpI2/2eN5v3lT7rz2it0zZABuqRvJ/3hF5eYs6BGhAypxCM1CezFzHmTWj5z1VVV+mjJa3poyiRNPPcMXTkoX1cO6q3bxozSG/OfVjBo/hf5MW/eEnUYBSqqTFvEyKt+pf6DT9V7r7yoFe+8Ue/+v945VQf27tZVN09Vp555kqQVb7+hhXMe0lcrPlJ2+w6mraU5RSa+b3hPSUmJHnzwQe3atatFjzNz3qSWz9zub7fovknX6eO3Xlennnk65+dX64zzR6tw9y79dfrtuufGaxSLr0Zj3rwj6i/XW72nWJsDZabVBnu3f6ubLvipklNSNHPxu8rMaSdJ+uiNxbpv8ngNOGWopj31vHy+mtZ82/qvVV1ZoW59jlNJoEj/dfpA9T95iO6cu8CkFdXnk9QzO1UDj86K2WvA3V566SWNHj1abdq00Q033KApU6aoY8eOzT7O7HmTWjZzhXt2aeU7SzT8ojFqm/rDF+J9V1amP/zyEm1c84Vumfm4Tj3nfNPWx7x5S9RHRgfKq0wdjA5dumrclAIVF+7XnGm3S5IC+/dpzvTblJKWrhvvfqA2iCSpW+9j1av/8UpMSjJxFU0zVPO+gWiFP/tVVlbq4YcfVo8ePTR58uRmj5TMnjepZTPX7uiOOufnV9cJIklqm5qq868eL0n6asVHpq6PefOWqMIoZBgqjsHh88/GXqWBpw3XR0sW64PFL+mxP/xOB4sO6Jqp09WhcxfTXy8aByuq+KUqTBEMBiMKpVjNm2TOzCUm1nwgTEhMNH19zJt3RBVGZTG8LtZv7rpfaZlZmj31Zq1c+qZOHH6Wzrzkihi9WsuFVPP+AbM0F0qxnDep9TP3zsJnJUknDB1m+tqYN++IKoxieTmSdkd31Mgrr1FVZYUSk5J0w50zYvZa0XL75VhgjcZCKdb7W2tm7s3n/qHP31+qH/34NJ047MyYrI9584aojqtjedhcXLhfbz43V5JUXVWlT5e9rbPHXBmz14vGj4cM0YYvV1u9DDhQJOcLBYNBBYNBzZo1Sw8++KC+2rRVUY5qRKKduU/ffUt/+987dFSnLpp070MxWx81nTfYLowenzZFBw8U6qpbpurVvz+mp++ZroGnDdNRnezxOyNJ+t2tU1RVXGj1MuBAn3/+uebMmdPsdj6fT8nJybr00kvV7qijpO1FMVtTNDP32Xvv6L5J45XVrr2mPf2CcjocHbP1EUbeEFUY+X2xuSjJslde1Cdv/VMnDj9LF183QR06d9Vfbr5Bj/z+FhX8/bmYvGY0Lr7oQuWmtLF6GXCghQsXNhlGfr9f6enpmjJliiZMmKDMzMyYXqMtmpn7bNnbmjHxOmXk5Gr60y/qmK7dY7Y+KXb/3sBeovqdUSx2jsI9u/T3u/5H6Vk5tZ310HMv1JAR5+nfyz/Qm8/ONf01o8VwwGx+v1+ZmZn64x//qG+//VZTp05VZmZmzX0x2t+imblwEKVnZWv60y+oY/eeMVnb4Zg3b4gqjBL95u8cj9xxi0oPFuu//ud/6xzyX1fwJ2XmttP/zfij9u7YbvrrRiMW7x/e1FQIhcVqf2vpzK16f6lmTLxOaVlZmv70C+rUo1dM1nUk5s0boqrpUpMS5JNMO930zWfnavWHyzRkxHk6/byL69yXldtO4wv+rPsmXadH7rhZBU8+J5/Pp+2b1uulObMlSZUVNV/EtWPzBj102+Tax/73n2eatMIf+FXz/oHW8Pl8ysjIqFPHNcbseZNaPnM7Nm/QvROuVVVlhfqfPEQfvvZyvec8qnNX/XT0WBNXybx5SdS/M8pKTjLlell7tm/T0/feqax27TV+2p8a3GbIiFE6bdRF+vC1l7Vk/tM65+dXK7Bvn5a9/Hyd7QL7694WizDKTE6iNkDU8vPz1atXL1177bXNhlCYmfMmRTdzXfL6qKqyQpL0r9dfafAx/U8eYnoYMW/eYZtr0zkB18qCVZg3uF3U16bLbpvkqcGQamqS7LbxuxYeEMa8we2iD6Nkb+4kOR5937AW8wa3izqMMpMT5bWTXPw+KSM5dn8JDzSGeYPbRR1Gfp9PXTJS5JX58EnqkpHCL1NhCeYNbhd1GElSr+xUz/TYhqS8nNRmtwNihXmDm7UqjHJT2ijLI4fRWcmJymnLJYBgHeYNbtaqMJKk/Jw0M9Zhe155n7A3r+yHXnmf+EGrw6hLRorrL9eR6K/p6wGrMW9wq1aHUYLfpzyXf4rJy0lTgsv/AYAzMG9wq1aHkST1zU1X2vfXz3ITn6S0pAT1zU23eilALeYNbmRKGCX4fTqpY7brzvQxJJ3cMZtPabAV5g1uZEoYSVK7lDbq7bL6oHdOGl+iB1ti3uA2poWRJPVrn+GK+iBcF/Rrn2H1UoBGMW9wE1PDKMHv08kds818SstQF8DumDe4ialhJNX8Yd7gTtlmP21cDe6UTV0AR2De4Bamh5Ekdc5I0aBjnPkdJIOOyVJn/sYBDsK8wQ1iEkaS1CMr1XEDMuiYLPXI4npYcB7mDU4X9Te9RmpHSblW7AxIki1PRQ231IM7ZfMJDY7HvMGpYh5GknSgvFIrdwVUWhWM9Uu1WFpSgk7uSGcN92De4ERxCSNJCoYMrd1fovVFpfLJ2k9t4dfvnZOmfu0zOIsHrsO8wWniFkZhheWV+tTiT218OoNXMG9wiriHkVTzqW3dgUPaWFSq6lD8Xj7x+4tM9s1N59MZPIN5gxNYEkZhwZCh7SXl2lBUquKKatPrBCMUks/vV3ZyovJy0tQlI4WhgGcdOW/B6molJJr3ZX3h+WXeEA1Lw+hwB8ortSlQpu0l5Qp/eGtpOB2+fXVlpTZ9vkK/HnMh3xgJHCYUCmnoWSP0i4m/Vad+x5syb35fzXct5eWkMm+Iim3CKCxkGCqpqFZRRZUC31XpQHmVDlZUKdTEY/ySMpOTlJuSpOy2ScpJTtLTf31Mv73lFu3du1fZ2dlxWj1gfx9++KFOP/10ffjhhxpy6qmmzFtGcqL8Po6CED3bhVFDQoahsqqgqkOGQkbNj9/nk9/nU6Lfp9SkhHqDsGPHDnXt2lVPPvmkxo0bZ9HKAfuZNGmSFixYoG3btsnvr/9379HMG9BajgijaJ1++unKzMzUa6+9ZvVSAFsIhULq2rWrLrvsMs2cOdPq5QC1YnY5IDu47LLL9NZbbykQCFi9FMAWli9frp07d+qyyy6zeilAHa4Oo0suuUTV1dV65ZVXrF4KYAsvvPCCOnfurCFDhli9FKAOV4dR586dNXToUD3//PNWLwWwXCgU0osvvqhLL720wd8VAVZy/R5JVQfUoKKDnbk+jKjqgBpUdLAz14cRVR1ARQf788ReSVUHr6Oig915Ioyo6uB1VHSwO0+EEVUdvIyKDk7gmT2Tqg5eRUUHJ/BMGFHVwauo6OAEngkjqjp4ERUdnMJTeydVHbyGig5O4akwoqqD11DRwSk8FUZUdfASKjo4ief2UKo6eAUVHZzEc2FEVQevoKKDk3gujKjq4AVUdHAaT+6lVHVwOyo6OI0nw4iqDm5HRQen8WQYUdXBzajo4ESe3VOp6uBWVHRwIs+GEVUd3IqKDk7k2TCiqoMbUdHBqTy9t1LVwW2o6OBUng4jqjq4DRUdnMrTYURVBzehooOTeX6PpaqDW1DRwck8H0ZUdXALKjo4mefDiKoObkBFB6djrxVVHZyPig5ORxiJqg7OR0UHpyOMRFUHZ6Oigxuw536Pqg5ORUUHNyCMvkdVB6eiooMbEEbfo6qDE1HRwS3Yew9DVQenoaKDWxBGh6Gqg9NQ0cEtCKPDUNXBSajo4CbswUegqoNTUNHBTQijI1DVwSmo6OAmhNERqOrgBFR0cBv24gZQ1cHuqOjgNoRRA6jqYHdUdHAbwqgBVHWwMyo6uBF7ciOo6mBXVHRwI8KoEVR1sCsqOrgRYdQIqjrYERUd3Iq9uQlUdbAbKjq4FWHUBKo62A0VHdyKMGoCVR3shIoObsYe3QyqOtgFFR3cjDBqBlUd7IKKDm5GGDWDqg52QEUHt2OvjgBVHaxGRQe3I4wiQFUHq1HRwe0IowhQ1cFKVHTwAvbsCFHVwSpUdPACwihCVHWwChUdvIAwihBVHaxARQevYO9uAao6xBsVHbyCMGoBqjrEGxUdvIIwagGqOsQTFR28hD28hajqEC9UdPASwqiFqOoQL1R08BLCqIWo6hAP4YrukksuoaKDJ7CXR4GqDrEWrujGjBlj9VKAuCCMokBVh1ijooPXEEZRoKpDLFHRwYvY06NEVYdYoaKDFxFGUaKqQ6xQ0cGLCKMoUdUhFqjo4FXs7a1AVQezUdHBqwijVqCqg9mo6OBVhFErUNXBTFR08DL2+FaiqoNZqOjgZYRRK1HVwSxUdPAywqiVqOpgBio6eB17vQmo6tBaVHTwOsLIBFR1aC0qOngdYWQCqjq0BhUdQBiZhqoO0aKiAwgj01DVIVpUdABhZBqqOkSDig6owd5vIqo6tBQVHVCDMDIRVR1aiooOqEEYmYiqDi1BRQf8gAkwGVUdIkVFB/yAMDIZVR0iRUUH/IAwMhlVHSJBRQfUxRTEAFUdmkNFB9RFGMUAVR2aQ0UH1EUYxQBVHZpCRQfUxyTECFUdGkNFB9RHGMUIVR0aQ0UH1EcYxQhVHRpCRQc0jGmIIao6HImKDmgYYRRDVHU4EhUd0DDCKIao6nA4KjqgcUxEjFHVIYyKDmgcYRRjVHUIo6IDGkcYxRhVHSQqOqA5TEUcUNWBig5oGmEUB1R1oKIDmkYYxQFVnbdR0QHNYzLihKrOu6jogOYRRnFCVeddVHRA8wijOKGq8yYqOiAyTEccUdV5DxUdEBnCKI6o6ryHig6IDGEUR1R13kJFB0SOCYkzqjrvoKIDIkcYxRlVnXdQ0QGRI4zijKrOG6jogJZhSixAVed+VHRAyxBGFqCqcz8qOqBlCCMLUNW5GxUd0HJMikWo6tyLig5oOcLIIlR17kVFB7QcYWQRqjp3oqIDosO0WGjMmDFUdS5DRQdEhzCyEFWd+1DRAdEhjCzUqVMnqjoXoaIDosfEWIyqzj2o6IDoEUYWo6pzDyo6IHqEkcWo6tyBig5oHabGBqjqnI+KDmgdwsgGqOqcj4oOaB3CyAao6pyNig5oPSbHJqjqnIuKDmg9wsgmqOqci4oOaD3CyCao6pyJig4wB9NjI1R1zkNFB5iDMLIRqjrnoaIDzEEY2QhVnbNQ0QHmYYJshqrOOajoAPMQRjZDVeccVHSAeQgjm6GqcwYqOsBcTJENUdXZHxUdYC7CyIao6uyPig4wF2FkQ1R19kZFB5iPSbIpqjr7oqIDzEcY2RRVnX1R0QHmI4xsiqrOnqjogNhgmmwsXNUVFRVZvRR8j4oOiA3CyMbCVd2rr75q9VLwPSo6IDYIIxujqrMXKjogdpgom+OsOvugogNihzCyOc6qsw8qOiB2CCObo6qzByo6ILaYKgegqrMeFR0QW4SRA1DVWY+KDogtwsgBqOqsRUUHxB6T5RBUddahogNijzByCKo661DRAbFHGDkEVZ01qOiA+GC6HISqLv6o6ID4IIwchKou/qjogPggjByEqi6+qOiA+GHCHIaqLn6o6ID4IYwchqoufqjogPghjByGqi4+qOiA+GLKHIiqLvao6ID4IowciKou9qjogPgijByIqi62qOiA+GPSHIqqLnao6ID4I4wciqoudqjogPgjjByKqi42qOgAazBtDkZVZz4qOsAahJGDUdWZj4oOsAZh5GBUdeaiogOsw8Q5HFWdeajoAOsQRg5HVWceKjrAOoSRw1HVmYOKDrAWU+cCVHWtR0UHWIswcgGqutajogOsRRi5AFVd61DRAdZj8lyCqi56VHSA9Qgjl6Cqix4VHWA9wsglqOqiQ0UH2APT5yJUdS1HRQfYA2HkIlR1LUdFB9gDYeQiVHUtQ0UH2AcT6DJUdZGjogPsgzByGaq6yFHRAfZBGLkMVV1kqOgAe2EKXYiqrnlUdIC9EEYuRFXXPCo6wF4IIxeiqmsaFR1gP0yiS1HVNY6KDrAfwsilqOoaR0UH2A9h5FJUdQ2jogPsiWl0Maq6+qjoAHsijFyMqq4+KjrAnggjF6Oqq4uKDrAvJtLlqOp+QEUH2Bdh5HJUdT+gogPsizByOaq6GlR0gL0xlR5AVUdFB9gdYeQBVHVUdIDdEUYe4PWqjooOsD8m0yO8XNVR0QH2Rxh5hJerOio6wP4II4/walVHRQc4A9PpIV6s6qjoAGcgjDzEi1UdFR3gDISRh3itqqOiA5yDCfUYL1V1VHSAcxBGHuOlqo6KDnAOwshjvFLVUdEBzsKUepAXqjoqOsBZCCMP8kJVR0UHOAth5EFur+qo6ADnYVI9ys1VHRUd4DyEkUe5uaqjogOchzDyKLdWdVR0gDMxrR7mxqqOig5wJsLIw9xY1VHRAc5EGHmY26o6KjrAuZhYj3NTVUdFBzgXYeRxbqrqqOgA5yKMPM4tVR0VHeBsTC1cUdVR0QHORhjBFVUdFR3gbIQRHF/VUdEBzsfkQpKzqzoqOsD5CCNIcnZVR0UHOB9hBEnOreqo6AB3YHpRy4lVHRUd4A6EEWo5saqjogPcgTBCLadVdVR0gHswwajDSVUdFR3gHoQR6nBSVUdFB7gHYYQ6nFLVUdEB7sIUox4nVHVUdIC7EEaoxwlVHRUd4C6EEeqxe1VHRQe4D5OMBtm5qqOiA9yHMEKD7FzVUdEB7kMYoUF2reqo6AB3YprRKDtWdVR0gDsRRmiUHas6KjrAnQgjNMpuVR0VHeBeTDSaZKeqjooOcC/CCE2yU1VHRQe4F2GEJtmlqqOiA9yNqUaz7FDVUdEB7kYYoVl2qOqo6AB3I4zQLKurOio6wP2YbETEyqqOig5wP8IIEbGyqqOiA9yPMEJErKrqqOgAb2C6EbGGqrp9+/Zpzpw5uuuuu1r13GVlZfrtb3+r559/XqWlpbW3U9EB3uAzDMOwehFwhp07d6pLly6aNWuWkpOTNX/+fL3//vsKhUJKSkrSd999F/XRy5dffqnjjz9ekpScnKxRo0Zp7NixWrZsmV599VVt27aNIyPAxQgjRGTfvn1auHChpkyZouLiYkmS3+9XKBSSJPXq1UsbN26M+vlLS0uVnp5e+98JCQkKBoOSpLy8PN19990aNWqU0tLSWvEuANgVYYRGFRYW6sUXX9Szzz6r9957T4ZhyOfz6chdxufz6dxzz9XixYtb9XodOnTQvn376t0eDr3k5GSdd955GjNmjM4//3ylpKS06vUA2Ae9Bxo1evRoXX/99Xr//fdrA6ihzy6JiYnq06dPq1+vsecIH31VVFTo5Zdf1tixY/X73/++1a8HwD4IIzRq6tSpSkpKajCADlddXa38/PxWv17fvn2VmJjY7HZHHXWUxo8f3+rXA2AfhBEaNWLECC1atEiJiYny+XyNbmcYhnr37t3q1+vdu3eTwZeQkKDc3Fx98MEHOvbYY1v9egDsgzBCkyINJDOOjPLz82tPWjgSQQS4G2GEZjUXSImJierWrVurX6exoyuCCHA/wggRaSqQunXrpoSEhFa/Rl5eXr3bCCLAGwgjRKyxQDruuONMef60tDQdddRRtf9NEAHeQRihRQ4PJKnmb4zMOK07LFzV+Xw+ggjwkObPowWOEA6kUaNGKRgMqlOnTg1uFzIMlVUFVR0yFDJqfvw+n/w+nxL9PqUmJch/ROWXk5MjScrKyiKIgBaIZt7shDBCVEaMGKG5c+fqqquuUl5enkKGoYMV1QpUVCnwXZUOlFfpYEWVQk08h19SZnKSclOSlN02SdnJSeqVl6c2bdpo+fLlBBHQCLPmLTM50TYBxeWA0CqFZRXaXFyu7SXlCn2/J/kktWSnOnx7v0/qnN5W+blpymnbxtzFAg53oLxSmwJlps5bl4wU5eWkWj5vhBFaLBgy9G1JuTYWlaq4orrFw9Cc8PNlJScqPydNXTJSlOC3x6c3IN68Mm+EESIWDBlaV3hIGwOlqg7Fb7dJ9PuUl5OmvrnphBI8w2vzRhghIoXllfp0V0ClVQ1fISEe0pISdHLHbOWmUN/B3bw4b4QRmhQMGVq7v0Tri0pNrwdaKvz6vXPS1K99BkdJcB0vzxthhEYdKK/USos/nTWGoyS4jdfnjTBCg3aUlGvFzoAkaz+dNSb8GW1wp2x1zuBL9uBszBthhAZsCZRp1Z5iq5cRsUHHZKlHVqrVywCiwrzV4HJAqMNpgyFJq3YXa0txmdXLAFqMefsBYYRaO0rKHTcYYat2F2tHSbnVywAixrzVRRhBUs0vT8OdtVOt2BnQgfJKq5cBNIt5q48wgoIhQyt3BaxehilW7gooGMc/EARainlrGGEErd1fotKqoC3P4mkJQ1JpVVBr95dYvRSgUcxbwwgjjyssr9T6olKrl2Gq9UWl1HWwJeatcYSRhwVDhj7dFZDbrmPgE3Ud7Id5axph5GHrDhxyRV1wpHB9sO7AIauXAtRi3ppGGHlUMGRoo8vqgiNtLCrl6Ai2wLw1jzDyqO0l5XG9LL0VqkOGtvO3R7AB5q15hJFHbXD5p7Qwr7xP2JtX9sPWvE/CyIMOlFequKLa6mXERXFFNWfWwVLMW2QIIw/aFChz3Rk9jfGp5v0CVmHeIkMYeUzIqOl13d1e/8BQTV8f4uL0sADzFjnCyGMOVlTLzN+jvj73b7qkbyc9OGVig/cfKg7oujMG6YqBvbRz80ZJ0vuLFuqeCb/Sb84eoisH9daVg/I16bzhevJPBSrcs8u8xX0vZEglHqlJYC92mLcj7f52q64clK9L+nbS4wVTzFvc96KdN8LIYwIVVaY+38irfqX+g0/Ve6+8qBXvvFHv/r/eOVUH9u7WVTdPVaeeeZKkD197Wds3rlefEwbpZ2Ov0tljfqGc9h302v89oZvO/6m2rf/a1DVKUpHJ7xuIhB3m7XChUEgP3z7Z1DU1JJp5I4w8JvBdlan9tc/n04S7H1Db1DQ99odbdbCosPa+j95YrA9fe1kDThmqc39xbe3tv501Rw/98wNNvm+2xk0p0NW3FWjaU8/r+j/OUOnBYj3/8P0mrrCmxw58RxgheiUlJerbt68mTJigHTt2RPw4O8zb4RY/NUffrP5MV0wy/4iodo2Kbt4II485UF5len/doUtXjZtSoOLC/Zoz7XZJUmD/Ps2ZfptS0tJ1490PyOf7YSTbJLdt8HlOPed8SdLubZtNXZ+hmvcNRGv//v36+uuvNXv2bPXo0SPiULLDvIVt37Re82fdq4vHT1CPvv1NXtUPop03wshDQoah4hjVVT8be5UGnjZcHy1ZrA8Wv6TH/vA7HSw6oGumTleHzl0ieo7Plr0tSerau6/p6ztYUcVJDDBFdXW1HnvssWZDyU7zFgwG9fBtk3VM95669PrJMVnT4aKZt8QYrQU2VBbj62L95q77ddP5P9XsqTerqrJCJw4/S2deckWj2//rn69q+4ZvVPFdub7d8I1Wf7hMHbp00+UTf2f62kKqef/pbdjl0XrBYFCS9Nhjj+nxxx/Xr3/9a91+++3q3Llz7TZ2mreX5jykTWu/1J+eXaykNm1iuKoa0cwbR0YeEuvLkbQ7uqNGXnmNqiorlJiUpBvunNHk9sv/uUjPz/6LXvnbo1r13jvqedwAFfz9WR3dpVtM1uf2y7Eg/oLBYKNHSnaZty3rvtILjzygC391g/IGHB/TNR2upe+fj4keEuuaqrhwv958bq4kqbqqSp8ue1tnj7my0e1/9+BfJUmlB4u1ae0azZ/5Z/3uknN060NP6Ec/Ps309b24cKGqDxaZ/rxwv/379zd5f/hI6dFHH9Wjjz6q4cOH64lnnovpmiKZt6rKSj102yQd062Hxky4OabrORI1HRoV6zB6fNoUHTxQqKtumapX//6Ynr5nugaeNkxHdWr6d0ZpmVn60Y+HKu+JZ/TfI0/Xg1Mm6dG3P1ZiUpKp65s160H957NPTH1OeIMR4eyEQiFJ0tKlS/Xxx58oue+gmK0pknl7ac5D2vbNOt01/1UltUmO2VoaQhihUf4GzrAxy7JXXtQnb/1TJw4/SxdfN0EdOnfVX26+QY/8/hYV/D2yT4ip6Rnqc8IgrXj7De3etkVd8nqbusb3lr2r3JTY9+Vwn82bN6tXr15NbpOYmKhgMKjLLrtMBQUFOqZnvpZtK2zyMdGKdN42/WeNQqGQbh97XoPP8+Zzc/Xmc3N18pkjdNvsJ01dY0v/vSGMPCRWYVS4Z5f+ftf/KD0rp7a3HnruhfpoyWv6aMlivfnsXP3s8l9E9FxFe/dIkhISzd81YxnG8K5wCI0ePVoFBQXq16+fpNj9bVtL5u2EU89QZk5uveco2rdXq957R5175avvoJPV87gBpq+TMEKjEv2x+cf4kTtuUenBYk2+b7ZyOhxde/t1BX/SVys/0v/N+KMGnv4TdejcReWHDunA3t3q3Cu/3vO8s2C+1v/7c3Xs3ksdu/c0fZ2xev/wpsZCqPZ+G8zbyCuvafA51nyyXKvee0f9Tx6iX0+/JybrbOn7J4w8JDUpQT7J1NNN33x2rlZ/uExDRpyn08+7uM59WbntNL7gz7pv0nV65I6bVfDkcyoJFGnSqGHKG3CCOvfKV26HY1R6sFgbvlytTWu/VGp6hv77zzNNXGENv2reP9BazYVQmB3mraE/fo2HaOaNU7s9xO/zKSvZvJMC9mzfpqfvvVNZ7dpr/LQ/NbjNkBGjdNqoi/Tlxx9qyfynlZnbTpfeMFltktvqi+Xva9FTj+v9RQtUVVWp88aN18zF7+rY/3eSaWsMy0xOoqZD1ML/qPt8Po0ePVpr1qzRc88912gQSfaYN6tEM28+I9LTROAKq/cUa3OgzDOXtJdqrpXVMztVA4/OsnopcCjDMPTYY49p2LBhTQbQkZi3yFHTeUx22yRPDYZUU5NktzX3NHF4i8/n0w033NDixzFvkaOm85hsE2sDJ8nx6PuGtZi3yBFGHpOZnCivnVTm90kZyZQAiD/mrQWPi8FaYGN+n09dMlJM/Y4VO/NJ6pKRwskLsATzFjnCyIN6Zad6psc2JOXlpFq9DHgY8xYZwsiDclPaKMsjtVVWcqJy2nIJIFiHeYsMYeRR+TlpVi8hLrzyPmFvXtkPW/M+CSOP6pKR4vrL4yT6a/p6wGrMW/MII49K8PuU5/JPa3k5aUpw+T8AcAbmrXmEkYf1zU1X2vfXz3ITn6S0pAT1zU23eilALeataYSRhyX4fTqpY7brzvQxJJ3cMZujItgK89Y0wsjj2qW0UW+X1Qe9c9L4Ej3YEvPWOMII6tc+wxX1Qbgu6Nc+w+qlAI1i3hpGGEEJfp9O7pht9TJMQT0Hu2PeGkYYQVLNH+YN7pRt9TJaZXCnbOo5OALzVh9hhFqdM1I06BhnfufPoGOy1Jm/KYKDMG91EUaoo0dWquMGZNAxWeqRxfXn4DzM2w/4plc0aEdJuVbsDEiSLU9FDbfUgztlc0QEx2PeCCM04UB5pVbuCqi0Kmj1UupJS0rQyR35HRHcw+vzRhihScGQobX7S7S+qFQ+WfupLfz6vXPS1K99BmfNwXW8PG+EESJSWF6pTy3+1MbRELzCi/NGGCFiwZChdQcOaWNRqapD8dttEr+/yGTf3HSOhuAZXps3wggtFgwZ2l5Srg1FpSquqDa9Tgg/X3ZyovJy0tQlI4UQgmd5Zd4II7TKgfJKbQqUaXtJucIf3lo6LIdv7/fVfPdLXk4q39AKHMHN80YYwRQhw1BJRbWKKqoU+K5KB8qrdLCiSqEmHuOXlJmcpNyUJGW3TVJOcpIykhPl93EUBDTFjfNGGCFmQoahsqqgqkOGQkbNj9/nk9/nU6Lfp9SkBNsMAuB0Tp83wggAYDkuBwQAsBxhBACwHGEEALAcYQQAsBxhBACwHGEEALAcYQQAsBxhBACwHGEEALAcYQQAsBxhBACw3P8HL9ovuvBL4d4AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Create a directed acyclic graph (DAG)\n",
    "G = nx.DiGraph()\n",
    "\n",
    "# Add edges based on the relationships in the provided figure\n",
    "G.add_edges_from([('X1', 'X2'), ('X1', 'X3'), ('X3', 'X4'), ('X2', 'X3')])\n",
    "\n",
    "# Define the layout to match the snapshot\n",
    "pos = {'X1': (0, 2), 'X2': (2, 2), 'X3': (1, 1), 'X4': (3, 1)}\n",
    "\n",
    "# Draw the DAG \n",
    "plt.figure(figsize=(4, 4))  # Reduced figure size for smaller display\n",
    "nx.draw(G, pos, with_labels=True, node_color='lightblue', node_size=2000, font_size=14, arrowsize=20)\n",
    "plt.title(\"Four Node DAG\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Factorizing with Markov Properties\n",
    "\n",
    "The local Markov assumption helps us simplify the factorization of joint distributions. If a distribution $P$ is Markov with respect to a DAG $\\mathcal{G}$, we can factorize it accordingly. Consider the following factorization for a four-variable distribution:\n",
    "\n",
    "$$\n",
    "P(x_1, x_2, x_3, x_4) = P(x_1)P(x_2 \\mid x_1)P(x_3 \\mid x_2, x_1)P(x_4 \\mid x_3, x_2, x_1)\n",
    "$$\n",
    "\n",
    "By applying the local Markov assumption to the DAG, where $X_4$ only depends on $X_3$, we can simplify the last factor:\n",
    "\n",
    "$$\n",
    "P(x_4 \\mid x_3, x_2, x_1) = P(x_4 \\mid x_3)\n",
    "$$\n",
    "\n",
    "\n",
    "Thus, the full factorization of the joint distribution becomes:\n",
    "\n",
    "$$\n",
    "P(x_1, x_2, x_3, x_4) = P(x_1)P(x_2 \\mid x_1)P(x_3 \\mid x_2, x_1)P(x_4 \\mid x_3)\n",
    "$$\n",
    "\n",
    "This factorization shows how each variable's probability depends on others based on the DAG structure.\n",
    "\n",
    "\n",
    "Depending on the graph structure, we may be able to simplify further. For instance, if the DAG has the structure $X_1 \\to X_2 \\to X_3 \\to X_4$, then the factorization can be reduced to:\n",
    "\n",
    "$$\n",
    "P(x_1, x_2, x_3, x_4) = P(x_1)P(x_2 \\mid x_1)P(x_3 \\mid x_1)P(x_4 \\mid x_3)\n",
    "$$\n",
    "\n",
    "### Parameter Reduction\n",
    "\n",
    "For the example of four binary variables $X_1, X_2, X_3, X_4$, the table below shows the parameters needed to model the distribution $P(x_4 \\mid x_3, x_2, x_1)$ when $n=4$ and all variables are binary:\n",
    "\n",
    "\n",
    "| $x_1$ | $x_2$ | $x_3$ | $P(x_4 \\mid x_3, x_2, x_1)$ |\n",
    "|-------|-------|-------|----------------------------|\n",
    "| 0     | 0     | 0     | $\\alpha_1$                 |\n",
    "| 0     | 0     | 1     | $\\alpha_2$                 |\n",
    "| 0     | 1     | 0     | $\\alpha_3$                 |\n",
    "| 0     | 1     | 1     | $\\alpha_4$                 |\n",
    "| 1     | 0     | 0     | $\\alpha_5$                 |\n",
    "| 1     | 0     | 1     | $\\alpha_6$                 |\n",
    "| 1     | 1     | 0     | $\\alpha_7$                 |\n",
    "| 1     | 1     | 1     | $\\alpha_8$                 |\n",
    "\n",
    "In this case, we need $2^{n-1} = 8$ parameters, $\\alpha_1$ to $\\alpha_8$. But we can reduce the complexity by modeling only local dependencies, such as $P(x_4 \\mid x_3)$, to significantly lower the number of parameters required.\n",
    "\n",
    "---\n",
    "\n",
    "### Bayesian Network Factorization\n",
    "\n",
    "The **Bayesian network factorization** follows directly from the local Markov assumption:\n",
    "\n",
    "$$\n",
    "P(x_1, \\dots, x_n) = \\prod_i P(x_i \\mid \\text{pa}_i)\n",
    "$$\n",
    "\n",
    "where $\\text{pa}_i$ denotes the set of parents of $x_i$ in the DAG. This factorization, also known as the **chain rule for Bayesian networks**, guarantees that the joint distribution factorizes according to the structure of the DAG. If $P$ and the DAG $\\mathcal{G}$ satisfy this factorization, then $P$ and $\\mathcal{G}$ are said to be **Markov compatible**.\n",
    "\n",
    "The **Minimality Assumption** strengthens the local Markov assumption by adding the condition that adjacent nodes in the DAG are dependent:\n",
    "\n",
    "$\\text{Minimality Assumption}$: \n",
    "1. Given its parents in the DAG $\\mathcal{G}$, a node $X$ is independent of all its non-descendants.\n",
    "2. Adjacent nodes in the DAG $\\mathcal{G}$ are dependent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 3.4.2. Global Markov Property\n",
    "\n",
    "The **Global Markov Property** states that any two sets of nodes in a DAG are conditionally independent if all paths between them are blocked by a set of nodes, according to the **d-separation** criterion. In mathematical terms, if $\\mathbf{X}$, $\\mathbf{Y}$, and $\\mathbf{Z}$ are disjoint sets of variables in a DAG $\\mathcal{G}$, then:\n",
    "\n",
    "$$\n",
    "\\mathbf{X} \\perp \\mathbf{Y} \\mid \\mathbf{Z} \\quad \\text{if} \\quad \\mathbf{Z} \\text{ d-separates } \\mathbf{X} \\text{ from } \\mathbf{Y} \\text{ in } \\mathcal{G}.\n",
    "$$\n",
    "\n",
    "An slighly diffrent notation is:\n",
    "\n",
    "$$\n",
    "X \\!\\perp\\!\\!\\!\\perp_G Y |\\{Z\\} \\Rightarrow X \\!\\perp\\!\\!\\!\\perp_P Y |\\{Z\\}\n",
    "$$\n",
    "\n",
    "* For all disjoint vertex sets $A,B,C$, the symbol $\\!\\perp\\!\\!\\!\\perp_{\\mathcal{G}}$ denotes d-separation.\n",
    "* Because of d-separation, we can read it $P$ is Markov with respect to $\\mathcal{G}$ or $P$ satisfy Markov assumption in respect to $\\mathcal{G}$.\n",
    "\n",
    "This is the broadest form of the Markov property and encapsulates the relationship between any non-adjacent nodes in the graph. It provides a basis for deriving conditional independence relationships from the graph structure.\n",
    "\n",
    "\n",
    "### Global Markov Example: a 3 Nodes DAG\n",
    "\n",
    "Consider a simple chain structure $A \\rightarrow B \\rightarrow C$. \n",
    "\n",
    "Here, $A \\perp C \\mid B$, which means $A$ and $C$ are conditionally independent given $B$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 426,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Create a simple chain structure for illustration\n",
    "G = nx.DiGraph()\n",
    "G.add_edges_from([('A', 'B'), ('B', 'C')])\n",
    "\n",
    "# Draw the graph\n",
    "pos = nx.spring_layout(G)\n",
    "nx.draw(G, pos, with_labels=True, node_color='skyblue', node_size=800, font_size=10, font_color='black', arrowsize=5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 3.4.3. Local Markov Property\n",
    "\n",
    "The **Local Markov Property** refers to the fact that in a DAG, each node is conditionally independent of its non-descendants, given its parents. Mathematically, for a node $X_i$, the local Markov property can be expressed as:\n",
    "\n",
    "$$\n",
    "X_i \\perp \\text{NonDescendants}(X_i) \\mid \\text{Parents}(X_i)\n",
    "$$\n",
    "\n",
    "This means that once we know the values of the parents of a node, that node becomes independent of all non-descendant variables in the graph.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Local Markov Example: a 4 Nodes Graph\n",
    "\n",
    "Given its parents in the DAG, a node $X$ is independent of all its predecessors. For example, let consider the graph below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 430,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define a directed graph (DAG) using NetworkX\n",
    "G = nx.DiGraph()\n",
    "\n",
    "# Add edges to represent the relationships in the graph\n",
    "G.add_edges_from([\n",
    "    (\"X1\", \"X2\"),\n",
    "    (\"X1\", \"X3\"),\n",
    "    (\"X2\", \"X3\"),\n",
    "    (\"X3\", \"X4\")\n",
    "])\n",
    "\n",
    "# Use spring_layout for consistent layout style\n",
    "pos = nx.spring_layout(G)\n",
    "\n",
    "# Draw the graph with custom styling for consistency\n",
    "nx.draw(G, pos, with_labels=True, node_color='lightblue', node_size=800, font_size=14, font_color='black', arrows=True, arrowstyle='-|>', arrowsize=10)\n",
    "plt.title(\"Local Markov Property Example\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the DAG above, we have:\n",
    "\n",
    "$$\n",
    "P(x_1, x_2, x_3, x_4) = P(x_1) P(x_2|x_1) P(x_3| x_2,x_1) P(x_4 | x_3, x_2, x_1)\n",
    "$$\n",
    "\n",
    "What happens with the *Local Markov Assumption*?\n",
    "\n",
    "$$\n",
    "P(x_1, x_2, x_3, x_4) = P(x_1) P(x_2|x_1) P(x_3| x_2,x_1) \\underbrace{P(x_4 | x_3, x_2, x_1)}_{P(x_4 | x_3)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 3.4.4. Pairwise Markov Property\n",
    "\n",
    "The **Pairwise Markov Property** asserts that any two **non-adjacent** nodes in a graph are conditionally independent given all the other nodes in the graph. Specifically, if there is no direct edge between two nodes in a **Markov Random Field** (undirected graph), then the two nodes are conditionally independent, given the rest of the nodes in the graph.\n",
    "\n",
    "The pairwise Markov property applies to **undirected graphs** (Markov Random Fields) and can be formally expressed as:\n",
    "\n",
    "$$\n",
    "X_i \\perp X_j \\mid \\{ X_k : X_k \\in V \\setminus \\{X_i, X_j\\} \\}\n",
    "$$\n",
    "\n",
    "Where:\n",
    "- $X_i$ and $X_j$ are two non-adjacent nodes.\n",
    "- $V$ is the set of all nodes in the graph.\n",
    "- $\\perp$ denotes conditional independence.\n",
    "\n",
    "This differs from the **Local Markov Property**, which focuses on the conditional independence of a node given its parents or neighbors.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 4. d-Separation in Graphs vs Conditional Independence in Distributions\n",
    "\n",
    "d-Separation is a graphical concept that helps determine conditional independence relations in a DAG. When two variables are d-separated, they are conditionally independent given a set of other variables. The concept of d-separation directly corresponds to the **Markov properties** and provides a graphical interpretation of conditional independence.\n",
    "\n",
    "Specifically, if two variables $X$ and $Y$ are d-separated by a set of variables $Z$ in a DAG, then $X$ and $Y$ are conditionally independent given $Z$ in the joint probability distribution that the DAG represents.\n",
    "\n",
    "Formally, this can be written as:\n",
    "\n",
    "$$\n",
    "X \\perp Y \\mid Z \\quad \\text{if and only if} \\quad Z \\text{ d-separates } X \\text{ from } Y \\text{ in the DAG}.\n",
    "$$\n",
    "\n",
    "This criterion allows us to infer conditional independence purely from the graphical structure of a DAG without needing to calculate probabilities directly.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 432,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Create a DAG\n",
    "G = nx.DiGraph()\n",
    "G.add_edges_from([('A', 'B'), ('B', 'C'), ('A', 'D'), ('D', 'C')])\n",
    "\n",
    "# Draw the graph\n",
    "pos = nx.spring_layout(G)\n",
    "nx.draw(G, pos, with_labels=True, node_color='lightblue', node_size=800, font_size=16, font_color='black', arrowsize=10)\n",
    "plt.title(\"Example of DAG for d-Separation\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this DAG, $A$ and $C$ are d-connected through both $B$ and $D$, meaning $A$ and $C$ are not conditionally independent unless we condition on both $B$ and $D$.\n",
    "\n",
    "If we condition on both $B$ and $D$, then $A$ and $C$ become d-separated, and thus independent.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 5. Markov Equivalence\n",
    "\n",
    "Two Directed Acyclic Graphs (DAGs) are said to be **Markov Equivalent** if they encode the same set of conditional independence relations. This means that despite having different structures, the two DAGs represent the same conditional independencies among variables.\n",
    "\n",
    "Markov Equivalent DAGs have:\n",
    "\n",
    "1. **Same Skeleton**: \n",
    "   - The skeleton of a graph is the undirected graph obtained by ignoring the direction of the edges. Two DAGs are Markov equivalent if they have the same skeleton, meaning they have the same edges between nodes, regardless of direction.\n",
    "   \n",
    "2. **Same v-Structures**: \n",
    "   - A v-structure is a specific type of structure in a DAG where two variables, $A$ and $B$, both have directed edges pointing to a third variable $C$ (i.e., $A \\rightarrow C \\leftarrow B$). The condition is that there should be no direct edge between $A$ and $B$ in the skeleton. Markov Equivalent graphs must have the same set of v-structures.\n",
    "\n",
    "3. **Conditional Independence Relations**:\n",
    "   - Since Markov Equivalent DAGs encode the same set of conditional independence relationships, they cannot be distinguished based solely on observational data. In other words, both graphs will imply the same conditional independence relations for a given joint probability distribution.\n",
    "\n",
    "### Why is Markov Equivalence Important?\n",
    "\n",
    "Markov Equivalence tells us that it's often impossible to determine the unique direction of causality from observational data alone. If two or more DAGs are Markov Equivalent, additional assumptions or interventional data (through experiments) are needed to distinguish between them. This concept is critical in causal inference since identifying the exact causal structure can be challenging without experimental intervention.\n",
    "\n",
    "### Example of Markov Equivalent DAGs\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define the updated DAG 1 and DAG 2 as per the new structure\n",
    "dag1_edges = [('A', 'B'), ('A', 'C'), ('B', 'D'), ('C', 'D'), ('D', 'E')]\n",
    "dag2_edges = [('B', 'A'), ('A', 'C'), ('B', 'D'), ('C', 'D'), ('D', 'E')]\n",
    "\n",
    "# Create directed graphs for both DAGs\n",
    "G1 = nx.DiGraph()\n",
    "G2 = nx.DiGraph()\n",
    "\n",
    "G1.add_edges_from(dag1_edges)\n",
    "G2.add_edges_from(dag2_edges)\n",
    "\n",
    "# Adjusted positions to make edges more uniform in length\n",
    "pos = {\n",
    "    'A': (0, 1),\n",
    "    'B': (1, 1),\n",
    "    'C': (0, 2),\n",
    "    'D': (2, 1),\n",
    "    'E': (3, 1)\n",
    "}\n",
    "\n",
    "# Draw the two DAGs for comparison\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 6))\n",
    "\n",
    "# Set uniform edge width for all graphs\n",
    "edge_width = 2\n",
    "\n",
    "# Draw DAG 1\n",
    "nx.draw(G1, pos, with_labels=True, node_color='lightblue', node_size=2000, font_size=16, \n",
    "        font_color='black', arrowsize=10, width=edge_width, ax=ax1)\n",
    "ax1.set_title('DAG 1: A -> B -> D, A -> C -> D -> E')\n",
    "\n",
    "# Draw DAG 2\n",
    "nx.draw(G2, pos, with_labels=True, node_color='lightcoral', node_size=2000, font_size=16, \n",
    "        font_color='black', arrowsize=10, width=edge_width, ax=ax2)\n",
    "ax2.set_title('DAG 2: B -> A -> C -> D -> E')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "The two DAGs are **Markov Equivalent** because they encode the same set of conditional independence relationships, despite having different edge directions. Specifically:\n",
    "\n",
    "1. **Same Skeleton**: \n",
    "   - The skeleton of a graph is the undirected version of the DAG, where edge directions are ignored. Both DAGs have the same skeleton, meaning the same undirected connections between nodes:\n",
    "     - $ A - B $, $ A - C $, $ B - D $, $ C - D $, $ D - E $.\n",
    "\n",
    "2. **Same v-Structures**: \n",
    "   - Both DAGs have the same v-structure $ B \\rightarrow D \\leftarrow C $, as well as no direct connection between $ B $ and $ C $. This ensures that both graphs represent the same conditional independence relationships between the variables.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Markov Equivalent DAGs\n",
    "To test whether the three graphs are Markov equivalent, we can write a second program that checks their skeletons (the undirected graph structure) and v-structures (collider structures). If both the skeletons and v-structures are the same, then the graphs are Markov equivalent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DAG 1 and DAG 2 are Markov Equivalent: True\n",
      "DAG 1 and DAG 3 are Markov Equivalent: False\n",
      "DAG 2 and DAG 3 are Markov Equivalent: False\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABv4AAAJOCAYAAAB/dnBOAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/TGe4hAAAACXBIWXMAAA9hAAAPYQGoP6dpAADCm0lEQVR4nOzdd3wUdf7H8ffsptGSUKSqKE0UC6KI7VAUCyKeCAomoSnNAuhZAMtZAPVOQUXs0kkApag0C0WwoCAISpEOIi3UUBKS3ez8/uCXXAgBQpLd787u6/l45PHIbHZn3nvJHe+bz853LNu2bQEAAAAAAAAAAABwNJfpAAAAAAAAAAAAAACKj8EfAAAAAAAAAAAAEAIY/AEAAAAAAAAAAAAhgMEfAAAAAAAAAAAAEAIY/AEAAAAAAAAAAAAhgMEfAAAAAAAAAAAAEAIY/AEAAAAAAAAAAAAhgMEfAAAAAAAAAAAAEAIY/AEAAAAAAAAAAAAhgMEfAAAAAAAAAAAAEAIY/KHEjBo1SpZl5X7FxMSoevXquu222zR06FAdOnTolK+/6qqrZFmW3n///VM+7/vvv9d9992nGjVqKCoqSnFxcWrSpIlefvll7dq167Q5d+zYoX79+qlZs2YqV66cLMvSd999dyZv9ZSys7NVvXp1WZalWbNmldh+S8LmzZuP+x1ZlqXY2Fg1bNhQw4YNU3Z2tumIkor/t1RYwfy7ynHw4EG99NJLuuyyy1S2bFmVKlVKF198sfr27avt27ebjqfvvvvuuN9VdHS0qlSpohtvvFGvvPKKdu/ebTricfL//ef96tmzp+l4AGCcU/rcnDlz9MADD6hevXoqXbq0atWqpa5du2rHjh1n9H7zO++88054/3Xr1tVTTz2lffv2FWvf/rB69ercnAcOHDAdp0AbNmxQjx49VKtWLcXExCg2NlbXXXed3n77bWVkZJiOpxdffPG433np0qV17rnnqlWrVho5cqQyMzNNR8yVv3fl/5owYYLpiAAQ9pzSpRYsWKC77rpL55xzjmJiYlS1alXdfvvt+vHHH8/o/Z5MMJ9vccq5sRx0qZJDl0I4iTAdAKHn5Zdf1vnnny+Px6OdO3fqu+++02OPPaYhQ4boyy+/1KWXXnrCa9atW6fFixfrvPPOU3Jysh566KEC9/3vf/9bAwYMUK1atdS5c2fVqlVLR48e1ZIlSzR48GCNHj1aGzZsOGW+NWvW6D//+Y/q1q2rSy65RAsXLiyR951j7ty52rFjR+57adGiRYnuvyTcf//9uuOOOyRJaWlpmjlzpnr16qUtW7bo9ddfN5zuf4ryt3Qmgv13tXHjRjVv3lx//fWX7r33XnXv3l1RUVH6/fffNXz4cE2dOlVr1641HVOS1Lt3bzVu3FjZ2dnavXu3fvrpJ73wwgsaMmSIPv30U910002mI+a65ZZb1LFjxxMer1evnoE0ABCcgr3P9e3bV/v27dO9996runXrauPGjRo2bJimT5+uZcuWqWrVqkV+7w0bNtQTTzwhSbm53nrrLc2fP1+LFi0q8n79Ydy4capatar279+vSZMmqWvXrqYjHWfGjBm69957FR0drY4dO+riiy9WVlaWfvjhBz311FNauXKlPvroI9MxJUnvv/++ypYtq8zMTG3btk1ff/21HnjgAb311luaPn26zjnnHNMRc+X0rvyuueYaA2kAAAUJ9i61du1auVwu9ezZM7dLjBs3Tk2bNtWMGTN0++23F+v9B/v5FskZ58boUv5Bl0JYsIESMnLkSFuSvXjx4hN+NmfOHLtUqVJ2zZo17fT09BN+/u9//9uuXLmyPXnyZNuyLHvTpk0nPGfChAm2JPu+++6zMzMzT/j5gQMH7BdeeOG0OQ8ePGjv3bvXtm3b/uyzz2xJ9rx58077usLq2LGj3ahRI/vtt9+2y5QpYx8+fLhY+9u9e7e9ffv2Esm2adMmW5L9+uuvH/e4z+ezGzdubFevXr3I+16/fr195MiR4ka0bbt4f0tnIph/Vx6Px77sssvs0qVL299///0JP09LS7OfeeaZIu1769at9r59+4ob0bZt2543b54tyf7ss89O+NmyZcvsypUr2/Hx8UX+z+Xw4cP2hg0bihszlyT7kUceKbH9AUCocUqfmz9/vp2dnX3CY5LsZ5999rSvP5maNWvaLVu2POHxJ5980pZkr127tkj7LcmOkMPn89nnnXee/a9//ctu3bq1feONNxZ7nyXZ5zZu3GiXLVvWrl+/foHvfd26dfZbb71VpH2vXr3azsrKKm5E27Zt+4UXXrAl2bt37z7hZ+PGjbNdLpfdpEmTIu8/UL0LABAcnNKlCnLkyBG7SpUq9m233Vak1+cVzOdbnHJujC51DF0KKBqW+kRA3HTTTXr++ee1ZcsWjRs37oSfp6SkqG3btrrzzjsVFxenlJSUE57z73//W5UqVdLw4cMVFRV1ws/j4uL04osvnjZLuXLlVKFChULl3rNnj/7880+lp6cX6vkZGRmaOnWq2rdvr/vuu08ZGRn64osvCvXak1mxYoXOPfdc/fOf/9SXX34pr9dbrP0VxLIsValSRRERRb8IeOzYsapWrZp69uypxYsXl2C6453ub6mwgv13NXnyZC1fvlzPPvusrr/++hN+Hhsbq0GDBhVp37Nnz1b16tWVmJioefPmybbtIuc8lcsuu0xvvfWWDhw4oGHDhhVpH7t371adOnV00003KSUlRUePHi3hlACAwgqmPte0aVO5XK4THqtQoYJWr1593ONn2ucKknMFYVG7kj/63I8//qjNmzerffv2at++vRYsWKC///67WPssyT733//+V4cPH9bw4cNVrVq1E35ep04d9enTp0j7fu2111SjRg09+eSTJ/y+S1JiYqK6du2qX375Rd9++22R9hGo3gUACH7B1KUKUrp0aZ111lknLB/OubHCo0sdjy4FmMPgDwHToUMHSdI333xz3OO//PKL1q9fr/vvv19RUVG65557lJycfNxz1q5dq7Vr1+ruu+9W2bJlA5Z52LBhuvDCCwu9rNOXX36pw4cPq3379qpatapuvPHGE97LmWrYsKGef/55/fHHH/rnP/+pc889V/3799e6deuKvM/09HTt2bNHe/bs0caNG/Xuu+/qq6++UqdOnYq8z4SEBCUmJmrixIm66qqrdOmll+rtt9/W3r17i7zPkznZ39KZCPbf1Zdffinpf++1JN16663q1auX5s6dq5tuukl16tTRoEGDtG3bthI/Vtu2bVWqVKki/66qVaumN954Q7t371ZiYqKqVaumRx99VL/99luRMx09ejT37z/vV1ZWVpH3CQDhIpj73OHDh3X48GFVqlTpuMfPtM95PJ7cfxv+/vtvTZs2TUOGDFHTpk11/vnnFymbP/pccnKyateurcaNG6tVq1YqXbq0xo8fX+T9SSXb56ZNm6ZatWrp2muvLVamgvTq1Uu333673n//fV100UW67rrrNGLECB0+fLjEj1Xc3umP3nXo0KECuwwnwgAg+AVblzp48GDuYO+ZZ57RihUrdPPNNx/3HM6NFR5d6kR0KcAQo9cbIqScajmDHHFxcfbll19+3GOPPvqofc4559g+n8+2bdv+5ptvbEn2b7/9lvucL774wpZ0wiXsPp/P3r1793FfHo+n0JlPt9RnzuXqhV0K9M4777Svu+663O2PPvrIjoiIsFNTUwud6WR8Pp89d+5cOykpyS5VqpQtyW7atKk9evToQi95mbOcQUFfDz30UO7voDgyMjLs5ORk++abb7Yty7Kjo6Ptdu3a2d98880JS3KdTFH/ls5EsP+uLr/8cjsuLq7YWU7F4/HYX3zxhX333XfbkZGRttvttu+44w57ypQphV7yoTDLJFx22WV2+fLli5130aJFds+ePe34+Hhbkn355Zfb7777rr1///5C7+Nkf/+S7PHjxxc7IwA4nRP7XI4BAwbYkuw5c+Yc9/iZ9LmaNWsW+G/EddddZ+/Zs+eMM+VXEh3Btm07KyvLrlix4nHLmiYkJNiXXXZZsTPadvH7XFpami3J/uc//1kieU51nA8//NBu0qSJLckuW7as/eCDD9o//fRTofdxquWpbNu29+/fb0uyW7duXaysJdm7Tva1Y8eOYmUEABSf07rUbbfdlvvvSFRUlN2jRw87IyPjuOdwbuzM0aX+hy4FmMHgDyWmMOWmRo0adp06dXK3PR6PfdZZZ9lPPvlk7mNer9euXLnycY+NHTvWlmR/8sknx+0v5x+PvF+nOn5+JXmPvz179tiRkZH2sGHDch/bu3fvCY+VhLS0NPuDDz7I/Yc5Li7O7tmz52nXvM4pN927d7e//fZb+9tvv7UnT55sP/LII7bL5bIfe+yxEs25efNm+8UXX7TPO+88W5Jds2ZN+5VXXjnt64ryt3QmnPC7ql27tn322WeXaJZT2bVrl/3GG2/YDRo0sCXl/nfwdOWpMIO/6667zo6IiCixrPkLdExMjJ2YmGhv2bLltK/NKc45f/95v3bu3FliGQHAqZzY52z72P39IiIi7Pvuu++MXpdfzZo17SZNmuT+2zB9+nR70KBBdnx8vH3ttdcW+/7CeRW1I9j2/078rVixIvexadOmnfBYSShKn9u6dastyU5KSirRLKeyatUq+8knn7SrVKliS7Ivuugi++OPPz7t6053ssrj8diS7ObNm5dY1uL2rn//+98FdpmC7vUEAAgsp3Wp3377zf7mm2/s4cOH202bNrW7dOliHzp0qLBv9wROON/ihHNjdKlTo0sBp8fgDyWmKJ9qmjFjhi3J/vTTT+1169blfrVr186uUaNG7qdgPv/88wI/1eTxeHL/x/mpp54yOvh79913bUn2jz/+eNx7uf766+1rrrnmlK/1er32jh07jvsqzD82GRkZ9nPPPWdblnXCJ8EKcrIbGNv2sU+XSbJ///33k74+PT39hJyFsXPnTrtVq1a5Rex0/H3FnxN+V8W94i8zM/OEnF6v97SvS0tLs7t27Zr7fxZOdzVdSV3xlz9rYU6sejwee+jQoXZUVJQtyZ46deppXyPJfuSRR077PAAIV07sc6tXr7YrVKhgN2zY0D548OAZvuPj1axZ027ZsuUJj0+aNMmWZA8dOvSkrw1UR7Bt27733nvt888//7j/vFetWmWXLl3a7t+//ylfG4g+VxKfUj906NBxGQt7lcD69evta665xpZUqCsgS+JT6sHUuwAAZjmxS+XIzMy0GzRoYLdp0+aMX5vDCedbnHBujC5FlwKKq+h3KwXO0N9//620tDTVqVMn97GcNb7vu+++Al8zf/58NWvWTPXr15d07Ga+eUVERKh58+a5+zcp571cd911Bf5848aNqlWrVoE/27p16wn3jJk3b55uvPHGAp+/ePFijRgxQhMmTNCBAwfUpEkTPfjgg7rwwguLnP/mm2/WsGHDtGDBAl1yySUFPmfixInq0qXLcY/ZJ1n/2uv1aubMmRo5cqRmzJgh27Z19913q1u3bkXOmKOgv6Uz4YTfVf369fXbb79p69atOuecc07zjk70008/qVmzZsc9tmnTJp133nknPNe2bX333XcaMWKEJk+erKNHj+rmm29W165dFRsbe8bHzsvj8Wjt2rW6+OKLT/m8/DeqHjlypDp37lzgc1evXq2RI0dq7Nix2rlzpxo0aKAHH3zwhPcLACh5wdbntm7dqltvvVVxcXGaOXOmypUrd0avL6yce90sWLBAvXr1OmmWQHSEgwcPatq0aTp69Kjq1q17ws9TUlI0aNAgWZZV4OsD0ediY2NVvXr1E37XZ+KNN97QSy+9lLtds2ZNbd68ucDnHj16VFOmTNHIkSM1Z84cxcTEKCkpSQ899FCRj58j5z2cqncGS+8CAAS/YOtSeUVFRemuu+7Sa6+9poyMDJUqVeqM9+GE8y2nEiznxuhSdCmguBj8IWDGjh0rSbrtttskSUeOHNEXX3yhdu3aqW3btic8v3fv3kpOTlazZs10wQUXqG7duvr888/11ltvqUyZMgHNfjqbNm3STz/9pEcffVQ33HDDcT/z+Xzq0KGDUlJS9NxzzxX4+qpVq+rbb7897rHLLrvsuO3U1FSNHTtWI0eO1MqVK1WxYkV17txZDz744GmHKoXh9Xol6ZQ38r3ttttOyJnfqlWrcocyu3btUr169TRgwAB17txZVapUKXZO6cS/pTPhlN9Vq1atNH78eI0bN079+/c/g3f4v0z5c1atWvW47c2bN2v06NEaNWqUNm/erLPPPltPPPGEHnzwwQLLVVFMmjRJGRkZp/1d5c/aoEGD47bT0tI0ceJEjRgxQr/88ovKli2rdu3aqWvXrrr66qtLJCsA4PSCqc/t3btXt956qzIzMzVnzpwTPkRSkgrTkwLVEaZMmaKjR4/q/fffV6VKlY772Zo1a/Tcc8/pxx9/1PXXX1/g6wPV5+6880599NFHWrhwoa655ppCvSavjh07HvceCjr5uGjRIo0cOVLjx49XWlqaLr/8cg0bNkwJCQmKj48/42MWpDC9M1h6FwAg+AVTlypIRkaGbNvWoUOHznjw55TzLacSTOfG6FJ0KaBYTF1qiNBzquUM5syZY5cqVco+//zzc28SnLM2+YIFCwrcX7du3ez4+Hj76NGjtm3bdnJysi3Jvv/++wtcs3nEiBElvtTn7t277dWrV9tHjhw55X4GDBhgS7L/+uuvAn9+yy232PXr1y90rrz++usv+5///KcdERFhW5ZlN2/e3J4wYUKR1p0+1XIGHTt2tCXZs2bNKlLOefPm5a6rXqpUKbtDhw72/Pnzi7SvM/1bOhNO+V1lZWXZl1xyiV2mTJkCb6p88OBB+5lnnilSzt9//z33/niRkZF269at7RkzZhRqGYX8TrVMwrJly+zKlSvb5cuXL/INkg8ePGgnJibm3rT76quvtj/55JMi33NALPUJAKfklD53+PBh+6qrrrLLlStn//rrr6d8bmH7nG2ffKnPnFx9+/Y97T4KUpId4eabb7Zr1apV4M+OHj1qly1b1u7Zs2eRcpZkn1u/fr1dpkwZ+6KLLirwPrrr168/Yamywpo0aVLuPV3i4+Pthx9+2F66dGmR9nWq5amSk5Ntl8t12qXJTiVQvQsAEByc0qV27dp1wmP79++3zznnHPucc8457nHOjRUeXep4dCnAHK74Q4mbNWuW/vzzT3m9Xu3atUtz587Vt99+q5o1a+rLL79UTEyMpGOX/1esWFHXXnttgfu566679PHHH2vGjBm65557lJCQoBUrVujVV1/VokWL1L59e51//vk6cuSIVqxYofHjx6tcuXIqX778aTMOHDhQkrRy5UpJxz598sMPP0jScZ88GjZsmF566aVTLi2Q814aNmx40iUZ77rrLvXq1UtLly5Vo0aNTpsvrw0bNmjp0qXq37+/HnjggRL5FMvSpUs1btw4SdKhQ4c0Z84cTZ48Wddee61uvfXWIu1z/vz58ng8eu+995SQkKC4uLhi5yzs35J07JM/559/vjp16qRRo0addJ9O+V1FRkZqypQpat68uZo2bar77rtP1113nSIjI7Vy5UqlpKSofPnyGjRo0Bnve8mSJfr777/1n//8R506dVLlypWLnDPH999/r6NHjyo7O1t79+7Vjz/+qC+//FJxcXGaOnXqCZ/UKqy9e/fq66+/Vs+ePfXggw+ecCVgUaxduzb37z+vKlWq6JZbbin2/gEgFAR7n0tMTNSiRYv0wAMPaPXq1Vq9enXuz8qWLau77747d7uwfS7Htm3bcv+dyMrK0vLly/Xhhx+qUqVKJ13m83RKqiNs375d8+bNU+/evQv8eXR0tG677TZ99tlnGjp0qCIjI89o/yXZ52rXrq2UlBS1a9dOF154oTp27KiLL75YWVlZ+umnn/TZZ5+ddFnv05kxY4YqVaqkMWPGqG3btkVaiiy/SZMmqWzZssrKytK2bdv09ddf68cff9Rll12mzz77rMj79Wfvyu/SSy/VpZdeWuz9AwCKL9i7VIsWLXT22WerSZMmqly5sv766y+NHDlS27dv18SJE497LufGCo8uRZcCgobpySNCR86nmnK+oqKi7KpVq9q33HKL/fbbb9sHDx7Mfe6uXbvsiIgIu0OHDifdX3p6ul26dOkTbv763Xff2W3btrWrVatmR0ZG2rGxsfaVV15pv/DCC4W+qihvzvxfeeV8auVkVwTatm0vWbLElmQ///zzJ33O5s2bbUn2448/Xqh8eaWnp+feyLm4cj7VlPcrIiLCrlWrlv3UU08V+Soq2z72yfuSciZ/Szn++OMPW5Ldr1+/k+7XSb+rHPv377f//e9/25dccoldunRpOyYmxr744ovt/v37F/kqupL8XeV8WirnKzIy0j7rrLPspk2b2oMGDSr0zaNPJisrq0if4DuZU/13/4Ybbiix4wCAUzmlz9WsWfOk/3tes2bN455bmD53sv26XC67cuXK9v3332+vX7/+tK8/mZLqCIMHD7Yl2XPmzDnpc0aNGmVLsr/44osz3n9JdoQca9eutbt162afd955dlRUlF2uXDn7uuuus995553cqxfOVEnmzPn7yPmKiYmxzz77bPvOO++0R4wYUeSMOfzZu/J/vfDCCyV2LABA0TilSw0bNsy+/vrr7UqVKtkRERH2WWedZbdq1arAKw85N1Z4dCm6FBAsLNs+yd1HAcBB3nvvPT399NPasGFDid1LEAAAAAAAAAAAJ3GZDgAAJSFn2SuGfgAAAAAAAACAcMUVfwAAAAAAAAAAAEAI4Io/AAAAAAAAAAAAIAQw+AMAAAAAAAAAAABCAIM/AAAAAAAAAAAAIAQw+AMAAAAAAAAAAABCAIM/AAAAAAAAAAAAIAQw+AMAAAAAAAAAAABCAIM/AAAAAAAAAAAAIAQw+AMAAAAAAAAAAABCAIM/AAAAAAAAAAAAIAQw+AMAAAAAAAAAAABCAIM/AAAAAAAAAAAAIAQw+AMAAAAAAAAAAABCAIM/AAAAAAAAAAAAIAQw+AMAAAAAAAAAAABCAIM/AAAAAAAAAAAAIAQw+AMAAAAAAAAAAABCAIM/AAAAAAAAAAAAIAQw+AMAAAAAAAAAAABCAIM/AAAAAAAAAAAAIAQw+AMAAAAAAAAAAABCAIM/AAAAAAAAAAAAIAREmA7gbz7bVronW16fLZ997MtlWXJZliJclkpHuuWyLNMxAQAAglK2na2DvoPy2l555ZXP9slluRShCEVYEYp1xcptuU3HBAAACEp2drZ8Bw5IHo9sr1fKzpbcblkREVJkpFzx8bLcdCkAAFByQmrw57NtHcz06kCmRweOerQvw6ODmR75TvEal6TY6EhVKBWp+JhIxUdHKjY6gmEgAAAIO9l2tvZl71NqdqpSs1O107tTe7L3yHeKNuWSS5XclVQ1oqoquyursruyKrgrMAwEAABhx87Olm/3bmXv2KHs7dvl3bZNvtTUY8O+k3G75apcWRE1ashdvbrc1arJddZZDAMBAECRWbZt26ZDFNe+jCxtPJCuvw9lyPf/78aSdCZvLO/zXZZ0drlSql2+tMrHRJVsWAAAgCCz07tTv2f+rrVZa5WtYyemXHKdcuCXX97nu+VWvah6uiz6MlWJqOKXzAAAAMHCu22bshYvlmflSsnrPfagyyX5Ct+ljnt+RIQiGzRQ1FVXKaJ69ZIPDAAAQppjB3/ZPltbD2Vow/4jSsv0nvGg73Ry9hcXHaE65cvo7HKl5HZxFSAAAAgNXturNVlrtDxzuXZn75YlS3YJtqmc/Z3lPksNoxuqXlQ9RVghtdgEAAAIY7bHI8+KFcpctEi+nTvPfNB3Ov+/P1fVqopu0kSRDRrIiowsuf0DAICQ5bjBX7bP1p97D2vDgSPy+gIXPcJlqXb5MqpfoSwDQAAA4Fhe26tFRxdp+dHlylJWwI4bpSg1jGmoxjGNGQACAADHsj0eZX7/vTIXLZIyMyXLkvx5ai1n/9HRir7qKkX/4x8MAAEAwCk5avC3NyNLv+44oCOeU6yN7mdlIt1qXC1eFUqxBCgAAHCWHd4d+vrI10rzpRk5viVLsa5Y3VbmNlWLqGYkAwAAQFF5t25VxtSp8h044N9h38lYllzx8Sp1zz2KOPvswB8fAAA4giMGf9k+W6v2HNK6/UdKfEnPM5Vz/Lrly+iiSuW4+g8AAAQ9r+3VwoyFWpq5tMSX9DxTOcdvFN1I15S6hqv/AABA0LM9Hh2dN09ZCxf6/wq/0/n/40ddc41imjXj6j8AAHCCoB/87cvI0mLDV/mdDFf/AQCAYGf6Kr9TiXPFcfUfAAAIat6//1bGlCnmrvI7Ga7+AwAAJxHUg79thzK0aPsBSWav8juZnGv9rqoerxrlShnNAgAAkN+6rHWadWSWJBm9yu9krP9vUy3KtFDdqLqG0wAAABzPs2qV0idPPjbwC8bTZ5YlWZZKt2mjyIsuMp0GAAAEiaAd/G0+kK6lu4Lvk+kn06hqnM6LK206BgAAgCRpReYKzUmfYzpGoTUv3VwNohuYjgEAACBJylq6VBnTppmOUWil7rpLUZdfbjoGAAAIAi7TAQritKGfJC3dmabNaemmYwAAADhu6CdJs9Nna2XmStMxAAAAHDf0k6SML79U1m+/mY4BAACCQNAN/rYdynDc0C/H0p1p2nYow3QMAAAQxtZlrXPc0C/H7PTZWpe1znQMAAAQxjyrVjlu6Jcj48sv5Vm1ynQMAABgWFAN/vZlZOXe08+pFm0/oH0ZWaZjAACAMLTDuyP3nn5ONevILO3w7jAdAwAAhCHv338fu6efg6VPnizv33+bjgEAAAwKmsFfts/W4h0HTMcoEYt3HFC2LyhvnQgAAEKU1/bq6yNfm45RIr4+8rW8ttd0DAAAEEZsj0cZU6ZItsPP59i2MqZMke3xmE4CAAAMCZrB36o9h3TEky2H1yvZko54srVqzyHTUQAAQBhZmLFQab402Q5vU7ZspfnS9HPGz6ajAACAMHJ03jz5DhwIicGf78ABHf3uO9NJAACAIUEx+NubkaV1+4+YjlGi1u0/wpKfAAAgIHZ4d2hp5lLTMUrUkswlLPkJAAACwrt1q7IWLnT+0C+HbSvrp59Y8hMAgDBlfPCX7bP1644DskwHKWGWWPITAAD4X84Sn1aItSlLFkt+AgAAv7M9HmVMnSpZodWlZFks+QkAQJgyPvj7c9/hkFjiM7+cJT//3HfYdBQAABDCFh9dHBJLfOaXs+Tn4qOLTUcBAAAhLPP770Njic/8/n/Jz8zvvzedBAAABJjRwV+2z9aGEFviM78N+49w1R8AAPALr+3VsqPLTMfwq2VHl3HVHwAA8Avb41HmokWhN/TLYdvKXLSIq/4AAAgzRgd/fx/KkDfEh2Jen62/D2WYjgEAAELQ2qy1ylJo31M4S1lam7XWdAwAABCCPCtXSpmZpmP4V2bmsfcJAADChtHB3/oQv9ovR7i8TwAAEFjLMpeZjuB3lqyweJ8AACDwMn/5JfTu7ZefZR17nwAAIGwYG/zty8hSWmZ4LNuUlunVvozQ/jQ+AAAIrJ3endqdvdt0DL+zZWt39m7t9O40HQUAAIQQ77Zt8u3cGbrLfOawbfl27pR32zbTSQAAQIBEmDrwxgPpsiQFql4t/3G+vp8+VX8u/VUH9qTKk5WlsvHxOrfuBWrU9GY1vauN4ipU9MuxLR17vxVKRfll/wAAIPz8nvm7LFmyA9Sm1sxboyWTlmjTok06uOugvFlelSlfRlXrV9VFt1ykK++7UmUrlfXLsS1Z+iPzD1WNqOqX/QMAgPCTtXix5HJJPl9AjjdvwwZ99scf+uWvv5R6+LAys7NVvlQpXVi5sm6pW1ftLr1UlcqU8c/BXS5l/fqrImrU8M/+AQBAULFsO/AfbfLZtr5ct1OBuL3fwf179eYTD+v3n76XJFWucY5qXnChokuV1oE9u7Xu96XKzMhQTOkyemHkRNW7rJFfcrgs6a66VeUK9SUkAACA32Xb2Xr/wPvKVrbfj3V472GN6TpGa+cfu89ehXMrqHqD6ooqHaVDqYe0ZckWZaVnKbpstB6a8pDOu/I8v+Rwy62H4x+WyzK6Uj0AAAgBdna2Dr72muT1/0pUe48c0YOTJ+u7jRslSefGx6tBlSoqExmpXYcPa8m2bUr3eFQ2Kkqfd+yoK88+2z9BIiIU27+/LBddCgCAUGfkir+Dmd6ADP2OHDqoZxPu1vZNG1SjVh31fPl1XXRlk+Oe48nK1Lypn2nisDe0f/cuv2Xx2dKhTK/iYiL9dgwAABAe9mXvC8jQL+NghobeMVSp61JVuW5ltXurnWpfU/u453gzvVo0fpG++s9XOrjroN+yZCtbe7P36qyIs/x2DAAAEB58u3cHZOiXdvSobh8xQuv27lW9SpX0VqtWurZmzeOek+n1avyyZXr1u++089Ah/4XxeuXbvVvuKlX8dwwAABAUjAz+DmR6AnKc4QOf0/ZNG1S5xjkalPKFysWXP+E5kVHRurVdkq66+TYdOZjm1zz7Mz0M/gAAQLGlZqcG5DiT+05W6rpUVTi3gvp81Udlyp+4/FREdISu7XytLrnjEqWnpfs1T2p2KoM/AABQbNk7dgTkOE/PnKl1e/fq3Ph4ff3AAypfuvQJz4mOiFDnK6/UHfXrK+3oUb/myd6+ncEfAABhwMj1/QeOeuTvBS93bt2i76dPlSR17vdigUO/vOIrnaUater4LY+lY+8bAACguFKzU+Xyc43bs3mPlk5aKkm6e+DdBQ798ipXuZyq1PXfiSSXXAEbeAIAgNCWvX37sfv7+dHmffs06Y8/JEmDbrutwKFfXpXLllXdSpX8F8jlCtjAEwAAmGVk8LcvwyN/r/S5ZN638mVnq0xsnK686VY/H+30bB173wAAAMW107tTPvn8eoyVX6+UL9unUnGldHGLi/16rMLwyaed3p2mYwAAgBDg3bZN8vm3S321dq2ybVtxMTG644IL/HqsQvH5jr1vAAAQ8gI++PPZttICsNTnhpW/S5JqXXSJ3G63349XGAczPfLZAbi5IQAACFnZdrb2ZO/x+3G2LtsqSTr7srPlchv5rNgJ9mTvkc/270k6AAAQ2uzsbPl27fL7cX7bvl2SdFm1anL7+erCwvLt2iXbzwNPAABgXsCbR7on2+9X+0nSwX17JUmxFSoG4GiF49Ox9w8AAFBUB30H/X61nyQd3nNYklS2Ulm/H6uwfPIpzeffezIDAIDQ5jtwwO9X+0nS3vRj9z4+q8ypl0sPqOxs+fbvN50CAAD4WcAHf15feF/xFu7vHwAAFI/X9pqOYFS4v38AAFBMnjC/DUu4v38AAMKAkaU+AyHnSr+cK/+CBUt9AgCA4vAqMIOvnCv9cq78CxbZYvUEAABQdLY3MF2qYunSkqTdR44E5HiFFaj3DwAAzAnZwV+tBpdKkjau+kPZ2cFzgojBHwAAKI5A3ePunMvOkST9vfxv+bKD514w2Xbw9DoAAOBAATpH1LB6dUnS8h07lB1M99ULonNkAADAPwI++HNZVkCOc+WNzeVyuXTkYJp+nftNQI5ZGIF6/wAAIDS5rMDUtwa3NZDlspSRlqEVs1YE5JiF4bbcpiMAAAAncwemS9xer55clqW0o0c1c82agByzUAL0/gEAgDkhO/ireu55ur7l3ZKkUf95SYcOnPrmxWl792jbxvV+z8XgDwAAFEeEIgJynErnV1KjNo0kSV88/4WO7D/1MlWHdh/SrnW7/J7LLU5WAQCAorMiAtOlzq9QQW0vvliS9NzXX2t/evopn7/78GGt27PH77kC9f4BAIA5AR/8RbgCN/h68LmBqlrzfKX+/ZeeS7xbq5f8csJzPFlZmjN5vJ5sfav+3rjO75kC+f4BAEDoibACd7KmzX/aqFKtStq7Za+GthiqjT9vPOE53iyvfh73s9648Q3tWuv/wV8g3z8AAAhBkZEBO9R/77hDtSpU0JYDB3T7iBFauGXLCc/J8no1dulSNf3wQ63Zvdv/oQL4/gEAgBkBP3NSOtItS1Ig7nRXNi5er6R8ocGP99TKRT/pucTWqnz2uap5wYWKjimltL17tO7333Q0/YhKly2nCpWr+jWPS8fePwAAQFHFumLlkks++f9eMaXjS6vPrD4a/eBorf9hvYbeMVQVa1ZUtQbVFFUqSod2H9JfS/9S5uFMxZSLUVzVOL/mccmlOJd/jwEAAEKbKz5ecrmkANx3L75UKX39wAPqMmmSfti8WS1GjlTN+Hg1qFJFpSMjlXrkiJZu26bDWVmKjY5WtXLl/BvI7ZarfHn/HgMAABhn2bYdiBncceZu3qMDmZ6AHvO37+fph+mf689lv+rA7lR5PVkqG19eNevWV6Mbm+uGu9qoXLx/y098dKRuOq+SX48BAABC3/iD45WanRrQY66evVpLpyzVpkWbdCj1kLyZXpWpUEbVLqymi269SFe2u1Jlypfxa4bK7sq6P/Z+vx4DAACEvkMffSTfjh0BPebsdes0acUKLdq6VamHDyvT61WF0qV1UeXKurVePbW/9FKVL13arxlc1aurXLdufj0GAAAwz8jgb9muNG06kB6Qq/6ChSXp/PjSaliFT6kDAIDimZc+TysyVwTkqr9g4ZJLF0dfrGalm5mOAgAAHC5jxgxlLV0akKv+gobLpagrrlCpO+4wnQQAAPhZwO/xJ0nxMZFhNfSTji1tGh/DOuoAAKD4Krsrh9XQT5J88qmyu7LpGAAAIAS4q1cPr6GfJPl8clerZjoFAAAIADODv+jwHICVD9P3DQAASla4DsDC9X0DAICSFa4DMHf16qYjAACAADAy+IuNjpDLMnFkc1yWVC46wnQMAAAQAiq4K8gtt+kYAeWWWxXdFU3HAAAAIcB11llSRJido4mIOPa+AQBAyDMy+HNZls4uV0rhMvuzJJ1drpRcVri8YwAA4E9uy616UfVkhUmbsmTpgqgL5LKMVFcAABBiLLdbkQ0aSK4w6RYulyIvvlhWuLxfAADCnLF/8WvFlw6b+/zZkmqXL206BgAACCGXRl8qO0zalC1bl0ZfajoGAAAIIVGNG4fPff58vmPvFwAAhAVjg78KpaIUFyZLX8ZFR6h8TJTpGAAAIIRUjaiqs9yhv1yTJUtnuc9SlYgqpqMAAIAQElGjhlxVq0qhvjqTZclVtaoiuL8fAABhw+g1/nXKlzF5+IAJl/cJAAACq2F0Q9MR/M6WHRbvEwAABF50kyaSHeIrKNj2sfcJAADChtHB39nlSinCFdqfrIpwHbufIQAAQEmrF1VPUQrtVQWiFKV6UfVMxwAAACEoskEDKTradAz/io4+9j4BAEDYMDr4c7ss1Q7xq+Fqly8jd4gPNwEAgBkRVoQaxjQ0HcOvGsY0VIQVHsvDAwCAwLIiIxV91VWhu9ynZSn6qqtkRUaaTgIAAALI6OBPkupXKKsykW6FWsWyJJWJdKt+hbKmowAAgBDWOKax4lxxskKsTVmyFOeKU+OYxqajAACAEBb9j3/IFR8fesM/y5KrfHlFN21qOgkAAAgw44M/t8vSldXiFWorqtuSGleL52o/AADgVxFWhG4rc5vsEGtTtmzdVuY2rvYDAAB+ZUVGqlTr1qF3rz/bVqnWrWVF0KUAAAg3xgd/klSxVJTqhtiSn3XLl1GFUqF9zx0AABAcqkVUU6PoRqZjlKgroq9QtYhqpmMAAIAwEHHOOYq65prQuerPshR17bWKOPts00kAAIABQTH4k6SLKpULiSU/c5b4vKhSOdNRAABAGLmm1DUhseRnzhKfV5e62nQUAAAQRmKaNQuNJT//f4nPmGbNTCcBAACGBM3gz+2y1LhavOkYJYIlPgEAQKDlLPkZCljiEwAABJoVGalS99wTEoM/lvgEACC8Bc3gT5IqlIrSVdXjTccolquqx7PEJwAAMKJaRDW1KNPCdIxiaVGmBUt8AgAAIyLOPlul27QxHaNYSrdpwxKfAACEuaAa/ElSjXKl1KhqnOkYRdKoapxqlCtlOgYAAAhjdaPqqnnp5qZjFEnz0s1VN6qu6RgAACCMRV50kUrddZfpGEVS6q67FHnRRaZjAAAAw4Ju8CdJ58WVdtzwr1HVOJ0XV9p0DAAAADWIbuC44V/z0s3VILqB6RgAAACKuvxyxw3/St11l6Iuv9x0DAAAEAQs27Zt0yFOZtuhDC3afkCSFIwhbdsnl+XSVdXjudIPAAAEnXVZ6zTryCxJkh2MbconWS5LLcq04Eo/AAAQdDyrVil98mTJto99BRmfJJfLpdJt2nClHwAAyBWUV/zlqFGulG44t6JKR7pNRzmBz+fTrq1/6WxvGkM/AAAQlOpG1dW95e5VrCvWdJQT+Hw+7dmyR1ekXsHQDwAABKXIiy5SmS5d5IqPlyzLdJzj+Hw+bdm/X7uaNmXoBwAAjhPUV/zlyPbZWrXnkNbtPyJLZq/+syT5bFtfDH9fE995Q/UvqKdFixYpOjraYCoAAICT89peLcxYqKWZS2XJMnr1nyVLPtunue/M1VevfaUL611IlwIAAEHN9nh0dN48ZS1ceGwAaPJUmmXJ9vk09Kef9Oq8eap30UV0KQAAcJygvuIvh9tl6ZLKsUFx9V/pSLeurRarpbOmKivzqH7//Xc988wzRjMBAACcSoQVoX+U/ofuK3efYl2xsmTuE+uxrli1jmmtjZ9tlOeohy4FAACCnhUZqVK33qoyDzxg9uo/y5IrPl5RHTro0+3bddTr1e+//65nn33WTB4AABCUHHHFX17ZPlt/7jusDfuPyOsLXPQIl6Xa5cuofoWycrss/f7772rcuLGysrIkSbNnz9bNN98csDwAAABF4bW9Wnx0sZYdXaYsZfn9eDlXGEYpSg1jGqpxTGNFWBF0KQAA4Ei2x6PM779X5qJFUmam/68AzNl/dLSir7pK0f/4h6zISLoUAAA4KccN/nJk+2z9fShD6/cfUVqmt8SXAM3ZX3x0hGqXL6Ozy5WS23X8J7qGDBmiJ554QpJUo0YN/f7776pQoUIJpgAAAPAPr+3V2qy1Wpa5TLuzd5f4EqA5+6vsrqzLoi9Tvah6irAijnsOXQoAADiV7fHIs3KlMn/5Rb6dOyWXS/L5Su4A/78/V7Vqir7qKkU2aCArMvK4p9ClAABAQRw7+MtrX0aWNh5I19+HMpRzEeCZDgLzPt9lSWeXK6Xa5UurfEzUSV/j8/l02223afbs2ZKktm3b6tNPP5UVZDd8BgAAOJWd3p36I/MPrclao2xlS5Jccsmnwp+8yvt8t9y6IOoCXRp9qapEVDnpa+hSAAAgFHi3bVPWr7/Ks2KF5PUee/BMB4F5nx8RoYiLLtLs3bt12a236rzzzivwJXQpAABQkJAY/OXw2bYOZXq1P9OjA0c92pfh0cFMzylPWbkkxUZHqkKpSMXHRKp8dKTKRUfIVciStG3bNl1yySXav3+/JGnUqFHq1KlT8d8MAABAgPlsn/Zm71VqdqpSs1O107tTe7L3nHIA6JJLldyVVDWiqiq7K6uyu7IquivKZRXuVtJ0KQAAECpsn0++3buVvX27snfskHfbNvl27ZKys0/+IrdbripVFFGjhtzVqsldvbpcZ52lu/75T02fPl1ut1sLFizQtddeW+DL6VIAACC/kBr8FcRn20r3ZMvrs7Vpyxb99NNPurdtW0VFRirCZal0pLvQQ76TmTRpku69915JUtmyZbV8+XLVqlWrJOIDAAAY5bN9SvOlyWt7tXHLRv2w8Ae1a9tO0RHRirAiFOeKK/SQ72ToUgAAIFTZPp98+/dLHo9sr/fYENDtlhURIUVGylW+vCzXiV2qRo0a2r59uySpdOnSmjt3rpo0aVLgMehSAAAgr5Af/OU4dOiQKlasKI/Ho8aNG2vRokUluv8uXbpo1KhRkqRrrrlGCxYsUERExKlfBAAA4BB0KQAAgMCpUqWKUlNTc7fLli2rmTNn6h//+EeBz6dLAQCAHMX7eLaDvPnmm/J4PJKkX3/9VevXry/R/Q8dOjT301QLFy7UK6+8UqL7BwAAMIkuBQAAEBgej0d79uw57rHDhw/r9ttv15w5cwp8DV0KAADkCIsr/g4fPqzzzjtPe/fuzX2sc+fOGjlyZIkeZ+HChbr++uvl8/nkdrv1448/nnQZBgAAAKegSwEAAATOpk2bTrpUZ3R0tH7++Wc1bNjwhJ/RpQAAgBQmV/y9++67x52okqSxY8eW+CfVr7nmGj333HOSpOzsbCUlJenw4cMlegwAAIBAo0sBAAAEzubNm0/6s8zMTM2aNavAn9GlAACAFAaDv8OHD+v1118/4fHs7GwNGjSoxI/3/PPP536aav369XrsscdK/BgAAACBQpcCAAAIrJMN/izLUosWLdSlS5eTvpYuBQAAQn7wV9An1HP445PqERERGjdunMqUKSNJGj58uKZOnVqixwAAAAgUuhQAAEBgRUdHF/j4888/r5kzZ6pq1aonfS1dCgAAhPzgb+bMmSf9WXZ2tr755psSP2adOnU0dOjQ3O2uXbtq+/btJX4cAAAAf6NLAQAABNa9996r//73vxo4cKBmzJiR+3je70+FLgUAQHgL+cHfgw8+qLPOOuu4T0u5XC5FR0erQYMGatmypV+O26VLF7Vu3VqStG/fPnXp0kU+n88vxwIAAPAXuhQAAEBgRUZG6qmnntKzzz6rO+64Q40aNZIkLVmyRGvWrCnUPuhSAACEr5Af/HXs2FGpqanatWtX7mO33HKLjh49qhUrVqhmzZp+Oa5lWfr4449VrVo1SdI333yjd955xy/HAgAA8Be6FAAAgFmJiYm536ekpBTqNXQpAADCV8gP/kyqWLGiRo0albvdt29f/fHHH+YCAQAAOEjFihU1evTo3G26FAAACEft2rWTZVmSjg3+bNsu1OvoUgAAhCcGf3526623qk+fPpKkzMxMJSYm6ujRo4ZTAQAAOMMtt9yixx57TBJdCgAAhKcaNWqoWbNmkqT169fr119/LfRr6VIAAIQfBn8B8Nprr+niiy+WJP3xxx969tlnDScCAABwjldffZUuBQAAwlpCQkLu98nJyWf0WroUAADhhcFfAMTExCg5OVlRUVGSpCFDhmj27NmGUwEAADgDXQoAAIS7Nm3a5HahCRMmKDs7u9CvpUsBABBeGPwFyKWXXqrXXnstd7tTp07au3evwUQAAADOQZcCAADhLD4+Xi1btpQk7dq1S/PmzTuj1xfUpfbt21eiGQEAQHBg8BdAffr0UfPmzSVJ27dvV48ePQp9Q2YAAIBwR5cCAADhrDjLfUp0KQAAwgWDvwByuVwaNWqUKlSoIEmaPHmyRo8ebTgVAACAM9ClAABAOGvZsqXKlSsn6VgPysjIOKPX5+9SkyZNoksBABCCGPwFWI0aNfTRRx/lbvfq1UsbNmwwmAgAAMA56FIAACBclSpVSm3atJEkHTp0SDNmzDjjfdClAAAIfQz+DGjTpo26dOkiSTp8+LA6dOggr9drOBUAAIAz0KUAAEC4yrvcZ0pKSpH2QZcCACC0Mfgz5O2331atWrUkSQsXLtQrr7xiOBEAAIBz0KUAAEA4uummm1SlShVJ0owZM3TgwIEi7YcuBQBA6GLwZ0i5cuU0btw4ud1uSdLLL7+sn3/+2XAqAAAAZ6BLAQCAcOR2u9W+fXtJUlZWliZPnlyk/dClAAAIXQz+DLrmmmv03HPPSZKys7OVlJSkQ4cOGU4FAADgDHQpAAAQjkpiuU+JLgUAQKhi8GfYc889pyZNmkiSNmzYoMcff9xwIgAAAOfI36Uee+wxs4EAAAD8rHHjxqpTp44kad68edq+fXuR98V5KQAAQg+DP8MiIiI0btw4lSlTRpI0fPhwTZ061XAqAAAAZ8jfpUaMGKEpU6YYTgUAAOA/lmXlXvVn27YmTJhQ5H1xXgoAgNDD4C8I1KlTR0OHDs3d7tq1a7E+rQUAABBO8nepbt260aUAAEBIK6nlPiXOSwEAEGoY/AWJLl266J577pEk7du3T507d5bP5zOcCgAAwBnoUgAAIJxccMEFuuKKKyRJS5Ys0Zo1a4q1P7oUAAChg8FfkLAsSx999JGqVasmSfr222/1zjvvGE4FAADgDAV1qbyfXAcAAAg1JXnVH+elAAAIHQz+gkjFihU1evTo3O2+ffvqjz/+MJgIAADAOfJ3qX79+tGlAABAyGrfvr0sy5J0bPBn23ax9sd5KQAAQgODvyBzyy236LHHHpMkZWZmKjExUUePHjUbCgAAwCHoUgAAIFxUr15dzZo1kyStX79eixcvLvY+6VIAADgfg78g9Oqrr+qSSy6RJP3xxx965plnDCcCAABwDroUAAAIFyW53GeO/F3q2WefLZH9AgCAwGDwF4RiYmKUnJysqKgoSdKbb76p2bNnG04FAADgDHQpAAAQLtq0aZPbeSZMmKDs7Oxi7zN/lxoyZAhdCgAAB2HwF6QuueQSvfbaa7nbnTp10t69ew0mAgAAcA66FAAACAfx8fFq2bKlJGnXrl2aO3duieyXLgUAgHMx+Atiffr0UfPmzSVJ27dvV48ePYp9o2YAAIBwQZcCAADhwB/LfUp0KQAAnIrBXxBzuVwaPXq0KlSoIEmaPHmyRo0aZTYUAACAQ9ClAABAOGjZsqViY2MlHes7GRkZJbLfgrrU6NGjS2TfAADAfxj8Bbnq1avr448/zt3u3bu3NmzYYDARAACAc9ClAABAqCtVqpTuueceSdKhQ4c0Y8aMEtt3/i7Vq1cvuhQAAEGOwZ8D3HPPPerSpYsk6fDhw+rQoYO8Xq/hVAAAAM5AlwIAAKEuMTEx9/uSXO5ToksBAOA0DP4c4u2331bt2rUlSQsXLtSgQYMMJwIAAHAOuhQAAAhlzZo1U5UqVSRJM2bM0P79+0t0/3QpAACcg8GfQ5QrV07jxo2T2+2WJA0YMEA///yz4VQAAADOQJcCAAChzO12q3379pKkrKwsTZkypUT3T5cCAMA5GPw5yNVXX63nn39ekpSdna2kpCQdOnTIcCoAAABnoEsBAIBQ5s/lPiW6FAAATsHgz2GeffZZXX311ZKkDRs26LHHHjMbCAAAwEHoUgAAIFRdeeWVqlOnjiRp3rx52rZtW4kfgy4FAEDwY/DnMBERERo3bpzKli0rSRoxYkSJL98AAAAQquhSAAAgVFmWpYSEBEmSbduaOHFiiR+DLgUAQPBj8OdAtWvX1tChQ3O3u3Xr5pdPcQEAAIQiuhQAAAhVOYM/yT/LfUoFd6nt27f75VgAAODMMfhzqM6dO6tNmzaSpH379qlLly7y+XyGUwEAADgDXQoAAISiCy64QFdccYUkacmSJVqzZo1fjpO/S3Xu3JkuBQBAkGDw51CWZenDDz9U9erVJUnffvvtcZ+2AgAAwMnRpQAAQKhKTEzM/d5fV/3RpQAACF4M/hysYsWKGjVqVO52v3799Mcff5gLBAAA4CB0KQAAEIratWsny7IkScnJybJt2y/HoUsBABCcGPw53C233KLHH39ckpSZmamEhAQdPXrUcCoAAABnoEsBAIBQU716dTVr1kyStGHDBi1evNhvx8rfpRITE+lSAAAYxuAvBLzyyiu65JJLJEkrVqzQM888YzgRAACAc9ClAABAqAnEcp858napP/74gy4FAIBhDP5CQExMjJKTkxUdHS1JevPNN/Xtt98aTgUAAOAMdCkAABBq7rnnHkVFRUmSJkyYIK/X67dj0aUAAAguDP5CxCWXXKLXXnstd7tz587au3evwUQAAADOQZcCAAChJD4+Xi1btpQk7dq1S/PmzfPr8ehSAAAEDwZ/IaR379665ZZbJEnbt29X9+7d/XYDZwAAgFBDlwIAAKEkkMt9Sid2qR49etClAAAwgMFfCHG5XBo1apQqVKggSZoyZYpGjRplNhQAAIBD0KUAAEAoadmypWJjYyVJkydPVkZGhl+Pl79LTZ48mS4FAIABDP5CTPXq1fXxxx/nbvfu3VsbNmwwmAgAAMA56FIAACBUxMTEqE2bNpKkQ4cOacaMGX4/Jl0KAADzGPyFoHvuuUcPPPCAJOnw4cNKSkry602cAQAAQgldCgAAhIqEhITc75OTkwNyTLoUAABmMfgLUW+//bZq164tSfr55581aNAgw4kAAACcI3+XGjhwoOFEAAAAZ65Zs2aqWrWqJGnmzJnav39/QI7LeSkAAMxh8BeiypYtq3HjxsntdkuSBgwYoJ9//tlwKgAAAGfI36UGDhyohQsXGk4FAABwZtxut9q3by9JysrK0pQpUwJyXM5LAQBgDoO/EHb11Vfr+eeflyRlZ2crMTFRhw4dMpwKAADAGfJ3qaSkJLoUAABwHBPLfUqclwIAwBQGfyHu2Wef1TXXXCNJ2rhxo/r06WM4EQAAgHPQpQAAgNNdeeWVqlOnjiTpu+++07Zt2wJ27Pxd6rHHHgvYsQEACFcM/kJcRESExo4dq7Jly0qSRo4cqcmTJxtOBQAA4AwREREaN24cXQoAADiWZVlKTEyUJNm2rYkTJwbs2Pm71IgRIwK23CgAAOGKwV8YqF27toYOHZq73b1794B+ugsAAMDJatWqpXfeeSd3my4FAACcxtRyn9KJXapbt250KQAA/IjBX5jo3Lmz2rRpI0nat2+fOnfuLJ/PZzgVAACAM3Tq1IkuBQAAHKtevXq68sorJUlLly7Vn3/+GdDj06UAAAgcBn9hwrIsffjhh6pevbokafbs2Xr77bcNpwIAAHAGuhQAAHC6vFf9paSkBPTYBXWpvKtTAQCAksPgL4xUrFhRo0ePzt3u16+f/vjjD4OJAAAAnIMuBQAAnKxdu3ayLEvSscGfbdsBPT5dCgCAwGDwF2aaN2+uxx9/XJKUlZWlhIQEHT161HAqAAAAZ6BLAQAAp6pevbpuuukmSdKGDRu0ePHigGdo3ry5/vWvf0mSMjMz6VIAAPgBg78w9Morr+iSSy6RJK1YsUL9+/c3nAgAAMA56FIAAMCp8i73mZycbCTDoEGD6FIAAPgRg78wFBMTo5SUFEVHR0uS3nrrLX3zzTeGUwEAADgDXQoAADjVPffco6ioKEnSxIkT5fV6A56hoC717bffBjwHAAChisFfmLr44ov1n//8J3e7c+fO2rt3r8FEAAAAzkGXAgAAThQfH68777xTkrRr1y7NmzfPSA66FAAA/sPgL4z16tVLt9xyiyRpx44d6t69e8Bv7AwAAOBUdCkAAOBEwbDcp3R8l9q+fTtdCgCAEsLgL4y5XC6NGjVKFStWlCRNmTJFI0eONJwKAADAGehSAADAiVq2bKnY2FhJx/pLRkaGkRwFdalRo0YZyQIAQChh8Bfmqlevro8//jh3u3fv3lq/fr3BRAAAAM5BlwIAAE4TExOjNm3aSJIOHTqk6dOnG8tSUJfasGGDsTwAAIQCBn9Q69at9eCDD0qSjhw5oqSkJCM3dwYAAHAiuhQAAHCavMt9pqSkGExyfJc6fPgwXQoAgGJi8AdJ0ltvvaXatWtLkn755RcNHDjQcCIAAADnoEsBAAAnadasmapWrSpJmjlzpvbv3280T94u9fPPP9OlAAAoBgZ/kCSVLVtWycnJcrvdkqQBAwZo4cKFhlMBAAA4A10KAAA4idvtVvv27SVJWVlZmjx5stE8+bvUwIED6VIAABQRgz/katKkif79739Lknw+n5KSknTo0CHDqQAAAJyBLgUAAJwkmJb7lI7vUtnZ2XQpAACKiMEfjvPMM8/ommuukSRt3LhRffr0MZwIAADAOehSAADAKa688krVrVtXkvTdd99p27ZthhPRpQAAKAkM/nCciIgIjRs3TmXLlpUkjRw50vhyDwAAAE5BlwIAAE5hWVbuVX+2bWvChAmGE9GlAAAoCQz+cIJatWrpnXfeyd3u1q1bUHzqCwAAwAnoUgAAwCmCbblP6cQu1b17d7oUAABngMEfCtSpUye1bdtWkrR//3517txZPp/PcCoAAABnyN+lOnXqRJcCAABBp169erryyislSUuXLtWff/5pONExebvUvn37OC8FAMAZYPCHAlmWpQ8//FDVq1eXJM2ePVtvv/224VQAAADOkL9LzZkzhy4FAACCUjBe9cd5KQAAio7BH06qQoUKGj16dO52v3799PvvvxtMBAAA4Bx0KQAA4ATt27eXZVmSjg3+bNs2nOgYuhQAAEXD4A+n1Lx5c/3rX/+SJGVlZSkxMVFHjx41nAoAAMAZ6FIAACDYVatWTTfddJMkacOGDVq0aJHhRP9DlwIA4Mwx+MNpvfLKK7r00kslSStWrFD//v0NJwIAAHCO/F2qX79+hhMBAAAcLxiX+8zBeSkAAM4Mgz+cVnR0tJKTkxUdHS1Jeuutt/TNN98YTgUAAOAM+bvU22+/TZcCAABBpU2bNrldZeLEifJ6vYYT/Q/npQAAODMM/lAoF198sf7zn//kbnfu3Fl79uwxmAgAAMA56FIAACCYxcXFqWXLlpKkXbt2ae7cuYYTHa+gLrV3716DiQAACF4M/lBovXr10q233ipJ2rFjh7p37x40N3wGAAAIdnQpAAAQzBITE3O/D7blPiW6FAAAhcXgD4Xmcrk0atQoVaxYUZI0depUjRw50nAqAAAAZyioS40YMcJwKgAAgGPuuOMOxcbGSpKmTJmijIwMw4mOl79LTZkyhfNSAAAUgMEfzki1atX08ccf52737t1b69evN5gIAADAOfJ3qT59+tClAABAUIiJiVGbNm0kSYcOHdL06dMNJzoR56UAADg9Bn84Y61bt9aDDz4oSTpy5IiSkpLk8XgMpwIAAHAGuhQAAAhWwb7cp1Rwl/J6vYZTAQAQPBj8oUjeeust1alTR5L0yy+/aODAgYYTAQAAOAddCgAABKMbb7xRVatWlSTNnDlT+/fvN5yoYHQpAABOjsEfiqRs2bIaN26c3G63JGngwIFauHCh4VQAAADOUFCX+umnnwynAgAA4c7tdqt9+/aSpKysLE2ePNlwooLl71IDBgzgvBQAAP+PwR+KrEmTJnrhhRckST6fT0lJSTp06JDhVAAAAM5AlwIAAMHICct9SnQpAABOhsEfiqV///669tprJUkbN25U7969DScCAABwjrxdatOmTXQpAABg3BVXXKG6detKkr777jtt27bNcKKTy39eqk+fPoYTAQBgHoM/FEtERITGjh2rcuXKSZJGjRqlSZMmGU4FAADgDHQpAAAQbCzLyr3qz7ZtTZgwwXCik8vfpUaOHBm0y5MCABAoDP5QbLVq1dI777yTu929e/eg/jQYAABAMKFLAQCAYHP//ffnfp+cnGwwyenl71LdunWjSwEAwhqDP5SIjh07qm3btpKk/fv3q1OnTvL5fIZTAQAAOEPHjh117733SqJLAQAA8+rVq6crr7xSkvTbb79p9erVhhOdGl0KAID/YfCHEmFZlj788EPVqFFDkjRnzhy99dZbZkMBAAA4hGVZ+uCDD+hSAAAgaOQs9ylJ48ePN5jk9ArqUm+//bbhVAAAmMHgDyWmQoUKGj16dO52//79tXz5coOJAAAAnIMuBQAAgkm7du1kWZakY8t92rZtONGp5e9S/fr10++//24wEQAAZjD4Q4m6+eab9cQTT0iSsrKylJiYqKNHjxpOBQAA4Ax0KQAAECyqVaumm266SZK0ceNGLVq0yHCi06NLAQDA4A9+MGjQIF166aWSpJUrV6pfv36GEwEAADgHXQoAAASLvMt9pqSkGExSeHm71IoVK+hSAICww+APJS46OlopKSmKjo6WJL399tv65ptvDKcCAABwBroUAAAIFvfcc09uJ5kwYYK8Xq/hRKdHlwIAhDsGf/CLBg0a6L///W/udqdOnbRnzx6DiQAAAJyDLgUAAIJBXFyc7rzzTklSamqq5s6dazhR4eTvUp07d6ZLAQDCBoM/+M2jjz6q2267TZK0c+dOde/ePehvBA0AABAsevXqdVyX6tatG10KAAAEXEJCQu73ycnJBpOcmbxdaseOHZyXAgCEDQZ/8BuXy6WRI0eqYsWKkqSpU6dqxIgRhlMBAAA4g2VZx3Wpzz//nC4FAAAC7o477lBcXJwkacqUKcrIyDCcqHDyd6mpU6dq5MiRhlMBAOB/DP7gV9WqVdMnn3ySu92nTx+tW7fOYCIAAADnoEsBAADTYmJi1KZNG0nS4cOHNX36dMOJCi9/l+rdu7fWr19vMBEAAP7H4A9+d/fdd6tr166SpCNHjigpKUkej8dwKgAAAGegSwEAANOcutynRJcCAIQfBn8IiDfffFN16tSRJC1atEgDBw40nAgAAMA56FIAAMCkG2+8UdWqVZMkzZw5U/v37zec6Mzk7VK//PILXQoAENIY/CEgypYtq3HjxsntdkuSBg4cqJ9++slwKgAAAGegSwEAAJPcbrfat28vSfJ4PJo8ebLhRGembNmySk5OPq5LLVy40HAqAAD8g8EfAqZJkyZ64YUXJEk+n09JSUk6ePCg4VQAAADOQJcCAAAmOXm5T0m66qqrTuhShw4dMpwKAICSx+APAdW/f39de+21kqRNmzapT58+hhMBAAA4R/4u1bt3b8OJAABAuLjiiitUr149SdL8+fP1999/G0505vJ2qY0bN9KlAAAhicEfAioiIkLjxo1TuXLlJEmjRo3SpEmTDKcCAABwhvxdavTo0frss88MpwIAAOHAsqzcq/5s29bEiRMNJzpznJcCAIQDBn8IuPPPP1/vvPNO7nb37t0d+SkxAAAAE/J3qR49etClAABAQDh9uU/pWJcaNmxY7nb37t21bds2g4kAAChZDP5gRMeOHXXvvfdKkvbv36/OnTvL5/MZTgUAAOAMdCkAAGBC3bp11bhxY0nSb7/9ptWrVxtOVDQdOnQ4rkt16tSJLgUACBkM/mCEZVn64IMPVKNGDUnSnDlz9NZbb5kNBQAA4BAFdak333zTcCoAABAO8l71l5KSYjBJ0XFeCgAQyhj8wZgKFSpozJgxudv9+/fX8uXLDSYCAABwjvxd6plnnqFLAQAAv2vXrp1crmOnFFNSUmTbtuFERZPTpSzLksR5KQBA6GDwB6NuuukmPfHEE5KkrKwsJSYmKiMjw3AqAAAAZ6BLAQCAQKtWrZpuuukmSdLGjRu1aNEiw4mKrqAudfToUcOpAAAoHgZ/MG7QoEG67LLLJEkrV65Uv379DCcCAABwDroUAAAItLzLfSYnJxtMUnwDBw6kSwEAQgqDPxgXHR2t5ORkxcTESJKGDh2qr7/+2nAqAAAAZ6BLAQCAQLvnnnsUHR0tSZo4caK8Xq/hREWXv0u9/fbb+uabbwynAgCg6Bj8ISg0aNBA//3vf3O3O3furD179hhMBAAA4Bx0KQAAEEhxcXG68847JUmpqamaO3eu4UTFk79LderUiS4FAHAsBn8IGo8++qhuu+02SdLOnTvVrVs3x94gGgAAINDoUgAAIJBCablP6cQu1b17d7oUAMCRGPwhaFiWpZEjR6pSpUqSpM8//1zDhw83nAoAAMAZ6FIAACCQ7rjjDsXFxUmSpkyZooyMDMOJiid/l5o6dapGjBhhOBUAAGeOwR+CSrVq1fTJJ5/kbvfp00fr1q0zmAgAAMA56FIAACBQYmJi1KZNG0nS4cOHNW3aNMOJio8uBQAIBQz+EHT++c9/qlu3bpKk9PR0JSUlyePxGE4FAADgDHQpAAAQKHmX+0xJSTGYpOTk7VJHjhyhSwEAHIfBH4LSkCFDVKdOHUnSokWLNGDAAMOJAAAAnIMuBQAAAuHGG29UtWrVJEkzZ87U/v37DScqGfm71MCBAw0nAgCg8Bj8ISiVLVtWycnJcrvdkqRBgwbpxx9/NJwKAADAGehSAAAgENxut9q3by9J8ng8mjRpkuFEJSN/lxo4cKB++uknw6kAACgcBn8IWldddZVefPFFSZLP51OHDh108OBBs6EAAAAcgi4FAAACITExMff7UFnuUzqxSyUlJdGlAACOwOAPQa1///667rrrJEmbNm1S7969DScCAABwDroUAADwt0aNGqlevXqSpPnz5+vvv/82nKjk5O9Sffr0MZwIAIDTY/CHoOZ2uzV27FiVK1dOkjR69Gh99tlnhlMBAAA4A10KAAD4m2VZSkhIkCTZtq0JEyYYTlRy8nepUaNGhcxypgCA0MXgD0Hv/PPP17Bhw3K3e/ToEVKfHgMAAPAnuhQAAPC3nMGfFFrLfUondqnu3bvTpQAAQY3BHxyhQ4cOuu+++yRJ+/fvV+fOneXz+QynAgAAcIb8XapTp050KQAAUGLq1q2rxo0bS5J+++03rV692nCiksV5KQCAkzD4gyNYlqUPPvhAZ599tiRpzpw5evPNNw2nAgAAcIb8XWru3Ll0KQAAUKJC+aq/gs5LvfXWW2ZDAQBwEgz+4Bjly5fX6NGjZVmWJOmZZ57R8uXLDacCAABwBroUAADwp3bt2snlOnaqMSUlRbZtG05UsvJ3qf79+9OlAABBicEfHOWmm27SE088IUnKyspSYmKiMjIyDKcCAABwhvxdKiEhgS4FAABKRLVq1XTTTTdJkjZu3KhffvnFcKKSx3kpAIATMPiD4wwcOFANGzaUJK1cuVL9+vUzGwgAAMBB8napVatW0aUAAECJSUxMzP0+1Jb7zMF5KQBAsGPwB8eJjo5WcnKyYmJiJElDhw7V119/bTgVAACAM9ClAACAv7Ru3VrR0dGSpIkTJ8rr9RpOVPLoUgCAYMfgD4500UUX6b///W/udufOnbV7926DiQAAAJyDLgUAAPwhLi5Od955pyQpNTVVc+bMMZzIPwrqUnv27DGYCACA/2HwB8d69NFHdfvtt0uSdu7cqe7du4fcjaMBAAD8JX+X6tatG10KAAAUWzgs9ynRpQAAwYvBHxzLsiyNHDlSlSpVkiR9/vnnGj58uOFUAAAAzpC/S33xxRd0KQAAUGwtWrRQXFycJGnKlClKT083nMg/CjovNWLECMOpAABg8AeHq1q1qj755JPc7T59+mjdunUGEwEAADgHXQoAAJS0mJgYtWnTRpJ0+PBhTZ8+3XAi/6FLAQCCEYM/ON4///lPdevWTZKUnp6uxMREeTwew6kAAACcgS4FAABKWrgs9ykd36WOHDmipKQkuhQAwCgGfwgJb775purWrStJWrx4sQYMGGA4EQAAgHPk71Ivv/yy4UQAAMDJbrjhBlWrVk2SNHPmTO3bt89wIv/K26UWLVrEeSkAgFEM/hASypQpo+TkZLndbknSoEGD9OOPPxpOBQAA4Aw5XSoiIkKS9Morr9ClAABAkbndbt1///2SJI/Ho8mTJxtO5F/5u9SgQYP0008/GU4FAAhXDP4QMho3bqwXX3xRkuTz+ZSUlKSDBw+aDQUAAOAQdCkAAFCSEhIScr8P9eU+JboUACB4MPhDSOnfv7+uu+46SdLmzZvVq1cvw4kAAACco1+/fnQpAABQIho1aqR69epJkubPn6+///7bcCL/y9ulNm3apN69extOBAAIRwz+EFLcbrfGjh2rcuXKSZLGjBmjTz/91HAqAAAAZ6BLAQCAkmJZlhITEyVJtm1rwoQJhhP5X/4uNXr0aH322WeGUwEAwg2DP4Sc888/X++++27uds+ePcPiU2UAAAAlIX+X6tGjB10KAAAUSc59/iQpOTnZYJLAoUsBAExj8IeQlJSUpPvuu0+StH//fnXq1Ek+n89wKgAAAGdISkpSu3btJEkHDhygSwEAgCKpW7euGjduLElatmyZVq1aZThRYOTtUvv371fnzp3pUgCAgGHwh5BkWZY++OADnX322ZKkuXPnasiQIYZTAQAAOINlWXr//ffpUgAAoNhylvuUpPHjxxtMEjj5u9ScOXP05ptvGk4FAAgXDP4QssqXL68xY8bIsixJ0jPPPKPly5cbTgUAAOAMBXWpZcuWmQ0FAAAcp127dnK5jp2CTElJkW3bhhMFBuelAACmMPhDSGvWrJmefPJJSZLH41FCQoIyMjIMpwIAAHCG/F0qMTGRLgUAAM5I1apVdfPNN0uSNm7cqF9++cVwosDJ26WysrLoUgCAgGDwh5A3YMAANWzYUJK0atUq9e3b12wgAAAAB6FLAQCA4kpISMj9PiUlxWCSwMvbpVauXKl+/fqZDQQACHkM/hDyoqOjlZycrJiYGEnSO++8o6+++spwKgAAAGegSwEAgOJq3bq1oqOjJUkTJ06U1+s1nChw8nepoUOH6uuvvzacCgAQyhj8ISxcdNFFev3113O3u3Tpot27dxtMBAAA4Bz5u1Tnzp3pUgAAoNDi4uLUqlUrSVJqaqrmzJljOFFgFdSl9uzZYzARACCUMfhD2HjkkUd0++23S5J27typbt26hc0NpQEAAIorb5fatWsXXQoAAJyRvMt9JicnG0xixiOPPKIWLVpI4rwUAMC/GPwhbFiWpZEjR6pSpUqSpC+++EKffPKJ4VQAAADOQJcCAADF0aJFC8XFxUmSpk6dqvT0dMOJAsuyLI0YMSK3S33++ecaPny44VQAgFDE4A9hpWrVqseVqscee0zr1q0zmAgAAMA5CupSa9euNZgIAAA4RUxMjNq2bStJOnz4sKZPn244UeDl71J9+vThvBQAoMQx+EPYueuuu9S9e3dJUnp6uhITE+XxeAynAgAAcIb8XSopKYkuBQAACiXcl/uU6FIAAP9j8IewNGTIENWtW1eStHjxYr388suGEwEAADgHXQoAABTFDTfcoOrVq0uSZs2apX379hlOZMaQIUNUr149SdKiRYs0YMAAw4kAAKGEwR/CUpkyZZScnKyIiAhJ0iuvvKIffvjBcCoAAABnoEsBAICicLvdat++vSTJ4/Fo8uTJhhOZkb9LDRo0SD/++KPhVACAUMHgD2GrcePGevHFFyVJPp9PHTp00MGDB82GAgAAcIiCulRaWprZUAAAIOix3OcxV1555XFdKikpifNSAIASweAPYa1fv366/vrrJUmbN29Wr169DCcCAABwjvxdqnfv3oYTAQCAYNeoUSNdcMEFkqQFCxZo69athhOZQ5cCAPgDgz+ENbfbrbFjx6pcuXKSpDFjxujTTz81nAoAAMAZ6FIAAOBMWZaVe9WfbduaMGGC4UTm5HSp2NhYSdLo0aP12WefGU4FAHA6Bn8Ie+edd57efffd3O0ePXqE9afNAAAAzgRdCgAAnKm8y32mpKQYTGJeQV3q77//NpgIAOB0DP4ASUlJSWrXrp0k6cCBA+rUqZN8Pp/hVAAAAM5AlwIAAGeiTp06uuqqqyRJy5Yt06pVqwwnMisxMTG3S+3fv58uBQAoFgZ/gI4tM/H+++/rnHPOkSTNmzdPQ4YMMZwKAADAGehSAADgTHHV3//k71Jz587Vm2++aTgVAMCpGPwB/698+fIaPXq0LMuSJD3zzDNatmyZ2VAAAAAOQZcCAABnol27dnK5jp2aTElJkW3bhhOZVb58eY0ZM+a4LrV8+XLDqQAATsTgD8ijWbNmevLJJyVJHo9HCQkJysjIMJwKAADAGehSAACgsKpWraqbb75ZkrRp0yb98ssvhhOZd+ONN+qpp56SJGVlZdGlAABFwuAPyGfAgAFq2LChJGn16tXq27ev2UAAAAAOkr9LPf3002YDAQCAoJV3uc/k5GSDSYLHyy+/nNulVq1axXkpAMAZY/AH5BMdHa2UlBTFxMRIkt555x199dVXhlMBAAA4Q/4uNWzYMM2aNctwKgAAEIzuueceRUdHS5ImTpwor9drOJF5nJcCABQXgz+gABdeeKHeeOON3O3OnTtr9+7dBhMBAAA4R/4u1aVLF7oUAAA4QWxsrFq1aiVJ2r17t2bPnm04UXCgSwEAioPBH3ASDz/8sFq0aCFJ2rVrl7p27Rr2N5oGAAAoLLoUAAAojLzLfaakpBhMElzydqmdO3eqW7dudCkAQKEw+ANOwrIsjRgxQpUqVZIkffnll/rkk08MpwIAAHCGgrrUxx9/bDgVAAAINnfccYfi4uIkSVOnTlV6errhRMEhf5f64osvNHz4cMOpAABOwOAPOIWqVatqxIgRuduPPfaY1q5dazARAACAc+TvUo8//jhdCgAAHCc6Olpt27aVJB0+fFjTpk0znCh45O9Sffr00bp16wwmAgA4AYM/4DRatWqlHj16SJLS09OVlJQkj8djOBUAAIAz0KUAAMDpJCYm5n7Pcp/Hy9+lEhMT6VIAgFNi8AcUwuDBg1WvXj1J0uLFi/XSSy8ZTgQAAOAcdCkAAHAqTZs2VfXq1SVJs2bN0r59+wwnCi75u9TLL79sOBEAIJgx+AMKoUyZMkpOTlZERIQk6dVXX9UPP/xgOBUAAIAz0KUAAMCpuN1utW/fXpLk8Xg0adIkw4mCS/4u9corr+jHH380nAoAEKwY/AGFdOWVV+Z+Ot3n86lDhw5KS0sznAoAAMAZ8neppKQkuhQAAMjFcp+nVlCXOnjwoOFUAIBgxOAPOAN9+/bV9ddfL0navHmzevXqZTgRAACAc+TtUlu2bKFLAQCAXJdffrkuuOACSdKCBQu0detWw4mCD+elAACFweAPOANut1tjx45VbGysJGns2LGaOHGi4VQAAADOQJcCAAAnY1mWEhISJEm2bWvChAmGEwWf/F1qzJgx+vTTTw2nAgAEGwZ/wBk677zz9O677+Zu9+zZk0+hAQAAFBJdCgAAnEzO4E9iuc+Tyd+levToob///ttgIgBAsGHwBxRBYmJi7k2nDxw4oE6dOsnn8xlOBQAA4Az5u1THjh3pUgAAQHXq1NFVV10lSVq2bJlWrVplOFFw4rwUAOBUGPwBRWBZlt577z2dc845kqR58+Zp8ODBhlMBAAA4Q/4u9d1339GlAACApGNDrRxc9Vew/F1q7ty5GjJkiOFUAIBgweAPKKLy5ctrzJgxsixLkvTss89q2bJlZkMBAAA4REFd6rfffjOcCgAAmHbffffJ5Tp2yjIlJUW2bRtOFJzyd6lnnnmG81IAAEkM/oBiufHGG/XUU09JkjwejxISEpSRkWE4FQAAgDPk71KJiYl0KQAAwlzVqlV18803S5I2bdqkn3/+2XCi4EWXAgAUhMEfUEwDBgxQw4YNJUmrV6/W008/bTYQAACAgwwYMECXX365JLoUAAA4huU+Cy9vl1q1apX69u1rOBEAwDQGf0AxRUVFKSUlRTExMZKkYcOGadasWYZTAQAAOENUVJSSk5PpUgAAIFfr1q0VHR0tSZo4caK8Xq/hRMErf5d655139NVXXxlOBQAwicEfUAIuvPBCvfHGG7nbXbp00e7duw0mAgAAcI6CulRqaqrBRAAAwKTY2Fi1atVKkrR7927Nnj3bcKLgxnkpAEBeDP6AEvLwww/rjjvukCTt2rVLXbt25QbUAAAAhZS/S3Xr1o0uBQBAGGO5zzOTt0vt3LmTLgUAYYzBH1BCLMvSiBEjdNZZZ0mSvvzyS3388ceGUwEAADgDXQoAAOTVokULxcfHS5KmTp2q9PR0s4GCXP4u9cUXX+iTTz4xnAoAYAKDP6AEValSRcOHD8/dfvzxx7V27VqDiQAAAJyDLgUAAHJER0erbdu2kqTDhw9r2rRphhMFv/xd6rHHHqNLAUAYYvAHlLBWrVqpR48ekqT09HQlJibK4/EYTgUAAOAMdCkAAJAjISEh93uW+yyc/F0qKSmJLgUAYYbBH+AHgwcPVr169SRJv/76q1566SXDiQAAAJyDLgUAACSpadOmql69uiRp1qxZ2rdvn+FEzpC3Sy1evFgvv/yy4UQAgEBi8Af4QZkyZZScnKyIiAhJ0quvvqoffvjBcCoAAABnKFOmjFJSUo7rUt9//73hVAAAINDcbrfuv/9+SZLH49GkSZMMJ3KG/F3qlVde4bwUAIQRBn+An1x55ZW5n073+XxKSkpSWlqa4VQAAADOcMUVV+R+Ot3n86lDhw50KQAAwhDLfRYNXQoAwheDP8CP+vbtq3/84x+SpC1btqhXr16GEwEAADjH008/fVyXevTRRw0nAgAAgXb55ZfrggsukCTNnz9fW7duNZzIOfJ2qc2bN6t3796GEwEAAoHBH+BHbrdbY8eOVWxsrCRp7NixmjhxouFUAAAAzpC/S40bN04TJkwwnAoAAASSZVlKTEzM3aYLFF7+LjVmzBh9+umnhlMBAPyNwR/gZzVr1tR7772Xu92zZ08+nQYAAFBI+bvUQw89RJcCACDM5NznT5KSk5MNJnGe/F2qR48edCkACHEM/oAASEhIUPv27SVJBw4cUMeOHZWdnW04FQAAgDPQpQAACG916tRRkyZNJEnLly/XypUrDSdylsTExNzh6YEDB9SpUyf5fD7DqQAA/sLgDwgAy7L0/vvv65xzzpEkfffddxo8eLDhVAAAAM5AlwIAAAkJCbnfp6SkGEziTO+9915ul5o3b56GDBliOBEAwF8Y/AEBEh8fr7Fjx8qyLEnSc889p99++81wKgAAAGegSwEAEN7atWsnl+vYqczx48fLtm3DiZwlf5d65plntGzZMrOhAAB+weAPCKAbbrhBTz/9tCTJ4/EoMTFR6enphlMBAAA4A10KAIDwVaVKFTVv3lyStGnTJv3888+GEzlP/i6VkJCgjIwMw6kAACWNwR8QYC+//LIuv/xySdLq1avVt29fw4kAAACcI3+Xyjl5BQAAQh/LfRYfXQoAQh+DPyDAoqKilJycrJiYGEnSsGHDNGvWLMOpAAAAnCF/l3r33Xc1c+ZMw6kAAEAgtG7dOrcDTJw4UR6Px3Ai5+G8FACEPgZ/gAEXXnihBg8enLvdpUsXpaamGkwEAADgHHQpAADCU2xsrFq1aiVJ2r17t+bMmWM4kTMV1KV2795tMBEAoCQx+AMMeeihh3THHXdIknbt2qWuXbtyY2oAAIBCytulUlNT6VIAAISJvMt9JicnG0zibJyXAoDQxeAPMMSyLI0YMUJnnXWWJGnatGn6+OOPDacCAABwhoK61EcffWQ4FQAA8LcWLVooPj5ekjR16lSlp6ebDeRQ+bvUl19+yXkpAAgRDP4Ag6pUqaIRI0bkbj/++ONau3atwUQAAADOUVCXWrNmjcFEAADA36Kjo9W2bVtJ0pEjRzRt2jTDiZyL81IAEJoY/AGG3XnnnerZs6ckKT09XYmJidycGgAAoJDydqmMjAy6FAAAYYDlPktO/vNSSUlJdCkAcDgGf0AQGDx4sC644AJJ0q+//qoXX3zRbCAAAAAHydullixZQpcCACDENW3aVDVq1JAkzZo1S3v37jWcyNnydqnFixfrpZdeMpwIAFAcDP6AIFC6dGklJycrIiJCkvTqq6/q+++/N5wKAADAGehSAACEF7fbrfbt20uSvF6vJk+ebDiRsxXUpX744QfDqQAARcXgDwgSV1xxhV5++WVJkm3b6tChg9LS0gynAgAAcAa6FAAA4YXlPktW3i7l8/mUlJRElwIAh2LwBwSRp59+Wk2bNpUkbdmyRY8++qjhRAAAAM5BlwIAIHxcfvnlql+/viRpwYIF2rp1q+FEzpe/S/Xq1ctwIgBAUTD4A4KI2+3WmDFjFBsbK0kaN26cJkyYYDgVAACAM9ClAAAIH5ZlHXfV3/jx4w2mCQ35u9TYsWM1ceJEw6kAAGeKwR8QZGrWrKn33nsvd7tnz57666+/DCYCAABwDroUAADhI+/gLyUlxWCS0FFQl+JqSgBwFgZ/QBBKTEzU/fffL0lKS0tTp06dlJ2dbTgVAACAM+TvUh07dqRLAQAQgmrXrq0mTZpIkpYvX66VK1caThQa8napAwcOqGPHjvL5fIZTAQAKi8EfEKTee+89nXvuuZKk7777ToMHDzacCAAAwDnee+89nXPOOZKk+fPn06UAAAhRXPXnH5yXAgDnYvAHBKn4+HiNGTNGlmVJkp577jktXbrUcCoAAABniI+P19ixY+lSAACEuHbt2snlOnaKMyUlRbZtG04UGvKfl3r22Wf122+/GU4FACgMBn9AELvhhhv09NNPS5I8Ho8SExOVnp5uOBUAAIAz0KUAAAh9VapUUfPmzSVJmzdv1s8//2w4UeigSwGAMzH4A4Lcyy+/rEaNGkmS/vzzz9zCBQAAgNOjSwEAEPryLveZnJxsMEnoydulVq9erb59+xpOBAA4HQZ/QJCLiopScnKySpUqJUl69913NXPmTMOpAAAAnIEuBQBA6GvdurViYmIkSZ9++qk8Ho/hRKEjf5caNmyYZs2aZTgVAOBUGPwBDlC/fn298cYbudtdunRRamqqwUQAAADOQZcCACC0xcbGqlWrVpKk3bt3a86cOYYThZb69etr8ODBudt0KQAIbgz+AId46KGH1LJlS0lSamqqunbtyg2rAQAACil/l3rwwQfpUgAAhBCW+/Svnj175napXbt2cV4KAIIYgz/AISzL0vDhw3XWWWdJkqZNm6aPPvrIcCoAAABnyN+lpk+fTpcCACCEtGjRQvHx8ZKkqVOnKj093WygEFPQeamPP/7YcCoAQEEY/AEOUqVKFY0YMSJ3+/HHH9eaNWsMJgIAAHAOuhQAAKErOjpabdu2lSQdOXJEX375peFEoaegLrV27VqDiQAABWHwBzjMnXfeqZ49e0qSMjIylJiYqKysLMOpAAAAnIEuBQBA6EpMTMz9PiUlxWCS0JW3S6WnpysxMVEej8dwKgBAXgz+AAcaPHiwLrjgAknSkiVL9NJLLxlOBAAA4Bz5u9SLL75oNhAAACgR//jHP1SjRg1J0qxZs7R3717DiUJT3i7166+/0qUAIMgw+AMcqHTp0kpOTlZERIQk6dVXX9X3339vOBUAAIAz5O9Sr732Gl0KAIAQ4Ha71b59e0mS1+vVpEmTDCcKTZyXAoDgxuAPcKgrrrhCAwYMkCTZtq0OHTooLS3NcCoAAABnoEsBABCaWO4zMOhSABC8GPwBDvbUU0+padOmkqQtW7bokUceMZwIAADAOehSAACEnoYNG6p+/fqSpAULFmjr1q2GE4Wu/F3q0UcfNZwIACAx+AMcze12a8yYMYqLi5MkJScna/z48YZTAQAAOANdCgCA0GNZlhISEnK3+bfdf/J3qXHjxmnChAmGUwEAGPwBDlezZk299957udsPPfSQ/vrrL4OJAAAAnIMuBQBA6Mk7+GO5T//K36V69uxJlwIAwxj8ASEgISEht9SmpaWpY8eOys7ONpwKAADAGehSAACEltq1a6tJkyaSpOXLl2vlypWGE4W2/F2qU6dOdCkAMIjBHxAi3n33XZ177rmSpPnz52vw4MGGEwEAADhH/i71xhtvGE4EAACKg6v+Aitvl/ruu+84LwUABjH4A0JEfHy8xowZI8uyJEnPPfecli5dajgVAACAM+TvUs8//zxdCgAAB2vXrp1crmOnPlNSUmTbtuFEoY3zUgAQPBj8ASHkhhtuUN++fSVJHo9HiYmJSk9PN5wKAADAGehSAACEjipVqqh58+aSpM2bN2vhwoWGE4U+uhQABAcGf0CIeemll9SoUSNJ0p9//qmnnnrKcCIAAADnoEsBABA6EhMTc79nuc/AyN+lnn76acOJACD8MPgDQkxUVJSSk5NVqlQpSdJ7772nmTNnGk4FAADgDAV1qRkzZhhOBQAAiuLuu+9WTEyMJOnTTz+Vx+MxnCj05e9S7777LuelACDAGPwBIah+/frH3US5S5cuSk1NNZgIAADAOfJ3qQceeIAuBQCAA8XGxqpVq1aSpN27d2v27NmGE4UHzksBgFkM/oAQ1bNnT915552SpNTUVD344IPcyBoAAKCQevbsqZYtW0qiSwEA4GQs92lG/vNSXbt2pUsBQIAw+ANClGVZGj58uCpXrixJmj59uj788EPDqQAAAJwhp0udddZZkuhSAAA41e233674+HhJ0tSpU3XkyBGzgcJE/vNS06ZN00cffWQ4FQCEBwZ/QAirXLmyhg8fnrv9r3/9S2vWrDGYCAAAwDmqVKmiESNG5G7/61//0p9//mkwEQAAOFPR0dFq27atJOnIkSOaNm2a4UThI/95qccff5zzUgAQAAz+gBB355136qGHHpIkZWRkKDExUVlZWYZTAQAAOANdCgAA52O5T3MK6lIej8dwKgAIbQz+gDDwxhtv6IILLpAkLVmyRC+++KLZQAAAAA6St0stXbqULgUAgMM0bdpUNWrUkCTNmjVLe/fuNZwovHBeCgACi8EfEAZKly6t5ORkRURESJJee+01LViwwHAqAAAAZ6BLAQDgbC6XS/fff78kyev1atKkSYYThZf8XerVV1/V999/bzgVAIQuBn9AmLjiiis0YMAASZJt2+rQoYPS0tIMpwIAAHCGgrrUgQMHzIYCAACFlpCQkPs9y30GHuelACBwGPwBYeSpp55S06ZNJUl//fWXHnnkEcOJAAAAnCN/l3r00UcNJwIAAIXVsGFD1a9fX5K0YMEC/fXXX4YThZ+8XWrLli10KQDwEwZ/QBhxu90aO3as4uLiJEnJyckaP3684VQAAADOQJcCAMC5LMtSYmJi7vaECRMMpglP+bvUuHHj+D0AgB8w+APCzLnnnqv33nsvd/uhhx7Sli1bDCYCAABwDroUAADOlXOfP4nlPk3J36V69uzJ1ZcAUMIY/AFhKCEhIXdt+7S0NHXq1EnZ2dmGUwEAADhD/i7VsWNHuhQAAA5Qu3ZtNWnSRJK0fPlyrVy50nCi8ESXAgD/YvAHhKl3331X5557riRp/vz5euONNwwnAgAAcI68XWrBggV0KQAAHCLvcp9c9WdO/vNSgwcPNpwIAEIHgz8gTMXHx2vs2LGyLEuS9Pzzz2vp0qWGUwEAADgDXQoAAGe677775HIdOyWakpIi27YNJwpP+bvUc889R5cCgBLC4A8IY02bNlXfvn0lSR6PRwkJCUpPTzecCgAAwBnoUgAAOE+VKlXUvHlzSdLmzZu1cOFCw4nCV/4ulZiYSJcCgBLA4A8Icy+99JIaNWokSVqzZo2eeuopw4kAAACcI3+XevLJJw0nAgAAp8Nyn8Ejb5f6888/OS8FACWAwR8Q5qKiopScnKxSpUpJkt577z3NmDHDcCoAAABnyN+l3n//fboUAABB7u6771ZMTIwkaeLEifJ4PIYTha+CzkvNnDnTcCoAcDYGfwBUv359DRkyJHf7gQceUGpqqsFEAAAAzlG/fn0NHjw4d5suBQBAcIuNjdVdd90lSdqzZ49mz55tOFF4y39eqkuXLnQpACgGBn8AJEk9evTQnXfeKUlKTU3VAw88wA2uAQAACqlnz550KQAAHCQhISH3e5b7NC//eakHH3yQLgUARcTgD4AkybIsDR8+XJUrV5YkzZgxQx9++KHhVAAAAM5QUJf64IMPDKcCAAAnc/vttys+Pl6SNHXqVB05csRsoDCXv0tNnz6d81IAUEQM/gDkqly5skaOHJm7/a9//Ut//vmnwUQAAADOUblyZY0YMSJ3+4knnqBLAQAQpKKjo3XvvfdKko4cOaJp06YZToSCzkutWbPGYCIAcCYGfwCOc8cdd+jhhx+WJGVkZCgxMVFZWVmGUwEAADhDy5Yt9dBDD0miSwEAEOzyLveZnJxsMAlycF4KAIqPwR+AE7z++uuqX7++JGnp0qV64YUXDCcCAABwjjfeeIMuBQCAAzRt2lQ1atSQJH311Vfau3ev4USQjj8vtWTJEr344otmAwGAwzD4A3CC0qVLKzk5WZGRkZKk//znP1qwYIHhVAAAAM5AlwIAwBlcLpfuv/9+SZLX69WkSZMMJ4J0Ypd67bXX6FIAcAYY/AEoUKNGjTRgwABJkm3b6tChgw4cOGA2FAAAgEPQpQAAcAaW+wxOBXWptLQ0w6kAwBkY/AE4qSeffFJNmzaVJP3111965JFHDCcCAABwDroUAADBr2HDhrnLSn7//ff666+/DCdCDroUABQNgz8AJ+V2uzV27FjFxcVJklJSUpSSkmI4FQAAgDPQpQAACH6WZSkxMTF3e8KECQbTIK/8XSo5OVnjx483nAoAgh+DPwCndO655+r999/P3X744Ye1ZcsWg4kAAACcgy4FAEDwy7nPn8Ryn8Emf5d66KGH6FIAcBoM/gCc1v3335/76be0tDR17NhR2dnZhlMBAAA4A10KAIDgVrt2bV199dWSpN9//10rVqwwnAh55e9SnTp1oksBwCkw+ANQKMOGDdO5554rSVqwYIFef/11w4kAAACcgy4FAEBwS0hIyP2epbmDT94uNX/+fL3xxhuGEwFA8GLwB6BQ4uPjNXbsWFmWJUl6/vnntXTpUsOpAAAAnKGgLrVkyRLDqQAAQI777rtPbrdb0rHBn23bhhMhL85LAUDhMfgDUGhNmzZVv379JEler1cJCQlKT083nAoAAMAZ8nepxMREuhQAAEGiSpUqat68uSRpy5YtWrhwoeFEyC9vl/J4PJyXAoCTYPAH4Iy8+OKLuuKKKyRJa9as0ZNPPmk4EQAAgHPQpQAACF55l/tMTk42mAQnk79LPfXUU4YTAUDwYfAH4IxERUVp3LhxKlWqlCTp/fff1/Tp0w2nAgAAcAa6FAAAwevuu+9WTEyMJOnTTz+Vx+MxnAj55e9S7733nmbMmGE4FQAEFwZ/AM5Y/fr1NWTIkNztBx54QLt27TKYCAAAwDnoUgAABKfY2FjdddddkqQ9e/Zo9uzZhhOhIAV1qdTUVIOJACC4MPgDUCQ9evRQq1atJEm7d+/Wgw8+yI2vAQAACokuBQBAcGK5T2fI26VSU1P1wAMP0KUA4P8x+ANQJJZl6ZNPPlHlypUlSTNmzNAHH3xgOBUAAIAz0KUAAAhOLVq0UPny5SVJn3/+uY4cOWI4EQpSUJf68MMPDacCgODA4A9AkVWuXFkjR47M3X7iiSf0559/GkwEAADgHHQpAACCT1RUlNq2bStJOnLkiKZNm2Y4EU4mf5f617/+RZcCADH4A1BMd9xxhx5++GFJUkZGhhITE5WVlWU4FQAAgDPQpQAACD4s9+kcdCkAOBGDPwDF9vrrr6t+/fqSpKVLl+qFF14wnAgAAMA56FIAAASXpk2bqkaNGpKkr776Snv37jWcCKdClwKA4zH4A1BspUuXVnJysiIjIyVJ//nPfzR//nzDqQAAAJyBLgUAQHBxuVy6//77JUler1efffaZ4UQ4lYK61IIFCwynAgBzGPwBKBGNGjXSgAEDJEm2batDhw46cOCA2VAAAAAOQZcCACC45F3uMyUlxWASFAZdCgD+h8EfgBLz5JNP6oYbbpAkbd26VY888ojhRAAAAM6Rv0vl3K8GAAAEXsOGDXXhhRdKkr7//nv99ddfhhPhdPJ2qb/++ovzUgDCFoM/ACXG7XZrzJgxiouLk3TsE3F8Kg4AAKBw8nep8ePH06UAADDEsqzjrvobP368wTQoDM5LAcAxDP4AlKhzzz1X77//fu72Qw89pC1bthhMBAAA4Bx0KQAAgkfOff4klvt0ivxd6uGHH6ZLAQg7DP4AlLj7779fiYmJkqSDBw+qQ4cOys7ONpwKAADAGehSAAAEh9q1a+vqq6+WJP3+++9asWKF4UQojLxdKi0tTR07dqRLAQgrDP4A+MW7776rmjVrSjq2Fv7rr79uOBEAAIBz0KUAAAgOeZf75Ko/58jbpRYsWECXAhBWGPwB8Iu4uDiNHTtWlmVJkp5//nktWbLEcCoAAABnoEsBABAc7rvvPrndbknHBn+2bRtOhMKgSwEIZwz+APjNP/7xD/Xr10+S5PV6lZiYqPT0dMOpAAAAnIEuBQCAeVWqVFHz5s0lSVu2bNFPP/1kOBEKiy4FIFwx+APgVy+++KKuuOIKSdKaNWv0xBNPGE4EAADgHHQpAADMY7lP58rfpZ588knDiQDA/xj8AfCrqKgoJScnq3Tp0pKkDz74QNOnTzecCgAAwBnoUgAAmNe6dWvFxMRIkj799FN5PB7DiVBY+bvU/7V37+FRlefex39rJpOQQEiCJJxFsKCCFURRPGDFSkXbBtSiYgy9VNrX424rtvVQhb1ftaJW2+25srevhYDiCbAqiKfWAwoaUSAoqICcAgQSiDnPzHr/iIkhBEggaz1rrfl+rstLJhlZ98r8HG6ee9azHn30UXopAIHH4A+A44466ijdf//9jY+vuOIKbd261WBFAAAA/kEvBQCAWenp6crNzZUklZSUaNGiRYYrQlvQSwFINAz+ALji17/+tX7+859LkrZv364rrriCG2IDAAC0Er0UAABmsd2nvzXvpa688kp6KQCBxeAPgCssy9L06dOVk5MjSXrllVf02GOPGa4KAADAH1rqpR599FHDVQEAkDjOPfdcZWVlSZLmzp2riooKwxWhLZr3Ui+//DLrUgACi8EfANfk5OToySefbHw8efJkff755wYrAgAA8I+WeqlVq1YZrAgAgMSRnJysX/ziF5KkiooKzZ8/33BFaCvWpQAkCgZ/AFx13nnn6dprr5UkVVVVKS8vT7W1tYarAgAA8IemvVR1dbUuu+wyeikAAFzCdp/+x7oUgETA4A+A6+655x4dffTRkqTCwkLdfvvthisCAADwD3opAADMOOOMM9SrVy9J0oIFC1RSUmK4IhyM5r3UlClTDFcEAO2LwR8A16WlpWnWrFmKRCKS6huuf/3rX4arAgAA8IeWeqm3337bbFEAACSAUCikCRMmSJKi0aiee+45wxXhYDTvpaZNm8a6FIBAYfAHwIjjjz9ed9xxhyTJtm3l5+errKzMbFEAAAA+0byXmjhxIr0UAAAuyMvLa/w12336F+tSAIKMwR8AYyZPnqwzzzxTkrRhwwZdc801ZgsCAADwkcmTJ+tHP/qRJHopAADcMmTIEB1zzDGSpHfeeUfr1683XBEOFutSAIKKwR8AY8LhsJ566illZGRIkmbPnq2CggLDVQEAAPhDOBzWP/7xD3opAABcZFmWLr300sbHTz/9tMFqcChaWpfiKk4AQcDgD4BRhx9+uB577LHGx9dccw2flgMAAGillnqpdevWmSsIAIAE0HTwx6DI35r3UldffTXrUgB8j8EfAOMuueQSXXbZZZKk3bt3Kz8/X7FYzHBVAAAA/tC8l5o4cSK9FAAADurfv79GjBghSfrss8+0YsUKwxXhULAuBSBoGPwB8ISHHnpIffv2lVS/R/4999xjuCIAAAD/oJcCAMBdXPUXLM17qXvvvddwRQBw8Bj8AfCEjIwMzZgxQ6FQ/dvS7bffro8++shwVQAAAP5ALwUAgLsuuugihcNhSfWDP9u2DVeEQ9G8l7rtttv08ccfG64KAA4Ogz8AnjFy5EjddNNNkqRoNKq8vDxVVFQYrgoAAMAf6KUAAHBPt27ddPbZZ0uS1q9fr/fff99wRThULfVSlZWVhqsCgLZj8AfAU6ZOnaoTTzxRkrR69WrdeOONhisCAADwD3opAADck5eX1/hrtvsMhqa91BdffKHJkycbrggA2o7BHwBPiUQimjlzptLS0iRJjz32mF566SXDVQEAAPgDvRQAAO4ZN26cOnToIEmaM2eO6urqDFeEQ9VSL/XPf/7TcFUA0DYM/gB4zlFHHaX777+/8fGVV16prVu3GqwIAADAP+ilAABwR3p6unJzcyVJJSUlWrRokeGK0B6a91JXXHEFvRQAX2HwB8CTfv3rXzc2z9u3b9cVV1zBjbIBAABaiV4KAAB3sN1nMNFLAfAzBn8APMmyLE2fPl3dunWTJL3yyit69NFHDVcFAADgD/RSAAC4Y8yYMcrKypIkzZ07VxUVFYYrQnuglwLgZwz+AHhWdna2/vd//7fx8eTJk7Vq1SqDFQEAAPgHvRQAAM5LTk7WL37xC0lSRUWF5s+fb7gitBd6KQB+xeAPgKedd955uvbaayVJ1dXVysvLU21treGqAAAA/IFeCgAA57HdZ3A176Uuu+wyeikAnsfgD4Dn3XvvvTrmmGMkSZ988oluv/12wxUBAAD4B70UAADOGjlypHr16iVJWrBggUpKSgxXhPbUtJcqLCyklwLgeQz+AHheamqqCgoKFIlEJEn33HOP3n77bbNFAQAA+AS9FAAAzgqFQpowYYIkKRqN6rnnnjNcEdoTvRQAv2HwB8AXjj/+eN1xxx2SJNu2NXHiRJWWlhquCgAAwB/opQAAcFbT7T4LCgoMVgIntNRLlZWVmS0KAPaBwR8A35g8ebLOPPNMSdKGDRt0zTXXyLZts0UBAAD4BL0UAADOGTJkSON2kO+++67Wr19vuCK0t5Z6KQDwIgZ/AHwjHA7rH//4hzIyMiRJTz/9NDfNBgAAaCV6KQAAnGNZ1h5X/T399NMGq4ETGnqpzMxMSdLs2bO5uhOAJzH4A+Arffr00WOPPdb4+JprrtG6devMFQQAAOAj9FIAADin4T5/Ett9BhW9FAA/YPAHwHcuueQSXXbZZZKk3bt3a+LEiYrFYoarAgAA8Ad6KQAAnNG/f3+NGDFCkrR8+XItX77ccEVwwsUXX0wvBcDTGPwB8KWHHnpIffv2lSS98847mjZtmuGKAAAA/INeCgAAZzTd7nP27NkGK4GTmvdS99xzj+GKAOB7DP4A+FJGRoZmzJihUKj+bWzKlCn66KOPDFcFAADgD/RSAAA4Y/z48QqHw5KkWbNmKR6PG64ITmjeS91+++30UgA8g8EfAN8aOXKkbrrpJklSNBpVXl6eKioqDFcFAADgD/RSAAC0v27duunss8+WJK1fv16LFy82XBGcQi8FwKsY/AHwtalTp+rEE0+UJK1evVqTJ082XBEAAIB/0EsBAND+mm73WVBQYLASOK15L3XjjTcarggAGPwB8LlIJKKCggKlpaVJkh5//HG99NJLhqsCAADwh5Z6qfnz5xuuCgAAfxs3bpxSU1MlSXPmzFFdXZ3hiuCU5r3UY489xroUAOMY/AHwvYEDB+qBBx5ofHzllVdq69atBisCAADwj5Z6qeLiYoMVAQDgb+np6crNzZUk7dixQ4sWLTJcEZzEuhQAr2HwByAQfvWrXzU21du3b9cVV1wh27YNVwUAAOAPTXupkpISXXnllfRSAAAcgksvvbTx12z3GXysSwHwEgZ/AALBsixNnz5d3bp1kyS98soreuSRRwxXBQAA4A/0UgAAtK8xY8YoKytLkjR37lxVVFQYrghOaqmXevTRRw1XBSBRMfgDEBjZ2dl68sknGx/feOONWrVqlcGKAAAA/KOlXqqoqMhgRQAA+FdycrLGjx8vSaqsrOQeugmgeS81efJk1qUAGMHgD0CgnHvuubruuuskSdXV1crLy1Ntba3hqgAAAPyBXgoAgPbDdp+Jh14KgBcw+AMQOPfcc4+OOeYYSdInn3yi2267zXBFAAAA/tG0l1q2bBm9FAAAB2nkyJHq3bu3JGnhwoUqKSkxXBHcwLoUANMY/AEInNTUVM2aNUuRSESSdO+99+rtt982WxQAAIBP0EsBANA+QqGQJkyYIEmKRqN67rnnDFcEN9BLATCNwR+AQBo6dKjuvPNOSZJt28rPz1dpaanhqgAAAPyBXgoAgPbBdp+JqXkvNXHiRHopAK5h8AcgsCZPnqxRo0ZJkjZu3KhrrrlGtm0brgoAAMAfmvdSV199Nb0UAABtNGTIkMZtH999912tX7/ecEVwS9NeasOGDaxLAXANgz8AgRUKhfTUU08pMzNTkvT000/z6ToAAIBWat5LPfPMM/RSAAC0kWVZysvLa3w8e/Zsg9XATaxLATCFwR+AQOvTp48ee+yxxsfXXnut1q1bZ64gAAAAH6GXAgDg0DXc50+SZs2aZbASuI1eCoAJDP4ABN7FF1+s/Px8SdLu3buVn5+vWCxmuCoAAAB/oJcCAODQ9O/fX6eccookafny5Vq+fLnhiuCm5r3UxIkT6aUAOIrBH4CE8OCDD6pv376S6vfUnzZtmuGKAAAA/INeCgCAQ3PppZc2/pqr/hJP017qnXfeoZcC4CgGfwASQkZGhmbOnKlQqP5tb8qUKfroo48MVwUAAOAP9FIAAByaiy66SOFwWFL9ff7i8bjhiuAmeikAbmLwByBhnH766br55pslSdFoVHl5eaqoqDBcFQAAgD/QSwEAcPBycnI0evRoSdL69eu1ePFiwxXBbfRSANzC4A9AQpkyZYpOPPFESdLq1as1efJkwxUBAAD4B70UAAAHr+l2nwUFBQYrgSn0UgDcwOAPQEKJRCIqKChQWlqaJOnxxx/X/PnzDVcFAADgD/RSAAAcvHHjxik1NVWSNGfOHNXV1RmuCG6jlwLgBgZ/ABLOwIED9cADDzQ+vvLKK1VcXGywIgAAAP+glwIA4OCkp6crNzdXkrRjxw699tprhiuCCfRSAJzG4A9AQvrVr36lsWPHSpJKSkp0+eWXy7Ztw1UBAAD4A70UAAAHp+l2n7NmzTJYCUxq3ktdccUV9FIA2g2DPwAJybIsPfHEE+rWrZskacGCBXrkkUcMVwUAAOAP9FIAABycMWPGKCsrS5I0d+5cVVRUGK4IJjTvpV599VV6KQDthsEfgISVnZ2tJ598svHxjTfeqKKiIoMVAQAA+Ae9FAAAbZecnKzx48dLkiorKzVv3jzDFcEUeikATmHwByChnXvuubruuuskSdXV1crLy1NNTY3hqgAAAPyBXgoAgLZju080oJcC4AQGfwAS3j333KNBgwZJkpYtW6bbbrvNcEUAAAD+QS8FAEDbjBw5Ur1795YkLVy4UCUlJYYrgknNe6nbb7/dcEUA/I7BH4CEl5qaqoKCAkUiEUnSfffdp7feestwVQAAAP5ALwUAQNuEQiFNmDBBkhSNRvXss88arggmNe+l7r33Xr399ttmiwLgawz+AEDS0KFDdeedd0qSbNvWxIkTVVpaargqAAAAf6CXAgCgbdjuE00176Xy8/PppQAcNAZ/APCdyZMna9SoUZKkjRs36uqrr5Zt24arAgAA8Ad6KQAAWm/IkCGN2zu+++67Wr9+veGKYBq9FID2wuAPAL4TCoX01FNPKTMzU5L0zDPPqKCgwGxRAAAAPtFSLzVz5kyzRQEA4FGWZe1x1d/s2bMNVgMvYF0KQHth8AcATfTp00ePP/544+Nrr71W69atM1cQAACAj9BLAQDQeg33+ZPY7hP16KUAtAcGfwDQzEUXXaT8/HxJ0u7du5Wfn69YLGa4KgAAAH9o2kuVl5fTSwEAsA/9+/fXKaecIklavny5li9fbrgieAHrUgAOFYM/AGjBQw89pCOOOEJS/V77d999t9mCAAAAfIReCgCA1mm63SdX/aEBvRSAQ8HgDwBa0LlzZ82YMUOhUP3b5NSpU7V06VLDVQEAAPgDvRQAAK1z0UUXKRwOS6q/z188HjdcEbyAXgrAoWDwBwD7cPrpp+vmm2+WJEWjUV122WWqqKgwXBUAAIA/NO+l8vLy6KUAAGgmJydHo0ePliStX79e77//vuGK4BWsSwE4WAz+AGA/pkyZouHDh0uSVq9erRtuuMFwRQAAAP7RtJdas2YNvRQAAC1gu0/sC+tSAA4Ggz8A2I9IJKKZM2cqLS1NkvT3v/9d8+bNM1wVAACAP9BLAQBwYOPGjVNqaqokac6cOaqrqzNcEbyCXgrAwWDwBwAHMHDgQP31r39tfDxp0iQVFxebKwgAAMBH6KUAANi/9PR05ebmSpJ27Nih1157zXBF8BJ6KQBtxeAPAFph0qRJGjt2rCSppKREl19+uWzbNlwVAACAP9BLAQCwf2z3if2hlwLQFgz+AKAVLMvSE088oe7du0uSFixYoIcffthwVQAAAP5ALwUAwP6NGTNGWVlZkqS5c+fq22+/NVwRvIReCkBbMPgDgFbKzs7Wk08+2fj497//vYqKigxWBAAA4B/0UgAA7FtycrLGjx8vSaqsrNT8+fMNVwSvoZcC0FoM/gCgDcaMGaPrr79eklRdXa28vDzV1NQYrgoAAMAf6KUAANg3tvvEgdBLAWgNBn8A0EbTpk3ToEGDJEnLli3TbbfdZrgiAAAA/6CXAgCgZSNHjlTv3r0lSQsXLlRJSYnhiuBF9FIADoTBHwC0UWpqqgoKChSJRCRJ9913n9566y3DVQEAAPgDvRQAAC0LhUKaMGGCJCkajerZZ581XBG8iF4KwIEw+AOAgzB06FDdddddkiTbtjVx4kSVlpYargoAAMAf6KUAAGhZXl5e46/Z7hP7Qi8FYH8Y/AHAQbrhhhs0atQoSdLGjRt11VVXybZtw1UBAAD4A70UAAB7O+644xq3cXz33Xe1fv16wxXBq5r3UldffTW9FABJDP4A4KCFQiE99dRTyszMlCTNmTNHM2fONFsUAACAT9BLAQCwN8uydOmllzY+nj17tsFq4GXNe6lnnnmGXgqAJAZ/AHBI+vTpo8cff7zx8bXXXqu1a9carAgAAMA/6KUAANhb08FfQUGBwUrgdfRSAFrC4A8ADtFFF12kiRMnSpLKy8uVn5+vaDRquCoAAAB/oJcCAGBP/fr10ymnnCJJWrFihZYvX264InhZS71ULBYzXBUAkxj8AUA7ePDBB3XEEUdIkt577z1NmzbNbEEAAAA+Qi8FAMCeml71N2vWLIOVwA+a91J333232YIAGMXgDwDaQefOnTVz5kyFQvVvq1OnTtXSpUsNVwUAAOAP9FIAAOzpoosuUjgcllQ/+IvH44YrgpfRSwFoisEfALST0047TbfccoskKRqNKi8vT99++63hqgAAAPyBXgoAgO/l5ORo9OjRkqRvvvlG77//vuGK4HX0UgAaMPgDgHZ0++23a/jw4ZKkNWvW6IYbbjBcEQAAgH/QSwEA8D22+0RbNe+lJk+ebLgiACYw+AOAdhSJRDRz5kylpaVJkp544gnNmzfPcFUAAAD+QC8FAMD3xo0bp9TUVEnSnDlzVFdXZ7gieF3zXurvf/87vRSQgBj8AUA7GzhwoP761782Pp40aZKKi4vNFQQAAOAj9FIAANRLT09Xbm6uJGnHjh167bXXDFcEP6CXAsDgDwAcMGnSJI0dO1aSVFJSossvv1y2bRuuCgAAwB/opQAAqJeXl9f464KCAoOVwE/opYDExuAPABxgWZamT5+u7t27S5IWLFighx56yHBVAAAA/kAvBQBAvXPOOUdZWVmSpHnz5unbb781XBH8oKVe6uGHHzZcFQC3MPgDAId07dpVTz75ZOPjP/zhD1q5cqXBigAAAPyDXgoAACk5OVnjx4+XJFVWVmr+/PmGK4JfNO+lfv/736uoqMhgRQDcwuAPABw0ZswYXX/99ZKk6upq5eXlqaamxnBVAAAA/kAvBQAA233i4DXvpS699FJ6KSABMPgDAIdNmzZNgwcPliR9+umn+tOf/mS4IgAAAP+glwIAJLrTTz9dvXv3liQtXLhQ27dvN1wR/IReCkg8DP4AwGGpqakqKChQcnKyJOkvf/mL3nzzTcNVAQAA+AO9FAAg0YVCIU2YMEGSFIvF9NxzzxmuCH5CLwUkHgZ/AOCCIUOG6M4775Qk2batX/7ylyotLTVcFQAAgD8076UmTpxILwUASChs94lDwboUkFgY/AGAS2644QadddZZkqSNGzfqqquukm3bhqsCAADwh6a91KZNm+ilAAAJ5bjjjtOgQYMkSe+9957WrVtntiD4DutSQOJg8AcALgmFQnrqqaeUlZUlSZozZ45mzJhhuCoAAAB/oJcCACQyy7L2uOpv9uzZBquBH9FLAYmDwR8AuKh37956/PHHGx9fd911Wrt2rcGKAAAA/INeCgCQyBru8ydJs2bNMlgJ/IpeCkgMDP4AwGXjx4/XxIkTJUnl5eXKz89XNBo1XBUAAIA/0EsBABJVv379dMopp0iSVqxYoeXLlxuuCH5ELwUEH4M/ADDgwQcfVL9+/STV781/9913G64IAADAP+ilAACJqul2nwUFBQYrgZ/RSwHBxuAPAAzo3LmzZsyYoVCo/m146tSpWrJkieGqAAAA/IFeCgCQqMaPH69wOCyp/j5/8XjccEXwI3opINgY/AGAIaeddppuvfVWSVIsFlNeXp4+//xznX/++Ro4cKA++OADwxUCAAB4F70UACAR5eTkaPTo0ZKkb775Ru+//77hiuBX9FJAcFm2bdumi3DDrl27lJmZKUk655xztGDBArMFAYCkuro6nX766Y2fqkpOTlZtba0k6aKLLtIzzzxjsjwAaEQvBcCL6KUAAIlo5syZys/PlyRdddVVevTRRw1XBL+ilwKCiSv+AMCgSCSixx57TElJSZLU2FxJ0qpVq0yVBQAA4Av0UgCARDR27FilpqZKkubMmbPHn39AW9BLAcGUZLoAp8VtW5V1MZXXxTVgyDBFIhHl9O2vsuo6JYUspUXCClmW6TIRUA35i8Ztxe36f0KWpZBlkT9Ikr766itdeOGFikaje31vzZo1isfjjfuttxX5g0nkLzhidky747tVapeq74l9FY6ElfmDTG2PbleSlaTOoc4KW2HTZSKgGvIXtaOKKqq4HVfICilJSeQPkpztpcgfTCJ/wWHHYoqXlUl1dbKjUSkWk8JhWUlJUiSiUGamrDCvJdomPT1dubm5euaZZ7Rz504tWrRIP/3pT/d6HvnDgTjZS5E/mJTo+QvUVp9x29bumqjKaupUVl2nnVV12l1Tp/3d4jYkqXNKRF1SI8rsEFFmSkSdU5JYjESbkT8cjGuuuWa/W3KsXbtWRxxxxAF/H/IHk8hfcMTsmHbGdmpbbJu2xbapOFqskliJ4vt5NUMKqWu4q7ondVdOOEc54Rx1CXdhMRJtRv5wMNqrlyJ/MIn8BYcdiym+fbtiW7Yotnmzops2Kb5tW/1i476Ewwrl5CipVy+Fe/ZUuEcPhbKzA70Yifbx0ksvKTc3V5I0YcIEFcyYQf7QZu3VS/H+B5PI394CMfjbWVWrr8sqtbG8SvHvzsaS1JYTa/r8kCX1Tk/VkVlpyuqQ3L7FInDIHw7Fa6+9pp///Of73JZjwYIFOuecc/b535M/mET+gqM4WqzPaj7T6trViqm+MQ4ptN8Fx+aaPj+ssAYmD9SQlCHqltTNkZoRHOQPh+JQeynyB5PIX3BEN21S7dKlqlu5Umq4aiYUkuKtfy33eH5SkiKDByv5pJOU1LNn+xeMQKitrVWPHj3Ut0MHXXXKKbp46NDvF7nJH1rpUHsp3v9gEvnbN98O/mJxWxvKq/RVaYV21UTbvNB4IA2/X0ZKkn6Q1VG901MVDnEVAuqRP7SndevWacqUKZoxY4aavyXfcsstuvPOO/f4GvmDSeQvOKJ2VF/UfqFPaz7V9th2WbJkt+Or2fD7ZYezNTRlqAYmD1SSFfhd5tFK5A/tqa29FPmDSeQvOOy6OtWtWKGaJUsULy5u+0LjgXz3+4W6d1fKyScrMniwrEik/X5/+FpD/r5+4QX1SEpSXSymSHtepUL+Ekpbeyne/2AS+Wsd3w3+YnFbn+/4Vl+VVSgad6/0pJClI7M66ugunViATGDkD0767LPPdMstt+jll19u/NpZZ52lN954QxL5g1nkLziidlRLqpfo0+pPVauWP9XphGQla2iHoRreYTgLkAmM/MFJB+qlyB9MIn/BYdfVqeadd1SzZIlUUyNZluTk0lrD75+SopSTTlLKyJG+XIBE+yB/cNKBeinyB5PIX9v4avC3o6pWH20pU0XdfvZmdVjHSFjDe2SqSypbkCUa8ge3LFq0SPn5+dq1a5eeffZZ/exnPyN/MIr8BceW6BYtrFioXfFdRo5vyVLnUGed0/Ec9UjqYaQGmEP+4JaWeinyB5PIX3BEN2xQ1YsvKl5W5uxi475YlkKZmUq94AIl9e7t/vFhFPmDW1rqpcgfTCJ/beeLwV8sbquopFxrSivafUuxtmo4/oCsjhrUNZ2rDxIA+YNJ5A8mkb/giNpRLa5arMKawnbfUqytGo4/LGWYTkk9hasPEgD5g0nkDyaRv+Cw6+pU/dZbql282PkrDA7ku+Mnn3KKOowa5aurD3BwyB9MIn8wifwdPM8P/nZW1Wqp4asM9oWrD4KP/MEk8geTyF9wmL7KYH8yQhlcfRBw5A8mkT+YRP6CI7pxo6peeMHcVQb74sOrD9B25A8mkT+YRP4OjacHf5vKq7Rkc5kks1cZ7EvDtQYn9cxUr/RUo7Wg/ZE/mET+YBL5C441tWv0asWrkmT0KoN9sb57Nc/teK4GJA8wXA3aG/mDSeQPJpG/4KgrKlLl88/XLzh6cfnMsiTLUtqFFyoyaJDpatDOyB9MIn8wifwdOs8O/taVVapwq/c+Gbcvw7pn6IiMNNNloJ2QP5hE/mAS+QuOFTUr9EblG6bLaLWz087W4JTBpstAOyF/MIn8wSTyFxy1hYWqeukl02W0WmpurpKPP950GWgn5A8mkT+YRP7aR8h0AS3x26KjJBUW79K6XZWmy0A7IH8wifzBJPIXHH5bdJSk1ytf18qalabLQDsgfzCJ/MEk8hccflt0lKSq+fNV+8knpstAOyB/MIn8wSTy1348N/jbVF7lu0XHBoXFu7SpvMp0GTgE5A8mkT+YRP6CY03tGt8tOjZ4vfJ1raldY7oMHALyB5PIH0wif8FRV1Tku0XHBlXz56uuqMh0GTgE5A8mkT+YRP7al6cGfzurahvvKeRXSzaXaWdVrekycBDIH0wifzCJ/AXHluiWxnsK+dWrFa9qS3SL6TJwEMgfTCJ/MIn8BUd048b6ewr5WOXzzyu6caPpMnAQyB9MIn8wify1P88M/mJxW0u3lJkuo10s3VKmWNyTt07EPpA/mET+YBL5C46oHdXCioWmy2gXCysWKmpHTZeBNiB/MIn8wSTyFxx2XZ2qXnhBsn3eT9q2ql54QXZdnelK0AbkDyaRP5hE/pzhmcFfUUm5Kupi8vnLK1tSRV1MRSXlpktBG5A/mET+YBL5C47FVYu1K75Lts9fTVu2dsV36YOqD0yXgjYgfzCJ/MEk8hcc1W+9pXhZWSAWHuNlZap++23TlaANyB9MIn8wifw5wxODvx1VtVpTWmG6jHa1prSCLcd8gvzBJPIHk8hfcGyJblFhTaHpMtrVxzUfs+WYT5A/mET+YBL5C47ohg2qXbzY/4uODWxbte+/76ktx7Bv5A8mkT+YRP6cY3zwF4vb+mhLmSzThbQzS2w55gfkDyaRP5hE/oKjYYsxK2CvpiUr4bcc8wPyB5PIH0wif8Fh19Wp6sUXJStYr6Usy1NbjqFl5A8mkT+YRP6cZXzw9/nObwOxxVhzDVuOfb7zW9OlYD/IH0wifzCJ/AXH0uqlgdhirLmGLceWVi81XQr2g/zBJPIHk8hfcNS8804wthhr7rstx2reecd0JdgP8geTyB9MIn/OMjr4i8VtfRWwLcaa+6q0IqGuOvAT8geTyB9MIn/BEbWjWla9zHQZjlpWvSyhrjrwE/IHk8gfTCJ/wWHX1almyZLgLTo2sG3VLFli/KoDtIz8wSTyB5PIn/OMDv42llcpGvBFuWjc1sbyKtNloAXkDyaRP5hE/oJjde1q1SrY9zSsVa1W1642XQZaQP5gEvmDSeQvOOpWrpRqakyX4ayamvrzhOeQP5hE/mAS+XOe0cHflwG/2qBBopyn3yTK65Io5+k3ifK6JMp5+k2ivC6JcJ7LapaZLsFxlqyEOE8/SoTXhfx5VyK8LuTPuxLhdUmU/NV8+GHw7i3UnGXVnyc8h/zBJPIHk8if84wN/nZW1WpXTfC3jZCkXTVR7awK9qcB/Yb8wSTyB5PIX3AUR4u1PbbddBmOs2Vre2y7iqPFpktBE+QPJpE/mET+giO6aZPixcXB3WasgW0rXlys6KZNpitBE+QPJpE/mET+3JFk5KiSvi6rlCW5ehvsG8aerfVfFCkpkqzp/y5UelYXV45rqf58u6Qmu3I8HJgb+bvqrJO0ffPGvb7eIS1N3focoWFnnKWxV1zleA7Jn/c4mb/mubMsSympaUpL76weffvpyME/1Knn5mrAccc7cPS9kT/vMfn+19y1dz2gsy642LE6gp6/z2o+kyVLtovd1D0j79HmlZsVTg7rv4r+Sx27dHTluJYsLa9Zru5J3V05Hg7Mjfz955D/VOmG0r2+ntwxWV2P6KpjRh+js647y/Eckj/vcTJ/zXNnWZaSOyarQ3oHZR+ZrT5D+mjouKHqe0Lfdj92S8if95h8/2tuwkMTdPKlJztWR9DzV7t0qRQKSfG4a8c87dFHtXLrViWHw/p88mR1SUtz58ChkGo/+khJvXq5czwckBv5++EDD2jDrl17fb1jJKIjunTRTwYM0PWnnup8Dsmf5ziZv+a5syR1TE5W55QU9T/sMA3t0UPnDx6sE3r3bvdjt4j8eY7J97/mHh47VnnHO7hGajB/RgZ/cbv+vjtuDv2+XL5M678okiRF62r1r5de0M8mTnLl2Lbq76c0rHuGQkG/hNUH3M7f0cOGq/vh/SRJth3Xzm3F+uKTj/TiE0X617zn9H8LXlT3Ps4tHJA/b3Erf01zV1tTpfLSUq1dtUIrl7yv+U8+rsHDT9E1d93vaPYk8uc1Jt//WtKj7xGOHj/I+YvZMa2uXe3q0O+bwm+0eeXm+uPXxvTRnI/0o6t+5Mqxbdn6ovYL/TjtxwpZRneqh9zPX7+T+6lr/66SJDtua3fxbq1dslab/7pZHz3zka5/+Xp1PaKrY8cnf97iVv6a5q6uqk4VOyu06bNN+vLdL/XWw2/pyNOO1IQHJziaPYn8eY3J97+WZPfPdvT4Qc6fHYvV33fHxaFf4aZNWrl1qySpNhbTM599pqtHjHDn4PG46laskP3zn8sKBeu19CO38zeiTx/161L/ofO4bau4vFxLNmzQA1u36ulPP9Wrl1+uI7o4+KF08ucpbuWvae6qo1HtqKzUZ1u26N116/TQ4sU6rW9fPTx2rLPZk8ifx5h8/2tJ/wDnz8jgb3dNVHGXr+R847nZkqQu3Xpo59YteuO52a4N/iQpbkvlNVFldIi4dky0zO38/fgXl+51RUvp9m26Pf8CbV73tWbce4d+/99POFoD+fMOt/LXUu5s21bhv9/Uk3dN0cqli3XrhFzd9fRL6tb7cEdrIX/e4YX3P7cFNX87YzsVU8zVY34w8wNJUkaPDO3asksfzPzAtcGfJMUU047YDmUnObvIiQNzO38j8kfsdUXL7q279eDPH9T2L7frpSkv6fKnLne0BvLnHW7lr6Xc2batVa+v0ou3vKiv3vtKfxvzN/124W91WN/DHK2F/HmHF97/3BbU/MW3b5ei7m5/P6OwUJLUMz1dm8vLNaOw0L3BnyRFo4pv365wt27uHRMtcjt/+cOG7XVFy9bycv30//0/fbljh25ftEj/uNjhv7eRP89wK38t5c62bS1as0Y3L1ig99av10/+53/02qRJOiIry9liyJ9neOH9z3WG8mdkzF1WU+fq8WqqKvXuy3MlSf8x7b/VIa2jvlm9Sl8uX+ZqHaUunzda5nb+WpKVnaOxV14tSVr+wbuuHJP8eYPJ/FmWpRN+9GNNe/Zl9ejbX2Ul2/Xon2505djkzxu88P5nQhDzty22zdXj1VbWqvD5+sWqyx67TCmdUrSlaIu+KfzG1TrcPm+0zAuvQ+dunXXWdWdJklb/e7Urx/TCecPs62BZlgaNHqTfvf47ZR+ZrfJt5Xr6N0+7cmzy5w2J+joE8bxjW7a4erzK2lo9v2KFJOmxCy5Qp+RkFW3bpkKX7/sT27zZ1eOhZW7nryXd0tP1H6eeKkn619q1rhyT/HmDyfxZlqWfDByoN371Kx3ZpYu2VVToP+bPd+XY5M8bvPD+Z4KJ/JkZ/FXXyc0Nt95f8E9VfluuwwccrR+OOE2nnZcr6furAN1gqf68YZ7b+duXzK45kqSYC59yIH/e4YX8deycoctv+U9J9YPnr1Z85ujxyJ93eCF/bgtq/rbFtinkYhu3bN4yVZdXq8cxPTRg5AAdP67+E3MNVwG6IaRQIBce/cjt/O1L526dJUnxmPPbxJA/7/BC/tIy0nT+XedLktb8e402LNvg6PHIn3d4IX9uC2r+Yps3199fyCVzi4q0u6ZGg3JydEa/fjp/8GBJ318F6IpQKGEXXL3G7fztS06nTpKkmBtb7pE/z/BC/jJTU/XnMWMkSf9eu1bLnB6KkD/P8EL+XGcof0Z+yjur6ly9v98bz9cP+M668JL6f19Q/+93X5mnmuoqV2qwVX/eMM/t/O3LmuWfSJL6DDjK8WORP+/wSv6GnXGWOmXUb6Xw6fv/cvRY5M87vJI/NwU1f8XRYsXl3j1pGgZ8J+edvMe/C18oVG1VrSs1xBVXcbTYlWNh/9zO376s/3i9JKn7Ud0dPxb58w6v5O+Ys49RWlaaJOmLt79w9Fjkzzu8kj83BTV/0U2bXL2/X8OAr2G7scu++/fzK1aoqs6lXjUerz9vGOd2/vbl4+/ycHS2C1v5kj/P8Er+Rg8YoKzUVEnSW1995ezByJ9neCV/rjKUP9cHf3Hb1i4Xt9zavPYrrfroQyVFIjoj90JJ0tHDhqtX/x+osny3Fi982bVadtfUKW4n2pKre1577TVNmjRJL730kux9/Jzdzt9ex4/HtWPrFr0y8381b/qjCoXD+sVVv3Hl2OTPWY888oiuu+46Fe7nE5um89eUZVnqP/hYSdKGL53fIo38Oaeqqkq33nqrbr31Vm3YsO8rDryUP7cFLX8xO6aSWIlrx9v25TZ9vfhrhSNhnXjRiZKkfif3U86AHFXvrtan8z91rZaSWInidst/SdiwYUPj/wtVVe58sCsRuZ2/5uLxuMo2l+mdJ97Rmw++qVA4pJ/c+BNXjr2//OHQtaaXMp2/pizLUu/jekuSij93fihC/pzT2l7KS/lzW9DyZ8diim/d6trxviwp0eJvvlEkFNLFxx0nSTr58MM1sGtX7a6p0byiItdqiW/dKjvRFlxd1Jp1Kbfz11w8Htfm3bv19w8/1H+/957ClqUbzzjDnWOTP0e1ppcynb+mLMvSkB49JEmrtm93/Hjkzzmt7aW8lD+3mchfkqtHk1RZF3P3ar8X6u+5cOKonyijy/c3XT/rwks049479OZzs3Xm2F+4Uktc9effKdn1H3tCyM/P17Zt2/Q///M/GjZsmKZOnaqf/exnsqzvN7ZzO3+S9PAtv9PDt/xur6//4IdDdfnNU3X0sJNcqYP8Oefrr7/WtddeK0l6+OGHlZubqylTpmjYsGF7PM9E/vYnPbOLJKm8rNTxY5E/58ydO1d33XWXJOm+++7TpEmTdNNNN6lPnz57PM9L738N/rFklTp2znC8jqDlb3d8t6tXG3xY8KEk6dgxx6pT106NXx+RN0Lzp87XBzM/0PCLh7tSS1xx7YrvUlb4+5u/b9iwQXfffbemT5+u2tr6qw+PPfZYTZgwwZWaEo3b+ZOk2dfN1uzr9t6i//Bhh2vcHePUf0R/V+poKX9oH63tpUzkb386HtZRklSxs8LxY5E/57S2l/LS+1+Du9bepbSMNMfrCFr+4mVlrl5tMPOT+t1+zj3qKHXt2LHx65cdf7xuX7RIMwoLdcmQIe4UE4spXlqq8GGHHfi5aLPWrEu5nT9JunbePF07b95eXx/Ws6fuGjNGIw4/3J1CyJ9jWttLmcjf/hyWVv9nWGllpfMHI3+OaW0v5aX3vwbr/vhHZX535amjDOTP9RWwaNy9ZcdYNKq35z4r6fttPhucOXa8Zj1wt4o++kDF36xT98OPcKUmN88/0Wxv8umQwsJC5ebm7tVomfj5Hz1suLof3q/xcXnpTq1fXaQvly/Tk3+eqt/c+5B6HuHOghX5c8b2Zp9Mmj9/vubPn79Xo+W1n7/93ad2m/4lxEleO/+g2Lbt+3uu1NbW6pFHHtH06dP3arS88P7XXFIk4lotQcpf1Hb+3rANYtGYlj69VJJ08mUn7/G94ZcM1z/v+Ke+fv9rlawtUdd+XV2pqeH8Wxr4NWj6/wXal5v5a9Dv5H7q2v/7fFXsqNDmlZv1TeE3mvunucp/PF/ZR7qwRZXMnH8iaHUv5bGfv/3dny2u9VIeO/+gaHUv5YH3v+aSIu4t6QQqf25trSkpGotp9qf1uyM0bO/Z4JIhQ/Rfb7yh99ev19qdO9WvSxd3inLx/BNNa9alTPz8R/Tps0e+dlZWauXWrSrcvFm3LFigJy68UEe6tRhN/hzR2l7Kaz//hp153OqlvHb+QdHaXsoL73/NJYfD7hXj8vm7Pvhzc6utj//1usq2b1OXbj009PQz9/heZtdsDTvjLC198zW98fzTyvvdTa7U9JMxY7SuaLkrx0o0LW2j0NBode3aVV988YWU2qmF/9JZP/7FpTrrgov3+FosGtXT/32vXvj7g7o9/0I9+Oo7Su3kfG3kzxl1+3jjbmi0TjjhBC1dutRzWw2Wl9Zf6dcpI9OV45E/Z1S28Mm4hkbrkUce0a9//Ws9/vjjRvLX0vufKV77/+9QROXewlvRa0XavXW3Mnpk6Oizjt7je+k56Ro0epBWvLpCHxZ8qJ/+6aeu1BRTTP/n//wf/f3vf9/nc2699VbdeeedrtSTaHoO6anL51zu6jFH5I/QyZfuOXiORWN69c+v6vUHXteDP39Qt3x4izqkd3C8ltFjRmvzZ5sdP06iaW0v5eb7X2s0XOnXcK8/p5E/Z7S2lzKRv5be/0yJKWa6hHZjR917LReuWaOt336rnunp+vEPfrDH93I6ddLoAQP06hdfaOYnn+i2H//YlZrGjB6tTxN0qzWntWZdqrOL+WuQP2xY4/0lG0RjMd311lu6/9139dMnn9TS669XekqK47WQP2e0tpdy8/2vNXZ892ewK1dcifw5pbW9lIn8tfT+Z4rb5x/owd8bz9VviVFXU63b8y/Y6/s7t9bfi+HtF+fokv/4vcIuTHgrKir2+hQGnFdSUqKCggJNuPLXpkuRJIWTkjTht3/U688WqHT7Vr0971mdm+f8Ihr5M+Pjjz/Wrl27FE92p5FpDdu2tXbVCklS34FHH+DZ7YP8mTFjxgxjgz8vCdL5u3mPnQ9mfiBJitZE9eDPHtzr+7u27JIkLZm9ROfefK5CYedvHx2zY5oxY8Z+n1NRUaGKCue33ktE6RXppkuQJIWTwjrv1vO0+B+Ltbt4t5Y+s1QjJ410/LjlleX8WWZAYy/V0TtbU9m2rU2fbZIk9RjUw5Vjkj8zvu+lvJM/E2J2cAZ/irl3LjO+u9dWdTSqnz755F7f31xeLkmatWyZbhk1SuGQ871UZTnvJSY0rEtdnZtruhRJUlI4rD+ddZaeKixU8bff6ulPP9WvTnL+VjTkz4yGXqqTi+9/B2Lbtj7bskWSNDgnx5Vjkj8zGnopN//89SSXz9/1wV/IpUt3S7dtVeG/35RUf/+qzwuX7vO5O7cVa9k7b+mEM892vK7s7Gz17+/Oto6J5uuvv97n93r16qXLL79ctW5dOt4KoVBI2b36aHfpTm38ao0rxyR/zqiurtbmzfv+9PWZZ56pjIwMlVZ7Z0uBwn+9oW93lUmShpz2I1eOSf6csWvXLu3YsaPF74VCIV199dX1v/bQ+58JQTr/kOX8gpAk7SrepVWLVkmqv6pl7Ydr9/3cLbu06o1VGvyTwY7XFbbCuvrqq/XAAw+0+KlqSTrssMOUkeH8/SMTUffs7qZLaBQKhdTl8C6q2FGhravd+eRut67dJP4oa3et7aWqYlUuVrV/RYuKVFlW/+nmo0Yd5coxyZ8zWt9LufPnr1eFLRe3wnKaS9t6FZeXa9Ga+r/r76yq0gcbNuzzuVvKy/X6l1/qnIEDHa+ra7du6u/m1mYJpDXrUiorc6+gAwiFQjo8M1M7Kiu12qVhCPlzRmt7qdi337pY1f69tmaNyqqrJUmjjjzSlWOSP2e0tpdy689fz3L5/AM7+HvrxTmKx2IaMGSY7n7mn/t83oz77tDc6Y/ojednuzL4m/vCC8rs4N49jRJJKBTaawHwjDPO0NSpU3XmmWfKsiyVeWjwEo/HtX1TfePfockNvp1E/pzx4YcfasSIEXt8zbIsTZgwQbfddpuOPrr+ijqvDB4qynfryT9PlSQNOfUM9TvmWFeOS/6c8be//U2//e1v9/hax44ddd1112ny5MnKzq6/75VX8mdKkM4/yaX2bcnsJYrH4up7Ql/9btHv9vm8+VPn683/flMfzvzQncGfwvrLX/6im266Sffdd58eeuihvbYWue222/Sb3/zG8VoS0fbods0qn2W6DEn1vdTOb3ZKklI6Or81lSTNe2GespPcuZ9gImltL+XW+9+BVO2u0txb50qSjjrzKPX+YW9Xjkv+nNHaXsor+TMlrOAs1llJ7ryWs5YtU8y2dWKvXnr9V7/a5/OmLFqkv733nmYUFroy+Hth3jyFu3vngzxB0pp1KS8NXuLxuL75bhDZMTnZlWOSP2e0tpdy6/3vQHZVV+uWBQskSaP699dxPdzZPYH8OaO1vZRX8meK2+fv+kfWkkLuLLy98cLTkqQzx43f7/N+NLb++x+//bp27Wx5Mt2e3Dr/RNS9yRv3GWecoTfffFNvv/22Ro0a1XiTWK/8/GPRqGb/dZp2l9YvVg0f9RNXjuuV8w+aptmzLEuXXnqpioqKVFBQ0NhcSeZ//rZtq/Dfb+qm8edpy/qvlZXdTVf93/tcO77p8w+qpvnr2LGj/vjHP2rt2rW6++67G5sriZ9/kM4/yXKnWfyw4ENJ0vAJw/f7vOEX139/5cKV+rbE+YWMhvPPzs7WtGnTtG7dOv3hD39QWtr399jq4dJfHBORW/k7kFg0plfufEUVO+q3dD12jDsfYvHK+QdNq3spwz9/27ZVtKhI9599v7Z/tV2du3fWxX9z7162ps8/qFrdSyX4zz9Q5x9x58OIMz/5RJI0YejQ/T7vkiFDJEkLV69WiRtblbt0/omoNetSXvn5R2Mx3fHmm433WDv3KHeuXvfK+QdNa3sp0z9/27a1aM0a/fiJJ/TVzp3q3qmT/ubm9rfkzxGt7aUS/ufv8vm73rmlRcKyJDl5p52VSxareP1aRZJTdPp5Y/f73MMHHKX+g36or4uW619zn1XuFVc5VldI9ecPZ8yZM0fPP/+8cnNzGz9J1Zwb+WvujedmaeWSxY2Py8t2av0XRSrZUn8J/oVX/UZHD9v/omp7IH/O6du3r5566imtWrVKv/zlL/dsqppwM39Nc1dXW6Pysp36euUKfburVJI0+KRTde1d9yunlzufUCd/zjn//PP15z//WbZta9KkSXs2VU144f2vuaGnnaGRP9/7HrztLWj56xzqrJBCisu5ew19+d6XKvm6REkpSRp2wbD9PrfHMT3Ue0hvbfx0o5Y+vVSjrhvlWF0hhZQR2nMLz4YB4I033qjp06fLsiyNGzfOsRoSnRv5a+6DGR/oy/e+bHxcubNSm1ZsUtmmMknS6Mmj1e/kfo7X0VL+0D5a20u5mb+muYvWRFWxo0IbP9uoytL6BdIfnP4DTXhwgrr06eJ4LRL5c1JreykvvP81d/Soo3XCL05wvI6g5S+UmSmFQlLcudfy3XXr9PXOnUoJh3Xhsfv/cMoxOTka0qOHPt2yRbM//VTXn3qqY3UpHFYoK8u53z/BtWZdyo38NTejsFDvrlvX+HhnVZVWFhdr4+7dkqQbR47UyYcf7nwh5M8xre2l3Mxf09zVxmLaUVmpT7dsUWlV/dbtpx9xhB4aO1aHZ2Y6Xosk8ueg1vZSXnj/a+6sI4/U+OOOc74QA/kzstVnRkpEZTXObbn4xvOzJUknjhqtThmZB3z+j8aN19dFy/XG87MdHfx1TokEaqsxrzn99NN1+umn7/c5buSvuc8Ll+5xj8mkSLKysnN02nm5+snFE3XsyQ429U2QP2dNnDjxgM9xM39Nc9chLU1pnTqr78CjdeSxx+m088bqBz8c6ngNTZE/5yQnJ+umm2464PO88P7XXMfOnV0Z/AUtf2ErrK7hrtoW2+bYMT6Y+YEkafA5g5WWmXaAZ9df9bfx0436YOYHjg7+uoa77vMeS9nZ2br55psdOzbquZG/5tZ+uHaPe0yGk8Pq3K2zjj//eJ16+akacPoAV+rYX/5w6FrTS7mZv6a5S+6YrNTOqeoxqIcOH3q4jj//eB0+zIUF0ibIn3Na20t54f2vudTOqa4M/oKWPyscVqhbN8W3bHHsGDMKCyVJY446SpmpqQd8/iVDhujTLVs0s7DQ0cFfqFs3WaHgvJZe05p1KTfy19wHGzbscY/J5HBY3Tp10gWDB+vyE0/UyH7Of4BKIn9Oa00v5Wb+muauYySizh06aFBOjo7v2VMXHHushvXq5XgNTZE/57S2l/LC+19zGR06uDL4M5E/y26++bQLlm3dpbVlla5edWCaJalfZpqGdgvOp+T8ivzBJPIHk8hfcLxV+ZZW1Kxw9aoD00IK6diUYzUqzbnBIlqH/MEk8geTyF9wVL38smoLC1296sC4UEjJJ5yg1PPOM11JwiN/MIn8wSTy5+JhXT3adzI7RBJq0VGq31ots0OC72PrEeQPJpE/mET+giMnnJNQi46SFFdcOeEc02VA5A9mkT+YRP6CI9yzZ2ItOkpSPK4w90H2BPIHk8gfTCJ/7jEz+EsJ3gJca2Ql6Hl7DfmDSeQPJpG/4AjiAlxrJOp5e02ivg6Jet5ek6ivQ6Ket9ck6usQxPNO1AXgcM+epkuAyB/MIn8wify5x8jgr3NKkkLBudVOq4QsKT3F9VsqogXkDyaRP5hE/oKjS7iLwgqbLsNVYYV1WPgw02VA5A9mkT+YRP6CI5SdLSUFr0fcr6Sk+vOGceQPJpE/mET+3GNk8BeyLPVOT1WirD1aknqnpypkJcoZexv5g0nkDyaRv+AIW2ENTB4oK0FeTUuWjko+SiGLm7F7AfmDSeQPJpG/4LDCYUUGD5ZCwTu3FoVCihx7rKxEOV+PI38wifzBJPLn4qFdP+J3+memJcx9hmxJR2almS4DTZA/mET+YBL5C47jUo6TnSCvpi1bx6UcZ7oMNEH+YBL5g0nkLziShw9PnPsMxeP15wvPIH8wifzBJPLnDmODvy6pycoI4NZbLclISVJWh2TTZaAJ8geTyB9MIn/B0T2pu7LDwd+uxJKl7HC2uiV1M10KmiB/MIn8wSTyFxxJvXop1L27FMDdIfZgWQp1764k7m/lKeQPJpE/mET+3GH0msofZHU0eXjXJMp5+k2ivC6Jcp5+kyivS6Kcp98kyuuSCOc5NGWo6RIcZ8tOiPP0o0R4XcifdyXC60L+vCsRXpdEyV/KySdLdsCv4LTt+vOE55A/mET+YBL5c57RwV/v9FQlhYI92U0K1d9PCd5D/mAS+YNJ5C84BiYPVLKCe1WjJCUrWQOTB5ouAy0gfzCJ/MEk8hcckcGDpZQU02U4KyWl/jzhOeQPJpE/mET+nGd08BcOWToy4J/GPzKro8IBX1z1K/IHk8gfTCJ/wZFkJWloh6Gmy3DU0A5DlWQlxva0fkP+YBL5g0nkLzisSEQpJ50U3O3GLEspJ50kKxIxXQlaQP5gEvmDSeTPeUYHf5J0dJdO6hgJK2gvsSWpYySso7t0Ml0K9oP8wSTyB5PIX3AM7zBcGaEMWQF7NS1ZyghlaHgHbsTuZeQPJpE/mET+giNl5EiFMjODt/hoWQplZSnljDNMV4L9IH8wifzBJPLnLOODv3DI0ok9MhW0HV1tScN7ZCbE1QZ+Rv5gEvmDSeQvOJKsJJ3T8RzZAXs1bdk6p+M5CXG1gZ+RP5hE/mAS+QsOKxJR6vnnB+9eQ7at1PPPl5WUOK+lH5E/mET+YBL5c5bxwZ8kHZaarAEB23JsQFZHdUkN9p7/QUH+YBL5g0nkLzh6JPXQsJRhpstoVyeknKAeST1Ml4FWIH8wifzBJPIXHEl9+ij5lFOCc9WBZSn51FOV1Lu36UrQCuQPJpE/mET+nOOJwZ8kDeqaHogtxxq2GBvUNd10KWgD8geTyB9MIn/BcUrqKYHYcqxhi7ERqSNMl4I2IH8wifzBJPIXHB1GjQrGlmPfbTHWYdQo05WgDcgfTCJ/MIn8OcMzg79wyNLwHpmmy2gXibbFWBCQP5hE/mAS+QuOhi3HgiDRthgLAvIHk8gfTCJ/wWFFIkq94IJALDx6YYsxtA35g0nkDyaRP2d4ZvAnSV1Sk3VSz0zTZRySk3pmJuQWY0FA/mAS+YNJ5C84eiT10LkdzzVdxiE5t+O5CbnFWBCQP5hE/mAS+QuOpN69lXbhhabLOCRpF17oiS3G0HbkDyaRP5hE/tqfpwZ/ktQrPVXDumeYLuOgDOueoV7pqabLwCEgfzCJ/MEk8hccA5IH6Oy0s02XcVDOTjtbA5IHmC4Dh4D8wSTyB5PIX3BEBg1Sam6u6TIOSmpuriKDBpkuA4eA/MEk8geTyF/78tzgT5KOyEjz3eLjsO4ZOiIjzXQZaAfkDyaRP5hE/oJjcMpg3y0+np12tganDDZdBtoB+YNJ5A8mkb/gSD7+eN8tPqbm5ir5+ONNl4F2QP5gEvmDSeSv/Vi2bdumi9iXTeVVWrK5TJLkxSIbdp09qWcmVxoEEPmDSeQPJpG/4FhTu0avVrwqSbI9+Gpa372a53Y8lysNAoj8wSTyB5PIX3DUFRWp8vnnJduu/8drLEuyLKVdeKHnrjTAoSN/MIn8wSTyd+g8PfiTpJ1VtVq6pUwVdTHTpeylYySs4T24p1CQkT+YRP5gEvkLji3RLVpYsVC74rtMl7KXjFCGzul4DvcUCjDyB5PIH0wif8ER3bhRVS+8oHhZmbcWHy1LocxMpV5wgafuKYT2Rf5gEvmDSeTv0Hh+8CdJsbitopJyrSmtkCWzVx80HH9AVkcN6pqucMg60H8CnyN/MIn8wSTyFxxRO6rFVYtVWFMoS5bRqw8ajn9CygkakTpCSVaSsVrgDvIHk8gfTCJ/wWHX1an6rbdUu3hx/af8TS6lfXf85FNPVYczz5QViZirBa4gfzCJ/MEk8nfwfDH4a7CjqlYfGb76gKsMEhf5g0nkDyaRv+BouPpgd3y3scVHrjJIXOQPJpE/mET+giO6YYOqXnzR3NUHPrnKAM4gfzCJ/MEk8td2vhr8SfVXH3y+81t9VVqhaNy90pNClo7M6qiju3TiKoMERv5gEvmDSeQvOKJ2VEurl2pZ9TLVqtbx4zVcYZCsZA3tMFTDOwznKoMERv5gEvmDSeQvOOy6OtW8845qliyRamqcvwKh4fdPSVHKSScpZeRIz19lAOeQP5hE/mAS+Wsb3w3+GsTitjaWV+nL0grtqom2+xZkDb9fZkqSjszqqN7pqSw4ohH5g0nkDyaRv+CI2lGtrl2tZTXLtD22vd23IGv4/XLCORqSMkQDkwey4IhG5A8mkT+YRP6Cw66rU93Klar58EPFi4ulUEiKx9vvAN/9fqEePZRy0kmKDB7sqwVHOIv8wSTyB5PIX+v4dvDX1M6qWn1dVqmN5VVquAihrQuRTZ8fsqTe6ak6MitNWR3YUgz7R/5gEvmDSeQvOIqjxVpes1xf1H6hmOq3dA0ppLha3zw3fX5YYR2VfJSOSzlO3ZK6OVIzgoP8wSTyB5PIX3BEN21S7UcfqW7FCikarf9iWxcimz4/KUmRY49V8vDhSurZs/0LRqCQP5hE/mAS+du3QAz+GsRtW+U1UZXW1Kmsuk47q+q0u6Zuvy1zSFLnlIi6pEaU2SGirJSI0lOSFLK4ugBtQ/5gEvmDSeQvOOJ2XDtiO7Qttk3bYttUHC1WSaxkvwuQIYXUNdxV3ZO6Kyeco5xwjg4LH6aQFXKxcgQB+YNJ5A8mkb/gsONxxbdvV2zzZsW2bFF00ybFt26VYvu5V3Y4rFC3bkrq1UvhHj0U7tlToexsWSFeS7QN+YNJ5A8mkb+9BWrw15K4bauyLqZo3Fbcrv8nZFkKWZaSQpbSImEWGeEY8geTyB9MIn/BEbfj2hXfpagdVUwxxeyYwlZYYYWVZCUpI5TBIiMcQ/5gEvmDSeQvOOx4XPHSUqmuTnY0Wr8IGQ7LSkqSIhGFsrICs8gI7yF/MIn8waREz1/gB38AAAAAAAAAAABAIgjuSBMAAAAAAAAAAABIIAz+AAAAAAAAAAAAgABg8AcAAAAAAAAAAAAEAIM/AAAAAAAAAAAAIAAY/AEAAAAAAAAAAAABwOAPAAAAAAAAAAAACAAGfwAAAAAAAAAAAEAAMPgDAAAAAAAAAAAAAoDBHwAAAAAAAAAAABAADP4AAAAAAAAAAACAAGDwBwAAAAAAAAAAAAQAgz8AAAAAAAAAAAAgABj8AQAAAAAAAAAAAAHA4A8AAAAAAAAAAAAIAAZ/AAAAAAAAAAAAQAAw+AMAAAAAAAAAAAACgMEfAAAAAAAAAAAAEAAM/gAAAAAAAAAAAIAAYPAHAAAAAAAAAAAABACDPwAAAAAAAAAAACAAGPwBAAAAAAAAAAAAAcDgDwAAAAAAAAAAAAgABn8AAAAAAAAAAABAADD4AwAAAAAAAAAAAALg/wOhPfXjCfMgawAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1800x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "from networkx.algorithms import isomorphism\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define the DAGs\n",
    "dag1_edges = [('A', 'B'), ('A', 'C'), ('B', 'D'), ('C', 'D'), ('D', 'E')]\n",
    "dag2_edges = [('B', 'A'), ('A', 'C'), ('B', 'D'), ('C', 'D'), ('D', 'E')]\n",
    "dag3_edges = [('A', 'B'), ('B', 'C'), ('B', 'D'), ('C', 'D'), ('D', 'E')]\n",
    "\n",
    "# Create directed graphs\n",
    "G1 = nx.DiGraph(dag1_edges)\n",
    "G2 = nx.DiGraph(dag2_edges)\n",
    "G3 = nx.DiGraph(dag3_edges)\n",
    "\n",
    "# Function to remove direction (skeleton) and check for v-structure similarity\n",
    "def are_markov_equivalent(G1, G2):\n",
    "    # Check if the skeletons (undirected versions) are the same\n",
    "    skeleton_G1 = nx.Graph(G1)\n",
    "    skeleton_G2 = nx.Graph(G2)\n",
    "    \n",
    "    if not isomorphism.GraphMatcher(skeleton_G1, skeleton_G2).is_isomorphic():\n",
    "        return False\n",
    "\n",
    "    # Check if v-structures are the same (v-structure: A -> C <- B)\n",
    "    v_structures_G1 = set((u, v, w) for u, v in G1.edges() for w in G1.predecessors(v) if u != w and not G1.has_edge(u, w))\n",
    "    v_structures_G2 = set((u, v, w) for u, v in G2.edges() for w in G2.predecessors(v) if u != w and not G2.has_edge(u, w))\n",
    "\n",
    "    return v_structures_G1 == v_structures_G2\n",
    "\n",
    "# Test Markov equivalence\n",
    "print(\"DAG 1 and DAG 2 are Markov Equivalent:\", are_markov_equivalent(G1, G2))\n",
    "print(\"DAG 1 and DAG 3 are Markov Equivalent:\", are_markov_equivalent(G1, G3))\n",
    "print(\"DAG 2 and DAG 3 are Markov Equivalent:\", are_markov_equivalent(G2, G3))\n",
    "\n",
    "# Adjusted positions to make edges more uniform in length\n",
    "pos = {\n",
    "    'A': (0, 1),\n",
    "    'B': (1, 1),\n",
    "    'C': (0, 2),\n",
    "    'D': (2, 1),\n",
    "    'E': (3, 1)\n",
    "}\n",
    "\n",
    "# Draw the three DAGs for comparison\n",
    "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(18, 6))\n",
    "\n",
    "# Set uniform edge width for all graphs\n",
    "edge_width = 2\n",
    "\n",
    "# Draw DAG 1\n",
    "nx.draw(G1, pos, with_labels=True, node_color='lightblue', node_size=2000, font_size=16, \n",
    "        font_color='black', arrowsize=10, width=edge_width, ax=ax1)\n",
    "ax1.set_title('DAG 1: A -> B -> D, A -> C -> D -> E')\n",
    "\n",
    "# Draw DAG 2\n",
    "nx.draw(G2, pos, with_labels=True, node_color='lightgreen', node_size=2000, font_size=16, \n",
    "        font_color='black', arrowsize=10, width=edge_width, ax=ax2)\n",
    "ax2.set_title('DAG 2: B -> A -> C -> D -> E')\n",
    "\n",
    "# Draw DAG 3\n",
    "nx.draw(G3, pos, with_labels=True, node_color='lightcoral', node_size=2000, font_size=16, \n",
    "        font_color='black', arrowsize=10, width=edge_width, ax=ax3)\n",
    "ax3.set_title('DAG 3: A -> B -> C -> D -> E')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Markov Blanket\n",
    "\n",
    "The **Markov Blanket** of a node is the minimal set of nodes that \"shield\" it from the rest of the network. Formally, the Markov blanket of a node $X_i$ in a DAG consists of:\n",
    "- Its parents\n",
    "- Its children\n",
    "- The other parents of its children\n",
    "\n",
    "<img src=\"img/ch3/emperor-penguins-family.png\" alt=\"img\" width=\"700\"/>\n",
    "\n",
    "Once you know the values of the nodes in the Markov blanket, $X_i$ is conditionally independent of all other nodes in the graph. The Markov blanket plays a key role in determining what information is necessary to predict a given node's behavior.\n",
    "\n",
    "### Markov Blanket Example:\n",
    "\n",
    "In this example, we define a DAG with five nodes and edges. The Markov blanket of node $B$ will be calculated, and the DAG will be visualized with the Markov blanket nodes highlighted.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Markov Blanket of B: {'C', 'D', 'A'}\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define a DAG with edges\n",
    "edges = [('A', 'B'), ('B', 'C'), ('B', 'D'), ('C', 'E'), ('D', 'E')]\n",
    "G = nx.DiGraph(edges)\n",
    "\n",
    "# Function to calculate the Markov blanket\n",
    "def markov_blanket(graph, node):\n",
    "    parents = set(graph.predecessors(node))\n",
    "    children = set(graph.successors(node))\n",
    "    co_parents = set()\n",
    "    for child in children:\n",
    "        co_parents.update(graph.predecessors(child))\n",
    "    co_parents.discard(node)  # Remove the original node from co-parents\n",
    "    return parents | children | co_parents\n",
    "\n",
    "# Calculate the Markov blanket for node 'B'\n",
    "markov_blanket_nodes = markov_blanket(G, 'B')\n",
    "print(f'Markov Blanket of B: {markov_blanket_nodes}')\n",
    "\n",
    "# Define positions for the nodes in the DAG for better visualization\n",
    "pos = nx.spring_layout(G)\n",
    "\n",
    "# Draw the entire DAG\n",
    "plt.figure(figsize=(6, 6))\n",
    "nx.draw(G, pos, with_labels=True, node_color='lightgray', node_size=2000, font_size=12, arrowsize=20)\n",
    "\n",
    "# Highlight the Markov blanket nodes in a different color\n",
    "nx.draw_networkx_nodes(G, pos, nodelist=markov_blanket_nodes, node_color='lightblue', node_size=2000)\n",
    "\n",
    "# Highlight the target node 'B' in a distinct color\n",
    "nx.draw_networkx_nodes(G, pos, nodelist=['B'], node_color='orange', node_size=2000)\n",
    "\n",
    "plt.title(\"DAG with Markov Blanket of Node 'B' Highlighted\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Example: A Simple DAG, with SCM, Factual Distributions, and Baysian Networks\n",
    "\n",
    "This simple example summarizes what we learned from working with DAG, SCM probabilistic distribution, and the Bayesian network.\n",
    "\n",
    "### Part 1: Creating the DAG\n",
    "\n",
    "Here's the DAG representation and graph-based explanations:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import necessary libraries\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Create a directed acyclic graph (DAG)\n",
    "G = nx.DiGraph()\n",
    "\n",
    "# Add edges to represent the relationships Z -> D -> Y, X -> D, X -> Y\n",
    "G.add_edges_from([('Z', 'D'), ('D', 'Y'), ('X', 'D'), ('X', 'Y')])\n",
    "\n",
    "# Draw the DAG\n",
    "plt.figure(figsize=(6, 4))\n",
    "pos = {'Z': (0, 1), 'X': (2, 1), 'D': (1, 0), 'Y': (3, 0)}\n",
    "nx.draw(G, pos, with_labels=True, node_color='lightblue', node_size=2000, font_size=14, arrowsize=10)\n",
    "plt.title(\"DAG Representation\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### DAG Explanations:\n",
    "\n",
    "- $X \\to D$, $X \\to Y$: $X$ is a parent of both $D$ and $Y$.\n",
    "- $Z \\to D$: $Z$ is a parent of $D$, so $D$ is a descendant of $Z$.\n",
    "- $D \\to Y$: $D$ is a parent of $Y$.\n",
    "- There is a **directed path** from $Z$ to $Y$ through $D$.\n",
    "- $D$ is a **collider** on the path $Z \\to D \\leftarrow X$.\n",
    "- There are no **cycles** (no directed paths that return to the same node).\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2: Structural Causal Model (SCM)\n",
    "The SCM defines how the variables interact based on the DAG structure. Each variable is expressed as a function of its parents and independent noise. In the next chapter, we will learn more about them.\n",
    "\n",
    "From the DAG structure, we can write the following SCM:\n",
    "\n",
    "- $Y := f_Y(D, X, U_Y)$\n",
    "- $D := f_D(Z, X, U_D)$\n",
    "- $X := U_X$\n",
    "- $Z := U_Z$\n",
    "\n",
    "Here, $U_Y, U_D, U_X, U_Z$ are exogenous noise terms that are mutually independent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 3: Factual Distributions\n",
    "\n",
    "Using the Markov factorization property of DAGs, we can express the joint distribution over all variables in terms of their conditional dependencies.\n",
    "\n",
    "We can factor the joint distribution $p(Y, D, X, Z)$ based on the DAG:\n",
    "\n",
    "$$\n",
    "p(y, d, x, z) = p(y \\mid d, x) \\cdot p(d \\mid x, z) \\cdot p(x) \\cdot p(z)\n",
    "$$\n",
    "\n",
    "By applying **Bayes' Law**, we can also regroupe the terms of the factorization to highlight specific dependencies. \n",
    "\n",
    "$$\n",
    "p(y, d, x, z) = p(y \\mid d, x) \\cdot p(d \\mid x, z) \\cdot p(x, z)\n",
    "$$\n",
    "\n",
    "- $p(y \\mid d, x)$: The conditional distribution of $Y$, given $D$ and $X$, since $Y$ depends on both $D$ and $X$.\n",
    "- $p(d \\mid x, z)$: The conditional distribution of $D$, given $X$ and $Z$, since $D$ depends on both $X$ and $Z$.\n",
    "- $p(x)$ and $p(z)$: The marginal distributions of $X$ and $Z$, respectively, since both are exogenous variables.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 4: Partial Ordering\n",
    "\n",
    "A **partial ordering** is a relation between the nodes in a directed acyclic graph (DAG) that defines the precedence or hierarchy of the nodes. In a DAG, **partial ordering** is a way of stating which nodes come before others, based on the direction of the edges. A strict partial order $\\prec$ on a set of nodes $V$ satisfies two main properties:\n",
    "\n",
    "1. **Transitivity**: If $A \\prec B$ ($A$ precedes $B$) and $B \\prec C$, then $A \\prec C$.\n",
    "2. **Irreflexivity**: No node precedes itself, i.e., $A \\not\\prec A$ for any $A$ in $V$.\n",
    "\n",
    "In the context of a DAG, partial ordering is derived from the directed edges. For example, if there is a directed edge $X \\to Y$, we say $X$ precedes $Y$ (denoted as $X \\prec Y$). Partial ordering defines the relative order in which nodes must appear, based on the edges of the DAG.\n",
    "\n",
    "#### Partial Ordering in the Current Example:\n",
    "\n",
    "Given the vertices $V = \\{Y, D, X, Z\\}$ and the edge set $E$, the adjacency matrix for the graph is:\n",
    "\n",
    "$$\n",
    "E = \\begin{pmatrix}\n",
    "0 & 0 & 0 & 0 \\\\\n",
    "1 & 0 & 0 & 0 \\\\\n",
    "1 & 1 & 0 & 0 \\\\\n",
    "0 & 1 & 0 & 0\n",
    "\\end{pmatrix}\n",
    "$$\n",
    "\n",
    "This matrix represents the following relationships:\n",
    "- $X \\to D$\n",
    "- $X \\to Y$\n",
    "- $Z \\to D$\n",
    "- $D \\to Y$\n",
    "\n",
    "From this, we can derive the following partial ordering:\n",
    "\n",
    "$$\n",
    "X \\prec D, \\quad X \\prec Y, \\quad Z \\prec D, \\quad D \\prec Y\n",
    "$$\n",
    "\n",
    "#### Explanation of the Partial Ordering:\n",
    "- $X \\prec D$: $X$ comes before $D$ because there is a directed edge from $X$ to $D$.\n",
    "- $X \\prec Y$: $X$ comes before $Y$ because there is a directed edge from $X$ to $Y$.\n",
    "- $Z \\prec D$: $Z$ comes before $D$ because there is a directed edge from $Z$ to $D$.\n",
    "- $D \\prec Y$: $D$ comes before $Y$ because there is a directed edge from $D$ to $Y$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Causal Assumptions\n",
    "\n",
    "* Causal Directed Acyclic Graphs (DAGs) rely on several assumptions to make meaningful inferences about causal structures. \n",
    "* These assumptions limit the possible causal models and provide a framework for drawing conclusions based on observed data. \n",
    "* The goal is not to magically discover causal relationships but to understand what causality can be learned given these assumptions.\n",
    "\n",
    "### Common Assumptions in Causal Discovery\n",
    "\n",
    "1. **Acyclicity** — The causal structure is represented by a Directed Acyclic Graph (DAG) $\\mathcal{G}$.\n",
    "\n",
    "    * This assumption, known as the **Acyclicity assumption** or the **no-feedback assumption**, states that the causal relationships among variables can be depicted by a DAG, where no feedback loops or cycles exist.\n",
    "    * It ensures that the causal relationships flow in a single direction, with no circular dependencies between variables.\n",
    "    * Without this assumption, causal inference would become much more complicated, as feedback loops would imply that variables could influence themselves.\n",
    "\n",
    "2. **Markov Property** — All variables are independent of their non-descendants when conditioned on their parents in the DAG.\n",
    "\n",
    "    * This assumption is also known as the **Markov condition** or **local independence**.\n",
    "    * It states that each variable is conditionally independent of its non-descendants given its parents (direct causes) in the DAG.\n",
    "    * This assumption allows us to isolate causal effects and make predictions based on direct relationships, without being influenced by unrelated variables in the system.\n",
    "\n",
    "3. **Faithfulness** — The DAG $\\mathcal{G}$ captures all conditional independencies in the true underlying distribution $p$.\n",
    "\n",
    "    * The **Faithfulness assumption** ensures that the causal model faithfully reflects the observed data.\n",
    "    * This means that all conditional independencies found in the data should be represented in the DAG, and conversely, any statistical dependence should correspond to a causal relationship in the model.\n",
    "    * In other words, if two variables are independent in the data, they must also be independent in the causal graph, and if two variables are dependent, the graph must reflect this relationship.\n",
    "\n",
    "4. **Sufficiency** — There are no unobserved confounders between any pair of variables in $\\mathcal{G}$.\n",
    "\n",
    "    * This assumption implies that any pair of variables in the DAG is not influenced by an unobserved common cause.\n",
    "    * **Sufficiency** ensures that the relationships between variables are not confounded by external factors that are not part of the model.\n",
    "    * In practice, this assumption is often challenged because unobserved variables (confounders) are common in real-world data. However, it provides a starting point for causal analysis by assuming that all relevant confounders are either observed or adequately controlled for.\n",
    "\n",
    "### Summary of Causal Assumptions:\n",
    "- **Acyclicity**: No feedback loops or cycles; causality flows in one direction.\n",
    "- **Markov Property**: Conditional independence of non-descendants, given parents.\n",
    "- **Faithfulness**: The DAG must represent all observed conditional independencies.\n",
    "- **Sufficiency**: No unobserved confounders; all relevant variables are included in the model.\n",
    "\n",
    "These assumptions are the foundation for most causal discovery algorithms, helping to draw causal conclusions from data while acknowledging the limitations imposed by the assumptions themselves.\n",
    "\n",
    "\n",
    "<br/>\n",
    "\n",
    "In this lecture, we are more focus on Markovian assumption. However, there is a comprehensive discussion of these four causal assumptions in [Kalainathan et al., 2018]( https://arxiv.org/abs/1803.04929). \n",
    "Also check this nice paper, [An introduction to causal inference](https://www.cmu.edu/dietrich/philosophy/docs/scheines/introtocausalinference.pdf), by Richard Scheines, CMU.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "c9e7f5186c4545eca8adbf149c8ad029",
    "deepnote_cell_height": 167.171875,
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "## References\n",
    "\n",
    "This chapter contents are inspired by following sources:\n",
    "\n",
    "1. An **Open Access** Book by By Jonas Peters and others, 2017, The [Elements of Causal Inference (Open Access) book](https://mitpress.mit.edu/books/elements-causal-inference) .\n",
    "\n",
    "\n",
    "2. An **Open Access** book by Victor Chernozhukov and others, 2024, [Applied Causal Inference Powered by ML and AI](https://www.causalml-book.org).\n",
    "\n",
    "3. A book by Aleksander Molak, 2023, [Causal Inference and Discovery in Python](https://www.packtpub.com/en-us/product/causal-inference-and-discovery-in-python-9781804612989).\n",
    "\n",
    "4. I also used a graph example from the [Introduction to Causal Inference](https://www.bradyneal.com/causal-inference-course) course by Brady Neal. He made a very nice **open-access** online course accompanied by videos on [YouTube](https://youtube.com/playlist?list=PLoazKTcS0Rzb6bb9L508cyJ1z-U9iWkA0).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Tags",
  "deepnote": {},
  "deepnote_execution_queue": [],
  "deepnote_notebook_id": "09b16480-942c-492c-be08-da138720dcc2",
  "interpreter": {
   "hash": "f82454df3ab4669350e470cecfad51160e6fdff8e76eafd19d8880dd92d922a3"
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}