{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 3: Network Topologies\n",
    "\n",
    "This tutorial explores complex network topologies in `braintools.conn`. You'll learn how to create biologically-plausible network architectures with specific graph properties.\n",
    "\n",
    "---\n",
    "\n",
    "## 1. Introduction to Network Topologies <a name=\"introduction\"></a>\n",
    "\n",
    "Network topology refers to the global structure of connections in a network, beyond local connectivity rules.\n",
    "\n",
    "### Why Network Topology Matters\n",
    "\n",
    "- **Computational Efficiency**: Topology affects information processing speed and capacity\n",
    "- **Robustness**: Network resilience to damage depends on topology\n",
    "- **Biological Realism**: Real brains exhibit specific topological features (small-world, modularity)\n",
    "- **Functional Specialization**: Modular structures support specialized processing\n",
    "\n",
    "### Common Network Properties\n",
    "\n",
    "- **Clustering Coefficient**: Local connectivity density\n",
    "- **Path Length**: Average distance between neurons\n",
    "- **Degree Distribution**: How connections are distributed\n",
    "- **Modularity**: Presence of distinct communities\n",
    "\n",
    "Let's start by importing the necessary libraries:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:10.379387Z",
     "start_time": "2025-10-01T16:46:06.982810Z"
    }
   },
   "source": [
    "import brainunit as u\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from braintools import conn, visualize as vis\n",
    "from braintools.init import Constant, Normal\n",
    "\n",
    "# Set random seed for reproducibility\n",
    "np.random.seed(42)\n",
    "\n",
    "# Configure matplotlib\n",
    "plt.rcParams['figure.figsize'] = (12, 4)\n",
    "plt.rcParams['font.size'] = 10\n",
    "\n",
    "print(\"✓ Imports successful\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "✓ Imports successful\n"
     ]
    }
   ],
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 2. Small-World Networks <a name=\"small-world\"></a>\n",
    "\n",
    "Small-world networks combine high local clustering with short global path lengths, a hallmark of brain connectivity.\n",
    "\n",
    "### 2.1 The Watts-Strogatz Model\n",
    "\n",
    "The Watts-Strogatz model creates small-world networks by:\n",
    "1. Starting with a regular ring lattice (high clustering, long paths)\n",
    "2. Rewiring edges with probability `p` (introducing shortcuts)\n",
    "\n",
    "Parameter `p` controls the transition:\n",
    "- `p = 0`: Regular lattice\n",
    "- `0 < p < 1`: Small-world\n",
    "- `p = 1`: Random graph"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:10.533789Z",
     "start_time": "2025-10-01T16:46:10.403587Z"
    }
   },
   "source": [
    "# Create small-world network\n",
    "n_neurons = 500\n",
    "\n",
    "small_world = conn.SmallWorld(\n",
    "    k=10,  # Each neuron connects to 10 neighbors (5 on each side)\n",
    "    p=0.1,  # 10% rewiring probability\n",
    "    weight=Constant(1.0 * u.nS),\n",
    "    seed=42\n",
    ")\n",
    "\n",
    "result_sw = small_world(pre_size=n_neurons, post_size=n_neurons)\n",
    "\n",
    "print(\"Small-World Network (Watts-Strogatz):\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Neurons: {n_neurons}\")\n",
    "print(f\"Neighbors (k): 10\")\n",
    "print(f\"Rewiring probability (p): 0.1\")\n",
    "print(f\"Total connections: {len(result_sw.pre_indices)}\")\n",
    "print(f\"Expected: {n_neurons * 10} (n × k)\")\n",
    "print(f\"Connections per neuron: {len(result_sw.pre_indices) / n_neurons:.1f}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Small-World Network (Watts-Strogatz):\n",
      "==================================================\n",
      "Neurons: 500\n",
      "Neighbors (k): 10\n",
      "Rewiring probability (p): 0.1\n",
      "Total connections: 5000\n",
      "Expected: 5000 (n × k)\n",
      "Connections per neuron: 10.0\n"
     ]
    }
   ],
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Effect of Rewiring Probability\n",
    "\n",
    "Let's compare networks with different rewiring probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:10.556066Z",
     "start_time": "2025-10-01T16:46:10.548934Z"
    }
   },
   "source": [
    "# Create networks with varying rewiring probability\n",
    "rewiring_probs = [0.0, 0.05, 0.1, 0.3, 0.5, 1.0]\n",
    "n_test = 200\n",
    "\n",
    "results_by_p = {}\n",
    "for p in rewiring_probs:\n",
    "    sw = conn.SmallWorld(k=6, p=p, seed=42)\n",
    "    result = sw(pre_size=n_test, post_size=n_test)\n",
    "    results_by_p[p] = result\n",
    "\n",
    "print(\"Rewiring Probability Effects:\")\n",
    "print(\"=\" * 60)\n",
    "print(f\"{'p':<10} {'Connections':<15} {'Description'}\")\n",
    "print(\"=\" * 60)\n",
    "for p in rewiring_probs:\n",
    "    result = results_by_p[p]\n",
    "    desc = \"Regular lattice\" if p == 0 else (\"Random graph\" if p == 1.0 else \"Small-world\")\n",
    "    print(f\"{p:<10.2f} {len(result.pre_indices):<15} {desc}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rewiring Probability Effects:\n",
      "============================================================\n",
      "p          Connections     Description\n",
      "============================================================\n",
      "0.00       1200            Regular lattice\n",
      "0.05       1200            Small-world\n",
      "0.10       1200            Small-world\n",
      "0.30       1200            Small-world\n",
      "0.50       1200            Small-world\n",
      "1.00       1200            Random graph\n"
     ]
    }
   ],
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 Degree Distribution Analysis\n",
    "\n",
    "Small-world networks maintain relatively uniform degree distribution:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:11.157316Z",
     "start_time": "2025-10-01T16:46:10.580398Z"
    }
   },
   "source": [
    "# Calculate degree distributions for different p values\n",
    "fig, axes = plt.subplots(2, 3, figsize=(16, 10))\n",
    "axes = axes.flatten()\n",
    "\n",
    "for idx, p in enumerate(rewiring_probs):\n",
    "    result = results_by_p[p]\n",
    "    in_degree = np.bincount(result.post_indices, minlength=n_test)\n",
    "\n",
    "    title = f\"p = {p:.2f} ({['Regular', 'Small-world', 'Small-world', 'Small-world', 'Small-world', 'Random'][idx]})\"\n",
    "\n",
    "    vis.distribution_plot(\n",
    "        in_degree,\n",
    "        bins=15,\n",
    "        alpha=0.7,\n",
    "        colors=['steelblue'],\n",
    "        edgecolor='black',\n",
    "        ax=axes[idx],\n",
    "        xlabel='In-Degree',\n",
    "        ylabel='Count',\n",
    "        title=title\n",
    "    )\n",
    "\n",
    "plt.suptitle('Degree Distributions Across Rewiring Probabilities', fontsize=14, y=1.00)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nKey Observations:\")\n",
    "print(\"- p=0.0 (Regular): All neurons have exactly k=6 connections\")\n",
    "print(\"- 0<p<1 (Small-world): Narrow distribution around k=6\")\n",
    "print(\"- p=1.0 (Random): Still centered on k=6 but with more variance\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1600x1000 with 6 Axes>"
      ],
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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Key Observations:\n",
      "- p=0.0 (Regular): All neurons have exactly k=6 connections\n",
      "- 0<p<1 (Small-world): Narrow distribution around k=6\n",
      "- p=1.0 (Random): Still centered on k=6 but with more variance\n"
     ]
    }
   ],
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 3. Scale-Free Networks <a name=\"scale-free\"></a>\n",
    "\n",
    "Scale-free networks have degree distributions following a power law, with a few highly connected \"hub\" neurons.\n",
    "\n",
    "### 3.1 Barabási-Albert Model\n",
    "\n",
    "The Barabási-Albert model creates scale-free networks through preferential attachment:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:11.215001Z",
     "start_time": "2025-10-01T16:46:11.167248Z"
    }
   },
   "source": [
    "# Create scale-free network\n",
    "scale_free = conn.ScaleFree(\n",
    "    m=3,  # Each new neuron connects to 3 existing neurons\n",
    "    weight=Constant(1.0 * u.nS),\n",
    "    seed=42\n",
    ")\n",
    "\n",
    "result_sf = scale_free(pre_size=n_neurons, post_size=n_neurons)\n",
    "\n",
    "print(\"Scale-Free Network (Barabási-Albert):\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Neurons: {n_neurons}\")\n",
    "print(f\"Edges per new neuron (m): 3\")\n",
    "print(f\"Total connections: {len(result_sf.pre_indices)}\")\n",
    "print(f\"Average degree: {len(result_sf.pre_indices) / n_neurons:.1f}\")\n",
    "\n",
    "# Analyze hub neurons\n",
    "in_degree_sf = np.bincount(result_sf.post_indices, minlength=n_neurons)\n",
    "out_degree_sf = np.bincount(result_sf.pre_indices, minlength=n_neurons)\n",
    "total_degree_sf = in_degree_sf + out_degree_sf\n",
    "\n",
    "print(f\"\\nHub Analysis:\")\n",
    "print(f\"  Max degree: {np.max(total_degree_sf)}\")\n",
    "print(f\"  Min degree: {np.min(total_degree_sf[total_degree_sf > 0])}\")\n",
    "print(f\"  Top 5 hubs (degree): {sorted(total_degree_sf, reverse=True)[:5]}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scale-Free Network (Barabási-Albert):\n",
      "==================================================\n",
      "Neurons: 500\n",
      "Edges per new neuron (m): 3\n",
      "Total connections: 2988\n",
      "Average degree: 6.0\n",
      "\n",
      "Hub Analysis:\n",
      "  Max degree: 188\n",
      "  Min degree: 6\n",
      "  Top 5 hubs (degree): [np.int64(188), np.int64(148), np.int64(130), np.int64(108), np.int64(64)]\n"
     ]
    }
   ],
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Scale-Free vs. Small-World Degree Distributions\n",
    "\n",
    "Compare the degree distributions:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:11.413918Z",
     "start_time": "2025-10-01T16:46:11.220089Z"
    }
   },
   "source": [
    "# Calculate degrees\n",
    "in_degree_sw = np.bincount(result_sw.post_indices, minlength=n_neurons)\n",
    "\n",
    "# Plot comparison\n",
    "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n",
    "\n",
    "vis.distribution_plot(\n",
    "    in_degree_sw,\n",
    "    bins=20,\n",
    "    alpha=0.7,\n",
    "    colors=['steelblue'],\n",
    "    edgecolor='black',\n",
    "    ax=axes[0],\n",
    "    xlabel='In-Degree',\n",
    "    ylabel='Count',\n",
    "    title='Small-World Network'\n",
    ")\n",
    "\n",
    "vis.distribution_plot(\n",
    "    in_degree_sf,\n",
    "    bins=20,\n",
    "    alpha=0.7,\n",
    "    colors=['coral'],\n",
    "    edgecolor='black',\n",
    "    ax=axes[1],\n",
    "    xlabel='In-Degree',\n",
    "    ylabel='Count',\n",
    "    title='Scale-Free Network'\n",
    ")\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nKey Differences:\")\n",
    "print(\"- Small-World: Narrow, bell-shaped distribution (homogeneous connectivity)\")\n",
    "print(\"- Scale-Free: Heavy-tailed distribution (heterogeneous, with hubs)\")\n",
    "print(f\"\\nCoefficient of Variation (std/mean):\")\n",
    "print(f\"  Small-World: {np.std(in_degree_sw) / np.mean(in_degree_sw):.3f}\")\n",
    "print(f\"  Scale-Free: {np.std(in_degree_sf) / np.mean(in_degree_sf):.3f}\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1400x500 with 2 Axes>"
      ],
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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Key Differences:\n",
      "- Small-World: Narrow, bell-shaped distribution (homogeneous connectivity)\n",
      "- Scale-Free: Heavy-tailed distribution (heterogeneous, with hubs)\n",
      "\n",
      "Coefficient of Variation (std/mean):\n",
      "  Small-World: 0.137\n",
      "  Scale-Free: 1.208\n"
     ]
    }
   ],
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 Log-Log Plot for Power Law\n",
    "\n",
    "Scale-free networks exhibit power-law degree distributions:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:11.704925Z",
     "start_time": "2025-10-01T16:46:11.421191Z"
    }
   },
   "source": [
    "# Calculate degree distribution\n",
    "unique_degrees, degree_counts = np.unique(in_degree_sf, return_counts=True)\n",
    "\n",
    "# Remove zero degree\n",
    "nonzero_mask = unique_degrees > 0\n",
    "unique_degrees = unique_degrees[nonzero_mask]\n",
    "degree_counts = degree_counts[nonzero_mask]\n",
    "\n",
    "# Plot log-log\n",
    "fig, ax = plt.subplots(figsize=(10, 6))\n",
    "ax.loglog(unique_degrees, degree_counts, 'o', markersize=8, alpha=0.7, color='coral')\n",
    "ax.set_xlabel('Degree (k)', fontsize=12)\n",
    "ax.set_ylabel('Count P(k)', fontsize=12)\n",
    "ax.set_title('Scale-Free Network: Log-Log Degree Distribution', fontsize=14)\n",
    "ax.grid(True, alpha=0.3, which='both')\n",
    "\n",
    "# Add power law reference line\n",
    "x_fit = np.array([unique_degrees.min(), 20])\n",
    "y_fit = 1000 * x_fit ** (-2.)  # Power law with exponent -2\n",
    "ax.loglog(x_fit, y_fit, '--', color='gray', linewidth=2, alpha=0.5, label='Power law (γ=-2)')\n",
    "ax.legend()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nIn a scale-free network, degree distribution follows P(k) ~ k^(-γ)\")\n",
    "print(\"The log-log plot shows an approximately linear relationship.\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "In a scale-free network, degree distribution follows P(k) ~ k^(-γ)\n",
      "The log-log plot shows an approximately linear relationship.\n"
     ]
    }
   ],
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 4. Regular Networks <a name=\"regular\"></a>\n",
    "\n",
    "Regular networks have deterministic, structured connectivity where all neurons have the same degree.\n",
    "\n",
    "### 4.1 k-Regular Networks"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:11.742543Z",
     "start_time": "2025-10-01T16:46:11.712394Z"
    }
   },
   "source": [
    "# Create regular network\n",
    "regular = conn.Regular(\n",
    "    degree=8,  # Each neuron has exactly 8 connections\n",
    "    weight=Constant(1.0 * u.nS),\n",
    "    seed=42\n",
    ")\n",
    "\n",
    "result_regular = regular(pre_size=200, post_size=200)\n",
    "\n",
    "print(\"Regular Network:\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Neurons: 200\")\n",
    "print(f\"Degree (k): 8\")\n",
    "print(f\"Total connections: {len(result_regular.pre_indices)}\")\n",
    "print(f\"Expected: {200 * 8} (n × k)\")\n",
    "\n",
    "# Verify regularity\n",
    "in_degree_reg = np.bincount(result_regular.post_indices, minlength=200)\n",
    "print(f\"\\nRegularity check:\")\n",
    "print(f\"  All in-degrees equal to {8}: {np.all(in_degree_reg == 8)}\")\n",
    "print(f\"  Unique in-degrees: {np.unique(in_degree_reg)}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Regular Network:\n",
      "==================================================\n",
      "Neurons: 200\n",
      "Degree (k): 8\n",
      "Total connections: 1600\n",
      "Expected: 1600 (n × k)\n",
      "\n",
      "Regularity check:\n",
      "  All in-degrees equal to 8: False\n",
      "  Unique in-degrees: [ 2  3  4  5  6  7  8  9 10 11 12 13 14 15]\n"
     ]
    }
   ],
   "execution_count": 8
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 Comparing Regular, Small-World, and Random\n",
    "\n",
    "Visualize the structural differences:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:12.009329Z",
     "start_time": "2025-10-01T16:46:11.749793Z"
    }
   },
   "source": [
    "# Create small test networks for visualization\n",
    "n_viz = 40\n",
    "\n",
    "regular_viz = conn.Regular(degree=4, seed=42)(pre_size=n_viz, post_size=n_viz)\n",
    "sw_viz = conn.SmallWorld(k=4, p=0.1, seed=42)(pre_size=n_viz, post_size=n_viz)\n",
    "random_viz = conn.Random(prob=0.1, seed=42)(pre_size=n_viz, post_size=n_viz)\n",
    "\n",
    "\n",
    "# Create connectivity matrices\n",
    "def result_to_matrix(result, size):\n",
    "    matrix = np.zeros((size, size))\n",
    "    matrix[result.pre_indices, result.post_indices] = 1\n",
    "    return matrix\n",
    "\n",
    "\n",
    "matrix_regular = result_to_matrix(regular_viz, n_viz)\n",
    "matrix_sw = result_to_matrix(sw_viz, n_viz)\n",
    "matrix_random = result_to_matrix(random_viz, n_viz)\n",
    "\n",
    "# Plot matrices\n",
    "fig, axes = plt.subplots(1, 3, figsize=(16, 5))\n",
    "\n",
    "vis.connectivity_matrix(matrix_regular, cmap='binary', center_zero=False,\n",
    "                        show_colorbar=False, ax=axes[0], title='Regular (k=4)')\n",
    "vis.connectivity_matrix(matrix_sw, cmap='binary', center_zero=False,\n",
    "                        show_colorbar=False, ax=axes[1], title='Small-World (k=4, p=0.1)')\n",
    "vis.connectivity_matrix(matrix_random, cmap='binary', center_zero=False,\n",
    "                        show_colorbar=False, ax=axes[2], title='Random (p=0.1)')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nMatrix Structures:\")\n",
    "print(\"- Regular: Clear banded structure (local connections)\")\n",
    "print(\"- Small-World: Bands with scattered long-range connections\")\n",
    "print(\"- Random: Uniform random distribution\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1600x500 with 3 Axes>"
      ],
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Matrix Structures:\n",
      "- Regular: Clear banded structure (local connections)\n",
      "- Small-World: Bands with scattered long-range connections\n",
      "- Random: Uniform random distribution\n"
     ]
    }
   ],
   "execution_count": 9
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 5. Modular Networks <a name=\"modular\"></a>\n",
    "\n",
    "Modular networks have distinct communities with dense intra-module and sparse inter-module connections.\n",
    "\n",
    "### 5.1 Modular Random Networks\n",
    "\n",
    "Create modules with different connection probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:12.097980Z",
     "start_time": "2025-10-01T16:46:12.016533Z"
    }
   },
   "source": [
    "# Create modular network with 4 modules\n",
    "modular = conn.ModularRandom(\n",
    "    n_modules=4,  # 4 distinct modules\n",
    "    intra_prob=0.3,  # 30% connectivity within modules\n",
    "    inter_prob=0.02,  # 2% connectivity between modules\n",
    "    weight=Constant(1.0 * u.nS),\n",
    "    seed=42\n",
    ")\n",
    "\n",
    "result_modular = modular(pre_size=400, post_size=400)\n",
    "\n",
    "print(\"Modular Random Network:\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Neurons: 400\")\n",
    "print(f\"Modules: 4 (100 neurons each)\")\n",
    "print(f\"Intra-module probability: 30%\")\n",
    "print(f\"Inter-module probability: 2%\")\n",
    "print(f\"Total connections: {len(result_modular.pre_indices)}\")\n",
    "print(f\"Average degree: {len(result_modular.pre_indices) / 400:.1f}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Modular Random Network:\n",
      "==================================================\n",
      "Neurons: 400\n",
      "Modules: 4 (100 neurons each)\n",
      "Intra-module probability: 30%\n",
      "Inter-module probability: 2%\n",
      "Total connections: 14189\n",
      "Average degree: 35.5\n"
     ]
    }
   ],
   "execution_count": 10
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.2 Custom Module Configurations\n",
    "\n",
    "Use `ModularGeneral` for flexible module sizes and connection probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:12.153176Z",
     "start_time": "2025-10-01T16:46:12.103842Z"
    }
   },
   "source": [
    "# Create custom modular network with different module sizes\n",
    "module_sizes = [80, 120, 100, 100]  # Unequal module sizes\n",
    "\n",
    "# Connection probability matrix (4×4 for 4 modules)\n",
    "prob_matrix = np.array([\n",
    "    [0.4, 0.05, 0.02, 0.01],  # Module 0: strongly connected internally\n",
    "    [0.05, 0.3, 0.1, 0.02],  # Module 1: moderate internal, some connection to 2\n",
    "    [0.02, 0.1, 0.35, 0.05],  # Module 2: moderate internal\n",
    "    [0.01, 0.02, 0.05, 0.25]  # Module 3: weaker internal connectivity\n",
    "])\n",
    "\n",
    "modular_general = conn.ModularGeneral(\n",
    "    intra_conn=[conn.Random(0.4), conn.Random(0.3), conn.Random(0.35), conn.Random(0.25)],\n",
    "    inter_conn_pair={\n",
    "        (0, 1): conn.Random(0.05),\n",
    "        (0, 2): conn.Random(0.02),\n",
    "        (0, 3): conn.Random(0.01),\n",
    "        (1, 2): conn.Random(0.1),\n",
    "        (1, 3): conn.Random(0.02),\n",
    "        (2, 3): conn.Random(0.05),\n",
    "        # bi\n",
    "        (1, 0): conn.Random(0.05),\n",
    "        (2, 0): conn.Random(0.02),\n",
    "        (3, 0): conn.Random(0.01),\n",
    "        (2, 1): conn.Random(0.1),\n",
    "        (3, 1): conn.Random(0.02),\n",
    "        (3, 2): conn.Random(0.05),\n",
    "    },\n",
    ")\n",
    "\n",
    "result_modular_gen = modular_general(pre_size=400, post_size=400)\n",
    "\n",
    "print(\"Custom Modular Network (ModularGeneral):\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Neurons: 400\")\n",
    "print(f\"Module sizes: {module_sizes}\")\n",
    "print(f\"Total connections: {len(result_modular_gen.pre_indices)}\")\n",
    "print(f\"\\nConnection probability matrix:\")\n",
    "print(prob_matrix)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Custom Modular Network (ModularGeneral):\n",
      "==================================================\n",
      "Neurons: 400\n",
      "Module sizes: [80, 120, 100, 100]\n",
      "Total connections: 17810\n",
      "\n",
      "Connection probability matrix:\n",
      "[[0.4  0.05 0.02 0.01]\n",
      " [0.05 0.3  0.1  0.02]\n",
      " [0.02 0.1  0.35 0.05]\n",
      " [0.01 0.02 0.05 0.25]]\n"
     ]
    }
   ],
   "execution_count": 11
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.3 Visualizing Modular Structure\n",
    "\n",
    "The block-diagonal structure reveals modularity:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:12.301335Z",
     "start_time": "2025-10-01T16:46:12.160556Z"
    }
   },
   "source": [
    "# Create smaller modular network for visualization\n",
    "modular_viz = conn.ModularRandom(\n",
    "    n_modules=4,\n",
    "    intra_prob=0.4,\n",
    "    inter_prob=0.05,\n",
    "    seed=42\n",
    ")(pre_size=120, post_size=120)\n",
    "\n",
    "matrix_modular = result_to_matrix(modular_viz, 120)\n",
    "\n",
    "# Plot\n",
    "fig, ax = plt.subplots(figsize=(10, 9))\n",
    "vis.connectivity_matrix(\n",
    "    matrix_modular,\n",
    "    cmap='binary',\n",
    "    center_zero=False,\n",
    "    show_colorbar=False,\n",
    "    ax=ax,\n",
    "    title='Modular Network Structure (4 modules of 30 neurons each)'\n",
    ")\n",
    "\n",
    "# Add module boundary lines\n",
    "module_size = 30\n",
    "for i in range(1, 4):\n",
    "    boundary = i * module_size\n",
    "    ax.axhline(boundary, color='red', linewidth=2, alpha=0.6)\n",
    "    ax.axvline(boundary, color='red', linewidth=2, alpha=0.6)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nRed lines mark module boundaries.\")\n",
    "print(\"Dense blocks on diagonal = intra-module connections.\")\n",
    "print(\"Sparse off-diagonal = inter-module connections.\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x900 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Red lines mark module boundaries.\n",
      "Dense blocks on diagonal = intra-module connections.\n",
      "Sparse off-diagonal = inter-module connections.\n"
     ]
    }
   ],
   "execution_count": 12
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 6. Hierarchical Networks <a name=\"hierarchical\"></a>\n",
    "\n",
    "Hierarchical networks organize neurons into levels with feedforward and feedback connections.\n",
    "\n",
    "### 6.1 Creating Hierarchical Structures"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:12.381617Z",
     "start_time": "2025-10-01T16:46:12.315607Z"
    }
   },
   "source": [
    "# Create hierarchical network with 3 levels\n",
    "hierarchical = conn.HierarchicalRandom(\n",
    "    n_levels=3,  # 3 hierarchical levels\n",
    "    feedforward_prob=0.3,  # Probability of feedforward connections\n",
    "    feedback_prob=0.1,  # Probability of feedback connections\n",
    "    recurrent_prob=0.2,  # Probability of lateral connections within level\n",
    "    weight=Constant(1.0 * u.nS),\n",
    "    seed=42\n",
    ")\n",
    "\n",
    "result_hierarchical = hierarchical(pre_size=300, post_size=300)\n",
    "\n",
    "print(\"Hierarchical Network:\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Neurons: 300 (100 per level)\")\n",
    "print(f\"Levels: 3\")\n",
    "print(f\"Forward probability: 30%\")\n",
    "print(f\"Backward probability: 10%\")\n",
    "print(f\"Lateral probability: 20%\")\n",
    "print(f\"Total connections: {len(result_hierarchical.pre_indices)}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hierarchical Network:\n",
      "==================================================\n",
      "Neurons: 300 (100 per level)\n",
      "Levels: 3\n",
      "Forward probability: 30%\n",
      "Backward probability: 10%\n",
      "Lateral probability: 20%\n",
      "Total connections: 13968\n"
     ]
    }
   ],
   "execution_count": 13
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.2 Visualizing Hierarchical Organization\n",
    "\n",
    "Hierarchical structure shows as off-diagonal bands:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:12.713905Z",
     "start_time": "2025-10-01T16:46:12.387105Z"
    }
   },
   "source": [
    "# Create smaller hierarchical network for visualization\n",
    "hierarchical_viz = conn.HierarchicalRandom(\n",
    "    n_levels=4,\n",
    "    feedforward_prob=0.4,\n",
    "    feedback_prob=0.15,\n",
    "    recurrent_prob=0.3,\n",
    "    seed=42\n",
    ")(pre_size=120, post_size=120)\n",
    "\n",
    "matrix_hierarchical = result_to_matrix(hierarchical_viz, 120)\n",
    "\n",
    "# Plot\n",
    "fig, ax = plt.subplots(figsize=(10, 9))\n",
    "vis.connectivity_matrix(\n",
    "    matrix_hierarchical,\n",
    "    cmap='binary',\n",
    "    center_zero=False,\n",
    "    show_colorbar=False,\n",
    "    ax=ax,\n",
    "    title='Hierarchical Network (4 levels of 30 neurons each)'\n",
    ")\n",
    "\n",
    "# Add level boundary lines\n",
    "level_size = 30\n",
    "for i in range(1, 4):\n",
    "    boundary = i * level_size\n",
    "    ax.axhline(boundary, color='blue', linewidth=2, alpha=0.6)\n",
    "    ax.axvline(boundary, color='blue', linewidth=2, alpha=0.6)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nBlue lines mark level boundaries.\")\n",
    "print(\"Diagonal blocks = lateral (within-level) connections.\")\n",
    "print(\"Upper off-diagonal = feedforward connections.\")\n",
    "print(\"Lower off-diagonal = feedback connections.\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x900 with 1 Axes>"
      ],
      "image/png": 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3pzfbbLPo379/+bw99NBD5Y/RP/300zFz5swolUrx8MMPt/qY9q9//evYcsstY7vttiu/1r9//zjyyCPj1VdfLX8FYIFDDjmk/OTzk/7xj3/EDjvsEHPnzo0HH3ywzWzZC3vvvfciImKFFVZYZNn48eNj7ty55Y8AZzFt2rS49957Y7/99osPPvigPMbvvfde7LzzzvHSSy/Fm2++GRER+++/f8ydOzduueWW8vZ33313NDc3x/777x8REaVSKW6++ebYfffdo1QqtbqGdt5555g+fXqbc6dfv37Rp0+fuP/+++P999/v8DG8/fbb8cwzz8SYMWNi4MCB5dc/85nPxBe/+MX49a9/3ZmhKfva174W99xzT1xzzTXx9a9/PSI+fvq9wIL/r62tXWTbvn37LrJ+W0aNGtXqCetnPvOZqKurK39HOMvYVlJbWxuHHnpoq9d+/etfx5AhQ+JrX/ta+bXevXvHMcccU37qv7D999+/1XxdcD0t6H9nz++SzNHa2tpywsh58+bFe++9F/37949Pf/rTrcbm5ptvjpVWWim+/e1vL7K/T95jKx3Xwha8bwDLNh8vB5YJW265ZYwYMWKR1zvyC9FLL70Uzz333CKB9AILEjEtMHz48MWud+WVV8aPf/zj+Otf/9rqY+2LW/+Try34Za6j5c0+GZgv+AXx/fffj7q6usVu8/LLL8fo0aMrtr0kx7GkDjzwwDjzzDPjjDPOiD333HOR5S+99FJExCIfZ17Y9OnTFxuYLtCzZ88YOXJkPPTQQxHxcdC9/fbbx3bbbRfz5s2LRx99NAYPHhzTpk1rFXS/9tpri627u/7665eXL3x+2huPb3zjG9GrV6944YUXYsiQIW2utzilT3zn/dVXX41zzz03LrroojbLiC2Jv/3tb1EqleKUU06JU045ZbHrvPPOO7HaaqvFJptsEuutt15cf/31cfjhh0fExx8tX2mlleILX/hCRHz8B6Pm5ua47LLL4rLLLmuzvcWpra2NpqamOPHEE2Pw4MGx9dZbx2677RYHH3xwu+P22muvRUTEpz/96UWWrb/++vHb3/42ZsyYEcsvv3zbA9GONddcs/yHkq997Wtx5JFHxqhRo2Ly5MnRr1+/8h9bZs+evci2s2bNioho8w8yC/vkdRzx8bW8IEDNMraVrLbaaot8JeK1116Lddddd5GqBwtfA+31f+H7UETnz++SzNH58+fHf/3Xf8XFF18cr7zySqtkdwtnkH/55Zfj05/+dPTqVflX40rHtbBSqdRlFRmA6iXoBqhg/vz58cUvfjFOOumkxS7/1Kc+1erfi/tl+n//939jzJgxseeee8Z3v/vdGDRoUPTs2TPOOeecxSbp6cgv5O3p2bPnYl//ZMC2pJb0OJbUgqfdY8aMWWzyoQVPsc8999w2vz/ekcBzu+22i7POOitmzZoVDz30UHz/+9+PhoaG2GijjeKhhx4qf683S0Ky9s7h3nvvHVdddVX813/9V5xzzjkdam9BgPD+++/H6quvXn791FNPjdVWWy123HHH8ne5p0yZEhEfB2WvvvpqrLHGGh0uD7dgjL/zne+Uv5P9Seuss075//fff/8466yz4t13340BAwbE7bffHl/72tfKwcuC9g466KA2/1jS3idOjjvuuNh9993jtttui9/+9rdxyimnxDnnnBP33ntvbLbZZh06ptT22WefuPzyy+PBBx+MnXfeOQYOHBi1tbXx9ttvL7LugtcWfJe4PZWu4yUZ27YCv4WD0IVlvQdFdOw+1JnzuyRz9Oyzz45TTjklDjvssDjzzDNj4MCB0aNHjzjuuOM6XVFgSe6v77//fjmnBLDsEnQDVLD22mvHhx9+2G7W6EpuuummWGutteKWW25p9cvvaaed1qHt11prrYj4uCRUKmuvvXbF9rMeR0ccdNBB8aMf/Sh++MMfLlLfdsFHbevq6iqej/aeLm2//fYxZ86cuPbaa+PNN98sB9ef+9znykH3pz71qVZJtdZcc83FZhf/61//Wl7eUd/+9rdjnXXWiVNPPTXq6+tj3LhxFbdZb731IiLilVdeiY033rj8+uuvvx5/+9vfynNkYUcddVREfPyLf0drlS9op3fv3h2a8/vvv3/88Ic/jJtvvjkGDx4cLS0tccABB5SXr7zyyjFgwICYN29ep6+htddeO0488cQ48cQT46WXXopNN900fvzjH8f//u//Lnb9BeeirfO10kordfop9+Is+Kj49OnTIyKiR48esfHGG8eTTz65yLqPPfZYrLXWWhWTqHXEkoztgqexzc3NrV7/5NPp9qy55prx3HPPxfz581v9Eacz18DClvT8Lskcvemmm+Lzn/98/OIXv2j1enNzc6tgeO21147HHnss5s6d26WlFF955ZXYZJNNuqw9oDr5TjdABfvtt1888sgj8dvf/naRZc3NzfHRRx9VbGPBk5GFn4Q89thj8cgjj3SoDyuvvHJ87nOfi1/+8pfx+uuvt1qW9en1AqNHj45nn312sbWyF+wj63F0xIKn3c8888wi5X8233zzWHvtteO8886LDz/8cJFt//nPf5b/f0FQ9ckgIyJiq622it69e0dTU1MMHDgwNtxww4j4OBh/9NFH44EHHljkKfeXv/zlePzxx1sd64wZM+Kyyy6LYcOGxQYbbLBEx3nKKafEd77znTj55JPjkksuqbj+5ptvHn369FkkkPvRj34Ut956a6ufM888MyIiTjrppLj11luXKMAcNGhQ7LjjjvGzn/1ssU9qFx7jiI8/WrzxxhvH9ddfH9dff32sssoq8bnPfa68vGfPnjF69Oi4+eabF/tHnU+2t7CZM2eWP469wNprrx0DBgxY7Ee3F1hllVVi0003jSuvvLLV+f/zn/8cd999d3z5y19uc9v2tNXXX/ziF1FTU9Mqs/w+++wTTzzxRKvzNXny5Lj33ntj33337dT+P2lJxnbBH6wWzkExb968Nj+Wvjhf/vKXY8qUKXH99deXX/voo4/iwgsvjP79+5fLr3VUZ8/vkszRnj17LnKPvPHGG8vf+V5g9OjR8e6778Z///d/L9JeZ++x06dPj5dffjm22WabTm0PdB+edANU8N3vfjduv/322G233WLMmDGx+eabx4wZM+JPf/pT3HTTTfHqq69W/PjgbrvtFrfcckvstdde8ZWvfCVeeeWVuPTSS2ODDTZYbPC4OBdccEFst9128dnPfjaOPPLIGD58eLz66qvxf//3f/HMM890yXHedNNNse+++8Zhhx0Wm2++eUybNi1uv/32uPTSS2OTTTbpkuPoiAXf7f7kcfXo0SN+/vOfx6677hobbrhhHHroobHaaqvFm2++Gffdd1/U1dXFHXfcEREfB6kREd///vfjgAMOiN69e8fuu+8eyy+/fCy33HKx+eabx6OPPlqu0R3x8ZPuGTNmxIwZMxYJuseNGxfXXntt7LrrrnHMMcfEwIED48orr4xXXnklbr755g5/fHth5557bkyfPj3Gjh0bAwYMiIMOOqjNdfv27Rtf+tKX4ne/+12cccYZ5dcXTuy2wIKn2ltsscVivxtfyUUXXRTbbbddbLzxxnHEEUfEWmutFVOnTo1HHnkk/vGPfyxS43j//fePU089Nfr27RuHH374ImMxfvz4uO+++2KrrbaKI444IjbYYIOYNm1aPP300/G73/0upk2btth+vPjii7HTTjvFfvvtFxtssEH06tUrbr311pg6dWqrp+mLc+6558auu+4aI0eOjMMPP7xcMqy+vj5OP/30JR6TiIizzjorfv/738cuu+wSa6yxRkybNi1uvvnmeOKJJ8qfXljgqKOOissvvzy+8pWvxHe+853o3bt3/OQnP4nBgwfHiSee2Kn9L05Hx3bDDTeMrbfeOk4++eSYNm1aDBw4MK677roO/dFwgSOPPDJ+9rOfxZgxY+Kpp56KYcOGxU033RS///3v4/zzz1/ip/dZzm9H5+huu+0WZ5xxRhx66KGxzTbbxJ/+9Ke4+uqrF/lkyMEHHxxXXXVVnHDCCfH444/H9ttvHzNmzIjf/e53cdRRR8Uee+yxRMcW8XHZulKp1KltgW5m6SZLB1i6Fi7RtDg77LBDxZJhpdLHpaFOPvnk0jrrrFPq06dPaaWVVipts802pfPOO680Z86cUqnUuvzVJ82fP7909tlnl9Zcc81SbW1tabPNNivdeeedpUMOOaS05pprltdrr41SqVT685//XNprr71KDQ0Npb59+5Y+/elPl0455ZTy8k+W2PrkOCxcLmhxx/nee++Vjj766NJqq61W6tOnT2n11VcvHXLIIeVyRB09jlJpyUuGfdLC5d4+eTx//OMfS3vvvXdpxRVXLNXW1pbWXHPN0n777VeaNGlSq/XOPPPM0mqrrVbq0aPHIsf/3e9+txQRpaamplbbrLPOOqWIKL388suL9Onll18u7bPPPuXx33LLLUt33nlnq3XaK0G1uPk4b9680te+9rVSr169Srfddlvbg1UqlW655ZZSTU1Nq/JUi5O1ZFip9PGxHnzwwaUhQ4aUevfuXVpttdVKu+22W+mmm25apI2XXnqpfK4efvjhxe5n6tSppbFjx5aGDh1a6t27d2nIkCGlnXbaqXTZZZe12Zd33323NHbs2NJ6661XWn755Uv19fWlrbbaqnTDDTdUPK5SqVT63e9+V9p2221L/fr1K9XV1ZV233330vPPP99qnSUZq7vvvru02267lVZdddVS7969SwMGDChtu+22pYkTJ7YqYbfAG2+8Udpnn31KdXV1pf79+5d222230ksvvdShvkdEaezYsYu8vrjrtiNjWyp9fE5HjRpVqq2tLQ0ePLj0ve99r3TPPfcstmTYJ++LC+/r0EMPLa200kqlPn36lDbeeONF5k571/XC94Ws57cjc3TWrFmlE088sbTKKquU+vXrV9p2221LjzzySGmHHXYo7bDDDq3amzlzZun73/9+afjw4eVx3Geffcr3go4e1wL7779/abvttuvQsQDdW02p1EWfSwQAkpo3b15ssMEGsd9++5U/Qg4Uz5QpU2L48OFx3XXXedINhKAbAKrI9ddfH9/61rfi9ddf75ISYUDXGzduXNx7773x+OOP590VoAAE3QAAAJCI7OUAAACQiKAbAAAAEhF0AwAAQCLqdEfE/Pnz46233ooBAwaUa7UCAABAW0qlUnzwwQex6qqrRo8ebT/P7jZB90UXXRTnnntuTJkyJTbZZJO48MILY8stt+zQtm+99VYMHTo0cQ8BAADobt54441YffXV21zeLYLu66+/Pk444YS49NJLY6uttorzzz8/dt5555g8eXIMGjSo4vYDBgyIiI8Hq66uLnV3l0h9fX2ytqdPn56s7fb6nXW/1Tgmlfpcab9Zjrn6z/PpEVEfEdP///93z/GqJOV1k2U8s56L9rbPet20J2XbeUp1f1x4PE49NWL69Ij6+ogzzkiyO6CDXI+Qr5aWlhg6dGg5nmxLtwi6f/KTn8QRRxwRhx56aEREXHrppfF///d/8ctf/jLGjRtXcfsFHymvq6srXNCdUl7HWuQx7o5jUv3H1Dci+kXE7ARtL6qo87Oox5y1X3nuO6+2q9HC41FbG9Gnz8f/NUyQL9cjFEOlryhXfSK1OXPmxFNPPRWjRo0qv9ajR48YNWpUPPLII4vdZvbs2dHS0tLqBwAAALpa1Qfd7777bsybNy8GDx7c6vXBgwfHlClTFrvNOeecE/X19eUf3+cGAAAghaoPujvj5JNPjunTp5d/3njjjby7BAAAQDdU9d/pXmmllaJnz54xderUVq9PnTo1hgwZsthtamtro7a2dml0DwAAgGVY1Qfdffr0ic033zwmTZoUe+65Z0R8XHd70qRJcfTRR+fbuf+vvS/Wl0qldrettDxL25W+8N/e9lm2rSRLrfQs+80qr3ORVcr5mcWCthsbI5qbIxoaIpqaGru07aUtr/OYddu87gV5yjKelSyN66YzUh4zACzLqj7ojog44YQT4pBDDokRI0bElltuGeeff37MmDGjnM0cAAAA8tAtgu79998//vnPf8app54aU6ZMiU033TTuuuuuRZKrAQAAwNLULYLuiIijjz66MB8nBwAAgIhlNHs5AAAALA2CbgAAAEik23y8vMjyyt6bMqtwyqzqWdrOM5NyyvHMojtmmk+ZZTnP7PnVWOmgyNnJU82TPM+zTPMAUH086QYAAIBEBN0AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJKBnWBfIsyVTUtquxDFV3lbUEUZa2u2a/4yOiISKaY8KEcR3ab6W28yqBlbLcUyXVWtIu1bYpr4us+061LQCQD0+6AQAAIBFBNwAAACQi6AYAAIBEBN0AAACQiKAbAAAAEhF0AwAAQCJKhi2kvr6+U9tlKT1TaduU5WFS9juLopZBy7LvPMv85FV2rqvmdmNjRHNzRENDRFNTY4e2yTK3i1pKT6moJZelBFte96E8S8MV9R4GANXOk24AAABIRNANAAAAiQi6AQAAIBFBNwAAACQi6AYAAIBEBN0AAACQiJJhC5k+fXrU1dUt8XYpy8PkWdZrWSwRk6VcT17jlbXEUF4l7fIs75ay31n2m/VcdlZepfSy7juv8cqqqOUYq3U8AaDoPOkGAACARATdAAAAkIigGwAAABIRdAMAAEAigm4AAABIRPbyhdTX17e5LFVGWRnGl66U2XmzZCTOkuE5ZdspM3XnOXeLmqU+r0oHKRU1w32elSGy6K7XJAB0Z550AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgESUDFvI9OnTo66ubom3q9bSM1mkLEOVsgxQJUUtJZXXHMoyt7uuxNX4iGiIiOaYMGFcu9t0tO1UY5a1LFeW0nBZ2s7zes4yZkW+l+Qlr3svANA2T7oBAAAgEUE3AAAAJCLoBgAAgEQE3QAAAJCIoBsAAAASEXQDAABAIkqGLaS+vr7NZalKz1RrCZeiluJJWbKpWmU5pjzn54K2GxsjmpsjGhoimpoaO9SvLLIcc7XOn2ot61XUfuU5D7pjiUoAqHaedAMAAEAigm4AAABIRNANAAAAiQi6AQAAIBFBNwAAACQie/lCpk+fHnV1dUt1n1mzyWbJVJtXZuo8swanzHqdRbVmFS5qpuS8znOembqL2naWfVfab5brPc8qClkqWmSRpe1qvUcBQBF40g0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgEQE3QAAAJCIoBsAAAASUTJsIfX19W0uy1LiJWWplZSlZ1KWI0u1bSXdscRQyrazjFee10UWRe1XJSnPcxZ5zu1U22aldBcALFs86QYAAIBEBN0AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJKBm2kOnTp0ddXd1il+VVSqqSopaeyWtMKo1HdywxlOf8S1myrrP77YhUpc6Kei4iinuvSDm38yr1mHLuZ+l3tZbxA4Bq50k3AAAAJCLoBgAAgEQE3QAAAJCIoBsAAAASEXQDAABAIrKXL6S+vr7NZUXN6lrULOF5ZTuupKhZmFNmVc9rjhQ5q39eWdfzPFepsnFXajfL3E85XkW9p1eSZTyr9ZgBoNp50g0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgEQE3QAAAJCIoBsAAAASUTJsIdOnT4+6uroubzdlKalUZYAqybP0TMpjzlJKqqjli/IqU1Wt5bFSlmQq6hwpqiKXncsiy30mZb8AgDQ86QYAAIBEBN0AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJKBm2FKQsQ1WtZb9SSTmeeW3bke2zbFvUY/638RHREBHNMWHCuA5tkVdZuSLL616RZ4mroh5zyn6113Z3ndsAUHSedAMAAEAigm4AAABIRNANAAAAiQi6AQAAIBFBNwAAACQi6AYAAIBElAxbSH19fZvLspT9SimvEi95lbzJs+08y3plUdQyQR3db2NjRHNzRENDRFNTY4e2yXLMKcuksXRluW/ndR/Ks7wgAJCGJ90AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJyF7eQSkz2eYlZYbnosorq3B3zUi8dLKuj4+IhohojgkTxiXb36L7Xbwsx5yl7axVEpbtObTk+82zKkV7ZNcHgOrjSTcAAAAkIugGAACARATdAAAAkIigGwAAABIRdAMAAEAigm4AAABIRMmwhUyfPj3q6ury7kYrKUsM5VX6KKtq7Xde+83rmIo61imlLDNV1BJXKfebdQ5lmWPVep/pjtcVAFQ7T7oBAAAgEUE3AAAAJCLoBgAAgEQE3QAAAJCIoBsAAAASEXQDAABAIkqG5SyvMj+p991e2ynL/OQpr/JtKRWh9FFjY0Rzc0RDQ0RTU2OXtJ1l7mfZNmXZr6LOoSyyjleWa7Kz7XZkeXuyXnPmEAAUjyfdAAAAkIigGwAAABIRdAMAAEAigm4AAABIRNANAAAAichenrM8M9GmzEzdXtsps/MWNTN6nlmBs4x3ln4XORNyqr5lrQiQKtt21u2rdR5kuVek2m+lfS+NigAAwNLlSTcAAAAkIugGAACARATdAAAAkIigGwAAABIRdAMAAEAigm4AAABIpNBB9znnnBNbbLFFDBgwIAYNGhR77rlnTJ48udU6s2bNirFjx8aKK64Y/fv3j9GjR8fUqVNz6vGSq6mpafenVCq1+1OtbXd2v0XW3nikbDvleU6pUr/z2nde++1Iman2frLMgyxSzq+sc6So/Uq1bcrzDAB0XqGD7gceeCDGjh0bjz76aNxzzz0xd+7c+NKXvhQzZswor3P88cfHHXfcETfeeGM88MAD8dZbb8Xee++dY68BAADgY73y7kB77rrrrlb/vuKKK2LQoEHx1FNPxec+97mYPn16/OIXv4hrrrkmvvCFL0RExMSJE2P99dePRx99NLbeeus8ug0AAAARUfAn3Z80ffr0iIgYOHBgREQ89dRTMXfu3Bg1alR5nfXWWy/WWGONeOSRR9psZ/bs2dHS0tLqBwAAALpa1QTd8+fPj+OOOy623Xbb2GijjSIiYsqUKdGnT59oaGhote7gwYNjypQpbbZ1zjnnRH19ffln6NChKbsOAADAMqpqgu6xY8fGn//857juuusyt3XyySfH9OnTyz9vvPFGF/QQAAAAWiv0d7oXOProo+POO++MBx98MFZfffXy60OGDIk5c+ZEc3Nzq6fdU6dOjSFDhrTZXm1tbdTW1qbsMgAAABQ76C6VSvHtb387br311rj//vtj+PDhrZZvvvnm0bt375g0aVKMHj06IiImT54cr7/+eowcOXKJ91dfX99uX1LIu2RTe9rrW8p+py7b1Nl9F7XkTlHPRaV+Zel3lrmbct8dKbWXqu0sqnUOZRnPPGUZ76xjkmq/AEDbCh10jx07Nq655pr41a9+FQMGDCh/T7u+vj769esX9fX1cfjhh8cJJ5wQAwcOjLq6uvj2t78dI0eOlLkcAACA3BU66L7kkksiImLHHXds9frEiRNjzJgxERHx05/+NHr06BGjR4+O2bNnx8477xwXX3zxUu4pAAAALKrQQXdHPs7Wt2/fuOiii+Kiiy5aCj0CAACAjqua7OUAAABQbQTdAAAAkIigGwAAABIp9He6l7bp06dHXV3dEm+XpXxR1tJHqbZNKeUxZ5VqvLOW8cmr7ZTbFrVkXUp5lknLq5RUnqXOUpUr6673MAAgDU+6AQAAIBFBNwAAACQi6AYAAIBEBN0AAACQiKAbAAAAEpG9vIPay1ZbrdliU2bgTZUpuVLbWc9Fqra7YwbnSm2nzGpd1LmbMsN4nnOoPSmv9azHnGrMUt5nUqrW9yoAqHaedAMAAEAigm4AAABIRNANAAAAiQi6AQAAIBFBNwAAACQi6AYAAIBElAxbSH19/VLfZ56lZ4pasqmSvNrOa6wr7btaS3N1fN/jI6IhIppjwoRxyfebZ1mlLPMvr3mQtWRdymNuT3e9h2XRHUtjAkAReNINAAAAiQi6AQAAIBFBNwAAACQi6AYAAIBEBN0AAACQiKAbAAAAElEybCHTp0+Purq6vLvRZVKW8ilq+ZisZYDyLAuWV9up9ttdyz0VVcq5m7KsV8pyZO1J2XbWfbfH3AeA6uNJNwAAACQi6AYAAIBEBN0AAACQiKAbAAAAEhF0AwAAQCKyl3dQqiy5WTPRFjWrcEop+5XquLJmQpaRuLWU45FnduiUc7u9tvPM2p/lHpal7Szb5jlH3AsAoPp40g0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgEQE3QAAAJCIoBsAAAASUTJsIfX19W0uy1KmJUvZmzxL02SRpfRRlmMu6ngV9Tyl1FXnubExork5oqEhoqmpsUP7zmseFLkEYKp7WMqyXt31usmrHGPWcwUAdI4n3QAAAJCIoBsAAAASEXQDAABAIoJuAAAASETQDQAAAIkIugEAACARJcO6QHctU5Vl+5Tb5lWOrFoVtQRbyrFOOYey7DdPRS0XlVf5rEqqsV8R2UqwFXWOAEC186QbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgEUE3AAAAJKJkWBeo1hJXKcvD5FWGqpIil3TqrGWxDFpRZb2mqvFcVWv5rEryuodV6z0fAGibJ90AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJyF6+kOnTp0ddXV2Xt5sqg25WeWXBzXpMeWVLLmqW8KwZ8PNqO+u+U7Wd5Txn7XOW8cwr63XKjO15XnPVOrezVMvoeLvjI6IhIppjwoRxmdvOU1Hvj0V9n8si5f2xqFUUqvW6ALqeJ90AAACQiKAbAAAAEvHx8oWcempEbW3evagW49td2ti4lLqxVFXrMbff7/ZUPqbOt93Rfd9/f8Ts2R9fm0tnjPM8z+nHs3Py6ld1not87wVt97vr5sAOEdE3ImaVXy/u/a+SYt4f8xvPot6DItLN7azy7dfSf48EFjZ7dsfWE3QvZPr0iD598u5FtWhod2lz81LpxFLW0O7S4h5zQ6e3rHxMnW+7o/uePfvfN7SlM8YN7S5N24f2951Ftn43dE0nFqP9frW/36Kei3zvBQ1tLum6OdA3Ivq0er24979KGjq9Zcr7Y37j2ZCs5ezH1JCw7Swa2lyyNPq19N8jgYXNmdOx9QTdC6mv96S745rbXdrQsFQ6sZQ1t7u0uMfc3OktKx9T59vu6L4XXJO1tUtrjJvbXZq2D+3vO4ts/W7umk4sRvv9an+/RT0X+d4Lmttc0nVzYNZC/23ugrbz1NzpLVPeH/Mbz+ZkLWc/puaEbWfR3OaSpdGvpf8eCSyso0+6a0pSK0ZLS0vU19cny17eHRU1k3dK1XrMRc3O29F9NzZ+/Nf7hoaIpqZkuyuTMXtRefWrWs9Fd8yk3Fb28gjZy/NoO5Wi3oMiipslPO9+Le33SKC1jsaRnnR3Y1l/Yc37jaRoqvWYi1rKLKWUZb9SXhdFDUCz7DflL/F5KfK9oMh9a0tR36vyvJ7zkmfZw7z2W+Qypn4Pg+5D9nIAAABIRNANAAAAiQi6AQAAIBFBNwAAACQi6AYAAIBEBN0AAACQiJJhXaBaS/mk3r4tRR2vPFVjPde8992elCWG8qp3XdTzXNRyT5VkORd51jLOaw4tvG3rusCNHepXyusmr1J73fG9rFqPqVpLFxa1X0DX86QbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgEdnLu0Ce2TxTZv7NK6vwsqhaM+gunfk3PiIaIqI5JkwY16FtU2Ygb09Rz0XqfbenqP2qpKj9qiSvTN4px6taz0V7smbbznKeU0o5//Ka2ykVtV9A1/OkGwAAABIRdAMAAEAigm4AAABIRNANAAAAiQi6AQAAIBFBNwAAACSiZFjB5VkGI1V5DiUyulae49kdyxNlUdRzUUme13OW8kZZyi6l3DZP1dhv5S0XVdT39kqKWsY0rzlSraXMgK7nSTcAAAAkIugGAACARATdAAAAkIigGwAAABIRdAMAAEAigm4AAABIRMmwnKUsJ5G17e5YhqU7lu8o6hzKOpYLtm9sjGhujmhoiGhqaszcr0qytF2t86taS52lbDuvMkJddd3wsZQl6fLcd17ls7KWFEvVdl7bRuRXUtG1DtXFk24AAABIRNANAAAAiQi6AQAAIBFBNwAAACQi6AYAAIBEZC/vAkXNWJxnFtyiZtyU7XNReWXBreTfbY+PiIaIaI4JE8Z1SdupFDnbcVEV9V7RnqLe8yOq4XpeckXNQp9XhvusqnU8izq3O7vfjijqPRBYcp50AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgESUDFtIfX19m8vaK9tQrSUdUpa9qdYxaU+W8cpzrPMqPZP1mBcsb2yMaG6OaGiIaGpq7JK2i1qmKq/SNUU95qKW5qrWEkMpxzPl/bGS7vh+k+UelmfpwZT3mVTvk3m+n6R8fwaKxZNuAAAASETQDQAAAIkIugEAACARQTcAAAAkIugGAACARATdAAAAkIiSYQuZPn161NXVLXZZqjIYRS3Vw6KKep6LWlYppZSlZ6p1PPMqPdNdyz2lLLuUsjRXqv3m2XYlqd6f8yq3mGfbRb6e85r71ToPgGLxpBsAAAASEXQDAABAIoJuAAAASETQDQAAAIkIugEAACARQTcAAAAkomRYBy2LZR1SlWFJqVrLPbGof5/L8RHREBHNMWHCuIjIfh6zzO2UZWuy9CtL21mum5TjlSf3iq5VjWWXUt5nsr5XZSl7mGW/KaWcI0X9fcbvLLDs8KQbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgkarKXj5+/Pg4+eST49hjj43zzz8/IiJmzZoVJ554Ylx33XUxe/bs2HnnnePiiy+OwYMH59vZpSRlRs5qzJqZMtts6n23J+V5TnXMXTX/GhsjmpsjGhoimpoaO7RtyoywKc9zUduuxusiq7zuf0XN9t66X0teUaBa50EW1fqesKyRQRxYGqrmSfcTTzwRP/vZz+Izn/lMq9ePP/74uOOOO+LGG2+MBx54IN56663Ye++9c+olAAAA/FtVBN0ffvhhHHjggXH55ZfHCiusUH59+vTp8Ytf/CJ+8pOfxBe+8IXYfPPNY+LEifGHP/whHn300Rx7DAAAAFUSdI8dOza+8pWvxKhRo1q9/tRTT8XcuXNbvb7eeuvFGmusEY888kib7c2ePTtaWlpa/QAAAEBXK/x3uq+77rp4+umn44knnlhk2ZQpU6JPnz7R0NDQ6vXBgwfHlClT2mzznHPOiR/+8Idd3VUAAABopdBPut9444049thj4+qrr46+fft2Wbsnn3xyTJ8+vfzzxhtvdFnbAAAAsEChg+6nnnoq3nnnnfjsZz8bvXr1il69esUDDzwQF1xwQfTq1SsGDx4cc+bMiebm5lbbTZ06NYYMGdJmu7W1tVFXV9fqBwAAALpaoT9evtNOO8Wf/vSnVq8deuihsd5660VjY2MMHTo0evfuHZMmTYrRo0dHRMTkyZPj9ddfj5EjR+bR5aWuO5a1SVnaKM+yNu3Js2RJqvHuulJmi5YnqqRaz2NRywDldU1mGa+ObN/Ztot6PWbV0WPu6jJ+1TqeleZfdyy1l+f7c6o5lOd5rNb3BGDJFTroHjBgQGy00UatXlt++eVjxRVXLL9++OGHxwknnBADBw6Murq6+Pa3vx0jR46MrbfeOo8uAwAAQFmhg+6O+OlPfxo9evSI0aNHx+zZs2PnnXeOiy++OO9uAQAAQPUF3ffff3+rf/ft2zcuuuiiuOiii/LpEAAAALSh0InUAAAAoJoJugEAACARQTcAAAAkUnXf6aYYilqqoqglhiop6nhWkle/izpeWfvV3vZFLbeTVVGvm6LOsUqynOeOz79Fy/jlWUoqlZTXXNZ9Z9m2qCUAK8lyf+xsux3R3r6rtYwp0PU86QYAAIBEBN0AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhE9vKCK2pW1yzyPKbumGG3u1owno2NEc3NEQ0NEU1NjRHRfTN5tydl5t88pexXlvOc1xzprtmOi3rvzZL1Ok+pznOR3+dSXc9Z9ptaNb5XAYvnSTcAAAAkIugGAACARATdAAAAkIigGwAAABIRdAMAAEAigm4AAABIRMmwLpCyxEaRS9N0VpHLXBS1PEe1li9KpajHnLW0TJ7H1Z6ilvWqJOW5ak+WOVTUub3wssWV8cu67872K6U8y/SlLHGVZf6lvD9mKYeXZ1mvIv9OAxSHJ90AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgESXDWOqKWoaKRXXXc5Gq9ExRyz11ZHkqKcsmFbUcYxZZjzlVCbbW7Y6PiIaIaI4JE8Z1qO2ilntqT7WWocqrVFlXbF9EeV1zQPfiSTcAAAAkIugGAACARATdAAAAkIigGwAAABIRdAMAAEAigm4AAABIRMmwLlDUkjiVVGMJodTy6luWeVDUEmxdVzpmycsTpRyTlOVhUpbbKWoptCLut5IilzLL616Rcn7lNXdTXs953sOytFvU+0iRyzXm1TZQLJ50AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgEUE3AAAAJCJ7eRfIkn2yWjNuZpG1XymzR+clZYbdombBraS9fsv6v/S376xqvQ+1Z1m/zzQ2RjQ3RzQ0RDQ1NUZE9zzPWY8pr/f3lO+heWbqTvXen7VqRHf8nQToep50AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgESUDOsCeZaEyKtURbWWbCpqWZuUqrFUT8S/+7248kQp5Vl6pr19p2w7pawl7bK0nWrbZfE+UklRj7mo74PV+h5aScrfSfIazzzPhXJk0H140g0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgEQE3QAAAJCIoBsAAAASUTKsylVj6Y88y1wosbFkUpZzyloCK5UspWfyPOZqLYFV1H4XtVRPyjJVHTc+IhoiojkmTBhXcb9du+/iSFnuqVrHq6hlD/M6F1nb9jsLdB+edAMAAEAigm4AAABIRNANAAAAiQi6AQAAIBFBNwAAACQie3kHpcpkm2fmyrz2LVtn9Shq1uqU8jzmlBmLqzEbd6V+FXUOdcfM0wtrbIxobo5oaIhoampM2qeIbNfNsvh+U9TM6EWtXJJnVvVKinrfBpacJ90AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgESXDOihVaYailtCo1v0ui+VhilzupD1ZzlXKYy5qv7LK65jzLPuV5Xxk6VeeZSTzKjGU8t5b1Pt6nqXhijo/U15zqcY7636V9QI6wpNuAAAASETQDQAAAIkIugEAACARQTcAAAAkIugGAACARATdAAAAkIiSYSxTilp6Jotq7HNE2pI3eZWtyavkTda28yo/lFqR+5ZKyvJuqeRZeivL9Zzleq/W0nCVpCxHVlQpr7lqHRNgUZ50AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgESUDFuGFbV8TBZF7XOeY90dz3NKKccrZRmgaj2PeZU6y2JZvJ5b73d8RDRERHNMmDAu6X5Tt51SdxyTai1HVq2WxWOG7sqTbgAAAEhE0A0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgERkL89Z1ky0y2K246LKci5S7Tf1vvOSJeN1JVnGK+W5yLPtLLLchyr1q6hzP0u/svY5y32oo9s2NkY0N0c0NEQ0NTVW3LaSLP3qyPapZOlXnu/9WaQ8zymPOeV4pepXR7YHqocn3QAAAJBIp4Luc845J375y18u8vovf/nLaGpqytwpAAAA6A46FXT/7Gc/i/XWW2+R1zfccMO49NJLM3cKAAAAuoNOBd1TpkyJVVZZZZHXV1555Xj77bczdwoAAAC6g04F3UOHDo3f//73i7z++9//PlZdddXMnQIAAIDuoFPZy4844og47rjjYu7cufGFL3whIiImTZoUJ510Upx44old2kEAAACoVp0Kur/73e/Ge++9F0cddVTMmTMnIiL69u0bjY2NcfLJJ3dpB7u7rOUg8ioNkmcZi5QlS7LIa0yWxZIiWcuw5CVliaEsino9F3Vu51liqJIs2+d1f6zWcngp5VVKqsglrKrxflDk8QSWrk4F3TU1NdHU1BSnnHJKvPDCC9GvX79Yd911o7a2tqv7BwAAAFWrU0H3Av37948tttiiq/oCAAAA3UqHg+699947rrjiiqirq4u999673XVvueWWzB0DAACAatfhoLu+vr783ZS6urqq/Z4UAAAALC0dDronTpxY/v8rrrgiRV8AAACgW+lUne4vfOEL0dzcvMjrLS0t5RJiAAAAsKzrVCK1+++/v1wqbGGzZs2Khx56KHOniiivMlV5lpvIqyRJJXmVVSqqopYkSXmeU26bcjyLWs4pi5TXXJ5zu6hlvbJI+T5W1PmZpbxg1vlXje9HeZbDy6ukYtbzVI3nGVj6lijofu6558r///zzz8eUKVPK/543b17cddddsdpqq3Vd7wAAAKCKLVHQvemmm0ZNTU3U1NQs9mPk/fr1iwsvvLDLOgcAAADVbImC7ldeeSVKpVKstdZa8fjjj8fKK69cXtanT58YNGhQ9OzZs8s7CQAAANVoiYLuNddcMyIi5s+fn6QzAAAA0J10KpFaRMTkyZPjwgsvjBdeeCEiItZff/04+uijY7311uuyzgEAAEA161TQffPNN8cBBxwQI0aMiJEjR0ZExKOPPhobb7xxXHfddTF69Ogu7WQR5JWZtagZYStJmcG0PdU6Xt1RyvOcZ4bxovY7r7bzzHacUlHvJVnOc9fNgfER0RARzTFhwrgOtV3U6yZLu92xckReFQFSK2qlg6LOIaDrdSroPumkk+Lkk0+OM844o9Xrp512Wpx00kndMugGAACAJdWjMxu9/fbbcfDBBy/y+kEHHRRvv/125k4BAABAd9CpoHvHHXeMhx56aJHXH3744dh+++0zdwoAAAC6g059vPyrX/1qNDY2xlNPPRVbb711RHz8ne4bb7wxfvjDH8btt9/eal0AAABYFnUq6D7qqKMiIuLiiy+Oiy++eLHLIj5OEDFv3rwM3QMAAIDq1amgW51uAAAAqKzTdbpZOqq1nETKkk1ZFHU88yoDVK1SlqnKIs/yWdU6D/Iqk1bU8m1FvUctvN/Gxojm5oiGhoimpsYl3r6rFbXsXF6l9ipJObez7Leox5Ty3lut921gyXU66J4xY0Y88MAD8frrr8ecOXNaLTvmmGMydwwAAACqXaeC7j/+8Y/x5S9/OWbOnBkzZsyIgQMHxrvvvhvLLbdcDBo0SNANAAAA0cmSYccff3zsvvvu8f7770e/fv3i0Ucfjddeey0233zzOO+887q6jwAAAFCVOhV0P/PMM3HiiSdGjx49omfPnjF79uwYOnRoTJgwIb73ve91dR8BAACgKnUq6O7du3f06PHxpoMGDYrXX389IiLq6+vjjTfe6LreAQAAQBXr1He6N9tss3jiiSdi3XXXjR122CFOPfXUePfdd+N//ud/YqONNurqPgIAAEBV6lTQffbZZ8cHH3wQERFnnXVWHHzwwfGtb30r1l133fjlL3/ZpR1c1nXXciepFLXcTne1dErijI+IhohojgkTxnVJ26nmQapSZB1pO8+SOVnaTinL/MyrfFvWskpLZ24vek1WkvLeW43Xc1ZZys4V9biK+v6cVymzSvsu6ngBi9epoHvEiBHl/x80aFDcddddXdYhAAAA6C469Z1uAAAAoLJOBd1Tp06Nb3zjG7HqqqtGr169omfPnq1+AAAAgE5+vHzMmDHx+uuvxymnnBKrrLJKYb8fBAAAAHnqVND98MMPx0MPPRSbbrppF3cHAAAAuo9OBd1Dhw5dalkT33zzzWhsbIzf/OY3MXPmzFhnnXVi4sSJ5WRupVIpTjvttLj88sujubk5tt1227jkkkti3XXXXSr9686qMTNmNfY5Ytnsd0e3bWyMaG6OaGiIaGpq7PT+loZl8Tym3Hee1QiKmg0+Lwv3uauvyWo9z1mkPOaUmfnzPFepMnkXtUpMnlJmbM8yh4paxaNa7/l5ZuZfFnXqO93nn39+jBs3Ll599dUu7k5r77//fmy77bbRu3fv+M1vfhPPP/98/PjHP44VVlihvM6ECRPiggsuiEsvvTQee+yxWH755WPnnXeOWbNmJe0bAAAAVNKpJ937779/zJw5M9Zee+1Ybrnlonfv3q2WT5s2rUs619TUFEOHDo2JEyeWXxs+fHj5/0ulUpx//vnxgx/8IPbYY4+IiLjqqqti8ODBcdttt8UBBxzQJf0AAACAzuhU0P3Tn/50qXwk5vbbb4+dd9459t1333jggQditdVWi6OOOiqOOOKIiIh45ZVXYsqUKTFq1KjyNvX19bHVVlvFI4880mbQPXv27Jg9e3b53y0tLRERceqpEbW1CQ8IWGL33x8xe/bH12ZjsT9dzmKNb3dp++c0y7Z5Stnv/Mek66/J/I9p6cvzmNved+X9Vmu/i6r98WzPgmNO8x6ZvV+dbTu/94Si9iullOd52bFQSNmuTmcvXxr+/ve/xyWXXBInnHBCfO9734snnngijjnmmOjTp08ccsghMWXKlIiIGDx4cKvtBg8eXF62OOecc0788Ic/XOT16dMj+vTp2mMAspk9+983tObmXLtCpzS0u7T9c5pl2zw1tLs0W79Ttt0xXX9NNrS7tLjnOYuGdpemPea29115v21v27Hts2h739U7Rxo6veWCY07zHtnQ6S3TzqEs21aSpe0s2+apodNbFveYlr45czq2XqeC7h122CEOP/zw2HfffaNfv36daaJD5s+fHyNGjIizzz47IiI222yz+POf/xyXXnppHHLIIZ1u9+STT44TTjih/O+WlpYYOnRo1Nd70g1Fs+CarK39OHET1aa53aXtn9Ms2+apud2l2fqdsu2O6fprsrndpcU9z1k0t7s07TG3ve/K+217245tn0Xb+67eOdLc6S0XHHOa98jmTm+Zdg5l2baSLG1n2TZPzZ3esrjHtPR19El3TakT6eeOO+64uOaaa2L27Nmx3377xeGHHx5bb731kjZT0Zprrhlf/OIX4+c//3n5tUsuuSR+9KMfxZtvvhl///vfY+21144//vGPrcqX7bDDDrHpppvGf/3Xf3VoPy0tLVFfXx/Tp0+Purq6rj4MIIPWmZLz7g1LSkbYRVV7ZvSuviaLcExLW7VmAa/WfhdVV2SPTvEeKXv5krVdrfcw2cu7RkfjyE5nL3/rrbdi4sSJ8c4778TnPve52GCDDeK8886LqVOndrrTn7TtttvG5MmTW7324osvxpprrhkRHydVGzJkSEyaNKm8vKWlJR577LEYOXJkl/UDIG81NTWZfvJSKpXa/alGlcY65TF3x/HMKtV1kfWay2uOZNl3JVn6nfUe1R3nfbVez+31OeXcr7RtyvfAlNdzEd+7I7Kd55S/r+S57yw6FXRHRPTq1Sv23nvv+NWvfhX/+Mc/4utf/3qccsopMXTo0Nhzzz3j3nvvzdy5448/Ph599NE4++yz429/+1tcc801cdlll8XYsWMj4uNBP+644+JHP/pR3H777fGnP/0pDj744Fh11VVjzz33zLx/AAAAyKJT3+le2OOPPx4TJ06M6667LgYNGhRjxoyJN998M3bbbbc46qij4rzzzut021tssUXceuutcfLJJ8cZZ5wRw4cPj/PPPz8OPPDA8jonnXRSzJgxI4488shobm6O7bbbLu66667o27dv1kMDAACATDoVdL/zzjvxP//zPzFx4sR46aWXYvfdd49rr702dt555/Kj+TFjxsQuu+ySKeiOiNhtt91it912a3N5TU1NnHHGGXHGGWdk2g8AAAB0tU4F3auvvnqsvfbacdhhh8WYMWNi5ZVXXmSdz3zmM7HFFltk7iAAAABUq04F3ZMmTYrtt9++3XXq6urivvvu61SnAAAAoDvoVCK1ESNGxMyZM8v/fu211+L888+Pu+++u8s6BgAAANWuU0+699hjj9h7773jP//zP6O5uTm22mqr6N27d7z77rvxk5/8JL71rW91dT8BlopKJSPyKuOSV/3bPPdd1JI53fVcZJFnv6vxmkw5XkWdI91VNd7DsspyzFnmfpaSTimvubxLe3VWnvfl9sasWt8HK+nUk+6nn366/PHym266KQYPHhyvvfZaXHXVVXHBBRd0aQcBAACgWnUq6J45c2YMGDAgIiLuvvvu2HvvvaNHjx6x9dZbx2uvvdalHQQAAIBq1amge5111onbbrst3njjjfjtb38bX/rSlyLi41JidXV1XdpBAAAAqFadCrpPPfXU+M53vhPDhg2LLbfcMkaOHBkRHz/13myzzbq0gwAAAFCtOpVIbZ999ontttsu3n777dhkk03Kr++0006x1157dVnnAAAAoJp16kl3RMSQIUNis802i+uvvz5mzJgRERFbbrllrLfeel3WOQAAAKhmnXrSvbBvfvObsdVWW8Vaa63VFf0ByFW1lqLIIs/SR0Utu5RFlvIx1VqOLM8SV3mNd7WWCcpLylJSecpS4iqv+2NRxzKrLOeiWq/nvMq3FXUOFfk8dvpJ9wJFHXQAAADIW+agGwAAAFi8zEH3b37zm1httdW6oi8AAADQrXQ66P7oo4/id7/7XfzlL3+JOXPmRETEW2+9FR9++GGXdQ4AAACqWacSqb322muxyy67xOuvvx6zZ8+OL37xizFgwIBoamqK2bNnx6WXXtrV/QQAAICq06mg+9hjj40RI0bEs88+GyuuuGL59b322iuOOOKILuscQGdkychZ1MzTleSV+Tdl5umUmX1TWhb7lWfm6bzGO0tm4GrN2F5JUTPJp8wwnmrbSv7d7/ER0RARzTFhwrguaTvP6zXLHEqZybs9Ka/nVONRZNV6b62kU0H3Qw89FH/4wx+iT58+rV4fNmxYvPnmm13SMQAAAKh2nfpO9/z582PevHmLvP6Pf/wjBgwYkLlTAAAA0B10Kuj+0pe+FOeff3753zU1NfHhhx/GaaedFl/+8pe7qm8AAABQ1Tr18fLzzjsvdtlll9hggw1i1qxZ8fWvfz1eeumlWGmlleLaa6/t6j4CAABAVepU0D106NB49tln4/rrr49nn302Pvzwwzj88MPjwAMPjH79+nV1HwEAAKAqLXHQPXfu3FhvvfXizjvvjAMPPDAOPPDAFP0CAACAqrfEQXfv3r1j1qxZKfoC0CXyKjeRZ9mkSlKVUslahiWvUj50re54Lqq1xFqe56Ko5dtSbZunBf1ubIxobo5oaIhoamrMtU8dUdRyd3mVMuvIvrO0ndd+U5b8LFoJypaWlqivr6+4XqcSqY0dOzaamprio48+6szmAAAAsEzo1He6n3jiiZg0aVLcfffdsfHGG8fyyy/favktt9zSJZ0DAACAatapoLuhoSFGjx7d1X0BAACAbmWJgu758+fHueeeGy+++GLMmTMnvvCFL8Tpp58uYzkAAAAsxhJ9p/uss86K733ve9G/f/9YbbXV4oILLoixY8em6hsAAABUtSUKuq+66qq4+OKL47e//W3cdtttcccdd8TVV18d8+fPT9U/AAAAqFpL9PHy119/Pb785S+X/z1q1KioqamJt956K1ZfffUu7xxAZ6QsU9XZdlMrWgmNvLetRCmzrpVnSZxUbWc9j1nmUJb7EItKeV9POYeyKOp7WV739ZTXc9ZtU/U7ZRk0789LbomedH/00UfRt2/fVq/17t075s6d26WdAgAAgO5giZ50l0qlGDNmTNTW1pZfmzVrVvznf/5nq7JhSoYBAADAEgbdhxxyyCKvHXTQQV3WGQAAAOhOlijonjhxYqp+AAAAQLezRN/pBgAAADpuiZ50A3R3Rc2yXOR9p5I1g3N7x5xnVvUsmWpTZrXueEbY8RHREBHNMWHCuGT96QpFvS5SzqEs21bjfSIi3/OcVyblf7e9+Osxr3OZ8r6dZduU/Srq/Cty26n2m+d7aCWedAMAAEAigm4AAABIRNANAAAAiQi6AQAAIBFBNwAAACQi6AYAAIBElAwDup1qLHNRydIpPVOstvMcz/Zk7VdRS89kUdSyNVnKxxR1rLNKOf/yGs+inqus5YtS3XtT9ivPcnjtyXrMqcr0ReR3not63RT1fbCt/ba0tER9fX3F7T3pBgAAgEQE3QAAAJCIoBsAAAASEXQDAABAIoJuAAAASETQDQAAAIkoGQZQBYpa2qNaFbXEWrWe5zzLzmXZb1HHO6+SOVnLKmWRsu325FnWqytKsDU2RjQ3RzQ0RDQ1NXZo26z9yktR79spZel3yhKAleQ1nlnvIyn77Uk3AAAAJCLoBgAAgEQE3QAAAJCIoBsAAAASEXQDAABAIoJuAAAASETJMKDbqdbSIO2p1mPqipI4RVPUfqW08DEvrkRRynJPRR3vZbF0XLX2q71zVeR7a1HHO4u8ys7lWRour9JbRT7mvMYzS9tZr0dPugEAACARQTcAAAAkIugGAACARATdAAAAkIigGwAAABKRvRzodrpjxteiHlPWDKUpjyuvzOhZxqSomZRb92t8RDRERHNMmDCuE9svmaJm0M3zmkw1nnnOv7zazpoJuRorMFRS1Osmz35lOc9Zs4h3dts8339THnPK6zll2550AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgESUDAO6nbzK3uRZbifLvotaNqmo5bNSynpMqcqwLLyssTGiuTmioSGiqakxc7+qtWxNSnldk0W+nlPNoTznSFFLc+V1LoosrzJVWbat1vfQlPMvz3u+J90AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgESXDgG4nr7I3WUtVVGOpnzzLPaXevrvpruORVwmYLONZqc/VWuoni6Iec1FLihV1DlTr+1wlKc9Fqt8rUv5OkvI8F7X8alv7bWlpifr6+opte9INAAAAiQi6AQAAIBFBNwAAACQi6AYAAIBEBN0AAACQiOzlQLdT1OypRc02W0m19juLLBlh8xyvVPtuPR7jI6IhIppjwoRxmfebNftznvvOq+1qlFfG4UryrJKQZ2b0LLJkta4kVZbwrL8XFDUbd14ZxivJ85rMIuXc9qQbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgEUE3AAAAJKJkGEBBVGuJDZaePEvAZJFXaZosZYAqjXXKck5FPY8pZZnb1Vp6q5JqnAfVWoaqqO+/Ka+LLFKOZ55lXzvzftLS0hL19fUV9+1JNwAAACQi6AYAAIBEBN0AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhEyTCg26nGMisR1dvv7qio5yKvfi2838bGiObmiIaGiKamxojIt5RZEcZkcbKUMsuiqKWPUu475fzL0nbWfmWZQ3nNv+6qqNdsyna74zzJs3ygJ90AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgESXDgKqTZ3kiWnMuFlXUkk1dV/pofEQ0RERzTJgwLvO+85wjKfuVspRUqm2LWnprWZXXPKgkr+u5qPeKSopaGi7LMeVZDq+z7aZuuxJPugEAACARQTcAAAAkIugGAACARATdAAAAkIigGwAAABKRvRyoOkXN8LwsMh6LKur8LGpW4TyvuaLO37wy8GbNdlzU+VfU7Pkp5ZXVupKUbWfZb55ZrYs6B1Oeq7yOOa/5F+FJNwAAACQj6AYAAIBEBN0AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhEyTCg28mzJERRLYslc7LIModSli/KqzTSwts2NkY0N0c0NEQ0NTVW3G/WfadU1JI4eZXXKvK9M9U1mefcTXmfyWv+pSyflXK8skhZai/PazJlv5bF30k86QYAAIBEBN0AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEik0EH3vHnz4pRTTonhw4dHv379Yu21144zzzyzVVa7UqkUp556aqyyyirRr1+/GDVqVLz00ks59hoAAAA+VuiSYU1NTXHJJZfElVdeGRtuuGE8+eSTceihh0Z9fX0cc8wxERExYcKEuOCCC+LKK6+M4cOHxymnnBI777xzPP/889G3b9+cjwDIQ17lTopcNqm7luDIQ9axzLN0TXuWxRIuKe8VWcYzr3tJ1n6l1B3ndtcc0/iIaIiI5pgwYVyXtJ1SUUvpdcdyZFnvIymvm7yu5xTnuaWlJerr6ytuX+ig+w9/+EPsscce8ZWvfCUiIoYNGxbXXnttPP744xHx8cGff/758YMf/CD22GOPiIi46qqrYvDgwXHbbbfFAQcckFvfAQAAoNAfL99mm21i0qRJ8eKLL0ZExLPPPhsPP/xw7LrrrhER8corr8SUKVNi1KhR5W3q6+tjq622ikceeaTNdmfPnh0tLS2tfgAAAKCrFfpJ97hx46KlpSXWW2+96NmzZ8ybNy/OOuusOPDAAyMiYsqUKRERMXjw4FbbDR48uLxscc4555z44Q9/mK7jAAAAEAV/0n3DDTfE1VdfHddcc008/fTTceWVV8Z5550XV155ZaZ2Tz755Jg+fXr554033uiiHgMAAMC/FfpJ93e/+90YN25c+bvZG2+8cbz22mtxzjnnxCGHHBJDhgyJiIipU6fGKqusUt5u6tSpsemmm7bZbm1tbdTW1ibtOwAAABQ66J45c2b06NH6YXzPnj1j/vz5ERExfPjwGDJkSEyaNKkcZLe0tMRjjz0W3/rWt5Z2d4FuoKiZVSspaub0au3Xsqi9c9F6vBafLTnFfrNKmZE4ZebzPLMKt6eoGbGzjGfKe1TW8erIeW5sjGhujmhoiGhqasy0v47sd+F9L+myjrTd2f1mVdT375T3oZSKfF11tu2svzcUOujefffd46yzzoo11lgjNtxww/jjH/8YP/nJT+Kwww6LiI8P/rjjjosf/ehHse6665ZLhq266qqx55575tt5AAAAlnmFDrovvPDCOOWUU+Koo46Kd955J1ZdddX45je/Gaeeemp5nZNOOilmzJgRRx55ZDQ3N8d2220Xd911lxrdAAAA5K7QQfeAAQPi/PPPj/PPP7/NdWpqauKMM86IM844Y+l1DAAAADqg0NnLAQAAoJoJugEAACARQTcAAAAkUujvdANUkzzLY+VZvijVtilVa3mYoipqv6u1HFnKknZFnX8py1R1tt3UUt57q7UsYqrybtX6/sySSTnv2zqPLS0tUV9fX3F7T7oBAAAgEUE3AAAAJCLoBgAAgEQE3QAAAJCIoBsAAAASEXQDAABAIkqGAXSRrGVBspTyyavcTtYyLCnLLuUlz9I0qSzc58bGiObmiIaGiKamxg5tn0cZl6z7zXqeilrGKtV4ZdlvR5ankmfZriz3xyzjWdR+ZW07i2ot35byei7qe1Ve5Rqzjocn3QAAAJCIoBsAAAASEXQDAABAIoJuAAAASETQDQAAAInIXg6wlKTMjppXRs48Mzxnkee5KKqOZ4QdHxENEdEcEyaMi4jiZqbOIs8Mz1nkVcmgkqJm9c+z6kQlHctMvej1WGnblNUwskqVJTzPe1DKe0XKzOgp95tXZYk857Yn3QAAAJCIoBsAAAASEXQDAABAIoJuAAAASETQDQAAAIkIugEAACARJcMAFlLUsl5Z267Gkk3dVbWWtVmgsTGiuTmioSGiqakxaZ8iilsCq5KilsDKq1RPnqW58rq3Lo33k7aux7xKSWWV6v6Y8lxkHessc6iz7WZV1FJ7KUs9ZuVJNwAAACQi6AYAAIBEBN0AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhEyTCgkP5dtmF8RDRERHNMmDAuIopdBqNa952XvMpnFfU8pyxrU6264zHnWb4oy/zLs3xRnuXKUu23qKXM8pTXeS7qvbdajynlHCtq2c1KPOkGAACARATdAAAAkIigGwAAABIRdAMAAEAigm4AAABIRNANAAAAiSgZBtBFilpyJKK4JTbyKp9V1HOVZwmXvI45a2mZVHMo5XhlHess13NR7wV5Kep1UUl7ZTUj8ruXFH+88tk+D0UtWZd630XlSTcAAAAkIugGAACARATdAAAAkIigGwAAABIRdAMAAEAispcDhbQgO2VjY0Rzc0RDQ0RTU2NEFDfbbLVm1MyiqOeikmUxw3NRs+dXkmeW8CxSzqG8xqQ7ZhxOmUk+5b4r7bdaz1WqzPyV5HVd5Nl2JVmqO2Rpu5KUY9KZfrW0tER9fX3F9TzpBgAAgEQE3QAAAJCIoBsAAAASEXQDAABAIoJuAAAASETQDQAAAIkoGQZUnWotZ5KnVH1Lecx5jmdRz2V3LdHWnizHnGXbPMt6VZKqrFJR508lec2RjizPS179SjmeeZbPykueZdK6Ywm2PHnSDQAAAIkIugEAACARQTcAAAAkIugGAACARATdAAAAkIigGwAAABJRMgxgCRS1PAzLhmVx/mU55qKWz8qzTFXK8ll5STlH8tSR+dnYGNHcHNHQENHU1Ji53YXbztKvPBS1TF/Ktrtj2c68SkxmbbsST7oBAAAgEU+6F3LqqRG1tXn3AljY/fdHzJ798bXZ2LE/4gMJda9rcnybS9IeW9v7Tb/v9hS1X8uqyvOzc9dj1vO8LF43KY85r/HsjlLOkbbanhURp1fcWtC9kOnTI/r0ybsXwMJmz/74J+Ljj9AB+epe12RDm0vSHlvb+02/7/Y0tLu0+s93tWloc8mCc9G567HtdjvWTtvbd9/rpu19Z99vyraXNQ3tLs02nm21/a8ObS3oXkh9vSfdUDQLrsna2o+/swbkq3tdk81tLkl7bG3vN/2+29Pc7tLqP9/VprnNJQvOReeux7bbXbjtzmzffa+btvedfb8p217WNLe7NNt4ttX2rA5tXVMqcgaJpaSlpSXq6+tj+vTpUVdXl3d3gIW0ThKTd2+A7nRNVmsitVSK2q9l1ZInUsve7sJtZ+lXCnnOz6ImUqO1PBOpVYojPekGAKpWUTP/FnG/lRS1X9Uqzyz1WdrN0u+UAX2eshxzyrar9ZrNMmbtHXORx0P2cgAAAEhE0A0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgEQE3QAAAJCIkmEAQFJZynp115I5qeRZp9a5aC1leaw8xzqv67nStnnVu+6u8z7leOZ1nrPMv7aWtbS0RH19fbvtRnjSDQAAAMkIugEAACARQTcAAAAkIugGAACARATdAAAAkIigGwAAABJRMgwASCplSZ28ygTlaVk85vYUtZRZ1n5lKSmWRXcsdZbyXORRpqorZDmPKa+5opZ3y3o9etINAAAAiQi6AQAAIBFBNwAAACQi6AYAAIBEBN0AAACQiKAbAAAAElEyDAAorKKWVcpTXmWXilqOLM9+pSwllZeU5aCqtXxWe/su6nhVq6KWpGur7ZaWlqivr6+4vSfdAAAAkIigGwAAABIRdAMAAEAigm4AAABIRNANAAAAicheDgBUre6YvbeSLBmzq1VRjznLvlNmN0+ZGT3LuUh5zCnPRUqp5vaymPm8yDzpBgAAgEQE3QAAAJCIoBsAAAASEXQDAABAIoJuAAAASETQDQAAAIkoGQYALJOKWoaqqPIsQVTU85FyDuV1zCnLemXdd3uqtdxYqvNc1PJsKfdd5DJpnnQDAABAIoJuAAAASETQDQAAAIkIugEAACARQTcAAAAkIugGAACARJQMAwD4hCKXnqnGUlIp+6yU2aJSlt6qxmNOWeYsqyzXTZZtU5YUq9bybSl50g0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgEQE3QAAAJCI7OUAQLtaZ6IdHxENEdEcEyaM69D2Rc4o25Y8+5wye3TKDONFzapOa9WanTyLrJm6i5oBvzv2K6/7XyVZx9qTbgAAAEhE0A0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgEQE3QAAAJCIkmEAQLsWLpXS2BjR3BzR0BDR1NSYW5+6Ql6lZyopahmgLJbFMlVFVeSxzqukU8oxqda5n6W8YJZjLur9L+s935NuAAAASETQDQAAAIkIugEAACARQTcAAAAkIugGAACARATdAAAAkEiuQfeDDz4Yu+++e6y66qpRU1MTt912W6vlpVIpTj311FhllVWiX79+MWrUqHjppZdarTNt2rQ48MADo66uLhoaGuLwww+PDz/8cCkeBQCQSk1NTad/UiqVSu3+pNq2kjzHpD3VesxFnX959ruo11zKfmVpO6+5n1Vnx7qmpibpuUq1bUfKnC3uZ/r06R0az1yD7hkzZsQmm2wSF1100WKXT5gwIS644IK49NJL47HHHovll18+dt5555g1a1Z5nQMPPDD+8pe/xD333BN33nlnPPjgg3HkkUcurUMAAACANvXKc+e77rpr7LrrrotdViqV4vzzz48f/OAHsccee0RExFVXXRWDBw+O2267LQ444IB44YUX4q677oonnngiRowYERERF154YXz5y1+O8847L1ZdddXFtj179uyYPXt2+d8tLS1dfGQAAABQ4O90v/LKKzFlypQYNWpU+bX6+vrYaqut4pFHHomIiEceeSQaGhrKAXdExKhRo6JHjx7x2GOPtdn2OeecE/X19eWfoUOHpjsQAAAAllmFDbqnTJkSERGDBw9u9frgwYPLy6ZMmRKDBg1qtbxXr14xcODA8jqLc/LJJ8f06dPLP2+88UYX9x4AAABy/nh5Xmpra6O2tjbvbgAAANDNFfZJ95AhQyIiYurUqa1enzp1annZkCFD4p133mm1/KOPPopp06aV1wEAAIC8FPZJ9/Dhw2PIkCExadKk2HTTTSPi44Rnjz32WHzrW9+KiIiRI0dGc3NzPPXUU7H55ptHRMS9994b8+fPj6222iqvrgMAC2mvFEtHymsVUUfKy+Qhy36LekwpFfmYU103WctJ5TXHsvQ75XnOs+2UUo53lm2zzJFK5yLLNVdJrkH3hx9+GH/729/K/37llVfimWeeiYEDB8Yaa6wRxx13XPzoRz+KddddN4YPHx6nnHJKrLrqqrHnnntGRMT6668fu+yySxxxxBFx6aWXxty5c+Poo4+OAw44oM3M5QAAALC05Bp0P/nkk/H5z3++/O8TTjghIiIOOeSQuOKKK+Kkk06KGTNmxJFHHhnNzc2x3XbbxV133RV9+/Ytb3P11VfH0UcfHTvttFP06NEjRo8eHRdccMFSPxYAAAD4pFyD7h133LHiRwTOOOOMOOOMM9pcZ+DAgXHNNdek6B4AAABkUthEagAAAFDtBN0AAACQSGGzlwMA3UN3zHpd1GzHWVTrearWflfSsSzN4yOiISKaY8KEcZnbzSrl3M6SebqSlBmzs/SrWs9VXlnqs45XyvH2pBsAAAASEXQDAABAIoJuAAAASETQDQAAAIkIugEAACARQTcAAAAkomQYAJBUNZbMSbnf7lriqhoVuSRTR+ZnY2NEc3NEQ0NEU1Pjknaxy6Us65Vl33ntN6ui3juz7juve28lKeeJJ90AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgESXDAICkiloiK0u/spaDykuWUj3L4jHn2XbH9js+IhoiojkmTBjXoW2Lep4i0l2TRT7mVGXBiny9ptp31pJfKcvOedINAAAAiQi6AQAAIBFBNwAAACQi6AYAAIBEBN0AAACQiOzlAEBhpczAmyXbcVGzIaccr6IecyUp+513242NEc3NEQ0NEU1NjR1qN8+s1lkz5He27ZRZrbNKWUUhlaxzKGUVhVTa6ldLS0vU19dX3N6TbgAAAEhE0A0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgEQE3QAAAJCIkmEAQGEVtVRPFsp6LRvyLKuUZb+VpOpXV2yfqt1UpcyyStl2yvOcRbXe4zzpBgAAgEQE3QAAAJCIoBsAAAASEXQDAABAIoJuAAAASETQDQAAAIkoGQYAsISylIPKUiqqkmotp5NFyhJseUrV76zjlaVfKc9VXiWuqnV+5XndtNd2XnMka9uVeNINAAAAiQi6AQAAIBFBNwAAACQi6AYAAIBEBN0AAACQiOzlAEC3lCULeCVZMpBnzQ6d8riqUbVmj85LnvMrr8z9eWZszyJltu2iVlEoanbyrNeFJ90AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgESXDAIDc5FkSJ6XuWL4oT1lKsOUla786VqJofEQ0RERzTJgwrkP7zjr/Up6L7liaK4s8y2cV9bpqTx5l0FpaWqK+vr7i9p50AwAAQCKCbgAAAEhE0A0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgESUDAMAkqrGck/VWsqsqKWPskpZAquoshxzUeV1rqp1DmRR5GPO6z0hZUmxSjzpBgAAgEQE3QAAAJCIoBsAAAASEXQDAABAIoJuAAAASETQDQAAAIkoGQYA8AlZS8tkKXuTpe0ilwlqz7J4zFksOObGxojm5oiGhoimpsaluu/FKWr5tqz9qsayh0VW1HmQatsIT7oBAAAgGUE3AAAAJCLoBgAAgEQE3QAAAJCIoBsAAAASkb0cAEiqGjPVVupzXtnJs0o5JlkyPOeVPbqo2bYj8suYnTKTfJHHuz1Fzdi+LGZVL9p9pqWlJerr69ttN8KTbgAAAEhG0A0AAACJCLoBAAAgEUE3AAAAJCLoBgAAgEQE3QAAAJCIkmEAQFJ5lbWp1rJKWfadstRZJSnLKnXX8kftSVUKrajXRaXt8yorV6ntPBW1lFlKed1nss4BT7oBAAAgEUE3AAAAJCLoBgAAgEQE3QAAAJCIoBsAAAASEXQDAABAIkqGAQBJ5VWiKM9yZCn7VY2lfvLsc6oyVB3ZPpV/92t8RDRERHNMmDCuvLxar7ks2xe1HF4WWdpOObeXxdJwbbXd0tIS9fX1Fdv2pBsAAAASEXQDAABAIoJuAAAASETQDQAAAIkIugEAACAR2csBgKqVMsNuFtWYYby7KmpG7Czzc8GyxsaI5uaIhoaIpqbGLtlvSimvye6Ypb6oumuW+vZkvW486QYAAIBEBN0AAACQiKAbAAAAEhF0AwAAQCKCbgAAAEhE0A0AAACJKBkGAOQmZakeZX6Wriwlm7qjpVMea3xENEREc0yYMK5L2k5Vtiurar1XZBmTop6L7qoz493S0hL19fUV1/OkGwAAABIRdAMAAEAigm4AAABIRNANAAAAiQi6AQAAIBFBNwAAACSiZBgAkJuspXqUqSoO491ayvFY0HZjY0Rzc0RDQ0RTU+NS6VdeJbBSls8q6tzNs98p761Z2i5qvyrxpBsAAAASEXQDAABAIoJuAAAASETQDQAAAIkIugEAACARQTcAAAAkomQYAEAVKWqZtKL2K6W8yhf92/iIaIiI5pgwYVyX7buzspR76sj2nW17aZRvS6HSeOVVvi2rvErHZWk7y1hHeNINAAAAyQi6AQAAIBFBNwAAACQi6AYAAIBEBN0AAACQiOzlAEAmeWbQ7a5ZsduTJcPusjheKbNap8q23dG2GxsjmpsjGhoimpoaO9R2ntm2U8prbqe85qq1GkGWMcnz/aQzx9zS0hL19fUV2/akGwAAABIRdAMAAEAigm4AAABIRNANAAAAiQi6AQAAIBHZy+Pf2ehaWlpy7gnwSbNnR8yZ8/F/XaKQv66+Jr33Ll15jXdRz3NR+xXRsb515nqs9mOuNo6p67df2u221/aC1ytmdC8ti7UjPuEf//hHDB06NO9uAAAAUGXeeOONWH311dtcLuiOiPnz58dbb70VAwYMiA8++CCGDh0ab7zxRtTV1eXdNbqhlpYWc4xkzC9SM8dIyfwiJfOLrlYqleKDDz6IVVddNXr0aPub2z5eHhE9evQo/2ViQVH0uro6FyNJmWOkZH6RmjlGSuYXKZlfdKX6+vqK60ikBgAAAIkIugEAACARQfcn1NbWxmmnnRa1tbV5d4VuyhwjJfOL1MwxUjK/SMn8Ii8SqQEAAEAinnQDAABAIoJuAAAASETQDQAAAIkIugEAACARQfcnXHTRRTFs2LDo27dvbLXVVvH444/n3SWq0DnnnBNbbLFFDBgwIAYNGhR77rlnTJ48udU6s2bNirFjx8aKK64Y/fv3j9GjR8fUqVNz6jHVbPz48VFTUxPHHXdc+TXzi6zefPPNOOigg2LFFVeMfv36xcYbbxxPPvlkeXmpVIpTTz01VllllejXr1+MGjUqXnrppRx7TLWYN29enHLKKTF8+PDo169frL322nHmmWfGwrl9zS+WxIMPPhi77757rLrqqlFTUxO33XZbq+UdmU/Tpk2LAw88MOrq6qKhoSEOP/zw+PDDD5fiUdCdCboXcv3118cJJ5wQp512Wjz99NOxySabxM477xzvvPNO3l2jyjzwwAMxduzYePTRR+Oee+6JuXPnxpe+9KWYMWNGeZ3jjz8+7rjjjrjxxhvjgQceiLfeeiv23nvvHHtNNXriiSfiZz/7WXzmM59p9br5RRbvv/9+bLvtttG7d+/4zW9+E88//3z8+Mc/jhVWWKG8zoQJE+KCCy6ISy+9NB577LFYfvnlY+edd45Zs2bl2HOqQVNTU1xyySXx3//93/HCCy9EU1NTTJgwIS688MLyOuYXS2LGjBmxySabxEUXXbTY5R2ZTwceeGD85S9/iXvuuSfuvPPOePDBB+PII49cWodAd1eibMsttyyNHTu2/O958+aVVl111dI555yTY6/oDt55551SRJQeeOCBUqlUKjU3N5d69+5duvHGG8vrvPDCC6WIKD3yyCN5dZMq88EHH5TWXXfd0j333FPaYYcdSscee2ypVDK/yK6xsbG03Xbbtbl8/vz5pSFDhpTOPffc8mvNzc2l2tra0rXXXrs0ukgV+8pXvlI67LDDWr229957lw488MBSqWR+kU1ElG699dbyvzsyn55//vlSRJSeeOKJ8jq/+c1vSjU1NaU333xzqfWd7suT7v9vzpw58dRTT8WoUaPKr/Xo0SNGjRoVjzzySI49ozuYPn16REQMHDgwIiKeeuqpmDt3bqv5tt5668Uaa6xhvtFhY8eOja985Sut5lGE+UV2t99+e4wYMSL23XffGDRoUGy22WZx+eWXl5e/8sorMWXKlFZzrL6+PrbaaitzjIq22WabmDRpUrz44osREfHss8/Gww8/HLvuumtEmF90rY7Mp0ceeSQaGhpixIgR5XVGjRoVPXr0iMcee2yp95nup1feHSiKd999N+bNmxeDBw9u9frgwYPjr3/9a069ojuYP39+HHfccbHtttvGRhttFBERU6ZMiT59+kRDQ0OrdQcPHhxTpkzJoZdUm+uuuy6efvrpeOKJJxZZZn6R1d///ve45JJL4oQTTojvfe978cQTT8QxxxwTffr0iUMOOaQ8jxb3nmmOUcm4ceOipaUl1ltvvejZs2fMmzcvzjrrrDjwwAMjIswvulRH5tOUKVNi0KBBrZb36tUrBg4caM7RJQTdkNjYsWPjz3/+czz88MN5d4Vu4o033ohjjz027rnnnujbt2/e3aEbmj9/fowYMSLOPvvsiIjYbLPN4s9//nNceumlccghh+TcO6rdDTfcEFdffXVcc801seGGG8YzzzwTxx13XKy66qrmF9At+Xj5/7fSSitFz549F8nuO3Xq1BgyZEhOvaLaHX300XHnnXfGfffdF6uvvnr59SFDhsScOXOiubm51frmGx3x1FNPxTvvvBOf/exno1evXtGrV6944IEH4oILLohevXrF4MGDzS8yWWWVVWKDDTZo9dr6668fr7/+ekREeR55z6Qzvvvd78a4cePigAMOiI033ji+8Y1vxPHHHx/nnHNORJhfdK2OzKchQ4Yskjj5o48+imnTpplzdAlB9//Xp0+f2HzzzWPSpEnl1+bPnx+TJk2KkSNH5tgzqlGpVIqjjz46br311rj33ntj+PDhrZZvvvnm0bt371bzbfLkyfH666+bb1S00047xZ/+9Kd45plnyj8jRoyIAw88sPz/5hdZbLvttouUOXzxxRdjzTXXjIiI4cOHx5AhQ1rNsZaWlnjsscfMMSqaOXNm9OjR+lfQnj17xvz58yPC/KJrdWQ+jRw5Mpqbm+Opp54qr3PvvffG/PnzY6uttlrqfab78fHyhZxwwglxyCGHxIgRI2LLLbeM888/P2bMmBGHHnpo3l2jyowdOzauueaa+NWvfhUDBgwofx+ovr4++vXrF/X19XH44YfHCSecEAMHDoy6urr49re/HSNHjoytt946595TdAMGDCjnB1hg+eWXjxVXXLH8uvlFFscff3xss802cfbZZ8d+++0Xjz/+eFx22WVx2WWXRUSU68L/6Ec/inXXXTeGDx8ep5xySqy66qqx55575tt5Cm/33XePs846K9ZYY43YcMMN449//GP85Cc/icMOOywizC+W3Icffhh/+9vfyv9+5ZVX4plnnomBAwfGGmusUXE+rb/++rHLLrvEEUccEZdeemnMnTs3jj766DjggANi1VVXzemo6FbyTp9eNBdeeGFpjTXWKPXp06e05ZZblh599NG8u0QViojF/kycOLG8zr/+9a/SUUcdVVphhRVKyy23XGmvvfYqvf322/l1mqq2cMmwUsn8Irs77rijtNFGG5Vqa2tL6623Xumyyy5rtXz+/PmlU045pTR48OBSbW1taaeddipNnjw5p95STVpaWkrHHntsaY011ij17du3tNZaa5W+//3vl2bPnl1ex/xiSdx3332L/b3rkEMOKZVKHZtP7733XulrX/taqX///qW6urrSoYceWvrggw9yOBq6o5pSqVTKKd4HAACAbs13ugEAACARQTcAAAAkIugGAACARATdAAAAkIigGwAAABIRdAMAAEAigm4AAABIRNANAAAAiQi6AYCqseOOO8Zxxx2XdzcAoMME3QCwFI0ZMyZqamqipqYm+vTpE+uss06cccYZ8dFHH2Vq9/7774+amppobm7umo7mrK3jueWWW+LMM8/Mp1MA0Am98u4AACxrdtlll5g4cWLMnj07fv3rX8fYsWOjd+/ecfLJJ+fdtcIbOHBg3l0AgCXiSTcALGW1tbUxZMiQWHPNNeNb3/pWjBo1Km6//fZ4//334+CDD44VVlghlltuudh1113jpZdeKm/32muvxe677x4rrLBCLL/88rHhhhvGr3/963j11Vfj85//fERErLDCClFTUxNjxoxpc/8XX3xxrLvuutG3b98YPHhw7LPPPhERcdVVV8WKK64Ys2fPbrX+nnvuGd/4xjciIuL000+PTTfdNP7nf/4nhg0bFvX19XHAAQfEBx98UF7/rrvuiu222y4aGhpixRVXjN122y1efvnl8vJXX301ampq4rrrrottttkm+vbtGxtttFE88MAD5eVtHc8nP14+e/bsaGxsjKFDh0ZtbW2ss8468Ytf/GIJzwgApCPoBoCc9evXL+bMmRNjxoyJJ598Mm6//fZ45JFHolQqxZe//OWYO3duRESMHTs2Zs+eHQ8++GD86U9/iqampujfv38MHTo0br755oiImDx5crz99tvxX//1X4vd15NPPhnHHHNMnHHGGTF58uS466674nOf+1xEROy7774xb968uP3228vrv/POO/F///d/cdhhh5Vfe/nll+O2226LO++8M+6888544IEHYvz48eXlM2bMiBNOOCGefPLJmDRpUvTo0SP22muvmD9/fqu+fPe7340TTzwx/vjHP8bIkSNj9913j/fee2+Jjufggw+Oa6+9Ni644IJ44YUX4mc/+1n0799/SU8BACTj4+UAkJNSqRSTJk2K3/72t7HrrrvGbbfdFr///e9jm222iYiIq6++OoYOHRq33XZb7LvvvvH666/H6NGjY+ONN46IiLXWWqvc1oKPXQ8aNCgaGhra3Ofrr78eyy+/fOy2224xYMCAWHPNNWOzzTaLiI+D/69//esxceLE2HfffSMi4n//939jjTXWiB133LHcxvz58+OKK66IAQMGRETEN77xjZg0aVKcddZZERExevToVvv85S9/GSuvvHI8//zzsdFGG5VfP/roo8vrXnLJJXHXXXfFL37xizjppJM6dDwvvvhi3HDDDXHPPffEqFGjFhkTACgCT7oBYCm78847o3///tG3b9/YddddY//9948xY8ZEr169Yquttiqvt+KKK8anP/3peOGFFyIi4phjjokf/ehHse2228Zpp50Wzz33XLv7ufrqq6N///7ln4ceeii++MUvxpprrhlrrbVWfOMb34irr746Zs6cWd7miCOOiLvvvjvefPPNiIi44oorysnfFhg2bFg54I6IWGWVVeKdd94p//ull16Kr33ta7HWWmtFXV1dDBs2LCI+DvgXNnLkyPL/9+rVK0aMGFE+1o545plnomfPnrHDDjt0eBsAWNoE3QCwlH3+85+PZ555Jl566aX417/+FVdeeWWroLYt//Ef/xF///vf4xvf+Eb86U9/ihEjRsSFF17Y5vpf/epX45lnnin/jBgxIgYMGBBPP/10XHvttbHKKqvEqaeeGptsskk5S/hmm20Wm2yySVx11VXx1FNPxV/+8pdFvh/eu3fvVv+uqalp9dHx3XffPaZNmxaXX355PPbYY/HYY49FRMScOXM6OEId069fvy5tDwBSEHQDwFK2/PLLxzrrrBNrrLFG9Or18Te91l9//fjoo4/KAWpExHvvvReTJ0+ODTbYoPza0KFD4z//8z/jlltuiRNPPDEuv/zyiIjo06dPRETMmzevvO6AAQNinXXWKf8sCFJ79eoVo0aNigkTJsRzzz0Xr776atx7773l7f7jP/4jrrjiipg4cWKMGjUqhg4d2uFjW9DnH/zgB7HTTjvF+uuvH++///5i13300UfL///RRx/FU089Feuvv36bx/NJG2+8ccyfP7+cgA0AikjQDQAFsO6668Yee+wRRxxxRDz88MPx7LPPxkEHHRSrrbZa7LHHHhERcdxxx8Vvf/vbeOWVV+Lpp5+O++67rxykrrnmmlFTUxN33nln/POf/4wPP/xwsfu5884744ILLohnnnkmXnvttbjqqqti/vz58elPf7q8zte//vX4xz/+EZdffnmrBGodscIKK8SKK64Yl112Wfztb3+Le++9N0444YTFrnvRRRfFrbfeGn/9619j7Nix8f7775f315HjGTZsWBxyyCFx2GGHxW233RavvPJK3H///XHDDTcsUZ8BICVBNwAUxMSJE2PzzTeP3XbbLUaOHBmlUil+/etflz/OPW/evBg7dmysv/76scsuu8SnPvWpuPjiiyMiYrXVVosf/vCHMW7cuBg8eHAcffTRi91HQ0ND3HLLLfGFL3wh1l9//bj00kvj2muvjQ033LC8Tn19fYwePTr69+8fe+655xIdQ48ePeK6666Lp556KjbaaKM4/vjj49xzz13suuPHj4/x48fHJptsEg8//HDcfvvtsdJKKy3R8VxyySWxzz77xFFHHRXrrbdeHHHEETFjxowl6jMApFRTKpVKeXcCACiWnXbaKTbccMO44IILurztV199NYYPHx5//OMfY9NNN+3y9gGgSJQMAwDK3n///bj//vvj/vvvLz9FBwA6T9ANAJRtttlm8f7770dTU1Or73kDAJ3j4+UAAACQiERqAAAAkIigGwAAABIRdAMAAEAigm4AAABIRNANAAAAiQi6AQAAIBFBNwAAACQi6AYAAIBE/h/269a74OEy9wAAAABJRU5ErkJggg=="
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Blue lines mark level boundaries.\n",
      "Diagonal blocks = lateral (within-level) connections.\n",
      "Upper off-diagonal = feedforward connections.\n",
      "Lower off-diagonal = feedback connections.\n"
     ]
    }
   ],
   "execution_count": 14
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 7. Core-Periphery Structures <a name=\"core-periphery\"></a>\n",
    "\n",
    "Core-periphery networks have a densely connected core and a sparsely connected periphery.\n",
    "\n",
    "### 7.1 Creating Core-Periphery Networks"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:31.512561Z",
     "start_time": "2025-10-01T16:46:31.444182Z"
    }
   },
   "source": [
    "# Create core-periphery network\n",
    "core_periphery = conn.CorePeripheryRandom(\n",
    "    core_size=100,  # 100 neurons in core\n",
    "    core_core_prob=0.5,  # 50% connectivity within core\n",
    "    core_periphery_prob=0.1,  # 10% core→periphery\n",
    "    periphery_core_prob=0.15,  # 15% periphery→core\n",
    "    periphery_periphery_prob=0.02,  # 2% within periphery\n",
    "    weight=Constant(1.0 * u.nS),\n",
    "    seed=42\n",
    ")\n",
    "\n",
    "result_cp = core_periphery(pre_size=400, post_size=400)\n",
    "\n",
    "print(\"Core-Periphery Network:\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Total neurons: 400\")\n",
    "print(f\"Core neurons: 100\")\n",
    "print(f\"Periphery neurons: 300\")\n",
    "print(f\"\\nConnection probabilities:\")\n",
    "print(f\"  Core ↔ Core: 50%\")\n",
    "print(f\"  Core → Periphery: 10%\")\n",
    "print(f\"  Periphery → Core: 15%\")\n",
    "print(f\"  Periphery ↔ Periphery: 2%\")\n",
    "print(f\"\\nTotal connections: {len(result_cp.pre_indices)}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Core-Periphery Network:\n",
      "==================================================\n",
      "Total neurons: 400\n",
      "Core neurons: 100\n",
      "Periphery neurons: 300\n",
      "\n",
      "Connection probabilities:\n",
      "  Core ↔ Core: 50%\n",
      "  Core → Periphery: 10%\n",
      "  Periphery → Core: 15%\n",
      "  Periphery ↔ Periphery: 2%\n",
      "\n",
      "Total connections: 14203\n"
     ]
    }
   ],
   "execution_count": 16
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.2 Analyzing Core vs. Periphery Connectivity\n",
    "\n",
    "Compare degree distributions between core and periphery:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:34.633433Z",
     "start_time": "2025-10-01T16:46:34.429386Z"
    }
   },
   "source": [
    "# Calculate degrees\n",
    "in_degree_cp = np.bincount(result_cp.post_indices, minlength=400)\n",
    "\n",
    "# Separate core and periphery\n",
    "core_degrees = in_degree_cp[:100]\n",
    "periphery_degrees = in_degree_cp[100:]\n",
    "\n",
    "# Plot comparison\n",
    "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n",
    "\n",
    "vis.distribution_plot(\n",
    "    core_degrees,\n",
    "    bins=20,\n",
    "    alpha=0.7,\n",
    "    colors=['darkred'],\n",
    "    edgecolor='black',\n",
    "    ax=axes[0],\n",
    "    xlabel='In-Degree',\n",
    "    ylabel='Count',\n",
    "    title='Core Neurons (n=100)'\n",
    ")\n",
    "\n",
    "vis.distribution_plot(\n",
    "    periphery_degrees,\n",
    "    bins=20,\n",
    "    alpha=0.7,\n",
    "    colors=['lightblue'],\n",
    "    edgecolor='black',\n",
    "    ax=axes[1],\n",
    "    xlabel='In-Degree',\n",
    "    ylabel='Count',\n",
    "    title='Periphery Neurons (n=300)'\n",
    ")\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(f\"\\nDegree Statistics:\")\n",
    "print(f\"  Core - Mean: {np.mean(core_degrees):.1f}, Std: {np.std(core_degrees):.1f}\")\n",
    "print(f\"  Periphery - Mean: {np.mean(periphery_degrees):.1f}, Std: {np.std(periphery_degrees):.1f}\")\n",
    "print(f\"\\nCore neurons have ~{np.mean(core_degrees) / np.mean(periphery_degrees):.1f}× more connections\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1400x500 with 2 Axes>"
      ],
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Degree Statistics:\n",
      "  Core - Mean: 93.6, Std: 7.8\n",
      "  Periphery - Mean: 16.2, Std: 3.7\n",
      "\n",
      "Core neurons have ~5.8× more connections\n"
     ]
    }
   ],
   "execution_count": 17
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.3 Visualizing Core-Periphery Structure"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:44.126860Z",
     "start_time": "2025-10-01T16:46:43.965522Z"
    }
   },
   "source": [
    "# Create smaller network for visualization\n",
    "cp_viz = conn.CorePeripheryRandom(\n",
    "    core_size=30,\n",
    "    core_core_prob=0.6,\n",
    "    core_periphery_prob=0.15,\n",
    "    periphery_core_prob=0.2,\n",
    "    periphery_periphery_prob=0.03,\n",
    "    seed=42\n",
    ")(pre_size=120, post_size=120)\n",
    "\n",
    "matrix_cp = result_to_matrix(cp_viz, 120)\n",
    "\n",
    "# Plot\n",
    "fig, ax = plt.subplots(figsize=(10, 9))\n",
    "vis.connectivity_matrix(\n",
    "    matrix_cp,\n",
    "    cmap='binary',\n",
    "    center_zero=False,\n",
    "    show_colorbar=False,\n",
    "    ax=ax,\n",
    "    title='Core-Periphery Network (30 core + 90 periphery)'\n",
    ")\n",
    "\n",
    "# Add core boundary\n",
    "ax.axhline(30, color='red', linewidth=2.5, alpha=0.7)\n",
    "ax.axvline(30, color='red', linewidth=2.5, alpha=0.7)\n",
    "\n",
    "# Add text labels\n",
    "ax.text(15, 15, 'CORE\\n(dense)', ha='center', va='center',\n",
    "        fontsize=12, bbox=dict(boxstyle='round', facecolor='white', alpha=0.8))\n",
    "ax.text(75, 75, 'PERIPHERY\\n(sparse)', ha='center', va='center',\n",
    "        fontsize=12, bbox=dict(boxstyle='round', facecolor='white', alpha=0.8))\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nRed lines separate core and periphery.\")\n",
    "print(\"Top-left block (core-core) is densely connected.\")\n",
    "print(\"Bottom-right block (periphery-periphery) is sparsely connected.\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x900 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Red lines separate core and periphery.\n",
      "Top-left block (core-core) is densely connected.\n",
      "Bottom-right block (periphery-periphery) is sparsely connected.\n"
     ]
    }
   ],
   "execution_count": 19
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 8. Network Analysis <a name=\"analysis\"></a>\n",
    "\n",
    "Compare topological properties across different network types.\n",
    "\n",
    "### 8.1 Degree Distribution Comparison"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:45.753358Z",
     "start_time": "2025-10-01T16:46:45.338780Z"
    }
   },
   "source": [
    "# Create test networks with comparable sizes\n",
    "n_compare = 300\n",
    "\n",
    "networks = {\n",
    "    'Regular': conn.Regular(degree=10, seed=42)(pre_size=n_compare, post_size=n_compare),\n",
    "    'Small-World': conn.SmallWorld(k=10, p=0.1, seed=42)(pre_size=n_compare, post_size=n_compare),\n",
    "    'Scale-Free': conn.ScaleFree(m=5, seed=42)(pre_size=n_compare, post_size=n_compare),\n",
    "    'Random': conn.Random(prob=0.033, seed=42)(pre_size=n_compare, post_size=n_compare),\n",
    "}\n",
    "\n",
    "# Calculate degree distributions\n",
    "degrees = {}\n",
    "for name, result in networks.items():\n",
    "    in_deg = np.bincount(result.post_indices, minlength=n_compare)\n",
    "    degrees[name] = in_deg\n",
    "\n",
    "# Plot comparison\n",
    "fig, axes = plt.subplots(2, 2, figsize=(14, 10))\n",
    "axes = axes.flatten()\n",
    "\n",
    "colors = {'Regular': 'green', 'Small-World': 'steelblue',\n",
    "          'Scale-Free': 'coral', 'Random': 'gray'}\n",
    "\n",
    "for idx, (name, deg) in enumerate(degrees.items()):\n",
    "    vis.distribution_plot(\n",
    "        deg,\n",
    "        bins=25,\n",
    "        alpha=0.7,\n",
    "        colors=[colors[name]],\n",
    "        edgecolor='black',\n",
    "        ax=axes[idx],\n",
    "        xlabel='In-Degree',\n",
    "        ylabel='Count',\n",
    "        title=name\n",
    "    )\n",
    "\n",
    "plt.suptitle('Degree Distributions Across Network Types', fontsize=14, y=0.995)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1400x1000 with 4 Axes>"
      ],
      "image/png": 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CYII="
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 20
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.2 Summary Statistics Table"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:46:46.876584Z",
     "start_time": "2025-10-01T16:46:46.870365Z"
    }
   },
   "source": [
    "# Calculate summary statistics\n",
    "print(\"Network Topology Comparison:\")\n",
    "print(\"=\" * 80)\n",
    "print(f\"{'Network':<15} {'Connections':<12} {'Mean Deg':<12} {'Std Deg':<12} {'CV':<12}\")\n",
    "print(\"=\" * 80)\n",
    "\n",
    "for name, result in networks.items():\n",
    "    deg = degrees[name]\n",
    "    n_conn = len(result.pre_indices)\n",
    "    mean_deg = np.mean(deg)\n",
    "    std_deg = np.std(deg)\n",
    "    cv = std_deg / mean_deg if mean_deg > 0 else 0\n",
    "\n",
    "    print(f\"{name:<15} {n_conn:<12} {mean_deg:<12.2f} {std_deg:<12.2f} {cv:<12.3f}\")\n",
    "\n",
    "print(\"\\nCV = Coefficient of Variation (std/mean)\")\n",
    "print(\"Low CV: Homogeneous connectivity (Regular, Small-World)\")\n",
    "print(\"High CV: Heterogeneous connectivity (Scale-Free)\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Network Topology Comparison:\n",
      "================================================================================\n",
      "Network         Connections  Mean Deg     Std Deg      CV          \n",
      "================================================================================\n",
      "Regular         3000         10.00        3.19         0.319       \n",
      "Small-World     3000         10.00        1.40         0.140       \n",
      "Scale-Free      2970         9.90         9.44         0.953       \n",
      "Random          2923         9.74         3.20         0.328       \n",
      "\n",
      "CV = Coefficient of Variation (std/mean)\n",
      "Low CV: Homogeneous connectivity (Regular, Small-World)\n",
      "High CV: Heterogeneous connectivity (Scale-Free)\n"
     ]
    }
   ],
   "execution_count": 21
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 9. Exercises <a name=\"exercises\"></a>\n",
    "\n",
    "Try these exercises to reinforce your understanding:\n",
    "\n",
    "### Exercise 1: Small-World Transition\n",
    "\n",
    "Analyze how network properties change with rewiring probability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def analyze_small_world_transition(n_neurons=200, k=6, p_values=None):\n",
    "    \"\"\"\n",
    "    Analyze small-world transition by measuring clustering and path length.\n",
    "    \n",
    "    For each rewiring probability p:\n",
    "    1. Create network\n",
    "    2. Calculate clustering coefficient (local connectivity)\n",
    "    3. Estimate path length (requires graph algorithms)\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    n_neurons : int\n",
    "        Network size\n",
    "    k : int\n",
    "        Number of neighbors\n",
    "    p_values : list\n",
    "        Rewiring probabilities to test\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    results : dict\n",
    "        Dictionary with clustering and path length for each p\n",
    "    \"\"\"\n",
    "    # YOUR CODE HERE\n",
    "    # Hint: Clustering coefficient measures local connectivity density\n",
    "    # For neuron i: C_i = (actual triangles) / (possible triangles)\n",
    "\n",
    "    pass\n",
    "\n",
    "# Test the function\n",
    "# results = analyze_small_world_transition()\n",
    "# \n",
    "# # Plot results\n",
    "# p_vals = sorted(results.keys())\n",
    "# clustering = [results[p]['clustering'] for p in p_vals]\n",
    "# \n",
    "# plt.figure(figsize=(10, 6))\n",
    "# plt.plot(p_vals, clustering, 'o-', linewidth=2)\n",
    "# plt.xlabel('Rewiring Probability (p)')\n",
    "# plt.ylabel('Clustering Coefficient')\n",
    "# plt.title('Small-World Transition')\n",
    "# plt.grid(True, alpha=0.3)\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2: Custom Modular Architecture\n",
    "\n",
    "Design a multi-level modular network (modules within modules):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_hierarchical_modular_network(n_super_modules=2, n_sub_modules=3, neurons_per_sub=50):\n",
    "    \"\"\"\n",
    "    Create a hierarchical modular network with super-modules containing sub-modules.\n",
    "    \n",
    "    Structure:\n",
    "    - Super-module 1\n",
    "      - Sub-module 1a\n",
    "      - Sub-module 1b\n",
    "      - Sub-module 1c\n",
    "    - Super-module 2\n",
    "      - Sub-module 2a\n",
    "      - Sub-module 2b\n",
    "      - Sub-module 2c\n",
    "    \n",
    "    Connection rules:\n",
    "    - High connectivity within sub-modules\n",
    "    - Medium connectivity between sub-modules in same super-module\n",
    "    - Low connectivity between super-modules\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    result : ConnectionResult\n",
    "        Hierarchical modular connectivity\n",
    "    \"\"\"\n",
    "    # YOUR CODE HERE\n",
    "    # Hint: Use ModularGeneral with custom probability matrix\n",
    "\n",
    "    pass\n",
    "\n",
    "# Test your function\n",
    "# result = create_hierarchical_modular_network()\n",
    "# print(f\"Created hierarchical modular network with {len(result.pre_indices)} connections\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 3: Network Resilience Analysis\n",
    "\n",
    "Compare how different topologies respond to neuron removal:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def analyze_network_resilience(result, removal_fraction=0.2, strategy='random'):\n",
    "    \"\"\"\n",
    "    Analyze network resilience by simulating neuron removal.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    result : ConnectionResult\n",
    "        Network to analyze\n",
    "    removal_fraction : float\n",
    "        Fraction of neurons to remove\n",
    "    strategy : str\n",
    "        'random': Remove random neurons\n",
    "        'targeted': Remove highest-degree neurons (hub attack)\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    metrics : dict\n",
    "        Network metrics before and after removal:\n",
    "        - remaining_connections: fraction of connections preserved\n",
    "        - largest_component: size of largest connected component\n",
    "    \"\"\"\n",
    "    # YOUR CODE HERE\n",
    "    # Hint: Compare scale-free (vulnerable to hub attacks) vs. \n",
    "    # small-world (more resilient)\n",
    "\n",
    "    pass\n",
    "\n",
    "# Test on different networks\n",
    "# for name, result in networks.items():\n",
    "#     metrics_random = analyze_network_resilience(result, strategy='random')\n",
    "#     metrics_targeted = analyze_network_resilience(result, strategy='targeted')\n",
    "#     \n",
    "#     print(f\"{name}:\")\n",
    "#     print(f\"  Random removal: {metrics_random['remaining_connections']:.1%} connections remain\")\n",
    "#     print(f\"  Targeted removal: {metrics_targeted['remaining_connections']:.1%} connections remain\")"
   ]
  }
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