{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 1: Basic Connectivity Patterns\n",
    "\n",
    "This tutorial introduces the fundamental connectivity patterns in `braintools.conn`. You'll learn how to create basic network topologies, understand connection results, and work with weights and delays.\n",
    "\n",
    "---\n",
    "\n",
    "## 1. Introduction to Connectivity <a name=\"introduction\"></a>\n",
    "\n",
    "Neural networks are defined not just by their neurons, but by how those neurons are connected. The `braintools.conn` module provides a comprehensive system for generating biologically-plausible connectivity patterns.\n",
    "\n",
    "### Why Connectivity Matters\n",
    "\n",
    "- **Network Dynamics**: Connection patterns determine how information flows through neural populations\n",
    "- **Computational Properties**: Different topologies enable different computations\n",
    "- **Biological Realism**: Real neural circuits exhibit specific connectivity motifs\n",
    "- **Efficiency**: Sparse connectivity reduces computational cost while maintaining function\n",
    "\n",
    "Let's start by importing the necessary libraries:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:00:42.778583Z",
     "start_time": "2025-10-01T16:00:39.601961Z"
    }
   },
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import brainunit as u\n",
    "from braintools import conn, visualize as vis\n",
    "from braintools.init import Constant, Normal, Uniform, LogNormal\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. Understanding ConnectionResult <a name=\"connectionresult\"></a>\n",
    "\n",
    "All connectivity patterns in `braintools.conn` return a `ConnectionResult` object. This object contains:\n",
    "\n",
    "- **`pre_indices`**: Array of presynaptic neuron indices\n",
    "- **`post_indices`**: Array of postsynaptic neuron indices\n",
    "- **`weights`**: Synaptic weights (optional)\n",
    "- **`delays`**: Synaptic delays (optional)\n",
    "- **`metadata`**: Additional information about the connectivity pattern\n",
    "\n",
    "Let's create a simple connection and examine its structure:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:00:42.833445Z",
     "start_time": "2025-10-01T16:00:42.823531Z"
    }
   },
   "source": [
    "# Create a simple random connectivity\n",
    "simple_conn = conn.Random(prob=0.1, seed=42)\n",
    "result = simple_conn(pre_size=10, post_size=10)\n",
    "\n",
    "print(\"ConnectionResult Structure:\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Number of connections: {len(result.pre_indices)}\")\n",
    "print(f\"\\nPresynaptic indices (first 10):\")\n",
    "print(result.pre_indices[:10])\n",
    "print(f\"\\nPostsynaptic indices (first 10):\")\n",
    "print(result.post_indices[:10])\n",
    "print(f\"\\nWeights: {result.weights}\")\n",
    "print(f\"Delays: {result.delays}\")\n",
    "print(f\"\\nMetadata:\")\n",
    "for key, value in result.metadata.items():\n",
    "    print(f\"  {key}: {value}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ConnectionResult Structure:\n",
      "==================================================\n",
      "Number of connections: 12\n",
      "\n",
      "Presynaptic indices (first 10):\n",
      "[0 1 3 3 4 4 6 6 7 8]\n",
      "\n",
      "Postsynaptic indices (first 10):\n",
      "[7 2 2 6 1 7 2 4 5 0]\n",
      "\n",
      "Weights: None\n",
      "Delays: None\n",
      "\n",
      "Metadata:\n",
      "  pattern: random\n",
      "  probability: 0.1\n",
      "  allow_self_connections: False\n",
      "  weight_initialization: None\n",
      "  delay_initialization: None\n"
     ]
    }
   ],
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Connection Density\n",
    "\n",
    "Let's calculate the connection density (ratio of actual connections to possible connections):"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:00:46.586764Z",
     "start_time": "2025-10-01T16:00:46.581628Z"
    }
   },
   "source": [
    "def calculate_density(result, allow_self_connections=False):\n",
    "    \"\"\"Calculate connection density from ConnectionResult.\"\"\"\n",
    "    pre_size = result.pre_size if isinstance(result.pre_size, int) else np.prod(result.pre_size)\n",
    "    post_size = result.post_size if isinstance(result.post_size, int) else np.prod(result.post_size)\n",
    "    \n",
    "    max_connections = pre_size * post_size\n",
    "    if not allow_self_connections and pre_size == post_size:\n",
    "        max_connections -= pre_size\n",
    "    \n",
    "    actual_connections = len(result.pre_indices)\n",
    "    density = actual_connections / max_connections\n",
    "    \n",
    "    return density, actual_connections, max_connections\n",
    "\n",
    "density, actual, maximum = calculate_density(result)\n",
    "print(f\"Connection density: {density:.1%}\")\n",
    "print(f\"Actual connections: {actual} / {maximum} possible\")\n",
    "print(f\"Expected density (prob=0.1): ~10%\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Connection density: 13.3%\n",
      "Actual connections: 12 / 90 possible\n",
      "Expected density (prob=0.1): ~10%\n"
     ]
    }
   ],
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 3. Random Connectivity <a name=\"random-connectivity\"></a>\n",
    "\n",
    "Random connectivity is the simplest and most fundamental pattern. Each potential connection is made with a fixed probability.\n",
    "\n",
    "### 3.1 Basic Random Connectivity\n",
    "\n",
    "The `Random` class (also aliased as `FixedProb`) creates connections with a specified probability:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:00:47.938122Z",
     "start_time": "2025-10-01T16:00:47.931886Z"
    }
   },
   "source": [
    "# Create random connectivity with 10% connection probability\n",
    "random_conn = conn.Random(prob=0.1, seed=42)\n",
    "result_random = random_conn(pre_size=100, post_size=100)\n",
    "\n",
    "print(f\"Random Connectivity (prob=0.1)\")\n",
    "print(f\"Generated {len(result_random.pre_indices)} connections\")\n",
    "\n",
    "density, actual, maximum = calculate_density(result_random)\n",
    "print(f\"Connection density: {density:.2%}\")\n",
    "print(f\"Expected: ~10%\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Random Connectivity (prob=0.1)\n",
      "Generated 1019 connections\n",
      "Connection density: 10.29%\n",
      "Expected: ~10%\n"
     ]
    }
   ],
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Effect of Connection Probability\n",
    "\n",
    "Let's examine how connection probability affects network density:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:00:49.367818Z",
     "start_time": "2025-10-01T16:00:49.348407Z"
    }
   },
   "source": [
    "# Test different probabilities\n",
    "probabilities = [0.01, 0.05, 0.1, 0.2, 0.3, 0.5]\n",
    "network_size = 100\n",
    "\n",
    "results_by_prob = {}\n",
    "for prob in probabilities:\n",
    "    conn_pattern = conn.Random(prob=prob, seed=42)\n",
    "    result = conn_pattern(pre_size=network_size, post_size=network_size)\n",
    "    density, n_conn, _ = calculate_density(result)\n",
    "    results_by_prob[prob] = (n_conn, density)\n",
    "\n",
    "# Display results\n",
    "print(\"\\nConnection Probability vs. Actual Density:\")\n",
    "print(\"=\" * 60)\n",
    "print(f\"{'Probability':<15} {'Connections':<15} {'Density':<15} {'Error'}\")\n",
    "print(\"=\" * 60)\n",
    "for prob in probabilities:\n",
    "    n_conn, density = results_by_prob[prob]\n",
    "    error = abs(density - prob) / prob * 100\n",
    "    print(f\"{prob:<15.2f} {n_conn:<15} {density:<15.4f} {error:>5.1f}%\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Connection Probability vs. Actual Density:\n",
      "============================================================\n",
      "Probability     Connections     Density         Error\n",
      "============================================================\n",
      "0.01            93              0.0094            6.1%\n",
      "0.05            486             0.0491            1.8%\n",
      "0.10            1019            0.1029            2.9%\n",
      "0.20            2021            0.2041            2.1%\n",
      "0.30            3021            0.3052            1.7%\n",
      "0.50            5021            0.5072            1.4%\n"
     ]
    }
   ],
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 Self-Connections\n",
    "\n",
    "By default, self-connections (neuron connecting to itself) are disabled. Let's see the difference:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:00:51.822975Z",
     "start_time": "2025-10-01T16:00:51.815972Z"
    }
   },
   "source": [
    "# Without self-connections (default)\n",
    "conn_no_self = conn.Random(prob=0.2, allow_self_connections=False, seed=42)\n",
    "result_no_self = conn_no_self(pre_size=50, post_size=50)\n",
    "\n",
    "# With self-connections\n",
    "conn_with_self = conn.Random(prob=0.2, allow_self_connections=True, seed=42)\n",
    "result_with_self = conn_with_self(pre_size=50, post_size=50)\n",
    "\n",
    "# Check for self-connections\n",
    "self_conn_mask = result_with_self.pre_indices == result_with_self.post_indices\n",
    "n_self_connections = np.sum(self_conn_mask)\n",
    "\n",
    "print(\"Self-Connections Comparison:\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Without self-connections: {len(result_no_self.pre_indices)} connections\")\n",
    "print(f\"With self-connections:    {len(result_with_self.pre_indices)} connections\")\n",
    "print(f\"Number of self-connections: {n_self_connections}\")\n",
    "print(f\"Expected self-connections: ~{50 * 0.2:.1f} (50 neurons × 20% prob)\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Self-Connections Comparison:\n",
      "==================================================\n",
      "Without self-connections: 519 connections\n",
      "With self-connections:    524 connections\n",
      "Number of self-connections: 9\n",
      "Expected self-connections: ~10.0 (50 neurons × 20% prob)\n"
     ]
    }
   ],
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 4. Regular Deterministic Patterns <a name=\"deterministic-patterns\"></a>\n",
    "\n",
    "In addition to random connectivity, `braintools.conn` provides deterministic connectivity patterns.\n",
    "\n",
    "### 4.1 All-to-All Connectivity\n",
    "\n",
    "The `AllToAll` pattern connects every presynaptic neuron to every postsynaptic neuron:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:00:53.120167Z",
     "start_time": "2025-10-01T16:00:53.116364Z"
    }
   },
   "source": [
    "# Create all-to-all connectivity\n",
    "all2all = conn.AllToAll(include_self_connections=False)\n",
    "result_all2all = all2all(pre_size=10, post_size=10)\n",
    "\n",
    "print(\"All-to-All Connectivity:\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Network size: 10 × 10\")\n",
    "print(f\"Connections: {len(result_all2all.pre_indices)}\")\n",
    "print(f\"Expected: 10 × 10 - 10 (self) = 90\")\n",
    "\n",
    "density, _, _ = calculate_density(result_all2all)\n",
    "print(f\"Density: {density:.1%}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All-to-All Connectivity:\n",
      "==================================================\n",
      "Network size: 10 × 10\n",
      "Connections: 90\n",
      "Expected: 10 × 10 - 10 (self) = 90\n",
      "Density: 100.0%\n"
     ]
    }
   ],
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 One-to-One Connectivity\n",
    "\n",
    "The `OneToOne` pattern creates one-to-one mappings, useful for identity mappings or layer-to-layer projections:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:00:54.193060Z",
     "start_time": "2025-10-01T16:00:54.187277Z"
    }
   },
   "source": [
    "# Equal sizes\n",
    "one2one_equal = conn.OneToOne()\n",
    "result_equal = one2one_equal(pre_size=10, post_size=10)\n",
    "\n",
    "print(\"One-to-One Connectivity (Equal Sizes):\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Pre size: 10, Post size: 10\")\n",
    "print(f\"Connections: {len(result_equal.pre_indices)}\")\n",
    "print(f\"Connection pairs (pre → post):\")\n",
    "for i in range(min(5, len(result_equal.pre_indices))):\n",
    "    print(f\"  {result_equal.pre_indices[i]} → {result_equal.post_indices[i]}\")\n",
    "\n",
    "# Different sizes (non-circular)\n",
    "one2one_diff = conn.OneToOne(circular=False)\n",
    "result_diff = one2one_diff(pre_size=8, post_size=12)\n",
    "\n",
    "print(f\"\\nOne-to-One Connectivity (Different Sizes, Non-Circular):\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Pre size: 8, Post size: 12\")\n",
    "print(f\"Connections: {len(result_diff.pre_indices)}\")\n",
    "print(f\"Note: Only first 8 neurons connected (min of 8 and 12)\")\n",
    "\n",
    "# Circular mapping\n",
    "one2one_circ = conn.OneToOne(circular=True)\n",
    "result_circ = one2one_circ(pre_size=8, post_size=12)\n",
    "\n",
    "print(f\"\\nOne-to-One Connectivity (Different Sizes, Circular):\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Pre size: 8, Post size: 12\")\n",
    "print(f\"Connections: {len(result_circ.pre_indices)}\")\n",
    "print(f\"Connection pairs (pre → post):\")\n",
    "for i in range(min(12, len(result_circ.pre_indices))):\n",
    "    print(f\"  {result_circ.pre_indices[i]} → {result_circ.post_indices[i]}\")\n",
    "print(f\"Note: Pre indices wrap around using modulo (% 8)\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "One-to-One Connectivity (Equal Sizes):\n",
      "==================================================\n",
      "Pre size: 10, Post size: 10\n",
      "Connections: 10\n",
      "Connection pairs (pre → post):\n",
      "  0 → 0\n",
      "  1 → 1\n",
      "  2 → 2\n",
      "  3 → 3\n",
      "  4 → 4\n",
      "\n",
      "One-to-One Connectivity (Different Sizes, Non-Circular):\n",
      "==================================================\n",
      "Pre size: 8, Post size: 12\n",
      "Connections: 8\n",
      "Note: Only first 8 neurons connected (min of 8 and 12)\n",
      "\n",
      "One-to-One Connectivity (Different Sizes, Circular):\n",
      "==================================================\n",
      "Pre size: 8, Post size: 12\n",
      "Connections: 12\n",
      "Connection pairs (pre → post):\n",
      "  0 → 0\n",
      "  1 → 1\n",
      "  2 → 2\n",
      "  3 → 3\n",
      "  4 → 4\n",
      "  5 → 5\n",
      "  6 → 6\n",
      "  7 → 7\n",
      "  0 → 8\n",
      "  1 → 9\n",
      "  2 → 10\n",
      "  3 → 11\n",
      "Note: Pre indices wrap around using modulo (% 8)\n"
     ]
    }
   ],
   "execution_count": 8
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 5. Working with Weights and Delays <a name=\"weights-delays\"></a>\n",
    "\n",
    "Synaptic weights and delays are crucial for realistic neural network simulations. `braintools.conn` supports flexible initialization through the `braintools.init` module.\n",
    "\n",
    "### 5.1 Constant Weights and Delays\n",
    "\n",
    "The simplest approach uses constant values with physical units:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:00:56.111913Z",
     "start_time": "2025-10-01T16:00:55.836357Z"
    }
   },
   "source": [
    "# Random connectivity with constant weights and delays\n",
    "conn_const = conn.Random(\n",
    "    prob=0.1,\n",
    "    weight=Constant(1.5 * u.nS),  # Synaptic conductance\n",
    "    delay=Constant(2.0 * u.ms),   # Transmission delay\n",
    "    seed=42\n",
    ")\n",
    "\n",
    "result_const = conn_const(pre_size=50, post_size=50)\n",
    "\n",
    "print(\"Connectivity with Constant Weights and Delays:\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Number of connections: {len(result_const.pre_indices)}\")\n",
    "print(f\"\\nWeight statistics:\")\n",
    "print(f\"  Mean: {np.mean(result_const.weights)}\")\n",
    "print(f\"  Std:  {np.std(result_const.weights)}\")\n",
    "print(f\"  All weights are identical: {np.all(result_const.weights == result_const.weights[0])}\")\n",
    "print(f\"\\nDelay statistics:\")\n",
    "print(f\"  Mean: {np.mean(result_const.delays)}\")\n",
    "print(f\"  Std:  {np.std(result_const.delays)}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Connectivity with Constant Weights and Delays:\n",
      "==================================================\n",
      "Number of connections: 263\n",
      "\n",
      "Weight statistics:\n",
      "  Mean: 1.5 * nsiemens\n",
      "  Std:  0.0 * nsiemens\n",
      "  All weights are identical: True\n",
      "\n",
      "Delay statistics:\n",
      "  Mean: 2.0 * msecond\n",
      "  Std:  0.0 * msecond\n"
     ]
    }
   ],
   "execution_count": 9
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.2 Stochastic Weight Distributions\n",
    "\n",
    "More realistic networks use stochastic weight distributions:\n",
    "\n",
    "#### Normal Distribution"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:00:57.429985Z",
     "start_time": "2025-10-01T16:00:57.292628Z"
    }
   },
   "source": [
    "# Normal (Gaussian) distribution\n",
    "conn_normal = conn.Random(\n",
    "    prob=0.15,\n",
    "    weight=Normal(mean=1.0 * u.nS, std=0.2 * u.nS),\n",
    "    delay=Normal(mean=1.5 * u.ms, std=0.3 * u.ms),\n",
    "    seed=42\n",
    ")\n",
    "\n",
    "result_normal = conn_normal(pre_size=100, post_size=100)\n",
    "\n",
    "print(\"Normal Distribution Weights and Delays:\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Number of connections: {len(result_normal.pre_indices)}\")\n",
    "print(f\"\\nWeight statistics:\")\n",
    "print(f\"  Mean: {np.mean(result_normal.weights):.3f}\")\n",
    "print(f\"  Std:  {np.std(result_normal.weights):.3f}\")\n",
    "print(f\"  Min:  {np.min(result_normal.weights):.3f}\")\n",
    "print(f\"  Max:  {np.max(result_normal.weights):.3f}\")\n",
    "print(f\"\\nDelay statistics:\")\n",
    "print(f\"  Mean: {np.mean(result_normal.delays):.3f}\")\n",
    "print(f\"  Std:  {np.std(result_normal.delays):.3f}\")\n",
    "print(f\"  Min:  {np.min(result_normal.delays):.3f}\")\n",
    "print(f\"  Max:  {np.max(result_normal.delays):.3f}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Normal Distribution Weights and Delays:\n",
      "==================================================\n",
      "Number of connections: 1515\n",
      "\n",
      "Weight statistics:\n",
      "  Mean: 1.004 * nsiemens\n",
      "  Std:  0.201 * nsiemens\n",
      "  Min:  0.233 * nsiemens\n",
      "  Max:  1.675 * nsiemens\n",
      "\n",
      "Delay statistics:\n",
      "  Mean: 1.493 * msecond\n",
      "  Std:  0.291 * msecond\n",
      "  Min:  0.323 * msecond\n",
      "  Max:  2.374 * msecond\n"
     ]
    }
   ],
   "execution_count": 10
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Uniform Distribution"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:01:14.553789Z",
     "start_time": "2025-10-01T16:01:14.537669Z"
    }
   },
   "source": [
    "# Uniform distribution\n",
    "conn_uniform = conn.Random(\n",
    "    prob=0.15,\n",
    "    weight=Uniform(low=0.5 * u.nS, high=2.0 * u.nS),\n",
    "    delay=Uniform(low=0.5 * u.ms, high=3.0 * u.ms),\n",
    "    seed=42\n",
    ")\n",
    "\n",
    "result_uniform = conn_uniform(pre_size=100, post_size=100)\n",
    "\n",
    "print(\"Uniform Distribution Weights and Delays:\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Weight range: [0.5, 2.0] nS\")\n",
    "print(f\"  Mean: {np.mean(result_uniform.weights):.3f}\")\n",
    "print(f\"  Std:  {np.std(result_uniform.weights):.3f}\")\n",
    "print(f\"  Min:  {np.min(result_uniform.weights):.3f}\")\n",
    "print(f\"  Max:  {np.max(result_uniform.weights):.3f}\")\n",
    "print(f\"\\nDelay range: [0.5, 3.0] ms\")\n",
    "print(f\"  Mean: {np.mean(result_uniform.delays):.3f}\")\n",
    "print(f\"  Std:  {np.std(result_uniform.delays):.3f}\")\n",
    "print(f\"  Min:  {np.min(result_uniform.delays):.3f}\")\n",
    "print(f\"  Max:  {np.max(result_uniform.delays):.3f}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uniform Distribution Weights and Delays:\n",
      "==================================================\n",
      "Weight range: [0.5, 2.0] nS\n",
      "  Mean: 1.258 * nsiemens\n",
      "  Std:  0.432 * nsiemens\n",
      "  Min:  0.500 * nsiemens\n",
      "  Max:  2.000 * nsiemens\n",
      "\n",
      "Delay range: [0.5, 3.0] ms\n",
      "  Mean: 1.749 * msecond\n",
      "  Std:  0.729 * msecond\n",
      "  Min:  0.500 * msecond\n",
      "  Max:  2.998 * msecond\n"
     ]
    }
   ],
   "execution_count": 12
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Log-Normal Distribution\n",
    "\n",
    "Log-normal distributions are common in biological synaptic weights:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:01:59.437821Z",
     "start_time": "2025-10-01T16:01:59.366569Z"
    }
   },
   "source": [
    "# Log-normal distribution (common in biological synapses)\n",
    "conn_lognormal = conn.Random(\n",
    "    prob=0.15,\n",
    "    weight=LogNormal(mean=1.0 * u.nS, std=0.5 * u.nS),\n",
    "    delay=Constant(1.0 * u.ms),\n",
    "    seed=42\n",
    ")\n",
    "\n",
    "result_lognormal = conn_lognormal(pre_size=100, post_size=100)\n",
    "\n",
    "print(\"Log-Normal Distribution Weights:\")\n",
    "print(\"=\" * 50)\n",
    "print(f\"Weight statistics:\")\n",
    "print(f\"  Mean: {np.mean(result_lognormal.weights):.3f}\")\n",
    "print(f\"  Std:  {np.std(result_lognormal.weights):.3f}\")\n",
    "print(f\"  Median: {u.math.median(result_lognormal.weights):.3f}\")\n",
    "print(f\"  Min:  {np.min(result_lognormal.weights):.3f}\")\n",
    "print(f\"  Max:  {np.max(result_lognormal.weights):.3f}\")\n",
    "print(f\"\\nNote: Log-normal has positive skew (long tail)\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log-Normal Distribution Weights:\n",
      "==================================================\n",
      "Weight statistics:\n",
      "  Mean: 1.011 * nsiemens\n",
      "  Std:  0.507 * nsiemens\n",
      "  Median: 0.898 * nsiemens\n",
      "  Min:  0.146 * nsiemens\n",
      "  Max:  4.410 * nsiemens\n",
      "\n",
      "Note: Log-normal has positive skew (long tail)\n"
     ]
    }
   ],
   "execution_count": 14
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.3 Visualizing Weight Distributions\n",
    "\n",
    "Let's compare the different weight distributions visually using `braintools.visualize`:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:04:01.351767Z",
     "start_time": "2025-10-01T16:04:01.042890Z"
    }
   },
   "source": [
    "# Extract weight values (remove units for plotting)\n",
    "weights_normal = u.get_mantissa(result_normal.weights)\n",
    "weights_uniform = u.get_mantissa(result_uniform.weights)\n",
    "weights_lognormal = u.get_mantissa(result_lognormal.weights)\n",
    "\n",
    "# Create figure with subplots\n",
    "fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n",
    "\n",
    "# Plot each distribution using vis.distribution_plot\n",
    "vis.distribution_plot(\n",
    "    weights_normal,\n",
    "    bins=30,\n",
    "    alpha=0.7,\n",
    "    colors=['blue'],\n",
    "    edgecolor='black',\n",
    "    ax=axes[0],\n",
    "    xlabel='Weight (nS)',\n",
    "    title='Normal Distribution'\n",
    ")\n",
    "\n",
    "vis.distribution_plot(\n",
    "    weights_uniform,\n",
    "    bins=30,\n",
    "    alpha=0.7,\n",
    "    colors=['green'],\n",
    "    edgecolor='black',\n",
    "    ax=axes[1],\n",
    "    xlabel='Weight (nS)',\n",
    "    title='Uniform Distribution'\n",
    ")\n",
    "\n",
    "vis.distribution_plot(\n",
    "    weights_lognormal,\n",
    "    bins=30,\n",
    "    alpha=0.7,\n",
    "    colors=['orange'],\n",
    "    edgecolor='black',\n",
    "    ax=axes[2],\n",
    "    xlabel='Weight (nS)',\n",
    "    title='Log-Normal Distribution'\n",
    ")\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nKey Observations:\")\n",
    "print(\"- Normal: Symmetric around mean\")\n",
    "print(\"- Uniform: Flat distribution within range\")\n",
    "print(\"- Log-Normal: Right-skewed with long tail (biologically realistic)\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1500x400 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",
      "Key Observations:\n",
      "- Normal: Symmetric around mean\n",
      "- Uniform: Flat distribution within range\n",
      "- Log-Normal: Right-skewed with long tail (biologically realistic)\n"
     ]
    }
   ],
   "execution_count": 19
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 6. Visualizing Connectivity <a name=\"visualization\"></a>\n",
    "\n",
    "Visualization helps us understand connectivity patterns. We'll use `braintools.visualize` for professional-quality plots.\n",
    "\n",
    "### 6.1 Connectivity Matrix\n",
    "\n",
    "A connectivity matrix shows which neurons connect to which. We'll use `vis.connectivity_matrix()`:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:04:10.760149Z",
     "start_time": "2025-10-01T16:04:10.524069Z"
    }
   },
   "source": [
    "def result_to_matrix(result):\n",
    "    \"\"\"Convert ConnectionResult to connectivity matrix.\"\"\"\n",
    "    pre_size = result.pre_size if isinstance(result.pre_size, int) else int(np.prod(result.pre_size))\n",
    "    post_size = result.post_size if isinstance(result.post_size, int) else int(np.prod(result.post_size))\n",
    "    \n",
    "    conn_matrix = np.zeros((pre_size, post_size))\n",
    "    conn_matrix[result.pre_indices, result.post_indices] = 1\n",
    "    \n",
    "    return conn_matrix\n",
    "\n",
    "# Compare different patterns\n",
    "conn_patterns = [\n",
    "    (conn.Random(prob=0.2, seed=42), \"Random (prob=0.2)\"),\n",
    "    (conn.AllToAll(include_self_connections=False), \"All-to-All\"),\n",
    "    (conn.OneToOne(), \"One-to-One\"),\n",
    "]\n",
    "\n",
    "fig, axes = plt.subplots(1, 3, figsize=(18, 5))\n",
    "\n",
    "for idx, (conn_pattern, name) in enumerate(conn_patterns):\n",
    "    result = conn_pattern(pre_size=30, post_size=30)\n",
    "    conn_mat = result_to_matrix(result)\n",
    "    \n",
    "    vis.connectivity_matrix(\n",
    "        conn_mat,\n",
    "        cmap='binary',\n",
    "        center_zero=False,\n",
    "        show_colorbar=False,\n",
    "        ax=axes[idx],\n",
    "        title=name\n",
    "    )\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1800x500 with 3 Axes>"
      ],
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 20
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.2 Weight Matrix Visualization\n",
    "\n",
    "When weights are present, we can visualize their distribution in the connectivity matrix:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:04:22.682005Z",
     "start_time": "2025-10-01T16:04:22.550700Z"
    }
   },
   "source": [
    "# Create connectivity with weights\n",
    "conn_weighted = conn.Random(\n",
    "    prob=0.2,\n",
    "    weight=LogNormal(mean=1.0 * u.nS, std=0.6 * u.nS),\n",
    "    seed=42\n",
    ")\n",
    "result_weighted = conn_weighted(pre_size=30, post_size=30)\n",
    "\n",
    "# Create weight matrix\n",
    "pre_size = 30\n",
    "post_size = 30\n",
    "weight_matrix = np.zeros((pre_size, post_size))\n",
    "weights = u.get_mantissa(result_weighted.weights)\n",
    "weight_matrix[result_weighted.pre_indices, result_weighted.post_indices] = weights\n",
    "\n",
    "# Plot using vis.connectivity_matrix\n",
    "fig, ax = plt.subplots(figsize=(10, 8))\n",
    "vis.connectivity_matrix(\n",
    "    weight_matrix,\n",
    "    cmap='viridis',\n",
    "    center_zero=False,\n",
    "    show_colorbar=True,\n",
    "    ax=ax,\n",
    "    title='Random Connectivity with Log-Normal Weights'\n",
    ")\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x800 with 2 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 21
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.3 Degree Distribution\n",
    "\n",
    "The degree distribution shows how many connections each neuron has:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:05:00.582430Z",
     "start_time": "2025-10-01T16:05:00.363028Z"
    }
   },
   "source": [
    "# Test with random connectivity\n",
    "conn_test = conn.Random(prob=0.15, seed=42)\n",
    "result_test = conn_test(pre_size=200, post_size=200)\n",
    "\n",
    "# Calculate degrees\n",
    "pre_size = 200\n",
    "post_size = 200\n",
    "out_degree = np.bincount(result_test.pre_indices, minlength=pre_size)\n",
    "in_degree = np.bincount(result_test.post_indices, minlength=post_size)\n",
    "\n",
    "# Plot using vis.distribution_plot\n",
    "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n",
    "\n",
    "vis.distribution_plot(\n",
    "    out_degree,\n",
    "    bins=20,\n",
    "    alpha=0.7,\n",
    "    colors=['blue'],\n",
    "    edgecolor='black',\n",
    "    ax=axes[0],\n",
    "    xlabel='Out-Degree (outgoing connections)',\n",
    "    ylabel='Count',\n",
    "    title='Out-Degree Distribution'\n",
    ")\n",
    "\n",
    "vis.distribution_plot(\n",
    "    in_degree,\n",
    "    bins=20,\n",
    "    colors=['green'],\n",
    "    edgecolor='black',\n",
    "    alpha=0.7,\n",
    "    ax=axes[1],\n",
    "    xlabel='In-Degree (incoming connections)',\n",
    "    ylabel='Count',\n",
    "    title='In-Degree Distribution'\n",
    ")\n",
    "\n",
    "plt.suptitle('Random Connectivity (prob=0.15)', fontsize=14, y=1.02)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(f\"Out-degree: mean={np.mean(out_degree):.2f}, std={np.std(out_degree):.2f}\")\n",
    "print(f\"In-degree:  mean={np.mean(in_degree):.2f}, std={np.std(in_degree):.2f}\")"
   ],
   "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": [
      "Out-degree: mean=29.86, std=4.74\n",
      "In-degree:  mean=29.86, std=5.55\n"
     ]
    }
   ],
   "execution_count": 22
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.4 Advanced Visualization: Correlation Matrix\n",
    "\n",
    "Let's visualize correlations between neurons' connectivity patterns:"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-01T16:05:04.601718Z",
     "start_time": "2025-10-01T16:05:04.452891Z"
    }
   },
   "source": [
    "# Create a network with some structure\n",
    "conn_struct = conn.Random(prob=0.15, seed=42)\n",
    "result_struct = conn_struct(pre_size=50, post_size=50)\n",
    "\n",
    "# Create connectivity matrix\n",
    "conn_mat = result_to_matrix(result_struct)\n",
    "\n",
    "# Sample subset for visualization clarity\n",
    "subset_size = 20\n",
    "conn_subset = conn_mat[:subset_size, :subset_size]\n",
    "\n",
    "# Plot correlation matrix\n",
    "fig, ax = plt.subplots(figsize=(10, 8))\n",
    "vis.correlation_matrix(\n",
    "    conn_subset,\n",
    "    method='pearson',\n",
    "    cmap='RdBu_r',\n",
    "    show_values=False,\n",
    "    ax=ax,\n",
    "    title='Connectivity Pattern Correlation (20×20 subset)'\n",
    ")\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nThis shows correlations between neurons' connectivity patterns.\")\n",
    "print(\"High correlation means neurons have similar connection patterns.\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x800 with 2 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "This shows correlations between neurons' connectivity patterns.\n",
      "High correlation means neurons have similar connection patterns.\n"
     ]
    }
   ],
   "execution_count": 23
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 7. Exercises <a name=\"exercises\"></a>\n",
    "\n",
    "Try these exercises to reinforce your understanding:\n",
    "\n",
    "### Exercise 1: Connection Probability Calibration\n",
    "\n",
    "Create a function that finds the connection probability needed to achieve a target number of connections:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_target_probability(pre_size, post_size, target_connections, tolerance=50, max_iterations=20):\n",
    "    \"\"\"\n",
    "    Find connection probability to achieve target number of connections.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    pre_size : int\n",
    "        Number of presynaptic neurons\n",
    "    post_size : int\n",
    "        Number of postsynaptic neurons\n",
    "    target_connections : int\n",
    "        Desired number of connections\n",
    "    tolerance : int\n",
    "        Acceptable deviation from target\n",
    "    max_iterations : int\n",
    "        Maximum search iterations\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    prob : float\n",
    "        Connection probability\n",
    "    actual : int\n",
    "        Actual connections achieved\n",
    "    \"\"\"\n",
    "    # YOUR CODE HERE\n",
    "    # Hint: Use binary search or gradient descent approach\n",
    "    # Start with initial probability estimate: target_connections / (pre_size * post_size)\n",
    "    \n",
    "    pass\n",
    "\n",
    "# Test your function\n",
    "# prob, actual = find_target_probability(pre_size=100, post_size=100, target_connections=1000)\n",
    "# print(f\"Target: 1000 connections\")\n",
    "# print(f\"Probability: {prob:.4f}\")\n",
    "# print(f\"Actual: {actual} connections\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2: Weight Scaling\n",
    "\n",
    "Create a custom weight initialization that scales weights inversely with the number of incoming connections (to maintain constant total input):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_scaled_weights(result, base_weight=1.0 * u.nS):\n",
    "    \"\"\"\n",
    "    Scale weights inversely with in-degree to maintain constant total input.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    result : ConnectionResult\n",
    "        Connectivity result\n",
    "    base_weight : Quantity\n",
    "        Base weight value\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    scaled_weights : array\n",
    "        Scaled weight array\n",
    "    \"\"\"\n",
    "    # YOUR CODE HERE\n",
    "    # Hint: Calculate in-degree for each post neuron\n",
    "    # Then scale weights: w_scaled = base_weight / in_degree\n",
    "    \n",
    "    pass\n",
    "\n",
    "# Test your function\n",
    "# conn_test = conn.Random(prob=0.1, seed=42)\n",
    "# result_test = conn_test(pre_size=100, post_size=100)\n",
    "# scaled_weights = create_scaled_weights(result_test, base_weight=1.0 * u.nS)\n",
    "# \n",
    "# # Verify constant total input\n",
    "# post_size = 100\n",
    "# total_inputs = np.zeros(post_size)\n",
    "# for post_idx in range(post_size):\n",
    "#     mask = result_test.post_indices == post_idx\n",
    "#     total_inputs[post_idx] = np.sum(u.get_mantissa(scaled_weights[mask]))\n",
    "# \n",
    "# print(f\"Total input per neuron - Mean: {np.mean(total_inputs):.3f}, Std: {np.std(total_inputs):.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 3: Connectivity Statistics\n",
    "\n",
    "Write a function that computes comprehensive connectivity statistics:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def analyze_connectivity(result):\n",
    "    \"\"\"\n",
    "    Compute comprehensive connectivity statistics.\n",
    "    \n",
    "    Should calculate:\n",
    "    - Connection density\n",
    "    - Mean/std of in-degree and out-degree\n",
    "    - Weight statistics (if present)\n",
    "    - Delay statistics (if present)\n",
    "    - Reciprocal connections (if pre_size == post_size)\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    stats : dict\n",
    "        Dictionary of statistics\n",
    "    \"\"\"\n",
    "    # YOUR CODE HERE\n",
    "    \n",
    "    pass\n",
    "\n",
    "# Test your function\n",
    "# conn_test = conn.Random(prob=0.15, weight=Normal(mean=1.0*u.nS, std=0.2*u.nS), seed=42)\n",
    "# result_test = conn_test(pre_size=100, post_size=100)\n",
    "# stats = analyze_connectivity(result_test)\n",
    "# \n",
    "# for key, value in stats.items():\n",
    "#     print(f\"{key}: {value}\")"
   ]
  }
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