Move LaTeX files into paper1 subfolder and add paper2 folder

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

LaTeX/paper1/activation_spreading.py

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+"""
+Simulate and visualize activation spreading in the Slipnet (Figure 2)
+Shows differential decay rates based on conceptual depth
+"""
+
+import matplotlib.pyplot as plt
+import numpy as np
+import networkx as nx
+from matplotlib.gridspec import GridSpec
+
+# Define simplified Slipnet structure
+nodes_with_depth = {
+    'sameness': 80,  # Initial activation source
+    'samenessGroup': 80,
+    'identity': 90,
+    'letterCategory': 30,
+    'a': 10, 'b': 10, 'c': 10,
+    'predecessor': 50,
+    'successor': 50,
+    'bondCategory': 80,
+    'left': 40,
+    'right': 40,
+}
+
+edges_with_strength = [
+    ('sameness', 'samenessGroup', 30),
+    ('sameness', 'identity', 50),
+    ('sameness', 'bondCategory', 40),
+    ('samenessGroup', 'letterCategory', 50),
+    ('letterCategory', 'a', 97),
+    ('letterCategory', 'b', 97),
+    ('letterCategory', 'c', 97),
+    ('predecessor', 'bondCategory', 60),
+    ('successor', 'bondCategory', 60),
+    ('sameness', 'bondCategory', 30),
+    ('left', 'right', 80),
+]
+
+# Create graph
+G = nx.Graph()
+for node, depth in nodes_with_depth.items():
+    G.add_node(node, depth=depth, activation=0.0, buffer=0.0)
+
+for src, dst, link_len in edges_with_strength:
+    G.add_edge(src, dst, length=link_len, strength=100-link_len)
+
+# Initial activation
+G.nodes['sameness']['activation'] = 100.0
+
+# Simulate activation spreading with differential decay
+def simulate_spreading(G, num_steps):
+    history = {node: [] for node in G.nodes()}
+
+    for step in range(num_steps):
+        # Record current state
+        for node in G.nodes():
+            history[node].append(G.nodes[node]['activation'])
+
+        # Decay phase
+        for node in G.nodes():
+            depth = G.nodes[node]['depth']
+            activation = G.nodes[node]['activation']
+            decay_rate = (100 - depth) / 100.0
+            G.nodes[node]['buffer'] -= activation * decay_rate
+
+        # Spreading phase (if fully active)
+        for node in G.nodes():
+            if G.nodes[node]['activation'] >= 95.0:
+                for neighbor in G.neighbors(node):
+                    strength = G[node][neighbor]['strength']
+                    G.nodes[neighbor]['buffer'] += strength
+
+        # Apply buffer
+        for node in G.nodes():
+            G.nodes[node]['activation'] = max(0, min(100,
+                G.nodes[node]['activation'] + G.nodes[node]['buffer']))
+            G.nodes[node]['buffer'] = 0.0
+
+    return history
+
+# Run simulation
+history = simulate_spreading(G, 15)
+
+# Create visualization
+fig = plt.figure(figsize=(16, 10))
+gs = GridSpec(2, 3, figure=fig, hspace=0.3, wspace=0.3)
+
+# Time snapshots: t=0, t=5, t=10
+time_points = [0, 5, 10]
+positions = nx.spring_layout(G, k=1.5, iterations=50, seed=42)
+
+for idx, t in enumerate(time_points):
+    ax = fig.add_subplot(gs[0, idx])
+
+    # Get activations at time t
+    node_colors = [history[node][t] for node in G.nodes()]
+
+    # Draw graph
+    nx.draw_networkx_edges(G, positions, alpha=0.3, width=2, ax=ax)
+    nodes_drawn = nx.draw_networkx_nodes(G, positions,
+                                         node_color=node_colors,
+                                         node_size=800,
+                                         cmap='hot',
+                                         vmin=0, vmax=100,
+                                         ax=ax)
+    nx.draw_networkx_labels(G, positions, font_size=8, font_weight='bold', ax=ax)
+
+    ax.set_title(f'Time Step {t}', fontsize=12, fontweight='bold')
+    ax.axis('off')
+
+    if idx == 2:  # Add colorbar to last subplot
+        cbar = plt.colorbar(nodes_drawn, ax=ax, fraction=0.046, pad=0.04)
+        cbar.set_label('Activation', rotation=270, labelpad=15)
+
+# Bottom row: activation time series for key nodes
+ax_time = fig.add_subplot(gs[1, :])
+
+# Plot activation over time for nodes with different depths
+nodes_to_plot = [
+    ('sameness', 'Deep (80)', 'red'),
+    ('predecessor', 'Medium (50)', 'orange'),
+    ('letterCategory', 'Shallow (30)', 'blue'),
+    ('a', 'Very Shallow (10)', 'green'),
+]
+
+time_steps = range(15)
+for node, label, color in nodes_to_plot:
+    ax_time.plot(time_steps, history[node], marker='o', label=label,
+                linewidth=2, color=color)
+
+ax_time.set_xlabel('Time Steps', fontsize=12)
+ax_time.set_ylabel('Activation Level', fontsize=12)
+ax_time.set_title('Activation Dynamics: Differential Decay by Conceptual Depth',
+                 fontsize=13, fontweight='bold')
+ax_time.legend(title='Node (Depth)', fontsize=10)
+ax_time.grid(True, alpha=0.3)
+ax_time.set_xlim([0, 14])
+ax_time.set_ylim([0, 105])
+
+# Add annotation
+ax_time.annotate('Deep nodes decay slowly\n(high conceptual depth)',
+                xy=(10, history['sameness'][10]), xytext=(12, 70),
+                arrowprops=dict(arrowstyle='->', color='red', lw=1.5),
+                fontsize=10, color='red')
+ax_time.annotate('Shallow nodes decay rapidly\n(low conceptual depth)',
+                xy=(5, history['a'][5]), xytext=(7, 35),
+                arrowprops=dict(arrowstyle='->', color='green', lw=1.5),
+                fontsize=10, color='green')
+
+fig.suptitle('Activation Spreading with Differential Decay\n' +
+             'Formula: decay = activation × (100 - conceptual_depth) / 100',
+             fontsize=14, fontweight='bold')
+
+plt.savefig('figure2_activation_spreading.pdf', dpi=300, bbox_inches='tight')
+plt.savefig('figure2_activation_spreading.png', dpi=300, bbox_inches='tight')
+print("Generated figure2_activation_spreading.pdf and .png")
+plt.close()