effective-plasticity

name	effective-plasticity
description	Network-based framework for quantifying plasticity as system_size/connectivity_ratio. Defines effective plasticity as normalized measure linked to critical regime. Plasticity drives criticality causally. Activation: effective plasticity, plasticity quantification, network plasticity measure, plasticity criticality, system size connectivity, Branchi plasticity.

Effective Plasticity: Network-Based Quantification Framework

Operationalizes plasticity as the ratio between system size and connectivity strength, defining effective plasticity as a normalized measure that links structural properties to dynamical regimes, with plasticity driving criticality.

Metadata

• Source: arXiv:2603.25180
• Authors: Igor Branchi
• Published: 2026-03-26
• Categories: q-bio.NC, cond-mat.dis-nn, cond-mat.stat-mech, nlin.AO, physics.bio-ph

Core Methodology

Key Innovation

Plasticity is transformed from a descriptive, retrospective concept into a predictive, quantitative measure by formalizing it as:

Plasticity = System_Size / Connectivity_Strength

Where:

• System size determines the dimensionality of the accessible state space
• Connectivity strength tunes the system's dynamical regime
• Effective plasticity emerges at intermediate connectivity, coinciding with the critical regime

Technical Framework

1. Define system size (N): Number of elements/nodes in the network
2. Define connectivity strength (C): Average coupling/interaction strength among elements
3. Compute plasticity ratio: P = N / C
4. Identify critical regime: The optimal range where P balances capacity for change vs. capacity to maintain coherence
5. Normalize as effective plasticity: Use critical regime as theoretically motivated benchmark

Causal Relationship: Plasticity → Criticality

The framework establishes that plasticity drives criticality, not merely accompanies it:

• Plasticity acts as a structural tuning parameter for criticality
• Larger systems can more robustly maintain critical dynamics through this relationship
• The relationship is causal: adjusting plasticity parameters shifts the system toward or away from criticality

Distinguishing Regime Shifts vs. Phase Changes

The framework distinguishes:

• Functional regime shifts: Changes in dynamic repertoire driven by plasticity tuning
• Thermodynamic phase changes: Physical state transitions

Plasticity is the system-level regulator that shapes and constrains the dynamic repertoire.

Applications

• Cross-system comparison: Normalized effective plasticity enables comparing adaptive efficacy across diverse systems (neural, ecological, economic, social)
• Psychopathology prediction: Anticipates transitions between mental states before they occur
• Neural network design: Optimal connectivity for balancing learning capacity and stability
• Complexity science: Unified measure for adaptive systems across domains
• Criticality engineering: Using plasticity as control knob for critical dynamics

Implementation Guide

Step-by-Step Analysis

1. Map the network: Identify nodes (N) and edges with weights
2. Compute system size: Count effective degrees of freedom
3. Estimate connectivity strength: Average absolute weight or coupling parameter
4. Calculate plasticity ratio: P = N / C
5. Compare to critical benchmark: Is P in the intermediate range associated with critical dynamics?
6. Track over time: Monitor how P changes and predict regime transitions

Code Example

import numpy as np

def compute_effective_plasticity(adjacency_matrix):
    """
    Compute effective plasticity from network adjacency matrix.
    
    Args:
        adjacency_matrix: N×N matrix of connection strengths
    
    Returns:
        plasticity_ratio, connectivity_strength, system_size
    """
    N = adjacency_matrix.shape[0]  # System size
    # Connectivity strength: mean absolute off-diagonal weight
    mask = ~np.eye(N, dtype=bool)
    C = np.mean(np.abs(adjacency_matrix[mask]))
    
    plasticity = N / C if C > 0 else float('inf')
    return plasticity, C, N

def is_critical(plasticity_ratio, critical_bounds=(0.5, 2.0)):
    """Check if system is in critical regime."""
    return critical_bounds[0] <= plasticity_ratio <= critical_bounds[1]

Pitfalls

• Domain-specific calibration: Critical bounds may vary across domains; use empirical calibration
• Dynamic systems: For time-varying networks, compute plasticity in sliding windows
• Not a standalone metric: Effective plasticity should be combined with dynamical analysis (Lyapunov exponents, etc.)
• Cross-domain comparison: Requires careful normalization of system size definition across domains

Related Skills

• complex-system-robustness-collapse
• brain-criticality-assessment
• brain-criticality-hypothesis-assessment
• brain-criticality-milro-assessment
• hierarchical-brain-criticality
• griffiths-phase-brain-criticality
• stochastic-synaptic-plasticity
• neuromodulated-synaptic-plasticity
• synaptic-weight-distributions-plasticity-geometry