Brain Criticality Theory
Project Overview
This research explores the hypothesis that the brain operates at or near a critical state, similar to physical systems at phase transitions. Critical systems exhibit unique properties like long-range correlations, power-law distributions, and optimal information processing.
Using computational models based on statistical physics, we investigate how neural networks might self-organize toward criticality and how this affects information processing capabilities.
Interactive Demonstration: Ising Model
The Ising model is a fundamental model in statistical physics that exhibits a phase transition. It serves as a useful analogy for understanding criticality in neural systems. This interactive simulation demonstrates how systems behave differently at, below, and above the critical temperature.
Ising Model Monte Carlo Simulation
This simulation demonstrates the phase transition in the 2D Ising model. The critical temperature is around 2.269 (in units of J/k_B).
Below the critical temperature, the system exhibits spontaneous magnetization (ordered phase). Above the critical temperature, the system is in a disordered paramagnetic phase.
Note: This simulation uses the Metropolis algorithm for Monte Carlo sampling of the 2D Ising model with periodic boundary conditions.
Each Monte Carlo step attempts to flip N² spins, where N is the lattice size.
Key Findings
Optimal Information Processing
Systems at criticality maximize information transmission, storage, and processing capabilities, potentially explaining why the brain might operate near this regime.
Scale-Free Dynamics
Neural activity patterns in critical systems exhibit scale-free properties, similar to neurophysiological recordings from real brains.
Self-Organized Criticality
Our models demonstrate how neural networks can self-organize toward critical states through plasticity mechanisms and homeostatic regulation.
Implications
Understanding brain criticality has profound implications for neuroscience, artificial intelligence, and treating neurological disorders:
- New perspectives on neural information processing and brain function
- Insights into neurological disorders as deviations from critical states
- Design principles for more efficient artificial neural networks
- Novel therapeutic approaches targeting the restoration of critical dynamics