Finite-size correlation behavior near a critical point: a simple metric for monitoring the state of a neural network

TL;DR

This paper introduces a simple correlation metric, $$, to identify the critical dynamical state of neuronal networks by analyzing how correlation length scales with observation size, applicable to both models and real brain data.

Contribution

The paper proposes a novel correlation metric $$ for detecting criticality in neuronal networks, validated on models and experimental brain recordings.

Findings

$$ accurately identifies critical states in neuronal models.

The metric correlates well with neuronal avalanche analysis.

Potential for application with optical imaging techniques.

Abstract

In this article, a correlation metric $\kappa_C$ is proposed for the inference of the dynamical state of neuronal networks. $\kappa_C$ is computed from the scaling of the correlation length with the size of the observation region, which shows qualitatively different behavior near and away from the critical point of a continuous phase transition. The implementation is first studied on a neuronal network model, where the results of this new metric coincide with those obtained from neuronal avalanche analysis, thus well characterizing the critical state of the network. The approach is further tested with brain optogenetic recordings in behaving mice from a publicly available database. Potential applications and limitations for its use with currently available optical imaging techniques are discussed.