Rounding of abrupt phase transitions in brain networks

TL;DR

This paper demonstrates that critical-like behavior in brain networks is robust and can emerge from hierarchical organization, with phase transitions becoming continuous in low-dimensional or disordered networks, explaining observed neural criticality.

Contribution

It reveals how hierarchical brain network structures cause rounding of phase transitions, enabling criticality despite models predicting discontinuous transitions.

Findings

Criticality is robust due to hierarchical organization.

Discontinuous transitions become continuous in low-dimensional or disordered networks.

Results explain observed critical behavior in brain activity measurements.

Abstract

The observation of critical-like behavior in cortical networks represents a major step forward in elucidating how the brain manages information. Understanding the origin and functionality of critical-like dynamics, as well as their robustness, is a major challenge in contemporary neuroscience. Here, we present an extensive numerical study of a family of simple dynamic models, which describe activity propagation in brain networks through the integration of different neighboring spiking potentials, mimicking basic neural interactions. The requirement of signal integration may lead to discontinuous phase transitions in networks that are well described by the mean field approximation, thus preventing the emergence of critical points in such systems. Here we show that criticality in the brain is instead robust, as a consequence of the hierarchical organization of the higher layers of cortical networks, which signals a departure from the mean-field paradigm. We show that, in finite-dimensional hierarchical networks, discontinuous phase transitions exhibit a rounding phenomenon and turn continuous for values of the topological dimension $D\le 2$, due to the presence of structural or topological disorder. Our results may prove significant in explaining the observation of traits of critical behavior in large-scale measurements of brain activity.