On the scaling of avalanche shape and activity power spectrum in neuronal networks

TL;DR

This study investigates how the activity power spectrum and avalanche shape scale in neuronal networks, confirming theoretical predictions at criticality and highlighting the spectrum's potential as a criticality indicator.

Contribution

The paper provides a numerical analysis linking avalanche profiles and power spectrum scaling in neuronal models, clarifying their behavior at and near criticality.

Findings

Avalanche profiles follow universal scaling at criticality.

Power spectrum exhibits Brown noise at criticality.

Near-critical systems show 1/f noise behavior.

Abstract

Many systems in Nature exhibit avalanche dynamics with scale-free features. A general scaling theory has been proposed for critical avalanche profiles in crackling noise, predicting the collapse onto a universal avalanche shape, as well as the scaling behaviour of the activity power spectrum as Brown noise. Recently, much attention has been given to the profile of neuronal avalanches, measured in neuronal systems in vitro and in vivo. Although a universal profile was evidenced, confirming the validity of the general scaling theory, the parallel study of the power spectrum scaling under the same conditions was not performed. The puzzling observation is that in the majority of healthy neuronal systems the power spectrum exhibits a behaviour close to $1/f$, rather than Brown, noise. Here we perform a numerical study of the scaling behaviour of avalanche shape and power spectrum for a model of integrate and fire neurons with a short-term plasticity parameter able to tune the system to criticality. We confirm that, at criticality, the average avalanche size and the avalanche profile fulfill the general avalanche scaling theory. However, the power spectrum consistently exhibits Brown noise behaviour, for both fully excitatory networks and systems with 30\% inhibitory networks. Conversely, a behaviour closer to $1/f$ noise is observed in systems slightly off-criticality. Results suggest that the power spectrum is a good indicator to determine how close neuronal activity is to criticality.