Measuring neuronal avalanches in disordered systems with absorbing states

TL;DR

This paper compares two definitions of neuronal avalanches in models and experiments, showing both can produce power-law distributions at criticality, but experimental definitions may suggest criticality outside the true critical region.

Contribution

It demonstrates that experimental avalanche definitions can produce power-law distributions even outside the critical point, highlighting the importance of definition choice.

Findings

Both avalanche definitions yield power-law distributions at criticality.

Experimental avalanche definition can produce power-laws outside the critical region.

Results depend on specific model details.

Abstract

Power-law-shaped avalanche-size distributions are widely used to probe for critical behavior in many different systems, particularly in neural networks. The definition of avalanche is ambiguous. Usually, theoretical avalanches are defined as the activity between a stimulus and the relaxation to an inactive absorbing state. On the other hand, experimental neuronal avalanches are defined by the activity between consecutive silent states. We claim that the latter definition may be extended to some theoretical models to characterize their power-law avalanches and critical behavior. We study a system in which the separation of driving and relaxation time scales emerges from its structure. We apply both definitions of avalanche to our model. Both yield power-law-distributed avalanches that scale with system size in the critical point as expected. Nevertheless, we find restricted power-law-distributed avalanches outside of the critical region within the experimental procedure, which is not expected by the standard theoretical definition. We remark that these results are dependent on the model details.