Subsampled directed-percolation models explain scaling relations experimentally observed in the brain

TL;DR

This study demonstrates that subsampled directed-percolation models within the same universality class as branching processes can reproduce experimental brain data, highlighting the importance of subsampling and data binning in interpreting critical exponents.

Contribution

The paper shows that subsampling and data binning in directed-percolation models can explain brain criticality data without requiring a different phase transition model.

Findings

Subsampling alters apparent critical exponents.

Experimental data matches models only near the phase transition.

Models reproduce key experimental scaling relations.

Abstract

Recent experimental results on spike avalanches measured in the urethane-anesthetized rat cortex have revealed scaling relations that indicate a phase transition at a specific level of cortical firing rate variability. The scaling relations point to critical exponents whose values differ from those of a branching process, which has been the canonical model employed to understand brain criticality. This suggested that a different model, with a different phase transition, might be required to explain the data. Here we show that this is not necessarily the case. By employing two different models belonging to the same universality class as the branching process (mean-field directed percolation) and treating the simulation data exactly like experimental data, we reproduce most of the experimental results. We find that subsampling the model and adjusting the time bin used to define avalanches (as done with experimental data) are sufficient ingredients to change the apparent exponents of the critical point. Moreover, experimental data is only reproduced within a very narrow range in parameter space around the phase transition.