The observation of power-law distributed neuronal avalanche sizes has inspired the “critical brain hypothesis”, which holds that the brain self-organizes to the critical point of a phase transition. This is proposed to be optimal for computation. However, most models of self-organized criticality lose criticality if external input is significant, i.e., when there is no longer a separation between the initiation of new avalanches and the cascades of old avalanches. Therefore, the obvious question is: Can the brain retain criticality when it is subjected to external driving? Here, we answer in the affirmative by studying a minimal model for neural activity which includes external driving .
External driving introduces two problems: (i) independent cascades might be fallaciously lumped together as a single avalanche and (ii) initially independent cascades might coalesce if they grow large enough. These problems can be resolved by using the network structure to separate avalanches, and we find a critical point for even strong driving. We find that the onset of avalanche coalescence introduces new scaling behaviour for large avalanches. Additionally, global indicators of criticality that are missing network information, such as the branching ratio and the overall level of neural activity, do not capture criticality with driving.
 D. J. Korchinski, J. G. Orlandi, S.-W. Son, and J. Davidsen, Criticality in Spreading Processes without Timescale Separation and the Critical Brain Hypothesis, Phys. Rev. X 11, 021059 (2021).
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