Neuronal Avalanches: Where Temporal Complexity and Criticality Meet
  The model of the current paper is an extension of a previous publication, wherein we used the leaky integrate-and-fire model on a regular lattice with periodic boundary conditions, and introduced the temporal complexity as a genuine signature of criticality. In that work, the power-law distribution of neural avalanches was manifestation of supercriticality rather than criticality. Here, however, we show that continuous solution of the model and replacing the stochastic noise with a Gaussian zero-mean noise leads to the coincidence of power-law display of temporal complexity and spatiotemporal patterns of neural avalanches at the critical point. We conclude that the source of inconsistency may in fact be a numerical artifact originated by the discrete description of the model, which may imply slow numerical convergence of avalanche distribution compared to temporal complexity. 
Mohammad Dehghani Habibabadi, Marzieh Zare, Farhad Shahbazi, Javad   Usefie-Mafahim, Paolo Grigolini
cond-mat.dis-nn nlin.AO physics.bio-ph