Critical Avalanches and Subsampling in Map-based Neural Networks
  We investigate the synaptic noise as a novel mechanism for creating critical avalanches in the activity of neural networks. We model neurons and chemical synapses by dynamical maps with a uniform noise term in the synaptic coupling. An advantage of utilizing maps is that the dynamical properties (action potential profile, excitability properties, post synaptic potential summation etc.) are not imposed to the system, but occur naturally by solving the system equations. We discuss the relevant neuronal and synaptic properties to achieve the critical state. We verify that networks of excitatory by rebound neurons with fast synapses present power law avalanches. We also discuss the measuring of neuronal avalanches by subsampling our data, shedding light on the experimental search for Self-Organized Criticality in neural networks. 
Mauricio Girardi-Schappo, Osame Kinouchi, Marcelo H. R. Tragtenberg
cond-mat.dis-nn nlin.AO physics.bio-ph q-bio.NC