Scaling and Renormalization Group for models of neural activity

In certain conditions, brain activity shows patterns typical of systems poised at a critical point, such as scale-free avalanches. However, whether the behavior of large number of neurons emerges from an underlying critical dynamic remains unclear. The authors of reference [1] have recently proposed a phenomenological Renormalization Group approach to the activity of a network of neurons, where the coarse-grained variables are defined by means of the pairwise correlations of the system. This coarse-graining procedure suggests that a non-trivial fixed point exists and seems to generate clear signatures of scaling behavior. In order to shed a light on these results, our aim is to test this phenomenological RG in the context of the contact process, a simplified model for the spreading of activity. In particular, we are interested in exploring whether such signatures appear at a real critical point as well, there the underlying dynamic really is at the edge of an absorbing phase transition, and if this procedure is able to discriminate between different phases. 1. L. Meshulam, J.L. Gauthier, C.D. Brody, D.W. Tank, W. Bialek, arXiv:1812.11904