Scale-Change Symmetry in the Rules Governing Neural Systems

Abstract

Similar universal phenomena can emerge in different complex systems when those systems share a common symmetry in their governing laws. In physical systems operating near a critical phase transition, the governing physical laws obey a fractal symmetry; they are the same whether considered at fine or coarse scales. This scale-change symmetry is responsible for universal critical phenomena found across diverse systems. Experiments suggest that the cerebral cortex can also operate near a critical phase transition. Thus we hypothesize that the laws governing cortical dynamics may obey scalechange symmetry. Here we develop a practical approach to test this hypothesis. We confirm, using two different computational models, that neural dynamical laws exhibit scale-change symmetry near a dynamical phase transition. Moreover, we show that as a mouse awakens from anesthesia, scale-change symmetry emerges. Scale-change symmetry of the rules governing cortical dynamics may explain observations of similar critical phenomena across diverse neural systems.

Fractal brain dynamics: from Mandelbrot to marmosets

“…Indeed, critical dynamics manifest with diverse scales of complex spatiotemporal dynamics, with occasional bouts of synchrony among diverse groups of neurons. According to theory, critical dynamics should also have fractal structure with essential contributions from a wide range of spatial and temporal scales (for example: Linkenkaer-Hansen et al 2001;Muñoz, 2018;Agrawal et al 2019). In this context, the fractal dynamics observed by Munn et al are consistent with the criticality hypothesis.…”