Global topological synchronization on simplicial and cell complexes

Abstract

Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However, the investigation of their collective phenomena is only at its infancy. Here we combine topology and nonlinear dynamics to determine the conditions for global synchronization of topological signals defined on simplicial or cell complexes. On simplicial complexes we show that topological obstruction impedes odd dimensional signals to globally synchronize. On the other hand, we show that cell complexes can overcome topological obstruction and in some structures signals of any dimension can achieve global synchronization.

Lorenzo Giambagli

PostDoc Department of Physics, Freie Universität Berlin

My research interests include Spectral analysis of Deep Neural Network (DNN), Structura Pruning, Bayesian Inference in DNN, Simplicial Complexes Dynamics, Theoretical Neuroscience