Studies on the Interplay between the Network Architecture and the Dynamical Criticality of the Brain

The critical brain hypothesis is a theory in neuroscience that suggests that the brain operates near a critical point between stability and instability where quantities like information flow diverge. In this thesis, we explore the brain's functional robustness and how its critical behavior relies on the structural components of its network. We demonstrate that the critical behavior of the brain network is linked to its Laplacian spectrum. Furthermore, we show that the brain's architecture can be reconstructed using Laplacian-based information maximization rewiring steps, referred to as adaptive rewiring. Through adaptive rewirings, the brain network undergoes an entropic phase transition, which allows it to maximize its functional abilities. These findings suggest a profound connection between the brain's structural determinants and its operational efficacy at the edge of criticality.