Special Condensed Matter Physics Seminar: Using random matrices to understand collective network dynamics, and vice versa

Abstract:

Motivated by experiments that highlight the heterogeneity of connectivity in the brain, we study the dynamics of neural networks with partially structured and partially random connectivity. These networks undergo a phase transition from a single fixed point to chaos, related to a large increase in the computational capacity. Surprisingly, finding the critical point of this transition leads to a new result in mathematics - the spectral radius of the network's connectivity matrix.