Published: Nov. 8, 2019

Katherine Morrison, School of Mathematical Sciences, University of Northern Colorado Predicting neural network dynamics from graph structure Neural networks often exhibit complex patterns of activity that are shaped by the intrinsic structure of the network. For example, spontaneous sequences of neural activity have been observed in cortex and hippocampus, and patterned motor activity arises in central pattern generators for locomotion. In this talk, we will focus on a simplified neural network model known as Combinatorial Threshold-Linear Networks (CTLNs) in order to understand how the pattern of neural connectivity, as encoded by a directed graph, shapes the emergent nonlinear dynamics of the corresponding network. We will see that important aspects of these dynamics are controlled by the stable and unstable fixed points of the network, and show how these fixed points can be determined via graph-based rules.