Math Modeling Seminar: Predicting neural network dynamics from graph structure

Math Modeling Seminar
Predicting neural network dynamics from graph structure

Dr. Katie Morrison
Associate Professor of Mathematical Sciences
University of Northern Colorado

You may attend this lecture in person at 2305 Gosnell Hall or virtually via Zoom.
If you’d like to attend virtually, you may register here for Zoom link.

Abstract:
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. We will then apply these theoretical results to produce a model CPG for quadruped gaits.

Speaker Bio:
Dr. Katie Morrison is an Associate Professor in the School of Mathematical Sciences at University of Northern Colorado. She received her BA from Swarthmore College, double majoring in mathematics and psychology, and her PhD in mathematics from the University of Nebraska. Her dissertation work was in algebraic coding theory, but she has since transitioned into mathematical neuroscience. Dr. Morrison’s current research focus is on the mathematical theory and analysis of neural networks and neural codes, using tools from algebra, discrete mathematics, differential equations, and topology. This work has been supported by an NIH BRAIN Initiative grant as well as two NSF mathematical biology grants.
Read more here.

Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.

The Math Modeling Seminar will recur each week throughout the semester on the same day and time. Find out more about upcoming speakers on the Mathematical Modeling Seminar Series webpage.
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