Predicting Neural Network Dynamics via Graphical Analysis

Katherine Morrison, Carina Curto

Research output: Chapter in Book/Report/Conference proceedingChapter

13 Scopus citations

Abstract

Neural network models in neuroscience allow one to study how the connections between neurons shape the activity of neural circuits in the brain. In this chapter, we study Combinatorial Threshold-Linear Networks in order to understand how the pattern of connectivity, as encoded by a directed graph, shapes the emergent nonlinear dynamics of the corresponding network. Important aspects of these dynamics are controlled by the stable and unstable fixed points of the network, and we show how these fixed points can be determined via graph-based rules. We also present an algorithm for predicting sequences of neural activation from the underlying directed graph, and examine the effect of graph symmetries on a network’s set of attractors.

Original languageEnglish (US)
Title of host publicationAlgebraic and Combinatorial Computational Biology
PublisherElsevier
Pages241-277
Number of pages37
ISBN (Electronic)9780128140666
ISBN (Print)9780128140697
DOIs
StatePublished - Jan 1 2018

All Science Journal Classification (ASJC) codes

  • General Mathematics

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