Research & Publications

The nematode C. elegans has a fully mapped connectome and can be imaged neuron by neuron, which makes it a test bed for connecting network structure to behavior. I build models, constrained by the connectome and fit to whole-brain imaging, of how neural activity switches the worm between behavioral states such as forward and reverse locomotion. Current work uses community detection and dimensionality reduction to find low-dimensional descriptions of these dynamics, and calibrated matching methods to identify neurons in whole-brain recordings. Earlier work studied memory retrieval in damaged Hopfield networks.

Koopman eigenfunctions turn a nonlinear system into a linear one in new coordinates. When those eigenfunctions can be found exactly, so can the solution of the ODE. I construct eigenfunctions from invariant manifolds, and in collaboration with Sonja Petrović, I study which polynomial ODEs have rational eigenfunctions and hence closed-form solutions.

Methods such as SINDy discover governing equations from data, but in biology data are often scarce while the library of candidate models is large. My group studies when the correct model can be identified in this regime, and how to choose sampling strategies that give the most information for model selection. Earlier work used discovered models to design control signals.

In signed networks, ties can be friendly or hostile. With Michael Gabbay and Nathan Kutz I studied structural balance dynamics on these networks: when communities can be detected, which factions emerge, and how a network of states can tip abruptly from peace into systemic war.