Control Theory for C. elegans Calcium Imaging Dynamics

Abstract

This thesis contains several projects under two main headings: data-driven modeling, and C. elegans applications. Most of these works build to the main core of this thesis: applying novel control theoretic methods to C. elegans Calcium imaging data. Sparse optimization techniques are used to provide a unsupervised solution to a pervasive problem in complex systems modeling: some features of the data lie outside the modeling assumptions, which can distort the entire model and interpretations thereof. The method divides the time series into regions that are explainable within a given modeling framework (intrinsic dynamics) and those that are not (control signals), and mathematically characterizes how they affect each other. In addition, previously uncharacterized neurons are identified that encode these control signals, which can inform future experimental work. Other projects include advances to the underlying mathematical methods, as well as attempts to reconstruct network structure from data, along with significant caveats.