My research is devoted to understanding biological clocks. I use techniques from many fields, including computer simulation, detailed mathematical modeling and mathematical analysis, to understand biological timekeeping. My research aims to generate predictions that can be experimentally verified. I study the mathematics of physiological factors which affect human performance such as sleep, proper timing by our internal daily (circadian) clock, and mood regulation. Applications of this work include an app to help travelers avoid jet lag, analysis of the sleep and circadian patterns of medical interns, and comparisons of performances of the Trio Sonatas by J. S. Bach.

My students, post-docs and I develop novel algorithms to measure these factors in the real world from smartphones, wearables or other sensors. This data has low signal to noise ratios, contains large gaps which create mathematical artifacts, and is masked by unexpected real-world events. I am also particularly interested how physiology, e.g., neuropeptide regulation, the electrical activity of neurons, and cellular biochemistry, affects human performance.  To understand this physiology, as well as differences that arise due to genetics or pharmacological intervention, we develop large-scale models to bridge scales from the genome to human behavior. Much of my time focuses on applying mathematical techniques from dynamical systems, numerical methods and machine learning to simulate and analyze such large-scale models, often using graphics processing units.