My research interests are in mathematical biology, applied probability, neural networks, and population and evolutionary genetics. In particular, I develop and analyze mathematical models to understand the roles of stochasticity, structure, and evolution in shaping the dynamics of biological systems. Stochasticity is fundamental to gene expression and also plays an under-appreciated role in physiological regulation at larger scales, such as the regulation of sleep and wake behavior. My current work focuses on modeling the neuronal network structure and stochastic dynamics involved in sleep-wake regulation. I explore these issues using random graph theory, specifically looking at stochastic processes occurring on random graphs, and also by investigating the accuracy of predictions made by deterministic approximations of stochastic processes on networks.
At the molecular level, I study the evolution of gene regulation using population genetic models to understand how factors such as mutation and selection influence the rate of this evolutionary process. I am also examining the effects of stochasticity in gene regulatory networks. See the links above for more information.
Computational Biomathematics Lab
Case Western Reserve University
10900 Euclid Ave, 210 Yost Hall
Cleveland, OH 44106
Mathematical Biosciences Institute (Long Term Visitor)
Ohio State University
1735 Neil Ave, 375 Jennings Hall
Columbus, OH 43210