Interest areas and publications
Probabilistic simulations
Computational studies of probabilistic systems implemented in R and C++. Most of these systems are related to mechanistic physiological problems, but focus on the qualitative nature of the random processes that govern their behavior. The dynamics of probabilistic cellular automata and Markov models are analyzed using techniques from nonlinear dynamics and stochastic processes.
Computational physiology
Models that employ combinations of differential equations, stochastic processes, and nonlinear dynamics are used for large-scale numerical simulations of human physiological processes in areas ranging from the molecular mechanisms in cardiac tissue to glucose-insulin dynamics to the pharmacokinetics of protein-based drugs. Models are mechanistic in nature, and an experimental approach is taken to study their behavior under varying conditions. Simulations are implemented in languages such as C++ and MATLAB, and in some cases are carried out on a high-performance computing cluster to produce detailed visual outputs.
Analysis of human performance and longitudinal outcome data
R, Stata, and SAS are used to analyze collected data from projects studying human performance in dance and weight training, and longitudinal outcomes in undergrauate computer science programs.
Research and Practice in Education
General approaches for investigations into undergraduate curriculum for students taking mathematics and statistics courses.