Research Topics

Image processing

Modeling of Transport in Groundwater




I've got several research projects in progress, and I'm always ready to bring a student on board for an honor's thesis project or an independent study project. If you are interested, email me!



Research projects include mathematical ecology (especially the modeling of population dynamics), statistical modeling and analysis of DNA data, stochastic modeling of cell proliferation, and physiological modeling, dynamics, and control. These projects involve theoretical problems (including mathematical understanding of a model's behavior) as well as computational and data analysis aspects.

One ecology problem of particular interest involves distributions of rates (e.g., fecundity, mortality, growth) among individuals in a population. We have been working on theoretical understanding of principles such as "survival of the fittest" and evolutionary stability, as well as application problems requiring fits to data and optimization (for stocking and population control in aquatic applications).

A physiology problem containing some interesting mathematical questions is the modeling of cartilage. Cartilage behaves in a way that couples electrical and mechanical phenomena. Degradation from arthritis affects the electromechanical properties of cartilage in some specific ways. Modeling and simulation in this area will support sensor development for early detection of arthritis.



Statistical Methods of Image Processing

Problems ranging from the detection of tumors from Magnetic Resonance Imaging to the correction of atmospheric aberrations in astronomical imagery rely on mathematical and statistical techniques for analyzing imagery data. Current projects are closely related to tracking problems for the Air Borne Laser defense system. Images observed over time are used to determine pointing angles toward targets. Atmospheric turbulence causes disturbances that must be rejected by the control system. Using advanced image processing algorithms together with Bayesian statistical techniques, we can greatly improve the pointing accuracy of the Air Borne Laser system.