I am a mathematician, and my specialty is in the area broadly known as applied mathematics. This means I am generally interested in mathematical problems related to physics, chemistry, epidemiology, biology, engineering, and many other areas of science. The problems that arise are often too difficult to understand using "traditional" analytical mathematical tools, i.e., they can't be "solved by hand," and so most of my work involves solving these problems numerically with computer algorithms. My current position is as an analyst, applying the tools of mathematics to solve problems with military and industry applications. A particular project I am working on uses Bayesian networks to identify military targets from constantly updated (dynamic) data. The underlying theory utilizes statistical inference combined with graph theory and geometry to turn large amounts of noisy data into a useful and accurate prediction of the state of the system. My previous research focused on the field of nonlinear dynamics, which is essentially the study of interactions of complex systems and the prediction of patterns and phenomena that emerge from them. Within this area, I was focused on dynamical systems which are coupled, but where the communication/feedback involves a time delay or lag, and on stochastic (noisy) dynamical systems, where the noise may induce transitions in the observed patterns or behaviors of the system. Other research I previously engaged in involved the development a multicomponent model of biofilm growth and drug interaction, and the theory and modeling of low temperature plasmas. Details on all of these projects, links to academic papers I've written, and other information can be found at this site. |