1: Biological Swarming
Biological and other natural systems involving large numbers of individuals moving based on self propulsion and pairwise interactions form interesting emergent patterns and structures. I'm studying the characteristics of these types of systems involving stochastic parameters.
2: Support Vector Machines
Classification of input to appropriate labels is applicable in areas from biological micro-array data to recognizing poker hands. The basic methodology for support vector machine problems is to maximize a margin volume around a hyperplane that partitions the training data in a Euclidean feature space. I'm exploring the alternative methods of training a multi-label classifier using Bayesian techniques and convex functional analysis.
3: Obscuration Maps
In tracking problems where an airborne observer is tracking a target on some generalized terrain, it is often advantageous for the tracker to know what areas of the terrain should be obscured to the observer. Assuming a digital elevation model of the terrain is known, generating an obscuration map efficiently becomes a problem applicable to military surveillance and targeting systems. Techniques I've explored involve concepts of ray tracing, shadow mapping generated by OpenGL, and 2D interpolation schemes.