Spatio-Temporal Dynamics: Research in the group is focused on how to implement modal decomposition on experimental data and how symmetries and other general characteristics of the modes can be used to gain theoretical understanding of turbulent flame flows. Genetic Networks: By now it is apparent that biological processes are affected by large collections of genes/proteins/metabolites. In general, neither the full membership of the gene network associated with a biological process nor the precise form of interactions between nodes is known. What is available, through microarrays or sequencing, are gene expression profiles of an organism or its viable mutants. Our group is developing a methodology whereby expression profiles of a selected group of mutants can be used to make predictions on how the network can be moved to a pre-specified state. We are collaborating with experimentalists to determine how Drosophila can be genetically altered to a sleep-deprived like state. Quantitative Finance: Physicists are motivated to study financial markets in the expectation that stochastic analysis developed in the context of statistical mechanics and nonlinear physics may find applications there. The relevant issues are the characteristics of the stochastic processes underlying financial markets. Recent analyses of financial markets have shown that the process is highly complex and that the intensity of fluctuations depends on the time of day and on variations in price during the day. Our research involves modeling and stochastic analyses of such processes. Models of Animal Behavior: Behavior of animals introduced into a novel arena is highly complex and includes a preference for boundaries and decay in activity as the novelty of the area is abrogated. We quantify the behavior by analyzing a large number of trajectories of Drosophila introduced into both (geometrically) simple and complex arenas. The results are used to gain a quantitative understanding of exploration.
Publications/Creative Works
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