Group Meetings

Abstract: HIV was first identified as the causative agent of AIDS over 25 years ago. During that time billions of dollars have been spent on research and prevention, yet rates of infection still increase. The disconnect between the magnitude of resources allocated and their limited effect is due our failure to base HIV prevention modalities on a empirically-supported, scientifically sound theory of infection transmission. Drawing on the fields of complex systems, phylogenetics, statistics, and epidemiology, I will discuss a framework for estimating site-specific parameters in a high-dimensional, mathematical model of HIV transmission using genetic sequence data. Topics discussed will include the philosophy of systems, mathematical modeling, the curse of dimensionality, and phylogenetics of HIV.

Abstract: In this talk, we will give an introduction to computations of both compressible and incompressible flows. Although these two types of flow problems are governed by different types of equations, a unified description of direct numerical simulations of multiphase compressible (or incompressible) flows in terms of interface tracking is available.

On the other hand, different numerical methodologies must be applied to them respectively. For compressible flows which are governed by the nonlinear hyperbolic partial differential equations, the major obstacles to the solutions are discontinuities. A careless treatment can introduce additional errors. This talk will present an interface tracking method for solving this class of flow problems and a conservative front tracking methodology to improve the numerical solution accuracy. For incompressible flows, a projection method together with the interface tracking is used to resolve the flow dynamics. In the end, we will also discuss the computation of the blood flow using this approach.

Abstract: The genetic network controlling early dorsal-ventral (DV) patterning has been studied extensively in Drosophila. This patterning is regulated by Dpp and its interactions with several other secreted factors including short gastrulation (Sog).  Recent experimental studies suggest that the DV patterning of zebrafish, a vertebrate development model, is
controlled by a similar gene network involving bone morphogenetic proteins (BMP, a homologue of Dpp) and an antagonist Chordin (a homologue of Sog): however, the pattern may also be established through a different mechanism.  In this talk, we present a computational model in three-dimension to study the detailed interactions in the complex gene network and to identify key components in the formation of morphogenetic BMP gradient in early dorsal-ventral patterning of the zebrafish embryo. Simulation results are presented for dynamics of the BMP gradient, cooperative action of the two feedbacks from BMP signals to BMP and Chordin synthesis, and pattern sensitivity with respect to BMP and Chordin dosage changes. Computational analysis shows that, unlike the case in Drosophila, synergy of the two feedbacks in the zygotic control along with maternal loading of the BMP and Chordin is critical for establishment of a desired stable BMP pattern and self-regulation of the gene-network during the early dorsal-ventral pattering of the zebrafish embryo. At last, I will talk about recent progress on Implicit Integrating factor (IIF) methods for stiff reaction diffusion equations.

Abstract: Dissipative structures in a reaction-diffusion systems will be introduced and numerical simulations of one and two dimension, which are consistent with analytical analysis, will be shown.