Brown University Center for Statistical Sciences Seminar
Abstract: This talk discusses the graph-theoretic limits on diffusion in dynamic networks. The work focuses on implications for disease & information diffusion, identifying contrasting effects for typical structural features (small world, degree distributions, etc.) and introducing new measures & graphical representations for diffusion over dynamic graphs.
Center for Computational Molecular Biology Seminar
Abstract: I'll talk about three areas of evolutionary biology using a combination of statistics and discrete math: viral population diversity, the evolution of drug resistance, and phylogenetics. Knowledge of the diversity of viral populations is important for understanding disease progression, vaccine design, and drug resistance, yet it is poorly understood. New technologies (pyrosequencing) allow us to read short, error-prone DNA sequences from an entire population at once. I will show how to assemble the reads into genomes using graph theory, allowing us to determine the population structure. Next, I will describe a new class of graphical models inspired by poset theory that describe the accumulation of (genetic) events with constraints on the order of occurrence. Applications of these models include calculating the risk of drug resistance in HIV and understanding cancer progression. Finally, I'll describe a polyhedral method for determining the sensitivity of phylogenetic algorithms to changes in the parameters. We will analyze several datasets where small changes in parameters lead to completely different trees and see how discrete geometry can be used to average out the uncertainty in parameter choice.
Center for Fluid Mechanics Seminar
Abstract: Nature has shown us that some hearts do not require valves to achieve unidirectional flow. In its earliest stages, the vertebrate heart consists of a primitive tube that drives blood through a simple vascular network nourishing tissues and other developing organ systems. We have shown that in the case of the embryonic zebrafish heart, an elastic wave resonance mechanism based on impedance mismatches at the boundaries of the heart tube is the likely mechanism responsible for the valveless pumping behavior. In this model, compared to peristalsis, fewer cells are required to actively contract in order to maintain the pumping action than are necessary in a peristaltic mechanism. When functioning normally, mature heart valves prevent intracardiac retrograde blood flow; before valves develop there is considerable regurgitation, resulting in oscillatory flow between the atrium and ventricle. As reversing flows are particularly strong stimuli to endothelial cells in culture, an attractive hypothesis is that heart valves form as a developmental response to oscillatory blood flow through the maturing heart. Here, we exploit the resonant pumping properties of the embryonic heart to reduce oscillatory flow during valvulogenesis by lowering heart rate. Reducing oscillatory flows across endocardial cushions leads to arrested valve growth. Using this assay, we identify Klf2a, a shear-responsive gene, as an essential valve inducer in the zebrafish heart. Klf2a is normally expressed in the valve precursors in response to oscillatory flow.
Brown Analysis Seminar
Department of Mathematics Colloquium
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