Scientific Computing Seminar
Abstract: We construct and analyze multilevel additive Schwarz preconditioners for the anisotropic cardiac Bidomain and Monodomain models in three dimensions. The Bidomain system is the most complete model to date of the bioelectrical activity of the heart tissue, consisting of a degenerate parabolic system of nonlinear reaction-diffusion equations coupled with a stiff system of several ordinary differential equations describing the dynamics of ionic currents through the cellular membrane. Due to the presence of very different scales in both space and time, the numerical discretization of this system by finite elements in space and semi-implicit methods in time produces very ill-conditioned linear systems that must be solved at each time step. The proposed multilevel algorithm employs a hierarchy of nested meshes with overlapping Schwarz preconditioners on each level and is fully additive, hence parallel, within and among levels. Convergence estimates can be proved, showing that the convergence rate of the resulting multilevel algorithm is independent of the number of subdomains (scalability), of the mesh sizes of each level and of the number of levels (optimality). Parallel numerical results, using the PETSc library and run on Linux Clusters, confirm the scalability and optimality of the method, as well as its parallel efficiency for large-scale simulations of a complete cardiac cycle on both cartesian and deformed domains in three dimensions.
Brown University Center for Statistical Sciences Seminar
Abstract: Building an emulator for a computer simulator using standard Gaussian process models can be computationally infeasible when the number of evaluated input values is large. As an alternative, we propose using compactly supported correlation functions, which produce sparse correlation matrices that can be more easily manipulated. Following the usual approach of taking the correlation to be a product of correlations in each input dimension, we show how to impose restrictions on the correlation range for each input, giving sparsity, while also allowing the ranges to trade-off against one another, thereby giving good predictive performance when the data are non-isotropic. As an illustration, the method is to construct an emulator of photometric red-shifts of cosmological objects. This is joint work with Salman Habib, Katrin Heitman (Los Alamos National Lab) and Cari Kaufman (UC Berkeley).
Lefschetz Center for Dynamical Systems Seminar
Abstract: Time-periodic shocks in systems of viscous conservation laws are shown to be nonlinearly stable. The result is obtained by representing the evolution associated to the linearized, time-periodic operator using a contour integral, similar to that of strongly continuous semigroups. This yields detailed pointwise estimates on the Green's function for the time-periodic operator. The evolution associated to the embedded zero eigenvalues is then extracted. Stability follows from a Gronwall- type estimate, proving algebraic decay of perturbations
Brown Analysis Seminar
CCMB Seminar Series
Abstract: Gene expression is often regulated by the binding of small RNAs or proteins to messenger RNA, and splicing of mRNA is one important example. We have developed physical-chemical models of binding which can be computed efficiently with our new oligo-binding algorithm BINDIGO. We have also developed a statistical method (Primary Sequence Ranking) which outperforms other tools for identifying splice sites. Bio: Daniel Aalberts is currently Associate Professor of Physics at Williams College. He has the distinction of having supervised two of the past ten Apker Award winners for outstanding undergraduate physics research. His RNA splicing research is supported by NIH; RNA pseudoknots, by NSF. Aalberts received his SB and PhD degrees from MIT, and did postdoctoral research at Leiden Univ. in the Netherlands and at the Center for Studies in Physics and Biology at Rockefeller Univ. in NYC.
Department of Mathematics Colloquium
Scientific Computing Seminar
Abstract: About one out of three individuals in the world is infected with Tuberculosis but TB associated mortality is relatively low today. The ability of the influenza virus to re-invent itself year after year generates fear of pandemics. Furthermore, it is well-known and documented that hospitals can be great reservoirs of resistant pathogens. Mathematical models are used to study the transmission dynamics, evolution and control of infectious disease at the population level. Their value will be illustrated in the context of intervention policies aim at combating the spread of resistance.
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