Center for Computational Molecular Biology
Seminar Series Lecture
Carnegie-Mellon University, Pittsburgh, PA | |
Abstract: Sequence alignment is a fundamental problem in computational biology, serving as the main component of many algorithms for protein structure and function prediction, phylogeny inference, and other tasks in sequence analysis.
Varying the objective function parameters of an alignment algorithm can greatly influence the quality of the resulting alignment. The goal of parametric sequence alignment is to study the parameter space decomposition and the optimality regions for all biologically meaningful settings of the parameters. Bounding the number of regions in the resulting space is an important problem because it indicates the complexity of finding all optimal alignments of biological or statistical interest.
In this talk, we will survey algorithmic and combinatorial problems arising from parametric sequence alignment and discuss special cases for which we can obtain tight bounds on the number of optimality regions.
Brown Analysis Seminar
Abstract: Many classical constructions and problems in dynamics have natural analogs over p-adic fields. After a brief description of p-adic fields and their basic properties, I will describe recent work on the p-adic Green function G_F associated to a holomorphic map F : P^N --> P^N, including its construction, Holder continuity, and the use of G_F to characterize the Fatou set of F. (Joint work with Shu Kawaguchi)
Transatlantic Seminar
NEW
Scientific Computing Seminar
Brown University, Division of Applied Mathematics | |
Abstract: In this talk, we will describe two recently developed discontinuous Galerkin schemes for solving the Hamilton-Jacobi equation and equations with higher order derivatives, respectively. Unlike the traditional DG schemes for treating these problems, both schemes do not need to rewrite the original equation into several other equations using auxiliary variables to compute the solution. For the Hamilton-Jacobi equation, our scheme works well when the Hamiltonian is convex or linear. An entropy correction is needed when the entropy condition is violated.
Stability and error estimates are available for the linear equations. The Eikonal equation is solved as an application of the scheme. For equations with higher order spatial derivatives, our scheme can give provable L2 stability and accuracy for a very general class of equations. Numerical tests show that this scheme is (k+1)-th order accurate when using piecewise k-th polynomials, under the condition that k+1 is greater than or equal to the order of the equation. This is a joint work with Chi-Wang Shu.
PDE Seminar
Department of Mathematics Colloquium
<--- 2006 Index