Center for Computational Molecular Biology Seminar
Abstract: Reconstruction of evolutionary histories is a fundamental problem in computational biology. It has been established that accurately representing complete evolutionary histories requires an underlying model that incorporates non-tree operations, corresponding to the mixing of genetic material from ancestral sequences. In this talk, we will address the problem of finding parsimonious evolutionary histories with both hybridization and mutation events (the Imperfect Ancestral Recombination Graph Reconstruction Problem). The power of our framework is the connection between our formulation and the Directed Steiner Arborescence Problem in combinatorial optimization. We implement linear programming techniques as well as heuristics for the Directed Steiner Arborescence Problem and apply these algorithms on simulated and benchmark data sets.
This is joint work with Ryan Tarpine and Sorin Istrail.
Hosted by: Sorin Istrail
Refreshments will be served at 3:45 p. m.
Scientific Computing Seminar
Abstract: We present implicit high-order hybridized discontinuous Galerkin (HDG) methods for the numerical solution of linear time-dependent convection-diffusion equations. In this method, the approximate solution and flux are expressed in an element-by-element fashion in terms of an approximate trace. This allows for elimination of both the approximate solution and flux to obtain a matrix equation in terms of the approximate trace only. The main disadvantages of a discontinuous Galerkin approximation --- a high number of globally coupled degrees of freedom for the same mesh and a low sparsity of the discrete system --- are thus eliminated to a significant extent. Moreover, the HDG method allows, in a single implementation, to use variable degrees and hanging nodes in different elements or subdomains of the computational domain. Finally, the HDG method appears attractive for the implicit time integration of the resulting system of ordinary differential equations. Numerical results for scalar and system cases are presented to assess the convergence and accuracy in both pure diffusion and pure convection limits.
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