Constrained Minkowski Sums: A Geometric Framework for Solving Interval Problems in Computational Biology Efficiency

By Dr. Friedrich Eisenbrand (EPFL, Lausanne)

Wednesday, December 9

Friedrich EisenbrandAbstract:: We introduce the notion of a constrained Minkowski sum which for two (finite) point-sets P,Q ⊆ R2 and a set of k inequalities Ax > b is defined as the point-set (P⊕Q)Ax>b = {x = p+q | p ∈ P, q ∈ Q, Ax > b}.We show that typical interval problems from computational biology can be solved by computing a set containing the vertices of the convex hull of an appropriately constrained Minkowski sum. Via this interpretation we not only obtain one common algorithm for many interval problems from the literature, but are also able to solve some of them more efficiently than previous special purpose algorithms. Joint work with Thorsten Bernholt and Thomas Hofmeister.

The Swarming Body - Exploring the Possibilities of Algorithmic Systems in Biology

By Dr. Christian Jacob (University of Calgary)

Tuesday, September 22

Christian JacobAbstract:: Mathematical and computational models are becoming more prominent in biological and bioinformatics research. However, the designing, programming, and utilization of computer models has not yet found the acceptance it deserves within the biological research community. Why are virtual biology labs not part of a biologist’s standard tool set? There seems to be a wide communication gap between how biologists think about biological “systems” and how computer scientists, bioinformaticians, and mathematical modelers implement their formal models of living systems. It turns out that the engineering of software, the building of computational models, and the investigation of biological systems faces similar challenges and approaches: modularization of subsystems to keep things organized, complex interaction networks among more basic computational units — elementary functions in software versus proteins and molecules in wetware. Creating a common language among “algorithmic systems biologists” and biologists who want to utilize “virtual laboratories” to study complex biological systems is highly important.

To illustrate this viewpoint, I will present a variety of models with visualization examples, that demonstrate our latest swarm intelligence-based approaches to explore gene regulatory systems, blood clotting, immune system processes, and bacterial ecosystems on various scales: from bodies to organs to cells to proteins.

Algorithm Stabilization and Acceleration in Computational Fluid Dynamics: Exploiting Recursive Properties of Fixed-Point Algorithms

By Dr. Aleksandar Jemcov (Fluent Inc.)

Thursday, June 4

Abstract: The current trend in applied computational science is the increase of the size and physical complexity of the problems that are being solved. This is evident in Computational Fluid Dynamics (CFD), where the steady increase of the size of the problems leads to computational simulations with several hundred millions of unknowns. In addition, new physical models that incorporate increasingly complex terms in the basic set of the Navier-Stokes equations also contribute to increased stiffness of the problems. Another source of difficulties is the inherent nonlinear nature of the Navier-Stokes system of equations. Modern CFD codes must be capable of handling these difficulties in an efficient manner. In this seminar, a stabilization and acceleration method based on recursive properties of fixed-point algorithms is described that is capable of handling various problems in CFD simulations. The method is equally applicable to iterative solvers used for the solution of systems of linear equations, as well as to nonlinear CFD algorithms. Examples of the use of these stabilization and acceleration algorithms will be demonstrated for 2D and 3D flows with various levels of difficulty.

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