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Optimization of Biosystems: Discrete structures, polytopes and suitable algorithms

March 30, 2004

Date: Tuesday, March 30th, 2004
Time: 11am-12:15pm
Location: Woodward 149

Stefan Wolfgang Pickl,
Department of Mathematics, Center for Applied Computer Science Cologne University of Cologne Current address: Department of Computer Science University of New Mexico

Abstract: This talk will give an introduction into the challenging field of the optimization of biosystems applying discrete structures and suitable algorithms. Many optimization problems can be described and solved with the aid of polytopes exploiting their geometrical and combinatorial structure. The presentation describes two cases where polytopes determine feasible sets (Example 1 - economathematics) and where polytopes are suitable tools ("keys") for optimization techniques (Example 2 - data analysis in the lifesciences). In these fields, a special representation form of polytopes may be used to construct an algorithm which is able to analyze and optimize a nonlinear time-discrete system. The underlying theory of the algorithm bases on the use of polytopes and linear programming techniques such that, successively only the extremal points of the polytope are regarded. Their topological behaviour can be used to get suitable decision criteria. Theoretical results are as well presented as numerical solutions. As an example, the project TEMPI (Technology Emissions Means Process Identification) is discussed.