On parametric nonlinear programming
Annals of Operations Research
A primal-dual potential reduction method for problems involving matrix inequalities
Mathematical Programming: Series A and B
DS '02 Proceedings of the 5th International Conference on Discovery Science
Reconstructing gene networks from large scale gene expression data
Reconstructing gene networks from large scale gene expression data
On optimization, dynamics and uncertainty: A tutorial for gene-environment networks
Discrete Applied Mathematics
Modeling and simulation of nitrogen regulation in Corynebacterium glutamicum
Discrete Applied Mathematics
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Many problems in the field of computational biology consist of the analysis of so-called gene-expression data. The successful application of approximation and optimization techniques, dynamical systems, algorithms and the utilization of the underlying combinatorial structures lead to a better understanding in that field. For the concrete example of gene-expression data we extend an algorithm, which exploits discrete information. This is lying in extremal points of polyhedra, which grow step by step, up to a possible stopping.We study gene-expression data in time, mathematically model it by a time-continuous system, and time-discretize this system. By our algorithm we compute the regions of stability and instability. We give a motivating introduction from genetics, present biological and mathematical interpretations of (in)stability, point out structural frontiers and give an outlook to future research.