Mixed-Integer Programming for Cycle Detection in Nonreversible Markov Processes
The main objective of this project is to develop an adaptive sampling strategy for the identification of cycles in transition networks. To analyse transition networks, methods of combinatorial optimization are required. This necessitates the design of new possibly heuristic methods and the development of exact mixed-integer programming (MIP) models to evaluate the quality of the heuristics. Experience has shown that the corresponding optimization problems exhibit a high degree of symmetry, which poses additional challenges to state-of-the-art MIP solvers. A long-term goal is to speed up the solver software SCIP in this respect. Previous work for the recognition and exploitation of symmetry in SCIP already exists. The cycle detection provides not only mathematical progress, but it also reveals an important element of natural processes: the micro-catalysis. Ion transport with the help of channel proteins is done by cyclic movements (pumping) of the proteins. The short time scales of these cycles are crucial for the long-term process. These movements are cyclically, because the protein must remain "intact" during the process. In particular, when we combine simulations of classical and quantum physics, such cycles are possible even on longer time scales.
Publications
2018 |
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Jakob Witzig, Isabel Beckenbach, Leon Eifler, Konstantin Fackeldey, Ambros Gleixner, Andreas Grever, Marcus Weber | Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes | Multiscale Modeling and Simulation, 16(1), pp. 248-265, 2018 (preprint available as ZIB-Report 16-39) |
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2017 |
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Leon Eifler | Mixed-Integer Programming for Clustering in Non-reversible Markov Processes | Master's thesis, Technische Universität Berlin, Thorsten Koch (Advisor), 2017 |
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2015 |
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Jessica Schöpke | Korrelation für lineare und nichtlineare Zusammenhänge | Master's thesis, Freie Universität Berlin, Marcus Weber (Advisor), 2015 |
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Annett Meier | Monte-Carlo-Verfahren zur Niedrig-Rang Approximation | Bachelor's thesis, Freie Universität Berlin, Marcus Weber (Advisor), 2015 |
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2014 |
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Ralf Banisch, Natasa Djurdjevac Conrad | Cycle-flow-based module detection in directed recurrence networks | EPL (Europhysics Letters), 108(6), 2014 |
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