TY - GEN A1 - Fischer, Alexander T1 - An Uncoupling-Coupling Technique for Markov Chain Monte Carlo Methods N2 - Uncoupling-coupling Monte Carlo (UCMC) combines uncoupling techniques for finite Markov chains with Markov chain Monte Carlo methodology. By determining almost invariant sets of the associated Markov operator, the Monte Carlo sampling splits by a hierarchical annealing process into the essential regions of the state space; therefore UCMC aims at avoiding the typical metastable behavior of Monte Carlo techniques. From the viewpoint of Monte Carlo, a slowly converging long-time Markov chain is replaced by a limited number of rapidly mixing short-time ones. The correct weighting factors for the various Markov chains are obtained via a coupling matrix, that connects the samplings from the different almost invariant sets. The underlying mathematical structure of this approach is given by a general examination of the uncoupling-coupling procedure. Furthermore, the overall algorithmic scheme of UCMC is applied to the $n$-pentane molecule, a well-known example from molecular dynamics. T3 - ZIB-Report - 00-04 KW - almost invariant sets KW - bridge sampling KW - cluster analysis KW - hierarchical annealing KW - Markov chains KW - Monte Carlo KW - $n$-pentane molecule KW - ratio of no Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5720 ER - TY - GEN A1 - Schütte, Christof A1 - Fischer, Alexander A1 - Huisinga, Wilhelm A1 - Deuflhard, Peter T1 - A Direct Approach to Conformational Dynamics based on Hybrid Monte Carlo N2 - Recently, a novel concept for the computation of essential features of the dynamics of Hamiltonian systems (such as molecular dynamics) has been proposed. The realization of this concept had been based on subdivision techniques applied to the Frobenius--Perron operator for the dynamical system. The present paper suggests an alternative but related concept that merges the conceptual advantages of the dynamical systems approach with the appropriate statistical physics framework. This approach allows to define the phrase ``conformation'' in terms of the dynamical behavior of the molecular system and to characterize the dynamical stability of conformations. In a first step, the frequency of conformational changes is characterized in statistical terms leading to the definition of some Markov operator $T$ that describes the corresponding transition probabilities within the canonical ensemble. In a second step, a discretization of $T$ via specific hybrid Monte Carlo techniques is shown to lead to a stochastic matrix $P$. With these theoretical preparations, an identification algorithm for conformations is applicable. It is demonstrated that the discretization of $T$ can be restricted to few essential degrees of freedom so that the combinatorial explosion of discretization boxes is prevented and biomolecular systems can be attacked. Numerical results for the n-pentane molecule and the triribonucleotide adenylyl\emph{(3'-5')}cytidylyl\emph{(3'-5')}cytidin are given and interpreted. T3 - ZIB-Report - SC-98-45 KW - conformation KW - conformational dynamics KW - hybrid Monte Carlo KW - reweighting KW - essential degrees of freedom KW - transition probabilities KW - Markov operator Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3889 ER - TY - GEN A1 - Fischer, Alexander A1 - Cordes, Frank A1 - Schütte, Christof T1 - Hybrid Monte Carlo with Adaptive Temperature in a Mixed-Canonical Ensemble: Efficient Conformational Analysis of RNA N2 - A hybrid Monte Carlo method with adaptive temperature choice is presented, which exactly generates the distribution of a mixed-canonical ensemble composed of two canonical ensembles at low and high temperature. The analysis of resulting Markov chains with the reweighting technique shows an efficient sampling of the canonical distribution at low temperature, whereas the high temperature component facilitates conformational transitions, which allows shorter simulation times. \\The algorithm was tested by comparing analytical and numerical results for the small n-butane molecule before simulations were performed for a triribonucleotide. Sampling the complex multi-minima energy landscape of these small RNA segments, we observed enforced crossing of energy barriers. T3 - ZIB-Report - SC-97-67 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3364 ER - TY - GEN A1 - Deuflhard, Peter A1 - Huisinga, Wilhelm A1 - Fischer, Alexander A1 - Schütte, Christof T1 - Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains N2 - The topic of the present paper bas been motivated by a recent computational approach to identify chemical conformations and conformational changes within molecular systems. After proper discretization, the conformations show up as almost invariant aggregates in reversible nearly uncoupled Markov chains. Most of the former work on this subject treated the direct problem: given the aggregates, analyze the loose coupling in connection with the computation of the stationary distribution (aggregation/disaggregation techniques). In contrast to that the present paper focuses on the inverse problem: given the system as a whole, identify the almost invariant aggregates together with the associated transition probabilites. A rather simple and robust algorithm is suggested and illustrated by its application to the n-pentane molecule. T3 - ZIB-Report - SC-98-03 KW - essential molecular dynamics KW - nearly reducible KW - nearly completely decomposable KW - nearly uncoupled Markov chain KW - almost invariant aggregates KW - trans Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3469 ER - TY - GEN A1 - Schütte, Christof A1 - Fischer, Alexander A1 - Huisinga, Wilhelm A1 - Deuflhard, Peter T1 - A Hybrid Monte Carlo Method for Essential Molecular Dynamics N2 - Recently, a novel concept for the computation of essential features of Hamiltonian systems (such as those arising in molecular dynamics) has been proposed. The realization of that concept was based on subdivision techniques applied to the Frobenius--Perron operator for the dynamical system. The present paper suggests an alternative but related concept based on statistical mechanics, which allows to attack realistic molecular systems. In a first step, the frequency of conformational changes is characterized in statistical terms leading to the definition of some Markov operator $T$ that describes the corresponding transition probabilities within the canonical ensemble. In a second step, a discretization of $T$ via hybrid Monte Carlo techniques (based on short term subtrajectories only) is shown to lead to a stochastic matrix $P$. With these theoretical preparations, an identification algorithm for conformations is applicable (to be presented elsewhere). Numerical results for the n-pentane molecule are given and interpreted. T3 - ZIB-Report - SC-98-04 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3474 ER - TY - GEN A1 - Fischer, Alexander A1 - Schütte, Christof A1 - Deuflhard, Peter A1 - Cordes, Frank T1 - Hierarchical Uncoupling-Coupling of Metastable Conformations N2 - Uncoupling-coupling Monte Carlo (UCMC) combines uncoupling techniques for finite Markov chains with Markov chain Monte Carlo methodology. UCMC aims at avoiding the typical metastable or trapping behavior of Monte Carlo techniques. From the viewpoint of Monte Carlo, a slowly converging long-time Markov chain is replaced by a limited number of rapidly mixing short-time ones. Therefore, the state space of the chain has to be hierarchically decomposed into its metastable conformations. This is done by means of combining the technique of conformation analysis as recently introduced by the authors, and appropriate annealing strategies. We present a detailed examination of the uncoupling-coupling procedure which uncovers its theoretical background, and illustrates the hierarchical algorithmic approach. Furthermore, application of the UCMC algorithm to the $n$-pentane molecule allows us to discuss the effect of its crucial steps in a typical molecular scenario. T3 - ZIB-Report - 01-03 KW - almost invariant sets KW - bridge sampling KW - metastability KW - hierarchical annealing KW - hybrid Monte Carlo KW - $n$-pentane molecule KW - ratio of normalizing co Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6296 ER - TY - CHAP A1 - Bock, Martin A1 - Skibina, Julia A1 - Fischer, Dorit A1 - Grunwald, Rüdiger A1 - Burger, Sven A1 - Beloglazov, Valentin A1 - Steinmeyer, Günter T1 - 10-fs pulse delivery through a fiber T2 - CLEO Y1 - 2012 U6 - https://doi.org/10.1364/CLEO_SI.2012.CTh3G.3 SP - CTh3G.3 PB - Optical Society of America ER - TY - JOUR A1 - Schütte, Christof A1 - Fischer, Alexander A1 - Huisinga, Wilhelm A1 - Deuflhard, Peter T1 - A Direct Approach to Conformational Dynamics Based on Hybrid Monte Carlo JF - J. Comput. Phys. Y1 - 1999 UR - http://www.zib.de/PaperWeb/abstracts/SC-98-45 VL - 151 SP - 146 EP - 168 ER - TY - JOUR A1 - Fischer, Alexander A1 - Cordes, Frank A1 - Schütte, Christof T1 - Hybrid Monte Carlo with Adaptive Temperature in Mixed–Canonical Ensemble: Efficient conformational analysis of RNA JF - J. Comp. Chem. Y1 - 1998 U6 - https://doi.org/10.1002/(SICI)1096-987X(19981130)19:15<1689::AID-JCC2>3.0.CO;2-J VL - 19 IS - 15 SP - 1689 EP - 1697 ER - TY - CHAP A1 - Fischer, Alexander A1 - Schütte, Christof A1 - Deuflhard, Peter A1 - Cordes, Frank ED - Schlick, T. ED - Gan, H. T1 - Hierarchical Uncoupling-Coupling of Metastable Conformations T2 - Computational Methods for Macromolecules Y1 - 2002 UR - http://www.zib.de/PaperWeb/abstracts/ZR-01-03 IS - 24 SP - 235 EP - 259 PB - Springer ER - TY - JOUR A1 - Deuflhard, Peter A1 - Huisinga, Wilhelm A1 - Fischer, Alexander A1 - Schütte, Christof T1 - Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains JF - Lin. Alg. Appl. Y1 - 2000 VL - 315 SP - 39 EP - 59 ER - TY - CHAP A1 - Enke, Harry A1 - Fiedler, Norman A1 - Fischer, Thomas A1 - Gnadt, Timo A1 - Ketzan, Erik A1 - Ludwig, Jens A1 - Rathmann, Torsten A1 - Stöckle, Gabriel A1 - Schintke, Florian ED - Enke, Harry ED - Ludwig, Jens T1 - Leitfaden zum Forschungsdaten-Management T2 - Leitfaden zum Forschungsdaten-Management Y1 - 2013 PB - Verlag Werner Hülsbusch, Glückstadt ER - TY - THES A1 - Fischer, Jens V. T1 - A Gossiping Framework for Scalaris Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-50685 ER - TY - CHAP A1 - Skibina, Julia A1 - Bock, Martin A1 - Fischer, Dorit A1 - Grunwald, Rüdiger A1 - Steinmeyer, Günter A1 - Wedell, Reiner A1 - Bretschneider, Mario A1 - Burger, Sven A1 - Beloglazov, Valentin T1 - 10-fs fiber based pulse delivery T2 - Conference on Lasers, Applications, and Technologies (LAT) Y1 - 2013 SP - LWF5 ER - TY - GEN A1 - Fischer, Frank A1 - Schlechte, Thomas T1 - Strong Relaxations for the Train Timetabling Problem using Connected Configurations N2 - The task of the train timetabling problem or track allocation problem is to find conflict free schedules for a set of trains with predefined routes in a railway network. Especially for non-periodic instances models based on time expanded networks are often used. Unfortunately, the linear programming relaxation of these models is often extremely weak because these models do not describe combinatorial relations like overtaking possibilities very well. In this paper we extend the model by so called connected configuration subproblems. These subproblems perfectly describe feasible schedules of a small subset of trains (2-3) on consecutive track segments. In a Lagrangian relaxation approach we solve several of these subproblems together in order to produce solutions which consist of combinatorially compatible schedules along the track segments. The computational results on a mostly single track corridor taken from the INFORMS RAS Problem Solving Competition 2012 data indicate that our new solution approach is rather strong. Indeed, for this instance the solution of the Lagrangian relaxation is already integral. T3 - ZIB-Report - 17-46 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64743 SN - 1438-0064 ER - TY - JOUR A1 - Fischer, Lisa A1 - Götschel, Sebastian A1 - Weiser, Martin T1 - Lossy data compression reduces communication time in hybrid time-parallel integrators JF - Comput. Vis. Sci. N2 - Parallel in time methods for solving initial value problems are a means to increase the parallelism of numerical simulations. Hybrid parareal schemes interleaving the parallel in time iteration with an iterative solution of the individual time steps are among the most efficient methods for general nonlinear problems. Despite the hiding of communication time behind computation, communication has in certain situations a significant impact on the total runtime. Here we present strict, yet no sharp, error bounds for hybrid parareal methods with inexact communication due to lossy data compression, and derive theoretical estimates of the impact of compression on parallel efficiency of the algorithms. These and some computational experiments suggest that compression is a viable method to make hybrid parareal schemes robust with respect to low bandwidth setups. Y1 - 2018 U6 - https://doi.org/10.1007/s00791-018-0293-2 VL - 19 IS - 1 SP - 19 EP - 30 ER - TY - THES A1 - Fischer, Lisa T1 - On the convergence of inexact time parallel time integration Y1 - 2017 ER - TY - CHAP A1 - Fischer, Frank A1 - Schlechte, Thomas ED - D'Angelo, Gianlorenzo ED - Dollevoet, Twan T1 - Strong Relaxations for the Train Timetabling Problem using Connected Configurations T2 - 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017) N2 - The task of the train timetabling problem or track allocation problem is to find conflict free schedules for a set of trains with predefined routes in a railway network. Especially for non-periodic instances models based on time expanded networks are often used. Unfortunately, the linear programming relaxation of these models is often extremely weak because these models do not describe combinatorial relations like overtaking possibilities very well. In this paper we extend the model by so called connected configuration subproblems. These subproblems perfectly describe feasible schedules of a small subset of trains (2-3) on consecutive track segments. In a Lagrangian relaxation approach we solve several of these subproblems together in order to produce solutions which consist of combinatorially compatible schedules along the track segments. The computational results on a mostly single track corridor taken from the INFORMS RAS Problem Solving Competition 2012 data indicate that our new solution approach is rather strong. Indeed, for this instance the solution of the Lagrangian relaxation is already integral. Y1 - 2017 SN - 978-3-95977-042-2 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2017.11 VL - 59 ER - TY - CHAP A1 - Fischer, Frank A1 - Grimm, Boris A1 - Klug, Torsten A1 - Schlechte, Thomas T1 - A Re-optimization Approach for Train Dispatching T2 - Operations Research Proceedings 2016 N2 - The Train Dispatching Problem (TDP) is to schedule trains through a network in a cost optimal way. Due to disturbances during operation existing track allocations often have to be re-scheduled and integrated into the timetable. This has to be done in seconds and with minimal timetable changes to guarantee smooth and conflict free operation. We present an integrated modeling approach for the re-optimization task using Mixed Integer Programming. Finally, we provide computational results for scenarios provided by the INFORMS RAS Problem Soling Competition 2012. Y1 - 2017 U6 - https://doi.org/10.1007/978-3-319-55702-1_85 SP - 645 EP - 651 ER - TY - CHAP A1 - Fischer, Frank A1 - Schlechte, Thomas T1 - Comparing two dual relaxations of large scale train timetabling problems T2 - Proceedings of Conference on Advanced Systems in Public Transport 2015 N2 - Railway transportation and in particular train timetabling is one of the basic and source application areas of combinatorial optimization and integer programming. We will discuss two well established modeling techniques for the train timetabling problem. In this paper we focus on one major ingredient - the bounding by dual relaxations. We compare two classical dual relaxations of large scale time expanded train timetabling problems - the Lagrangean Dual and Lagrangean Decomposition. We discuss the convergence behavior and show limitations of the Lagrangean Decomposition approach for a configuration based model. We introduce a third dualization approach to overcome those limitations. Finally, we present promising preliminary computational experiments that show that our new approach indeed has superior convergence properties. Y1 - 2015 ER -