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ON A UNIQUE TWO-DIMENSIONAL INTEGRAL OPERATOR HOMOGENEOUS WITH RESPECT TO ALL ORIENTATION PRESERVING LINEAR TRANSFORMATIONS

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arXiv 2025年

作者： Avetisyan, Zhirayr Karapetyants, Alexey Mirotin, Adolf Department of Mathematics: Analysis Logic and Discrete Mathematics University of Ghent Krijgslaan 281 Building S8 GhentB 9000 Belgium Regional Mathematical Center Southern Federal University Rostov-on-Don344090 Russia Institute of Mathematics Mechanics and Computer Sciences Regional Mathematical Center Southern Federal University Rostov-on-Don344090 Russia Department of Mathematics and Programming Technologies Francisk Skorina Gomel State University Gomel246019 Belarus

In this paper, we consider a two-dimensional operator with an antisymmetric integral kernel, recently introduced by Z. Avetisyan and A. Karapetyants in connection to the study of general homogeneous operators. This is the unique two-dimensional operator that has an antisymmetric kernel homogeneous with respect to all orientation-preserving linear transformations of the plane. It is shown that the operator under consideration interacts naturally, both in Cartesian and polar coordinates, with projective tensor products of some classical functional spaces, such as Lebesgue, Hardy, and Hölder spaces;conditions for their boundedness as operators acting from these spaces to Banach lattices of measurable functions and estimates of their norms are *** Codes 44A05, 44A15 Copyright © 2025, The Authors. All rights reserved.

关键词： Linear transformations

The worst-case complexity of symmetric strategy improvement

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arXiv 2023年

作者： van Dijk, Tom Loho, Georg Maat, Matthew T. Formal Methods and Tools University of Twente Netherlands Discrete Mathematics and Mathematical Programming University of Twente Netherlands

Symmetric strategy improvement is an algorithm introduced by Schewe et al. (ICALP 2015) that can be used to solve two-player games on directed graphs such as parity games and mean payoff games. In contrast to the usual well-known strategy improvement algorithm, it iterates over strategies of both players simultaneously. The symmetric version solves the known worst-case examples for strategy improvement quickly, however its worst-case complexity remained open. We present a class of worst-case examples for symmetric strategy improvement on which this symmetric version also takes exponentially many steps. Remarkably, our examples exhibit this behaviour for any choice of improvement rule, which is in contrast to classical strategy improvement where hard instances are usually hand-crafted for a specific improvement rule. We present a generalized version of symmetric strategy iteration depending less rigidly on the interplay of the strategies of both players. However, it turns out it has the same shortcomings. © 2023, CC BY.

关键词： Directed graphs

Multi-objective optimization of traffic externalities using tolls

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Multi-objective optimization of traffic externalities using ...

Congress on Evolutionary Computation

作者： Anthony E. Ohazulike Ties Brands Centre for Transport Studies (CTS) Discrete Mathematics and Mathematical Programming (DMMP) University of Twente Netherlands Centre for Transport Studies (CTS) University of Twente Netherlands

ISBN: (纸本)9781479904532

Genetic algorithms (GAs) are widely accepted by researchers as a method of solving multi-objective optimization problems (MOPs), at least for listing a high quality approximation of the Pareto front of a MOP. In traffic management, it has been long established that tolls can be used to optimally distribute traffic in a network with aim of combating some traffic externalities such as congestion, emission, noise, safety issues. Formulating the multi-objective toll problem as a one point solution problem fails to give the general overview of the objective space of the MOP. Therefore, in this paper we develop a game theoretic approach that gives the general overview of the objective space of the multiobjective problem and compare the results with those of the wellknown genetic algorithm non-dominated sorting genetic algorithm II (NSGA-II). Results show that the game theoretic approach presents a promising tool for solving multi-objective problems, since it produces similar non-dominated solutions as NSGA-II, indicating that competing objectives (or stakeholders in the game setting) can still produce Pareto optimal solutions. Most fascinating is that a range of non-dominated solutions is generated during the game, and almost all generated solutions are in the neighborhood of the Pareto set. This indicates that good solutions are generated very fast during the game.

关键词： Games Roads Genetic algorithms Vectors Optimization Pricing Game theory

High-throughput screening of cell-surface topographic interactions

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High-throughput screening of cell-surface topographic intera...

14th International Conference on Miniaturized Systems for Chemistry and Life Sciences 2010, MicroTAS 2010

作者： Unadkat, Hemant V. Hulsman, Marc Cornelissen, Kamiel Papenburg, Bernke Truckenmüller, Roman K. Post, Gerhard F. Uetz, Marc Reinders, Marcel J.T. Stamatialis, Dimitrios Van Blitterswijk, Clemens De Boer, Jan MIRA Research Institute Department of Tissue Regeneration University of Twente Postbus 217 7500 AE Enschede Netherlands Discrete Mathematics and Mathematical Programming University of Twente Postbus 217 7500 AE Enschede Netherlands Membrane Science and Technology Group University of Twente Postbus 217 7500 AE Enschede Netherlands Delft Bioinformatics Lab. Delft University of Technology Mekelweg 4 Delft Netherlands

ISBN: (纸本)9781618390622

High throughput biomaterials screening largely remains unexplored. The present study was an attempt to explore the area of high throughput as well as high content screening of cell surface topographic interaction. An array of surface topographies called TopoChip was fabricated using a widely used polymer in tissue engineering, Poly (DL-lactic acid). The topographies were subsequently screened for their mitogenic effect on cells. We were able to detect topographic parameters responsible for mitogenic effect of surface topographies.

关键词： Cytology

Enabling Research through the SCIP Optimization Suite 8.0

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arXiv 2023年

作者： Bestuzheva, Ksenia Besançon, Mathieu Chen, Wei-Kun Chmiela, Antonia Donkiewicz, Tim van Doornmalen, Jasper Eifler, Leon Gaul, Oliver Gamrath, Gerald Gleixner, Ambros Gottwald, Leona Graczyk, Christoph Halbig, Katrin Hoen, Alexander Hojny, Christopher van der Hulst, Rolf Koch, Thorsten Lübbecke, Marco Maher, Stephen J. Matter, Frederic Mühmer, Erik Müller, Benjamin Pfetsch, Marc E. Rehfeldt, Daniel Schlein, Steffan Schlösser, Franziska Serrano, Felipe Shinano, Yuji Sofranac, Boro Turner, Mark Vigerske, Stefan Wegscheider, Fabian Wellner, Philipp Weninger, Dieter Witzig, Jakob Zuse Institute Berlin Department AIS2T Takustr. 7 Berlin14195 Germany ZIB-AIS2T Germany School of Mathematics and Statistics Beijing Institute of Technology Beijing100081 China RWTH Aachen University Lehrstuhl für Operations Research Kackertstr. 7 Aachen52072 Germany Eindhoven University of Technology Department of Mathematics and Computer Science Netherlands ZIB-AIS2T I2DAMO GmbH Englerallee 19 Berlin14195 Germany ZIB-AIS2T HTW Berlin Germany Friedrich-Alexander Universität Erlangen-Nürnberg Department of Data Science Cauerstr. 11 Erlangen91058 Germany University of Twente Department of Discrete Mathematics and Mathematical Programming P.O. Box 217 Enschede7500 AE Netherlands Technische Universität Berlin Software and Algorithms for Discrete Optimization Straße des 17. Juni 135 Berlin10623 Germany ZIB Department A2IM Takustr. 7 Berlin14195 Germany RWTH Aachen-Lehrstuhl für OR Germany University of Exeter College of Engineering Mathematics and Physical Sciences Exeter United Kingdom Technische Universität Darmstadt Fachbereich Mathematik Dolivostr. 15 Darmstadt64293 Germany TU Darmstadt Fachbereich Mathematik Germany ZIB-A2IM Germany TU Berlin Germany ZIB-A2IM Software and Algorithms for Discrete Optimization Institute of Mathematics TU Berlin Germany GAMS Software GmbH c/o ZIB-AIS2T Germany

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this paper is on the role of the SCIP Optimization Suite in supporting research. SCIP's main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP's application as a research tool and as a platform for further developments. Further, the paper gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon *** Codes 90C05, 90C10, 90C11, 90C30, 90C90, 65Y05 Copyright © 2023, The Authors. All rights reserved.

关键词： Integer programming

The SCIP optimization suite 8.0

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arXiv 2021年

作者： Bestuzheva, Ksenia Besançon, Mathieu Chen, Wei-Kun Chmiela, Antonia Donkiewicz, Tim Van Doornmalen, Jasper Eifler, Leon Gaul, Oliver Gamrath, Gerald Gleixner, Ambros Gottwald, Leona Graczyk, Christoph Halbig, Katrin Hoen, Alexander Hojny, Christopher Van Der Hulst, Rolf Koch, Thorsten Lübbecke, Marco Maher, Stephen J. Matter, Frederic Mühmer, Erik Müller, Benjamin Pfetsch, Marc E. Rehfeldt, Daniel Schlein, Steffan Schlösser, Franziska Serrano, Felipe Shinano, Yuji Sofranac, Boro Turner, Mark Vigerske, Stefan Wegscheider, Fabian Wellner, Philipp Weninger, Dieter Witzig, Jakob Zuse Institute Berlin Department AIS2T Takustr. 7 Berlin14195 Germany School of Mathematics and Statistics Beijing Institute of Technology Beijing100081 China RWTH Aachen University Lehrstuhl für Operations Research Kackertstr. 7 Aachen52072 Germany Technische Universiteit Eindhoven Department of Mathematics and Computer Science P.O. Box 513 Eindhoven5600 MB Netherlands I2DAMO GmbH Englerallee 19 Berlin14195 Germany Friedrich-Alexander Universität Erlangen-Nürnberg Department of Data Science Cauerstr. 11 Erlangen91058 Germany University of Twente Department of Discrete Mathematics and Mathematical Programming P.O. Box 217 Enschede7500 AE Netherlands Technische Universität Berlin Software and Algorithms for Discrete Optimization Straße des 17. Juni 135 Berlin10623 Germany Zuse Institute Berlin Department A2IM Takustr. 7 Berlin14195 Germany University of Exeter College of Engineering Mathematics and Physical Sciences Exeter United Kingdom Technische Universität Darmstadt Fachbereich Mathematik Dolivostr. 15 Darmstadt64293 Germany Technische Universität Berlin Straße des 17. Juni 135 Berlin10623 Germany Software and Algorithms for Discrete Optimization Institute of Mathematics Technische Universität Berlin Straße des 17. Juni 135 Berlin10623 Germany GAMS Software GmbH C/o Zuse Institute Berlin Department AIS2T Takustr. 7 Berlin14195 Germany

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints are handled. Additionally, SCIP 8.0 now supports interfaces for Julia as well as Matlab. Further, UG now includes a unified framework to parallelize all solvers, a utility to analyze computational experiments has been added to GCG, dual solutions can be postsolved by PaPILO, new heuristics and presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in *** Codes 90C05, 90C10, 90C11, 90C30, 90C90, 65Y05 Copyright © 2021, The Authors. All rights reserved.

关键词： Integer programming

The SCIP Optimization Suite 9.0

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arXiv 2024年

作者： Bolusani, Suresh Besançon, Mathieu Bestuzheva, Ksenia Chmiela, Antonia Dionísio, João Donkiewicz, Tim van Doornmalen, Jasper Eifler, Leon Ghannam, Mohammed Gleixner, Ambros Graczyk, Christoph Halbig, Katrin Hedtke, Ivo Hoen, Alexander Hojny, Christopher van der Hulst, Rolf Kamp, Dominik Koch, Thorsten Kofler, Kevin Lentz, Jurgen Manns, Julian Mexi, Gioni Mühmer, Erik Pfetsch, Marc E. Schlösser, Franziska Serrano, Felipe Shinano, Yuji Turner, Mark Vigerske, Stefan Weninger, Dieter Xu, Liding Gaul, Oliver Zuse Institute Berlin Department AIS2T Takustr. 7 Berlin14195 Germany Université Grenoble Alpes Inria LIG Grenoble38000 France CMUP Department of Computer Science Faculty of Sciences University of Porto R Campo Alegre Porto4169-007 Portugal RWTH Aachen University Lehrstuhl für Operations Research Kackertstr. 7 Aachen52072 Germany Eindhoven University of Technology Department of Mathematics and Computer Science P.O. Box 513 Eindhoven5600 MB Netherlands Friedrich-Alexander Universität Erlangen-Nürnberg Department of Data Science Cauerstr. 11 Erlangen91058 Germany Schenker AG Global Data & AI Kruppstr. 4 Essen45128 Germany University of Twente Department of Discrete Mathematics and Mathematical Programming P.O. Box 217 Enschede7500 AE Netherlands University of Bayreuth Universitaetsstr. 30 Bayreuth95440 Germany Technische Universität Berlin Straße des 17. Juni 135 Berlin10623 Germany Zuse Institute Berlin Department A2IM Takustr. 7 Berlin14195 Germany DAGOPT Optimization Technologies GmbH Austria Technische Universität Darmstadt Fachbereich Mathematik Dolivostr. 15 Darmstadt64293 Germany Fair Isaac Germany GmbH Takustr. 7 Berlin14195 Germany COPT GmbH Berlin Germany GAMS Software GmbH c/o Zuse Institute Berlin Department AIS2T Takustr. 7 Berlin14195 Germany Friedrich-Alexander Universität Erlangen-Nürnberg Department of Mathematics Cauerstr. 11 Erlangen91058 Germany École polytechnique LIX CNRR Rue Honoré d’Estienne d’Orves. 1 Palaiseau9120 France

MSC Codes 90C05, 90C10, 90C11, 90C30, 90C90, 65Y05The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming (CIP) framework SCIP. This report discusses the enhancements and extensions included in SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a new cut generator and two new cut selection schemes, a new branching rule, a new LP interface, and several bugfixes. SCIP Optimization Suite 9.0 also features new Rust and C++ interfaces for SCIP, new Python interface for SoPlex, along with enhancements to existing interfaces. SCIP Optimization Suite 9.0 also includes new and improved features in the LP solver SoPlex, the presolving library PaPILO, the parallel framework UG, the decomposition framework GCG, and the SCIP extension SCIP-SDP. These additions and enhancements have resulted in an overall performance improvement of SCIP in terms of solving time, number of nodes in the branch-and-bound tree, as well as the reliability of the solver. Copyright © 2024, The Authors. All rights reserved.

关键词： Mixed-integer linear programming