TY - CHAP A1 - Gonnermann-Müller, Jana A1 - Brandenburger, Bonny A1 - Vladova, Gergana A1 - Gronau, Norbert T1 - To What Extent Can Individualisation in Terms of Different Types of Mode Improve Learning Outcomes and Learner Satisfaction? A Pre-study T2 - Proceedings of the Hawaii International Conference on System Sciences Y1 - 2023 ER - TY - JOUR A1 - Combettes, Cyrille A1 - Pokutta, Sebastian T1 - Revisiting the Approximate Carathéodory Problem via the Frank-Wolfe Algorithm JF - Mathematical Programming A Y1 - 2023 U6 - https://doi.org/10.1007/s10107-021-01735-x VL - 197 SP - 191 EP - 214 ER - TY - JOUR A1 - Sperber, Wolfram T1 - Mathematische Gesellschaft der DDR – die Vorgeschichte JF - Mathematische Semesterberichte N2 - ZusammenfassungDie Mathematische Gesellschaft der DDR (MGDDR) ist seit 1991 Geschichte. Die MGDDR spaltete sich 1962 auf Betreiben der Sozialistischen Einheitspartei (SED) der DDR von der Deutschen Mathematiker-Vereinigung (DMV) ab und beschloss 1990 den Zusammenschluss mit der DMV. Die Geschichte der MGDDR ist spannend, angefangen von der Vorgeschichte, ihren Aktivitäten in der DDR-Zeit bis zur Neupositionierung nach der Wende. Und die MGDDR hat ihre Spuren in der DMV hinterlassen. Etliche Ansätze und Aktivitäten der MGDDR wurden von der DMV fortgeführt und weiterentwickelt. Aus der Literatur sind bisher nur Darstellungen einzelner Aspekte der MGDDR bekannt. Dieser Artikel unternimmt den Versuch einer Gesamtdarstellung der Geschichte der MGDDR und soll die Ausführungen in [1] und [2] ergänzen und erweitern. Die MGDDR war ein Ergebnis des Kalten Krieges und – wesentlich stärker als bisher der Öffentlichkeit bekannt – ein Produkt der Wissenschaftspolitik von Partei und Staat der DDR. Der politische Einfluss wird in diesem Artikel durch Unterlagen belegt, die in verschiedenen Archiven gefunden wurden. Von besonderer Bedeutung bei der Recherche war das Archivgut der Stiftung Archiv der Parteien und Massenorganisationen der DDR im Bundesarchiv(SAPMO), wo seit 1990 die Unterlagen der SED, staatlicher Stellen und Massenorganisatioen der DDR systematisch aufbereitet und verfügbar gemacht worden sind. Die Mathematiker der DDR standen der Vereinnahmung durch Partei und Staat mehrheitlich kritisch gegenüber. Dies gilt insbesondere für die Zeit vor dem Mauerbau. Nach dem Mauerbau und den Einschränkungen des Reiseverkehrs war für die meisten Mathematiker der DDR die Gründung einer eigenen Fachgesellschaft alternativlos. Diese erfolgte am 8. Juni 1962. Nach dem Mauerbau war für die Mathematiker in der DDR wissenschaftlicher Austausch ohne Einbeziehung der MGDDR nahezu unmöglich. Für die Arbeit der MGDDR standen aber immer mathematische Ziele im Zentrum und die MGDDR war dabei – trotz einiger Behinderungen – durchaus erfolgreich. Nach der Wende positionierte sich die MGDDR neu und beschloss auf dem Mathematiker-Kongress der DDR im September 1990 den Zusammenschluss mit der DMV. Der vorliegende Artikel umfasst die Vorgeschichte der MGDDR bis zu deren Gründung am 08.06.1962. In zwei weiteren Publikationen soll die Arbeit der MGDDR bis zur Wende und dem Zusammenschluss mit der DMV dargestellt werden. Y1 - 2023 U6 - https://doi.org/10.1007/s00591-023-00350-5 SN - 0720-728X VL - 70 IS - 2 SP - 103 EP - 146 PB - Springer Science and Business Media LLC ER - TY - THES A1 - Danecker, Fabian T1 - A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization N2 - This thesis introduces the novel hybrid algorithm DisCOptER for globally optimal flight planning. DisCOptER (Discrete-Continuous Optimization for Enhanced Resolution) com- bines discrete and continuous optimization in a two-stage approach to find optimal trajectories up to arbitrary precision in finite time. In the discrete phase, a directed auxiliary graph is created in order to define a set of candidate paths that densely covers the relevant part of the trajectory space. Then, Yen’s algorithm is employed to identify a set of promising candidate paths. These are used as starting points for the subsequent stage in which they are refined with a locally convergent optimal control method. The correctness, accuracy, and complexity of DisCOptER are intricately linked to the choice of the switch-over point, defined by the discretization coarseness. Only a sufficiently dense graph enables the algorithm to find a path within the convex domain surrounding the global minimizer. Initialized with such a path, the second stage rapidly converges to the optimum. Conversely, an excessively dense graph poses the risk of overly costly and redundant computations. The determination of the optimal switch-over point necessitates a profound understanding of the local behavior of the problem, the approximation properties of the graph, and the convergence characteristics of the employed optimal control method. These topics are explored extensively in this thesis. Crucially, the density of the auxiliary graph is solely dependent on the en- vironmental conditions, yet independent of the desired solution accuracy. As a consequence, the algorithm inherits the superior asymptotic convergence properties of the optimal control stage. The practical implications of this computational efficiency are demonstrated in realistic environments, where the DisCOptER algorithm consistently delivers highly accurate globally optimal trajectories with exceptional computational efficiency. This notable improvement upon existing approaches underscores the algorithm’s significance. Beyond its technical prowess, the DisCOptER algorithm stands as a valuable tool contributing to the reduction of costs and the overall enhancement of flight operations efficiency. Y1 - 2023 UR - http://dx.doi.org/10.17169/refubium-43526 ER - TY - CHAP A1 - Andrés Arcones, Daniel A1 - Weiser, Martin A1 - Koutsourelakis, Faidon-Stelios A1 - Unger, Jörg F. T1 - Evaluation of Model Bias Identification Approaches Based on Bayesian Inference and Applications to Digital Twins T2 - 5th ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering N2 - In recent years, the use of simulation-based digital twins for monitoring and assessment of complex mechanical systems has greatly expanded. Their potential to increase the information obtained from limited data makes them an invaluable tool for a broad range of real-world applications. Nonetheless, there usually exists a discrepancy between the predicted response and the measurements of the system once built. One of the main contributors to this difference in addition to miscalibrated model parameters is the model error. Quantifying this socalled model bias (as well as proper values for the model parameters) is critical for the reliable performance of digital twins. Model bias identification is ultimately an inverse problem where information from measurements is used to update the original model. Bayesian formulations can tackle this task. Including the model bias as a parameter to be inferred enables the use of a Bayesian framework to obtain a probability distribution that represents the uncertainty between the measurements and the model. Simultaneously, this procedure can be combined with a classic parameter updating scheme to account for the trainable parameters in the original model. This study evaluates the effectiveness of different model bias identification approaches based on Bayesian inference methods. This includes more classical approaches such as direct parameter estimation using MCMC in a Bayesian setup, as well as more recent proposals such as stat-FEM or orthogonal Gaussian Processes. Their potential use in digital twins, generalization capabilities, and computational cost is extensively analyzed. Y1 - 2023 UR - https://2023.uncecomp.org/proceedings/pdf/19795.pdf SP - 1 EP - 15 ER - TY - JOUR A1 - Andrés Arcones, Daniel A1 - Weiser, Martin A1 - Koutsourelakis, Faidon-Stelios A1 - Unger, Jörg F. T1 - A Bayesian Framework for Simulation-based Digital Twins of Bridges JF - EUROSTRUCT 2023:European Association on Quality Control of Bridges and Structures: Digital Transformation in Sustainability N2 - Simulation-based digital twins have emerged as a powerful tool for evaluating the mechanical response of bridges. As virtual representations of physical systems, digital twins can provide a wealth of information that complements traditional inspection and monitoring data. By incorporating virtual sensors and predictive maintenance strategies, they have the potential to improve our understanding of the behavior and performance of bridges over time. However, as bridges age and undergo regular loading and extreme events, their structural characteristics change, often differing from the predictions of their initial design. Digital twins must be continuously adapted to reflect these changes. In this article, we present a Bayesian framework for updating simulation-based digital twins in the context of bridges. Our approach integrates information from measurements to account for inaccuracies in the simulation model and quantify uncertainties. Through its implementation and assessment, this work demonstrates the potential for digital twins to provide a reliable and up-to-date representation of bridge behavior, helping to inform decision-making for maintenance and management. Y1 - 2023 U6 - https://doi.org/10.1002/cepa.2177 VL - 6 IS - 5 SP - 734 EP - 740 ER - TY - JOUR A1 - Gupta, Pranshu A1 - Hamann, Fabian A1 - Müyesser, Alp A1 - Sgueglia, Amedeo A1 - Parczyk, Olaf T1 - A general approach to transversal versions of Dirac-type theorems JF - Bulletin of the London Mathematical Society Y1 - 2023 VL - 55 IS - 6 SP - 2817 EP - 2839 ER - TY - JOUR A1 - Kohayakawa, Yoshiharu A1 - Mota, Guilherme O. A1 - Schnitzer, Jakob A1 - Parczyk, Olaf T1 - Anti-Ramsey threshold of complete graphs for sparse graphs JF - Discrete Mathematics Y1 - 2023 ER - TY - THES A1 - Bena, Noor-Cella T1 - Finding Rules and Patterns in Egyptological Research Objects using Boolean Polynomial Rings Y1 - 2023 ER - TY - THES A1 - Kunt, Tim T1 - The n-Queens Problem in Higher Dimensions N2 - How many mutually non-attacking queens can be placed on a d-dimensional chessboard of size n? The n-queens problem in higher dimensions is a generalization of the well-known n-queens problem. We provide a comprehensive overview of theoretical results, bounds, solution methods, and the interconnectivity of the problem within topics of discrete optimization and combinatorics. We present an integer programming formulation of the n-queens problem in higher dimensions and several strengthenings through additional valid inequalities. Compared to recent benchmarks, we achieve a speedup in computational time between 15-70x over all instances of the integer programs. Our computational results prove optimality of certificates for several large instances. Breaking additional, previously unsolved instances with the proposed methods is likely possible. On the primal side, we further discuss heuristic approaches to constructing solutions that turn out to be optimal when compared to the IP. We conclude with preliminary results on the number and density of the solutions. T3 - ZIB-Report - 24-05 KW - Integer Programming KW - Maximum Independent Set KW - n-Queens Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-96468 ER -