@inproceedings{RickertGaoUrbanetal.2022, author = {Rickert, Lucas and Gao, Timm and Urban, Felix and Große, Jan and Srocka, Nicole and Rodt, Sven and Musial, Anna and Zolnacz, Kinga and Mergo, Pawel and Dybka, Kamil and Urbanczyk, Waclaw and Sek, Grzegorz and Burger, Sven and Reitzenstein, Stephan and Heindel, Tobias}, title = {A Plug\&Play Telecom-Wavelength Single-Photon Source for Quantum Key Distribution}, booktitle = {Quantum 2.0}, doi = {10.1364/QUANTUM.2022.QTu4C.6}, pages = {QTu4C.6}, year = {2022}, language = {en} } @article{ErlekamZumbansenWeber2022, author = {Erlekam, Franziska and Zumbansen, Maximilian and Weber, Marcus}, title = {Parameter estimation on multivalent ITC data sets}, volume = {12}, journal = {Scientific Reports}, doi = {10.1038/s41598-022-17188-x}, pages = {13402}, year = {2022}, abstract = {The Wiseman fitting can be used to extract binding parameters from ITC data sets, such as heat of binding, number of binding sites, and the overall dissociation rate. The classical Wiseman fitting assumes a direct binding process and neglects the possibility of intermediate binding steps. In principle, it only provides thermodynamic information and not the kinetics of the process. In this article we show that a concentration dependent dissociation constant could possibly stem from intermediate binding steps. The mathematical form of this dependency can be exploited with the aid of the Robust Perron Cluster Cluster Analysis method. Our proposed extension of the Wiseman fitting rationalizes the concentration dependency, and can probably also be used to determine the kinetic parameters of intermediate binding steps of a multivalent binding process. The novelty of this paper is to assume that the binding rate varies per titration step due to the change of the ligand concentration and to use this information in the Wiseman fitting. We do not claim to produce the most accurate values of the binding parameters, we rather present a novel method of how to approach multivalent bindings from a different angle.}, language = {en} } @misc{PlockAndrleBurgeretal.2022, author = {Plock, Matthias and Andrle, Kas and Burger, Sven and Schneider, Philipp-Immanuel}, title = {Research data and example scripts for the paper "Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction"}, journal = {Zenodo}, doi = {10.5281/zenodo.6359594}, year = {2022}, language = {en} } @misc{BinkowskiBetzHammerschmidtetal.2022, author = {Binkowski, Felix and Betz, Fridtjof and Hammerschmidt, Martin and Schneider, Philipp-Immanuel and Zschiedrich, Lin and Burger, Sven}, title = {Source code and simulation data for Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators}, journal = {Zenodo}, doi = {10.5281/zenodo.6614951}, year = {2022}, language = {en} } @article{FrankSikorskiRoeblitz2024, author = {Frank, Anna-Simone and Sikorski, Alexander and R{\"o}blitz, Susanna}, title = {Spectral clustering of Markov chain transition matrices with complex eigenvalues}, volume = {444}, journal = {Journal of Computational and Applied Mathematics}, arxiv = {http://arxiv.org/abs/2206.14537}, doi = {10.1016/j.cam.2024.115791}, pages = {115791}, year = {2024}, abstract = {The Robust Perron Cluster Analysis (PCCA+) has become a popular spectral clustering algorithm for coarse-graining transition matrices of nearly decomposable Markov chains with transition states. Originally developed for reversible Markov chains, the algorithm only worked for transition matrices with real eigenvalues. In this paper, we therefore extend the theoretical framework of PCCA+ to Markov chains with a complex eigen-decomposition. We show that by replacing a complex conjugate pair of eigenvectors by their real and imaginary components, a real representation of the same subspace is obtained, which is suitable for the cluster analysis. We show that our approach leads to the same results as the generalized PCCA+ (GPCCA), which replaces the complex eigen-decomposition by a conceptually more difficult real Schur decomposition. We apply the method on non-reversible Markov chains, including circular chains, and demonstrate its efficiency compared to GPCCA. The experiments are performed in the Matlab programming language and codes are provided.}, language = {de} } @misc{KostreSunkaraSchuetteetal.2022, author = {Kostr{\´e}, Margarita and Sunkara, Vikram and Sch{\"u}tte, Christof and Djurdjevac Conrad, Nataša}, title = {Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-86764}, year = {2022}, abstract = {Spreading processes are important drivers of change in social systems. To understand the mechanisms of spreading it is fundamental to have information about the underlying contact network and the dynamical parameters of the process. However, in many real-wold examples, this information is not known and needs to be inferred from data. State-of-the-art spreading inference methods have mostly been applied to modern social systems, as they rely on availability of very detailed data. In this paper we study the inference challenges for historical spreading processes, for which only very fragmented information is available. To cope with this problem, we extend existing network models by formulating a model on a mesoscale with temporal spreading rate. Furthermore, we formulate the respective parameter inference problem for the extended model. We apply our approach to the romanization process of Northern Tunisia, a scarce dataset, and study properties of the inferred time-evolving interregional networks. As a result, we show that (1) optimal solutions consist of very different network structures and spreading rate functions; and that (2) these diverse solutions produce very similar spreading patterns. Finally, we discuss how inferred dominant interregional connections are related to available archaeological traces. Historical networks resulting from our approach can help understanding complex processes of cultural change in ancient times.}, language = {en} } @article{BoltzSirbuStelzeretal.2022, author = {Boltz, Horst-Holger and Sirbu, Alexei and Stelzer, Nina and de Lanerolle, Primal and Winkelmann, Stefanie and Annibale, Paolo}, title = {The Impact of Membrane Protein Diffusion on GPCR Signaling}, volume = {11}, journal = {Cells}, number = {10}, doi = {10.3390/cells11101660}, pages = {1660}, year = {2022}, abstract = {Spatiotemporal signal shaping in G protein-coupled receptor (GPCR) signaling is now a well-established and accepted notion to explain how signaling specificity can be achieved by a superfamily sharing only a handful of downstream second messengers. Dozens of Gs-coupled GPCR signals ultimately converge on the production of cAMP, a ubiquitous second messenger. This idea is almost always framed in terms of local concentrations, the differences in which are maintained by means of spatial separation. However, given the dynamic nature of the reaction-diffusion processes at hand, the dynamics, in particular the local diffusional properties of the receptors and their cognate G proteins, are also important. By combining some first principle considerations, simulated data, and experimental data of the receptors diffusing on the membranes of living cells, we offer a short perspective on the modulatory role of local membrane diffusion in regulating GPCR-mediated cell signaling. Our analysis points to a diffusion-limited regime where the effective production rate of activated G protein scales linearly with the receptor-G protein complex's relative diffusion rate and to an interesting role played by the membrane geometry in modulating the efficiency of coupling}, language = {en} } @article{SchneiderManleyKruegeretal.2022, author = {Schneider, Philipp-Immanuel and Manley, Phillip and Kr{\"u}ger, Jan and Zschiedrich, Lin and K{\"o}ning, Rainer and Bodermann, Bernd and Burger, Sven}, title = {Reconstructing phase aberrations for high-precision dimensional microscopy}, volume = {12137}, journal = {Proc. SPIE}, doi = {10.1117/12.2620762}, pages = {121370I}, year = {2022}, language = {en} } @inproceedings{JaegerSutterTockhornetal.2022, author = {J{\"a}ger, Klaus and Sutter, Johannes and Tockhorn, Philipp and Hammerschmidt, Martin and Schneider, Philipp-Immanuel and Albrecht, Steve and Becker, Christiane}, title = {Improving perovskite/silicon tandem solar cells with optical simulations}, volume = {PC12150}, booktitle = {Proc. SPIE}, doi = {10.1117/12.2621255}, pages = {PC1215001}, year = {2022}, language = {en} } @article{AvalosOvandoSantiagoMovsesyanetal.2022, author = {Avalos-Ovando, Oscar and Santiago, Eva Yazmin and Movsesyan, Artur and Kong, Xiang-Tian and Yu, Peng and Besteiro, Lucas V. and Khosravi Khorashad, Larousse and Okamoto, Hiromi and Slocik, Joseph M. and Correa-Duarte, Miguel and Comesana-Hermo, Miguel and Liedl, Tim and Markovich, Gil and Burger, Sven and Govorov, Alexander O.}, title = {Chiral Bioinspired Plasmonics: A Paradigm Shift for Optical Activity and Photochemistry}, volume = {9}, journal = {ACS Photon.}, doi = {10.1021/acsphotonics.2c00445}, pages = {2219}, year = {2022}, language = {en} } @article{BremerJimenezThieleetal.2022, author = {Bremer, Lucas and Jimenez, Carlos and Thiele, Simon and Weber, Ksenia and Huber, Tobias and Rodt, Sven and Herkommer, Alois and Burger, Sven and H{\"o}fling, Sven and Giessen, Harald and Reitzenstein, Stephan}, title = {Numerical optimization of single-mode fiber- coupled single-photon sources based on semiconductor quantum dots}, volume = {30}, journal = {Opt. Express}, arxiv = {http://arxiv.org/abs/2202.09562}, doi = {10.1364/OE.456777}, pages = {15913}, year = {2022}, language = {en} } @article{DassKuenPosnjaketal.2022, author = {Dass, Mihir and Kuen, Lilli and Posnjak, Gregor and Burger, Sven and Liedl, Tim}, title = {Visible wavelength spectral tuning of absorption and circular dichroism of DNA-assembled Au/Ag core-shell nanorod assemblies}, volume = {3}, journal = {Mater. Adv.}, doi = {10.1039/D1MA01211H}, pages = {3438}, year = {2022}, language = {en} } @article{PlockAndrleBurgeretal.2022, author = {Plock, Matthias and Andrle, Kas and Burger, Sven and Schneider, Philipp-Immanuel}, title = {Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction}, volume = {5}, journal = {Adv. Theory Simul.}, arxiv = {http://arxiv.org/abs/2202.11559}, doi = {10.1002/adts.202200112}, pages = {2200112}, year = {2022}, language = {en} } @article{VolkovaHeupelTrofimovetal.2022, author = {Volkova, Kseniia and Heupel, Julia and Trofimov, Sergei and Betz, Fridtjof and Colom, R{\´e}mi and MacQueen, Rowan W. and Akhundzada, Sapida and Reginka, Meike and Ehresmann, Arno and Reithmeier, Johann Peter and Burger, Sven and Popov, Cyril and Naydenov, Boris}, title = {Optical and Spin Properties of NV Center Ensembles in Diamond Nano-Pillars}, volume = {12}, journal = {Nanomaterials}, doi = {10.3390/nano12091516}, pages = {1516}, year = {2022}, language = {en} } @article{WangVannucciBurgeretal.2022, author = {Wang, Yujing and Vannucci, Luca and Burger, Sven and Gregersen, Niels}, title = {Near-unity efficiency in ridge waveguide-based, on-chip single-photon sources}, volume = {2}, journal = {Mater. Quantum Technol.}, arxiv = {http://arxiv.org/abs/2207.02665}, doi = {10.1088/2633-4356/aca8e8}, pages = {045004}, year = {2022}, language = {en} } @article{LopezFraguasBinkowskiBurgeretal.2022, author = {Lopez-Fraguas, Eduardo and Binkowski, Felix and Burger, Sven and Hagedorn, Sylvia and Garcia-Camara, Braulio and Vergaz, Ricardo and Becker, Christiane and Manley, Phillip}, title = {Tripling the light extraction efficiency of a deep ultraviolet LED using a nanostructured p-contact}, volume = {12}, journal = {Sci. Rep.}, doi = {10.1038/s41598-022-15499-7}, pages = {11480}, year = {2022}, language = {en} } @misc{BetzColomBurgeretal.2022, author = {Betz, Fridtjof and Colom, Remi and Burger, Sven and Naydenov, Boris}, title = {Scripts for quantifying the effect of diamond nano-pillars on the fluorescence of NV centers}, journal = {Zenodo}, doi = {10.5281/zenodo.6558815}, year = {2022}, language = {en} } @phdthesis{Niemann2022, author = {Niemann, Jan-Hendrik}, title = {Learning Reduced Models for Large-Scale Agent-Based Systems}, doi = {10.17169/refubium-35245}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-refubium-35530-6}, pages = {130}, year = {2022}, abstract = {Modeling social systems and studying their dynamical behavior plays an important role in many fields of research. Agent-based modeling provides a high degree of detail into artificial societies by describing the model from the perspective of the agents. The interactions of agents, often characterized by simple rules, lead to complex, time-evolving patterns. Their understanding is of great importance, e.g., for predicting and influencing epidemics. Analysis and simulation, however, often becomes prohibitively time-consuming when the number of agents or the time scale of interest is large. Therefore, this thesis is devoted to learn significantly reduced models of large-scale agent-based systems from simulation data. We show how data-driven methods based on transfer operators can be used to find reduced models represented by ordinary or stochastic differential equations that describe the dynamical behavior of larger groups or entire populations and thus enable the analysis and prediction of agent-based systems. To this end, we first present an extension of EDMD (extended dynamic mode decomposition) called gEDMD to approximate the Koopman generator from data. This method can be used to compute eigenfunctions, eigenvalues, and modes of the generator, as well as for system identification and model reduction of both deterministic and non-deterministic dynamical systems. Secondly, we analyze the long-term behavior of certain agent-based models and their pathwise approximations by stochastic differential equations for large numbers of agents using transfer operators. We show that, under certain conditions, the transfer operator approach connects the pathwise approximations on finite time scales with methods for describing the behavior on possibly exponentially long time scales. As a consequence, we can use the finite-time, pathwise approximations to characterize metastable behavior on long time scales using transfer operators. This can significantly reduce the computational cost. The third part addresses the data-driven model reduction since in many cases no analytical limit models are known or existent. We show how the Koopman operator theory can be used to infer the governing equations of agent-based systems directly from simulation data. Using benchmark problems, we demonstrate that for sufficiently large population sizes the data-driven models agree well with analytical limit equations and, moreover, that the reduced models allow predictions even in cases far from the limit or when no limit equations are known. Lastly, we demonstrate the potential of the presented approach. We present an ansatz for the multi-objective optimization of agent-based systems with the help of data-driven surrogate models based on the Koopman generator. In particular, when limit models are unknown or non-existent, this approach makes multi-objective optimization problems solvable that would otherwise be computationally infeasible due to very expensive objective functions.}, language = {en} } @article{BeronVeraOlascoagaHelfmannetal.2023, author = {Beron-Vera, Francisco Javier and Olascoaga, Maria Josefina and Helfmann, Luzie and Miron, Philippe}, title = {Sampling-Dependent Transition Paths of Iceland-Scotland Overflow Water}, volume = {53}, journal = {Journal of Physical Oceanography}, number = {4}, arxiv = {http://arxiv.org/abs/2208.09499}, doi = {10.1175/JPO-D-22-0172.1}, pages = {1151 -- 1160}, year = {2023}, abstract = {In this note, we apply Transition Path Theory (TPT) from Markov chains to shed light on the problem of Iceland-Scotland Overflow Water (ISOW) equatorward export. A recent analysis of observed trajectories of submerged floats demanded revision of the traditional abyssal circulation theory, which postulates that ISOW should steadily flow along a deep boundary current (DBC) around the subpolar North Atlantic prior to exiting it. The TPT analyses carried out here allow to focus the attention on the portions of flow from the origin of ISOW to the region where ISOW exits the subpolar North Atlantic and suggest that insufficient sampling may be biasing the aforementioned demand. The analyses, appropriately adapted to represent a continuous input of ISOW, are carried out on three time-homogeneous Markov chains modeling the ISOW flow. One is constructed using a high number of simulated trajectories homogeneously covering the flow domain. The other two use much fewer trajectories which heterogeneously cover the domain. The trajectories in the latter two chains are observed trajectories or simulated trajectories subsampled at the observed frequency. While the densely sampled chain supports a well-defined DBC, the more heterogeneously sampled chains do not, irrespective of whether observed or simulated trajectories are used. Studying the sampling sensitivity of the Markov chains, we can give recommendations for enlarging the existing float dataset to improve the significance of conclusions about time-asymptotic aspects of the ISOW circulation.}, language = {en} } @article{BartelsFisikopoulosWeiser2023, author = {Bartels, Tinko and Fisikopoulos, Vissarion and Weiser, Martin}, title = {Fast Floating-Point Filters for Robust Predicates}, volume = {63}, journal = {BIT Numerical Mathematics}, arxiv = {http://arxiv.org/abs/2208.00497}, doi = {10.1007/s10543-023-00975-x}, year = {2023}, abstract = {Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information systems and computer-aided design. With floating-point arithmetic, these geometric predicates can incur round-off errors that may lead to incorrect results and inconsistencies, causing computations to fail. This issue has been addressed using a combination of exact arithmetic for robustness and floating-point filters to mitigate the computational cost of exact computations. The implementation of exact computations and floating-point filters can be a difficult task, and code generation tools have been proposed to address this. We present a new C++ meta-programming framework for the generation of fast, robust predicates for arbitrary geometric predicates based on polynomial expressions. We combine and extend different approaches to filtering, branch reduction, and overflow avoidance that have previously been proposed. We show examples of how this approach produces correct results for data sets that could lead to incorrect predicate results with naive implementations. Our benchmark results demonstrate that our implementation surpasses state-of-the-art implementations.}, language = {en} } @inproceedings{DhanakotiMaddocksWeiser2022, author = {Dhanakoti, Siva Prasad Chakri and Maddocks, John and Weiser, Martin}, title = {Navigation of Concentric Tube Continuum Robots using Optimal Control}, booktitle = {Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics}, doi = {10.5220/0011271000003271}, pages = {146 -- 154}, year = {2022}, abstract = {Recently developed Concentric Tube Continuum Robots (CTCRs) are widely exploited in, for example in minimally invasive surgeries which involve navigating inside narrow body cavities close to sensitive regions. These CTCRs can be controlled by extending and rotating the tubes in order to reach a target point or perform some task. The robot must deviate as little as possible from this narrow space and avoid damaging neighbouring tissue. We consider \emph{open-loop} optimal control of CTCRs parameterized over pseudo-time, primarily aiming at minimizing the robot's working volume during its motion. External loads acting on the system like tip loads or contact with tissues are not considered here. We also discussed the inclusion of tip's orientation in the optimal framework to perform some tasks. We recall a quaternion-based formulation of the robot configuration, discuss discretization, develop optimization objectives addressing different criteria, and investigate their impact on robot path planning for several numerical examples. This optimal framework can be applied to any backbone based continuum robots.}, language = {en} } @article{BinkowskiBetzHammerschmidtetal.2022, author = {Binkowski, Felix and Betz, Fridtjof and Hammerschmidt, Martin and Schneider, Philipp-Immanuel and Zschiedrich, Lin and Burger, Sven}, title = {Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators}, volume = {5}, journal = {Commun. Phys.}, arxiv = {http://arxiv.org/abs/2203.11101}, doi = {10.1038/s42005-022-00977-1}, pages = {202}, year = {2022}, language = {en} } @article{TockhornSutterCruzetal.2022, author = {Tockhorn, Philipp and Sutter, Johannes and Cruz, Alexandros and Wagner, Philipp and J{\"a}ger, Klaus and Yoo, Danbi and Lang, Felix and Grischek, Max and Li, Bor and Li, Jinzhao and Shargaieva, Oleksandra and Unger, Eva and Al-Ashouri, Amran and K{\"o}hnen, Eike and Stolterfoth, Martin and Neher, Dieter and Schlatmann, Rutger and Rech, Bernd and Stannowski, Bernd and Albrecht, Steve and Becker, Christiane}, title = {Nano-optical designs for high-efficiency monolithic perovskite-silicon tandem solar cells}, volume = {17}, journal = {Nat. Nanotechnol.}, doi = {10.1038/s41565-022-01228-8}, pages = {1214}, year = {2022}, language = {en} } @article{MovsesyanSantiagoBurgeretal.2022, author = {Movsesyan, Artur and Santiago, Eva Yazmin and Burger, Sven and Correa-Duarte, Miguel and Besteiro, Lucas V. and Wang, Zhiming and Govorov, Alexander O.}, title = {Plasmonic nanocrystals with complex shapes for photocatalysis and growth: Contrasting anisotropic hot-electron generation with the photothermal effect}, volume = {10}, journal = {Adv. Opt. Mater.}, arxiv = {http://arxiv.org/abs/2203.00930}, doi = {10.1002/adom.202102663}, pages = {2102663}, year = {2022}, language = {en} } @misc{ColomBinkowskiBetzetal.2022, author = {Colom, Remi and Binkowski, Felix and Betz, Fridtjof and Kivshar, Yuri and Burger, Sven}, title = {Source code and simulation results for nanoantennas supporting an enhanced Purcell factor due to interfering resonances}, journal = {Zenodo}, doi = {10.5281/zenodo.6565850}, year = {2022}, language = {en} } @article{KlusDjurdjevacConrad2022, author = {Klus, Stefan and Djurdjevac Conrad, Natasa}, title = {Koopman-based spectral clustering of directed and time-evolving graphs}, volume = {33}, journal = {Journal of Nonlinear Science}, arxiv = {http://arxiv.org/abs/2204.02951}, doi = {10.1007/s00332-022-09863-0}, pages = {8}, year = {2022}, abstract = {While spectral clustering algorithms for undirected graphs are well established and have been successfully applied to unsupervised machine learning problems ranging from image segmentation and genome sequencing to signal processing and social network analysis, clustering directed graphs remains notoriously difficult. Two of the main challenges are that the eigenvalues and eigenvectors of graph Laplacians associated with directed graphs are in general complex-valued and that there is no universally accepted definition of clusters in directed graphs. We first exploit relationships between the graph Laplacian and transfer operators and in particular between clusters in undirected graphs and metastable sets in stochastic dynamical systems and then use a generalization of the notion of metastability to derive clustering algorithms for directed and time-evolving graphs. The resulting clusters can be interpreted as coherent sets, which play an important role in the analysis of transport and mixing processes in fluid flows.}, language = {en} } @article{BennerBurgerGoeddekeetal.2022, author = {Benner, Peter and Burger, Michael and G{\"o}ddeke, Dominik and G{\"o}rgen, Christiane and Himpe, Christian and Heiland, Jan and Koprucki, Thomas and Ohlberger, Mario and Rave, Stephan and Reidelbach, Marco and Saak, Jens and Sch{\"o}bel, Anita and Tabelow, Karsten and Weber, Marcus}, title = {Die mathematische Forschungsdateninitiative in der NFDI: MaRDI (Mathematical Research Data Initiative)}, journal = {GAMM Rundbrief}, number = {1}, pages = {40 -- 43}, year = {2022}, language = {de} } @article{TillmannJaegerKarsentietal.2022, author = {Tillmann, Peter and J{\"a}ger, Klaus and Karsenti, Asher and Kreinin, Lev and Becker, Christiane}, title = {Model-Chain Validation for Estimating the Energy Yield of Bifacial Perovskite/Silicon Tandem Solar Cells}, volume = {6}, journal = {Sol. RRL}, doi = {10.1002/solr.202200079}, pages = {2200079}, year = {2022}, language = {en} } @article{EngelOliconMendezWehlitzetal.2024, author = {Engel, Maximilian and Olic{\´o}n-M{\´e}ndez, Guillermo and Wehlitz, Nathalie and Winkelmann, Stefanie}, title = {Synchronization and random attractors in reaction jump processes}, journal = {Journal of Dynamics and Differential Equations}, arxiv = {http://arxiv.org/abs/2207.00602}, doi = {10.1007/s10884-023-10345-4}, year = {2024}, abstract = {This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. Based on Gillespie's stochastic simulation algorithm, a corresponding random dynamical system is formulated in a two-step procedure, at first for the states of the embedded discrete-time Markov chain and then for the augmented Markov chain including random jump times. We uncover a time-shifted synchronization in the sense that—after some initial waiting time—one trajectory exactly replicates another one with a certain time delay. Whether or not such a synchronization behavior occurs depends on the combination of the initial states. We prove this partial time-shifted synchronization for the special setting of a birth-death process by analyzing the corresponding two-point motion of the embedded Markov chain and determine the structure of the associated random attractor. In this context, we also provide general results on existence and form of random attractors for discrete-time, discrete-space random dynamical systems.}, language = {en} } @misc{BorndoerferDaneckerWeiser2023, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-91309}, year = {2023}, abstract = {The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition.}, language = {en} } @phdthesis{Danecker2023, author = {Danecker, Fabian}, title = {A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization}, year = {2023}, abstract = {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.}, language = {en} } @article{BorndoerferDaneckerWeiser2021, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {A Discrete-Continuous Algorithm for Free Flight Planning}, volume = {14}, journal = {Algorithms}, number = {1}, publisher = {MDPI}, issn = {1438-0064}, doi = {10.3390/a14010004}, pages = {4}, year = {2021}, abstract = {We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach.}, language = {en} } @misc{BorndoerferDaneckerWeiser2023, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Newton's Method for Global Free Flight Trajectory Optimization}, doi = {10.12752/8987}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-89876}, year = {2023}, abstract = {Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case.}, language = {en} } @inproceedings{BorndoerferDaneckerWeiser2023, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization}, volume = {115}, booktitle = {23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)}, doi = {10.4230/OASIcs.ATMOS.2023.3}, pages = {3:1 -- 3:6}, year = {2023}, abstract = {The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition.}, language = {en} } @article{BorndoerferDaneckerWeiser2023, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Newton's Method for Global Free Flight Trajectory Optimization}, volume = {4}, journal = {Operations Research Forum}, doi = {10.1007/s43069-023-00238-z}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-91846}, year = {2023}, abstract = {Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case.}, language = {en} } @article{BorndoerferDaneckerWeiser2023, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Error Bounds for Discrete-Continuous Free Flight Trajectory Optimization}, volume = {198}, journal = {Journal of Optimization Theory and Applications}, doi = {10.1007/s10957-023-02264-7}, pages = {830 -- 856}, year = {2023}, abstract = {Flight planning, the computation of optimal routes in view of flight time and fuel consumption under given weather conditions, is traditionally done by finding globally shortest paths in a predefined airway network. Free flight trajectories, not restricted to a network, have the potential to reduce the costs significantly, and can be computed using locally convergent continuous optimal control methods. Hybrid methods that start with a discrete global search and refine with a fast continuous local optimization combine the best properties of both approaches, but rely on a good switchover, which requires error estimates for discrete paths relative to continuous trajectories. Based on vertex density and local complete connectivity, we derive localized and a priori bounds for the flight time of discrete paths relative to the optimal continuous trajectory, and illustrate their properties on a set of benchmark problems. It turns out that localization improves the error bound by four orders of magnitude, but still leaves ample opportunities for tighter bounds using a posteriori error estimators.}, language = {en} } @inproceedings{BorndoerferDaneckerWeiser2022, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization}, volume = {106}, booktitle = {22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)}, doi = {10.4230/OASIcs.ATMOS.2022.2}, pages = {1 -- 13}, year = {2022}, abstract = {We present an efficient algorithm that finds a globally optimal solution to the 2D Free Flight Trajectory Optimization Problem (aka Zermelo Navigation Problem) up to arbitrary precision in finite time. The algorithm combines a discrete and a continuous optimization phase. In the discrete phase, a set of candidate paths that densely covers the trajectory space is created on a directed auxiliary graph. Then Yen's algorithm provides a promising set of discrete candidate paths which subsequently undergo a locally convergent refinement stage. Provided that the auxiliary graph is sufficiently dense, the method finds a path that lies within the convex domain around the global minimizer. From this starting point, the second stage will converge rapidly to the optimum. The density of the auxiliary graph depends solely on the wind field, and not on the accuracy of the solution, such that the method inherits the superior asymptotic convergence properties of the optimal control stage.}, language = {en} } @misc{BorndoerferDaneckerWeiser2020, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {A Discrete-Continuous Algorithm for Free Flight Planning}, issn = {1438-0064}, doi = {10.3390/a14010004}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81343}, year = {2020}, abstract = {We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach.}, language = {en} } @article{WidlerKaminskaMartinsetal.2026, author = {Widler, Valeria and Kaminska, Barbara and Martins, Andre C. R. and Puga-Gonzalez, Ivan}, title = {An Investigation into the Causal Mechanism of Political Opinion Dynamics: A Model of Hierarchical Coarse-Graining with Community-Bounded Social Influence}, journal = {Computational Social Science of Social Cohesion and Polarization}, edition = {Computational Social Science of Social Cohesion and Polarization}, publisher = {Springer, Cham.}, arxiv = {http://arxiv.org/abs/2504.00877}, doi = {10.1007/978-3-032-01373-6_10}, pages = {225 -- 256}, year = {2026}, abstract = {The increasing polarization in democratic societies is an emergent outcome of political opinion dynamics. Yet, the fundamental mechanisms behind the formation of political opinions, from individual beliefs to collective consensus, remain unknown. Understanding that a causal mechanism must account for both bottom-up and top-down influences, we conceptualize political opinion dynamics as hierarchical coarse-graining, where microscale opinions integrate into a macro-scale state variable. Using the CODA (Continuous Opinions Discrete Actions) model, we simulate Bayesian opinion updating, social identity-based information integration, and migration between social identity groups to represent higher-level connectivity. This results in coarse-graining across micro, meso, and macro levels. Our findings show that higher-level connectivity shapes information integration, yielding three regimes: independent (disconnected, local convergence), parallel (fast, global convergence), and iterative (slow, stepwise convergence). In the iterative regime, low connectivity fosters transient diversity, indicating an informed consensus. In all regimes, time-scale separation leads to downward causation, where agents converge on the aggregate majority choice, driving consensus. Critically, any degree of coherent higher-level information integration can overcome misalignment via global downward causation. The results highlight how emergent properties of the causal mechanism, such as downward causation, are essential for consensus and may inform more precise investigations into polarized political discourse.}, language = {en} } @article{Marco2025, author = {Marco, Reidelbach}, title = {MaRDMO: Future Gateway to FAIR Mathematical Data}, journal = {E-Science-Tage 2025: Research Data Management: Challenges in a Changing World}, doi = {10.11588/heibooks.1652.c23913}, pages = {40 -- 53}, year = {2025}, abstract = {Mathematical research data plays a crucial role across scientific disciplines, yet its documentation and dissemination remain challenging due to the lack of standardized research data management practices. The MaRDMO Plugin addresses these challenges by integrating mathematical models, algorithms, and interdisciplinary workflows into the established framework of the Research Data Management Organiser (RDMO). Built on FAIR principles, MaRDMO enables structured documentation and retrieval of mathematical research data through guided questionnaires. It connects to multiple knowledge graphs, including MathModDB, MathAlgoDB, and the MaRDI Portal. Users can document and search for models, algorithms, and workflows via dynamic selection interfaces that also leverage other sources such as Wikidata. The plugin facilitates the export to the individual MaRDI services, ensuring data quality through automated validation. By embedding mathematical research data management into the widely adopted RDMO platform, MaRDMO represents a significant step toward making mathematical research data more findable, accessible, and reusable.}, language = {en} } @article{CardereraPokuttaSchuetteetal.2025, author = {Carderera, Alejandro and Pokutta, Sebastian and Sch{\"u}tte, Christof and Weiser, Martin}, title = {An efficient first-order conditional gradient algorithm in data-driven sparse identification of nonlinear dynamics to solve sparse recovery problems under noise}, volume = {470}, journal = {Journal of Computational and Applied Mathematics}, doi = {10.1016/j.cam.2025.116675}, year = {2025}, abstract = {Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the potential to transform data-rich fields where well-established dynamical models remain unknown. This work contributes to the recent trend in data-driven sparse identification of nonlinear dynamics of finding the best sparse fit to observational data in a large library of potential nonlinear models. We propose an efficient first-order Conditional Gradient algorithm for solving the underlying optimization problem. In comparison to the most prominent alternative framework, the new framework shows significantly improved performance on several essential issues like sparsity-induction, structure-preservation, noise robustness, and sample efficiency. We demonstrate these advantages on several dynamics from the field of synchronization, particle dynamics, and enzyme chemistry.}, language = {en} } @article{SchemberaWuebbelingShehuetal.2025, author = {Schembera, Bj{\"o}rn and W{\"u}bbeling, Frank and Shehu, Aurela and Biedinger, Christine and Fiedler, Jochen and Reidelbach, Marco and Schmidt, Burkhard and Ferrer, Eloi and Koprucki, Thomas}, title = {FAIR Representation of Mathematical Research Data: MathModDB and MathAlgoDB as Knowledge Graphs for Mathematical Models and Numerical Algorithms}, journal = {2nd Conference on Research Data Infrastructure (CoRDI)}, doi = {10.5281/zenodo.16735911}, year = {2025}, language = {en} } @misc{Villani2025, type = {Master Thesis}, author = {Villani, Paolo}, title = {Regression Techniques for Surrogate Modelling in Bayesian Inverse Problems}, pages = {59}, year = {2025}, abstract = {For many real-world applications, a system of interest can be represented via a mathematical model which depends on a set of parameters. In order to identify the parameters, a set of observations is available and an Inverse Problem is formulated. Identifying the parameters from the observations is often a challenging task, especially when the model is expensive to evaluate. This is the case for Partial Differential Equations models, where numerical simulations which are both inexact and computationally expensive are required to obtain the model output. To ease the computational costs, surrogate models can be used to approximate the forward model. In this work, we present two different regression techniques, Gaussian Process Regression and Lipschitz Regression. After reformulating the Inverse Problem to account for the surrogate model, we develope an adaptive training strategy to train the surrogate model. The proposed training strategy aims at optimizing not only the training points' positions but also their evaluation accuracies. Moreover, interleaved sampling of the posterior distribution of the unknown parameters is performed while the surrogate model is trained, providing a solution for the Inverse Problem. The quality of the surrogating techniques as well as the effectiveness of the adaptive training strategy are tested through different numerical experiments.}, language = {en} } @article{SikelerKempterSekulicetal.2025, author = {Sikeler, Christoph and Kempter, Susanne and Sekulic, Ivan and Burger, Sven and Liedl, Tim}, title = {Chiral Plasmonic Crystals Self-Assembled by DNA Origami}, volume = {129}, journal = {J. Phys. Chem. C}, number = {10}, doi = {10.1021/acs.jpcc.4c08768}, pages = {5116 -- 5121}, year = {2025}, language = {en} } @misc{ZhangSchuette2017, author = {Zhang, Wei and Sch{\"u}tte, Christof}, title = {Reliable approximation of long relaxation timescales in molecular dynamics}, issn = {1438-0064}, doi = {10.3390/e19070367}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-63718}, year = {2017}, abstract = {Many interesting rare events in molecular systems like ligand association, protein folding or con- formational changes happen on timescales that often are not accessible by direct numerical simulation. Therefore rare event approximation approaches like interface sampling, Markov state model building or advanced reaction coordinate based free energy estimation have attracted huge attention recently. In this article we analyze the reliability of such approaches: How precise is an estimate of long relaxation timescales of molecular systems resulting from various forms of rare event approximation methods? Our results give a theoretical answer to this question by relating it with the transfer operator approach to molecular dynamics. By doing so they also allow for understanding deep connections between the different approaches.}, language = {en} } @article{GonnermannMuellerHaaseLeinsetal.2026, author = {Gonnermann-M{\"u}ller, Jana and Haase, Jennifer and Leins, Nicolas and Igel, Moritz and Fackeldey, Konstantin and Pokutta, Sebastian}, title = {FACET: Multi-Agent AI Supporting Teachers in Scaling Differentiated Learning for Diverse Students}, journal = {arXiv}, arxiv = {http://arxiv.org/abs/2601.22788}, doi = {https://arxiv.org/abs/2601.22788}, year = {2026}, abstract = {Classrooms are becoming increasingly heterogeneous, comprising learners with diverse performance and motivation levels, language proficiencies, and learning differences such as dyslexia and ADHD. While teachers recognize the need for differentiated instruction, growing workloads create substantial barriers, making differentiated instruction an ideal that is often unrealized in practice. Current AI educational tools, which promise differentiated materials, are predominantly student-facing and performance-centric, ignoring other aspects that shape learning outcomes. We introduce FACET, a teacher-facing multi-agent framework designed to address these gaps by supporting differentiation that accounts for motivation, performance, and learning differences. Developed with educational stakeholders from the outset, the framework coordinates four specialized agents, including learner simulation, diagnostic assessment, material generation, and evaluation within a teacher-in-the-loop design. School principals (N = 30) shaped system requirements through participatory workshops, while in-service K-12 teachers (N = 70) evaluated material quality. Mixed-methods evaluation demonstrates strong perceived value for inclusive differentiation. Practitioners emphasized both the urgent need arising from classroom heterogeneity and the importance of maintaining pedagogical autonomy as a prerequisite for adoption. We discuss implications for future school deployment and outline partnerships for longitudinal classroom implementation.}, language = {en} } @article{AndresArconesWeiserKoutsourelakisetal.2026, author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Phaedon-Stelios and Unger, J{\"o}rg F.}, title = {Embedded Model Form Uncertainty Quantification with Measurement Noise for Bayesian Model Calibration}, volume = {7}, journal = {Data-Centric Engineering}, arxiv = {http://arxiv.org/abs/2410.12037}, doi = {10.1017/dce.2025.10035}, year = {2026}, abstract = {A key factor in ensuring the accuracy of computer simulations that model physical systems is the proper calibration of their parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian methods provide a robust framework for quantifying and propagating these uncertainties to model predictions. Nevertheless, Bayesian methods paired with inexact models usually produce predictions unable to represent the observed datapoints. Additionally, the quantified uncertainties of these overconfident models cannot be propagated to other Quantities of Interest (QoIs) reliably. A promising solution involves embedding a model inadequacy term in the inference parameters, allowing the quantified model form uncertainty to influence non-observed QoIs. This paper introduces a more interpretable framework for embedding the model inadequacy compared to existing methods. To overcome the limitations of current approaches, we adapt the existing likelihood models to properly account for noise in the measurements and propose two new formulations designed to address their shortcomings. Moreover, we evaluate the performance of this inadequacy-embedding approach in the presence of discrepancies between measurements and model predictions, including noise and outliers. Particular attention is given to how the uncertainty associated with the model inadequacy term propagates to the QoIs, enabling a more comprehensive statistical analysis of prediction's reliability. Finally, the proposed approach is applied to estimate the uncertainty in the predicted heat flux from a transient thermal simulation using temperature bservations.}, language = {en} } @article{MehrmannJohnyEbbinghausetal.2026, author = {Mehrmann, Carolin and Johny, Jacob and Ebbinghaus, Petra and Hammerschmidt, Martin and Das, Ankita and Wei, Xin and Tesch, Marc F. and Rabe, Martin}, title = {Nano IR spectroscopy on Silicon-Supported Organic-Inorganic Hybrid Materials}, journal = {Phys. Chem. Chem. Phys.}, publisher = {Royal Society of Chemistry (RSC)}, doi = {10.1039/D5CP03815D}, year = {2026}, language = {en} } @article{FariasBasultoMehlhopOttoetal.2025, author = {Farias-Basulto, Guillermo and Mehlhop, Thede and Otto, Nicolas J. and Bertram, Tobias and J{\"a}ger, Klaus and Gall, Stefan and Weinberger, Nikolaus and Schlatmann, Rutger and Lauermann, Iver and Klenk, Reiner and List-Kratochvil, Emil and Kaufmann, Christian A.}, title = {Improving Perovskite/CIGS Tandem Solar Cells for Higher Power Conversion Efficiency through Light Management and Bandgap Engineering}, volume = {17}, journal = {ACS Appl. Mater. Interfaces}, doi = {10.1021/acsami.5c15458}, pages = {56250}, year = {2025}, language = {en} } @article{LelievreZhang2019, author = {Leli{\`e}vre, Tony and Zhang, Wei}, title = {Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates}, journal = {Multiscale Modeling and Simulation}, number = {17}, arxiv = {http://arxiv.org/abs/1805.01928}, doi = {10.1137/18M1186034}, pages = {1019 -- 1051}, year = {2019}, abstract = {Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Leli{\`e}vre, Nonlinearity, 2010] to approximate the essential dynamics of high-dimensional diffusion processes along a given reaction coordinate. The approximation error of the effective dynamics when it is used to approximate the behavior of the original dynamics has been considered in recent years. As a continuation of the previous work [F. Legoll, T. Leli{\`e}vre, and S. Olla, Stoch. Process. Appl, 2017], in this paper we obtain pathwise estimates for effective dynamics when the reaction coordinate function is either nonlinear or vector-valued.}, language = {en} }