TY - THES A1 - Binkowski, Felix T1 - Riesz-projection-based methods for the numerical simulation of resonance phenomena in nanophotonics Y1 - 2023 U6 - https://doi.org/10.17169/refubium-41230 ER - TY - JOUR A1 - Ernst, Ariane A1 - Falkenhagen, Undine A1 - Winkelmann, Stefanie T1 - Model reduction for calcium-induced vesicle fusion dynamics JF - Proceedings in Applied Mathematics & Mechanics N2 - In this work, we adapt an established model for the Ca2+-induced fusion dynamics of synaptic vesicles and employ a lumping method to reduce its complexity. In the reduced system, sequential Ca2+-binding steps are merged to a single releasable state, while keeping the important dependence of the reaction rates on the local Ca2+ concentration. We examine the feasibility of this model reduction for a representative stimulus train over the physiologically relevant site-channel distances. Our findings show that the approximation error is generally small and exhibits an interesting nonlinear and non-monotonic behavior where it vanishes for very low distances and is insignificant at intermediary distances. Furthermore, we give expressions for the reduced model’s reaction rates and suggest that our approach may be used to directly compute effective fusion rates for assessing the validity of a fusion model, thereby circumventing expensive simulations. Y1 - 2023 U6 - https://doi.org/10.1002/pamm.202300184 VL - 23 IS - 4 ER - TY - GEN A1 - Colom, Rémi A1 - Mikheeva, Elena A1 - Achouri, Karim A1 - Zuniga-Perez, Jesus A1 - Bonod, Nicolas A1 - Martin, Olivier J.F. A1 - Burger, Sven A1 - Genevet, Patrice T1 - Crossing of the Branch Cut: The Topological Origin of a Universal 2π-Phase Retardation in Non-Hermitian Metasurfaces (Laser Photonics Rev. 17(6)/2023) T2 - Laser Photonics Rev. Y1 - 2023 U6 - https://doi.org/10.1002/lpor.202370029 VL - 17 SP - 2370029 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 - 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 - Betz, Fridtjof A1 - Binkowski, Felix A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Cover Picture: Resonance Expansion of Quadratic Quantities with Regularized Quasinormal Modes JF - Phys. Status Solidi A Y1 - 2023 U6 - https://doi.org/10.1002/pssa.202370013 VL - 220 SP - 2370013 ER - TY - CHAP A1 - Kuen, Lilli A1 - Betz, Fridtjof A1 - Binkowski, Felix A1 - Schneider, Philipp-Immanuel A1 - Hammerschmidt, Martin A1 - Heermeier, Niels A1 - Rodt, Sven A1 - Reitzenstein, Stephan A1 - Burger, Sven T1 - Applying a Riesz-projection-based contour integral eigenvalue solver to compute resonance modes of a VCSEL T2 - Proc. SPIE Y1 - 2023 U6 - https://doi.org/10.1117/12.2665490 VL - 12575 SP - 125750J ER - TY - JOUR A1 - Mikheeva, Elena A1 - Colom, Rémi A1 - Achouri, Karim A1 - Overvig, Adam A1 - Binkowski, Felix A1 - Duboz, Jean-Yves A1 - Cueff, Sébastien A1 - Fan, Shanhui A1 - Burger, Sven A1 - Alù, Andrea A1 - Genevet, Patrice T1 - Asymmetric phase modulation with light with parity-symmetry broken metasurfaces JF - Optica Y1 - 2023 U6 - https://doi.org/10.1364/OPTICA.495681 VL - 10 SP - 1287 ER - TY - GEN A1 - Binkowski, Felix A1 - Betz, Fridtjof A1 - Colom, Remi A1 - Genevet, Patrice A1 - Burger, Sven T1 - Source code and simulation results: Poles and zeros of electromagnetic quantities in photonic systems T2 - Zenodo Y1 - 2023 U6 - https://doi.org/10.5281/zenodo.8063931 SP - 8063931 ER - TY - JOUR A1 - Zonker, Johannes A1 - Padilla-Iglesias, Cecilia A1 - Djurdjevac Conrad, Natasa T1 - Insights into drivers of mobility and cultural dynamics of African hunter-gatherers over the past 120 000 years JF - Royal Society Open Science N2 - Humans have a unique capacity to innovate, transmit and rely on complex, cumulative culture for survival. While an important body of work has attempted to explore the role of changes in the size and interconnectedness of populations in determining the persistence, diversity and complexity of material culture, results have achieved limited success in explaining the emergence and spatial distribution of cumulative culture over our evolutionary trajectory. Here, we develop a spatio-temporally explicit agent-based model to explore the role of environmentally driven changes in the population dynamics of hunter–gatherer communities in allowing the development, transmission and accumulation of complex culture. By modelling separately demography- and mobility-driven changes in interaction networks, we can assess the extent to which cultural change is driven by different types of population dynamics. We create and validate our model using empirical data from Central Africa spanning 120 000 years. We find that populations would have been able to maintain diverse and elaborate cultural repertoires despite abrupt environmental changes and demographic collapses by preventing isolation through mobility. However, we also reveal that the function of cultural features was also an essential determinant of the effects of environmental or demographic changes on their dynamics. Our work can therefore offer important insights into the role of a foraging lifestyle on the evolution of cumulative culture. Y1 - 2023 U6 - https://doi.org/10.1098/rsos.230495 VL - 10 IS - 11 ER - TY - GEN A1 - Betz, Fridtjof A1 - Binkowski, Felix A1 - Burger, Sven T1 - RPExpand (Version 1) T2 - Zenodo Y1 - 2023 U6 - https://doi.org/10.5281/zenodo.7840116 SP - doi: 10.5281/zenodo.7840116 ER - TY - JOUR A1 - Betz, Fridtjof A1 - Binkowski, Felix A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Resonance expansion of quadratic quantities with regularized quasinormal modes JF - Phys. Status Solidi A Y1 - 2023 U6 - https://doi.org/10.1002/pssa.202200892 VL - 220 SP - 2200892 ER - TY - JOUR A1 - Ben Soltane, Isam A1 - Colom, Rémi A1 - Stout, Brian A1 - Bonod, Nicolas T1 - Derivation of the Transient and Steady Optical States from the Poles of the S-Matrix JF - Laser Photon. Rev. Y1 - 2023 U6 - https://doi.org/10.1002/lpor.202200141 VL - 17 SP - 2200141 ER - TY - JOUR A1 - Helfmann, Luzie A1 - Conrad, Natasa Djurdjevac A1 - Lorenz-Spreen, Philipp A1 - Schütte, Christof T1 - Modelling opinion dynamics under the impact of influencer and media strategies JF - Scientific Reports N2 - Digital communication has made the public discourse considerably more complex, and new actors and strategies have emerged as a result of this seismic shift. Aside from the often-studied interactions among individuals during opinion formation, which have been facilitated on a large scale by social media platforms, the changing role of traditional media and the emerging role of "influencers" are not well understood, and the implications of their engagement strategies arising from the incentive structure of the attention economy even less so. Here we propose a novel opinion dynamics model that accounts for these different roles, namely that media and influencers change their own positions on slower time scales than individuals, while influencers dynamically gain and lose followers. Numerical simulations show the importance of their relative influence in creating qualitatively different opinion formation dynamics: with influencers, fragmented but short-lived clusters emerge, which are then counteracted by more stable media positions. Mean-field approximations by partial differential equations reproduce this dynamic. Based on the mean-field model, we study how strategies of influencers to gain more followers can influence the overall opinion distribution. We show that moving towards extreme positions can be a beneficial strategy for influencers to gain followers. Finally, we demonstrate that optimal control strategies allow other influencers or media to counteract such attempts and prevent further fragmentation of the opinion landscape. Our modelling framework contributes to better understanding the different roles and strategies in the increasingly complex information ecosystem and their impact on public opinion formation. Y1 - 2023 U6 - https://doi.org/10.1038/s41598-023-46187-9 VL - 13 SP - 19375 ER - TY - JOUR A1 - Wolf, Sarah A1 - Fürst, Steffen A1 - Geiges, Andreas A1 - Laublichler, Manfred A1 - Mielke, Jahel A1 - Steudle, Gesine A1 - Winter, Konstantin A1 - Jaeger, Carlo T1 - The Decision Theatre Triangle for societal challenges – an example case and research needs JF - Journal of Cleaner Production N2 - Tackling societal challenges relating to sustainability requires both an understanding of the underlying complex socio-ecological systems and participation of scientists as well as relevant stakeholders, such as practice experts, decision makers, and citizens. This paper introduces the Decision Theatre Triangle, a method which combines empirical information, mathematical modelling and simulation, and a format for dialogue between scientists and stakeholders. While it builds on previous Decision Theatre work, the new structuring into these three elements emphasizes what is needed for setting up a Decision Theatre for a given challenge. Based on experience with a specific example – sustainable mobility in Germany – it is argued that agent-based models are particularly suitable for Decision Theatres and that the method is useful not only for decision support but also for science communication and co-creation of a deeper knowledge of the system under discussion. As a step towards facilitating a broader use of the Decision Theatre Triangle method, the paper then sketches research needs for each of its three elements, with a focus on mathematical modelling and simulation. Y1 - 2023 U6 - https://doi.org/10.1016/j.jclepro.2023.136299 VL - 394 SP - 136299 ER - TY - JOUR A1 - Ernst, Ariane A1 - Unger, Nathalie A1 - Schütte, Christof A1 - Walter, Alexander A1 - Winkelmann, Stefanie T1 - Rate-limiting recovery processes in neurotransmission under sustained stimulation JF - Mathematical Biosciences N2 - At chemical synapses, an arriving electric signal induces the fusion of vesicles with the presynaptic membrane, thereby releasing neurotransmitters into the synaptic cleft. After a fusion event, both the release site and the vesicle undergo a recovery process before becoming available for reuse again. Of central interest is the question which of the two restoration steps acts as the limiting factor during neurotrans-mission under high-frequency sustained stimulation. In order to investigate this question, we introduce a novel non-linear reaction network which involves explicit recovery steps for both the vesicles and the release sites, and includes the induced time-dependent output current. The associated reaction dynamics are formulated by means of ordinary differential equations (ODEs), as well as via the associated stochastic jump process. While the stochastic jump model describes a single release site, the average over many release sites is close to the ODE solution and shares its periodic structure. The reason for this can be traced back to the insight that recovery dynamics of vesicles and release sites are statistically almost independent. A sensitivity analysis on the recovery rates based on the ODE formulation reveals that neither the vesicle nor the release site recovery step can be identified as the essential rate-limiting step but that the rate- limiting feature changes over the course of stimulation. Under sustained stimulation the dynamics given by the ODEs exhibit transient dynamics leading from an initial depression of the postsynaptic response to an asymptotic periodic orbit, while the individual trajectories of the stochastic jump model lack the oscillatory behavior an asymptotic periodicity of the ODE-solution. Y1 - 2023 U6 - https://doi.org/10.1016/j.mbs.2023.109023 VL - 362 ER - TY - JOUR A1 - Secker, Christopher A1 - Fackeldey, Konstantin A1 - Weber, Marcus A1 - Ray, Sourav A1 - Gorgulla, Christoph A1 - Schütte, Christof T1 - Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists JF - Journal of Cheminformatics N2 - Opioids are essential pharmaceuticals due to their analgesic properties, however, lethal side effects, addiction, and opioid tolerance are extremely challenging. The development of novel molecules targeting the μ-opioid receptor (MOR) in inflamed, but not in healthy tissue, could significantly reduce these unwanted effects. Finding such novel molecules can be achieved by maximizing the binding affinity to the MOR at acidic pH while minimizing it at neutral pH, thus combining two conflicting objectives. Here, this multi-objective optimal affinity approach is presented, together with a virtual drug discovery pipeline for its practical implementation. When applied to finding pH-specific drug candidates, it combines protonation state-dependent structure and ligand preparation with high-throughput virtual screening. We employ this pipeline to characterize a set of MOR agonists identifying a morphine-like opioid derivative with higher predicted binding affinities to the MOR at low pH compared to neutral pH. Our results also confirm existing experimental evidence that NFEPP, a previously described fentanyl derivative with reduced side effects, and recently reported β-fluorofentanyls and -morphines show an increased specificity for the MOR at acidic pH when compared to fentanyl and morphine. We further applied our approach to screen a >50K ligand library identifying novel molecules with pH-specific predicted binding affinities to the MOR. The presented differential docking pipeline can be applied to perform multi-objective affinity optimization to identify safer and more specific drug candidates at large scale. Y1 - 2023 U6 - https://doi.org/10.1186/s13321-023-00746-4 VL - 15 ER - TY - CHAP A1 - Gander, Lia A1 - Krause, Rolf A1 - Weiser, Martin A1 - Costabal, Francisco A1 - Pezzuto, Simone T1 - On the Accuracy of Eikonal Approximations in Cardiac Electrophysiology in the Presence of Fibrosis T2 - Functional Imaging and Modeling of the Heart. FIMH 2023. N2 - Fibrotic tissue is one of the main risk factors for cardiac arrhythmias. It is therefore a key component in computational studies. In this work, we compare the monodomain equation to two eikonal models for cardiac electrophysiology in the presence of fibrosis. We show that discontinuities in the conductivity field, due to the presence of fibrosis, introduce a delay in the activation times. The monodomain equation and eikonal-diffusion model correctly capture these delays, contrarily to the classical eikonal equation. Importantly, a coarse space discretization of the monodomain equation amplifies these delays, even after accounting for numerical error in conduction velocity. The numerical discretization may also introduce artificial conduction blocks and hence increase propagation complexity. Therefore, some care is required when comparing eikonal models to the discretized monodomain equation. Y1 - 2023 U6 - https://doi.org/10.1007/978-3-031-35302-4_14 VL - 13958 PB - Springer, Cham ER - TY - JOUR A1 - Semler, Phillip A1 - Weiser, Martin T1 - Adaptive Gaussian Process Regression for Efficient Building of Surrogate Models in Inverse Problems JF - Inverse Problems N2 - In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model y with a surrogate model y(s) that can be evaluated quickly leads to a significant speedup. The approximation quality of the surrogate model depends strongly on the number, position, and accuracy of the sample points. With an additional finite computational budget, this leads to a problem of (computer) experimental design. In contrast to the selection of sample points, the trade-off between accuracy and effort has hardly been studied systematically. We therefore propose an adaptive algorithm to find an optimal design in terms of position and accuracy. Pursuing a sequential design by incrementally appending the computational budget leads to a convex and constrained optimization problem. As a surrogate, we construct a Gaussian process regression model. We measure the global approximation error in terms of its impact on the accuracy of the identified parameter and aim for a uniform absolute tolerance, assuming that y(s) is computed by finite element calculations. A priori error estimates and a coarse estimate of computational effort relate the expected improvement of the surrogate model error to computational effort, resulting in the most efficient combination of sample point and evaluation tolerance. We also allow for improving the accuracy of already existing sample points by continuing previously truncated finite element solution procedures. Y1 - 2023 U6 - https://doi.org/10.1088/1361-6420/ad0028 VL - 39 IS - 12 SP - 125003 ER - TY - THES A1 - Tillmann, Peter T1 - Optimizing bifacial tandem solar cells for realistic operation conditions Y1 - 2023 U6 - https://doi.org/10.17169/refubium-39571 ER - TY - CHAP A1 - Mukherjee, Deshabrato A1 - Kalas, Benjámin A1 - Burger, Sven A1 - Sáfrán, György A1 - Serényi, Miklós A1 - Fried, Miklós A1 - Petrik, Péter T1 - Nanostructures for in-situ surface-enhanced Kretschmann-Raether ellipsometry T2 - Proc. SPIE Y1 - 2023 U6 - https://doi.org/10.1117/12.2649080 VL - 12428 SP - 124280S ER - TY - JOUR A1 - Straube, Arthur A1 - Winkelmann, Stefanie A1 - Höfling, Felix T1 - Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles JF - The Journal of Physical Chemistry B N2 - This theoretical study concerns a pH oscillator based on the urea-urease reaction confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyse the structure of the phase flow and of the limit cycle, which controls the dynamics for giant vesicles and dominates the pronouncedly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, which are amenable to analytic treatments that are complemented by numerical solutions, and obtain the period and amplitude of the oscillations as well as the parameter domain, where oscillatory behavior persists. We show that the accuracy of these predictions is highly sensitive to the employed reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The faithful modeling of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms. Y1 - 2023 U6 - https://doi.org/10.1021/acs.jpcb.2c09092 VL - 127 IS - 13 SP - 2955 EP - 2967 ER - TY - JOUR A1 - Rickert, Lucas A1 - Betz, Fridtjof A1 - Plock, Matthias A1 - Burger, Sven A1 - Heindel, Tobias T1 - High-performance designs for fiber-pigtailed quantum-light sources based on quantum dots in electrically-controlled circular Bragg gratings JF - Opt. Express Y1 - 2023 U6 - https://doi.org/10.1364/OE.486060 VL - 31 SP - 14750 ER - TY - JOUR A1 - del Razo, Mauricio A1 - Winkelmann, Stefanie A1 - Klein, Rupert A1 - Höfling, Felix T1 - Chemical diffusion master equation: formulations of reaction-diffusion processes on the molecular level JF - Journal of Mathematical Physics N2 - The chemical diffusion master equation (CDME) describes the probabilistic dynamics of reaction--diffusion systems at the molecular level [del Razo et al., Lett. Math. Phys. 112:49, 2022]; it can be considered the master equation for reaction--diffusion processes. The CDME consists of an infinite ordered family of Fokker--Planck equations, where each level of the ordered family corresponds to a certain number of particles and each particle represents a molecule. The equations at each level describe the spatial diffusion of the corresponding set of particles, and they are coupled to each other via reaction operators --linear operators representing chemical reactions. These operators change the number of particles in the system, and thus transport probability between different levels in the family. In this work, we present three approaches to formulate the CDME and show the relations between them. We further deduce the non-trivial combinatorial factors contained in the reaction operators, and we elucidate the relation to the original formulation of the CDME, which is based on creation and annihilation operators acting on many-particle probability density functions. Finally we discuss applications to multiscale simulations of biochemical systems among other future prospects. Y1 - 2023 U6 - https://doi.org/10.1063/5.0129620 VL - 64 IS - 1 ER - TY - JOUR A1 - Lücke, Marvin A1 - Heitzig, Jobst A1 - Koltai, Péter A1 - Molkethin, Nora A1 - Winkelmann, Stefanie T1 - Large population limits of Markov processes on random networks JF - Stochastic Processes and their Applications N2 - We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each discrete state in the system, or in certain subsystems, and general conditions for the convergence of the collective variable dynamics to a mean-field ordinary differential equation are proved. We discuss the convergence to this mean-field limit for a continuous-time noisy version of the so-called "voter model" on Erdős-Rényi random graphs, on the stochastic block model, as well as on random regular graphs. Moreover, a heterogeneous population of agents is studied. For each of these types of interaction networks, we specify the convergence conditions in dependency on the corresponding model parameters. Y1 - 2023 U6 - https://doi.org/10.1016/j.spa.2023.09.007 VL - 166 ER - TY - CHAP A1 - Steyer, Joshua A1 - Chegini, Fatemeh A1 - Potse, Mark A1 - Loewe, Axel A1 - Weiser, Martin T1 - Continuity of Microscopic Cardiac Conduction in a Computational Cell-by-Cell Model T2 - 2023 Computing in Cardiology Conference (CinC) N2 - Conduction velocity in cardiac tissue is a crucial electrophysiological parameter for arrhythmia vulnerability. Pathologically reduced conduction velocity facilitates arrhythmogenesis because such conduction velocities decrease the wavelength with which re-entry may occur. Computational studies on CV and how it changes regionally in models at spatial scales multiple times larger than actual cardiac cells exist. However, microscopic conduction within cells and between them have been studied less in simulations. In this work, we study the relation of microscopic conduction patterns and clinically observable macroscopic conduction using an extracellular-membrane-intracellular model which represents cardiac tissue with these subdomains at subcellular resolution. By considering cell arrangement and non-uniform gap junction distribution, it yields anisotropic excitation propagation. This novel kind of model can for example be used to understand how discontinuous conduction on the microscopic level affects fractionation of electrograms in healthy and fibrotic tissue. Along the membrane of a cell, we observed a continuously propagating activation wavefront. When transitioning from one cell to the neighbouring one, jumps in local activation times occurred, which led to lower global conduction velocities than locally within each cell. Y1 - 2023 U6 - https://doi.org/10.22489/CinC.2023.385 SN - 2325-887X VL - 50 PB - Computing in Cardiology ER - TY - GEN A1 - Betz, Fridtjof A1 - Binkowski, Felix A1 - Burger, Sven A1 - Kuen, Lilli T1 - RPExpand (Version 2.0) T2 - Zenodo Y1 - 2023 U6 - https://doi.org/10.5281/zenodo.10371002 SP - doi: 10.5281/zenodo.10371002 ER - TY - CHAP A1 - Chegini, Fatemeh A1 - Froehly, Algiane A1 - Huynh, Ngoc Mai Monica A1 - Pavarino, Luca A1 - Potse, Mark A1 - Scacchi, Simone A1 - Weiser, Martin T1 - Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution T2 - 10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023 N2 - The cardiac extracellular-membrane-intracellular (EMI) model enables the precise geometrical representation and resolution of aggregates of individual myocytes. As a result, it not only yields more accurate simulations of cardiac excitation compared to homogenized models but also presents the challenge of solving much larger problems. In this paper, we introduce recent advancements in three key areas: (i) the creation of artificial, yet realistic grids, (ii) efficient higher-order time stepping achieved by combining low-overhead spatial adaptivity on the algebraic level with progressive spectral deferred correction methods, and (iii) substructuring domain decomposition preconditioners tailored to address the complexities of heterogeneous problem structures. The efficiency gains of these proposed methods are demonstrated through numerical results on cardiac meshes of different sizes. Y1 - 2023 UR - https://www.scipedia.com/public/2023f U6 - https://doi.org/10.23967/c.coupled.2023.004 ER - TY - JOUR A1 - Trepte, Philipp A1 - Secker, Christopher A1 - Kostova, Simona A1 - Maseko, Sibusiso B. A1 - Gang Choi, Soon A1 - Blavier, Jeremy A1 - Minia, Igor A1 - Silva Ramos, Eduardo A1 - Cassonnet, Patricia A1 - Golusik, Sabrina A1 - Zenkner, Martina A1 - Beetz, Stephanie A1 - Liebich, Mara J. A1 - Scharek, Nadine A1 - Schütz, Anja A1 - Sperling, Marcel A1 - Lisurek, Michael A1 - Wang, Yang A1 - Spirohn, Kerstin A1 - Hao, Tong A1 - Calderwood, Michael A. A1 - Hill, David E. A1 - Landthaler, Markus A1 - Olivet, Julien A1 - Twizere, Jean-Claude A1 - Vidal, Marc A1 - Wanker, Erich E. T1 - AI-guided pipeline for protein-protein interaction drug discovery identifies a SARS-CoV-2 inhibitor JF - bioRxiv Y1 - 2023 U6 - https://doi.org/10.1101/2023.06.14.544560 ER - TY - JOUR A1 - Beron-Vera, Francisco Javier A1 - Olascoaga, Maria Josefina A1 - Helfmann, Luzie A1 - Miron, Philippe T1 - Sampling-Dependent Transition Paths of Iceland-Scotland Overflow Water JF - Journal of Physical Oceanography N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1175/JPO-D-22-0172.1 VL - 53 IS - 4 SP - 1151 EP - 1160 ER - TY - JOUR A1 - Bartels, Tinko A1 - Fisikopoulos, Vissarion A1 - Weiser, Martin T1 - Fast Floating-Point Filters for Robust Predicates JF - BIT Numerical Mathematics N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1007/s10543-023-00975-x VL - 63 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 - JOUR A1 - Zhang, Wei A1 - Schütte, Christof T1 - Understanding recent deep-learning techniques for identifying collective variables of molecular dynamics BT - Special Issue: 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) JF - Proceedings in Applied Mathematics and Mechanics N2 - High-dimensional metastable molecular dynamics (MD) can often be characterised by a few features of the system, that is, collective variables (CVs). Thanks to the rapid advance in the area of machine learning and deep learning, various deep learning-based CV identification techniques have been developed in recent years, allowing accurate modelling and efficient simulation of complex molecular systems. In this paper, we look at two different categories of deep learning-based approaches for finding CVs, either by computing leading eigenfunctions of transfer operator associated to the underlying dynamics, or by learning an autoencoder via minimisation of reconstruction error. We present a concise overview of the mathematics behind these two approaches and conduct a comparative numerical study of these two approaches on illustrative examples. Y1 - 2023 U6 - https://doi.org/10.1002/pamm.202300189 VL - 23 IS - 4 ER -