TY - JOUR A1 - Jäger, Klaus A1 - Tillmann, Peter A1 - Katz, Eugene A. A1 - Becker, Christiane T1 - Perovskite/silicon tandem solar cells: Effect of luminescent coupling and bifaciality JF - Sol. RRL Y1 - 2021 U6 - https://doi.org/10.1002/solr.202000628 VL - 5 SP - 2000628 ER - TY - JOUR A1 - Manley, Phillip A1 - Segantini, Michele A1 - Ahiboz, Doguscan A1 - Hammerschmidt, Martin A1 - Arnaoutakis, Georgios A1 - MacQueen, Rowan W. A1 - Burger, Sven A1 - Becker, Christiane T1 - Double-layer metasurface for enhanced photon up-conversion JF - APL Photon. Y1 - 2021 U6 - https://doi.org/10.1063/5.0040839 VL - 6 SP - 036103 ER - TY - JOUR A1 - Pakhomov, Anton V. A1 - Hammerschmidt, Martin A1 - Burger, Sven A1 - Pertsch, Thomas A1 - Setzpfand, Frank T1 - Modeling of surface-induced second-harmonic generation from multilayer structures by the transfer matrix method JF - Opt. Express Y1 - 2021 U6 - https://doi.org/10.1364/OE.417066 VL - 29 SP - 9098 ER - TY - JOUR A1 - Binkowski, Felix A1 - Wu, Tong A1 - Lalanne, Philippe A1 - Burger, Sven A1 - Govorov, Alexander O. T1 - Hot Electron Generation through Near-Field Excitation of Plasmonic Nanoresonators JF - ACS Photonics Y1 - 2021 U6 - https://doi.org/10.1021/acsphotonics.1c00231 VL - 8 SP - 1243 ER - TY - JOUR A1 - Cvetkovic, Nada A1 - Conrad, Tim A1 - Lie, Han Cheng T1 - A Convergent Discretisation Method for Transition Path Theory for Diffusion Processes JF - Multiscale Modeling & Simulation Y1 - 2021 U6 - https://doi.org/10.1137/20M1329354 VL - 19 IS - 1 SP - 242 EP - 266 PB - Society for Industrial and Applied Mathematics ER - TY - BOOK A1 - Deuflhard, Peter A1 - Weiser, Martin T1 - Numerische Mathematik 3. Adaptive Lösung partieller Differentialgleichungen Y1 - 2020 SN - 978-3-11-069168-9 U6 - https://doi.org/10.1515/9783110689655 PB - de Gruyter ET - 2 ER - TY - JOUR A1 - Sikorski, Alexander A1 - Weber, Marcus A1 - Schütte, Christof T1 - The Augmented Jump Chain JF - Advanced Theory and Simulations N2 - Modern methods of simulating molecular systems are based on the mathematical theory of Markov operators with a focus on autonomous equilibrated systems. However, non-autonomous physical systems or non-autonomous simulation processes are becoming more and more important. A representation of non-autonomous Markov jump processes is presented as autonomous Markov chains on space-time. Augmenting the spatial information of the embedded Markov chain by the temporal information of the associated jump times, the so-called augmented jump chain is derived. The augmented jump chain inherits the sparseness of the infinitesimal generator of the original process and therefore provides a useful tool for studying time-dependent dynamics even in high dimensions. Furthermore, possible generalizations and applications to the computation of committor functions and coherent sets in the non-autonomous setting are discussed. After deriving the theoretical foundations, the concepts with a proof-of-concept Galerkin discretization of the transfer operator of the augmented jump chain applied to simple examples are illustrated. Y1 - 2021 U6 - https://doi.org/10.1002/adts.202000274 VL - 4 IS - 4 PB - Wiley-VCH ER - TY - JOUR A1 - Sechi, Renata A1 - Sikorski, Alexander A1 - Weber, Marcus T1 - Estimation of the Koopman Generator by Newton's Extrapolation JF - Multiscale Modeling and Simulation N2 - This article addresses the problem of estimating the Koopman generator of a Markov process. The direct computation of the infinitesimal generator is not easy because of the discretization of the state space, in particular because of the trade-off inherent in the choice of the best lag time to study the process. Short lag times implies a strong discretization of the state space and a consequent loss of Markovianity. Large lag times bypass events on fast timescales. We propose a method to approximate the generator with the computation of the Newton polynomial extrapolation. This technique is a multistep approach which uses as its input Koopman transfer operators evaluated for a series of lag times. Thus, the estimated infinitesimal generator combines information from different time resolutions and does not bias only fast- or slow-decaying dynamics. We show that the multi-scale Newton method can improve the estimation of the generator in comparison to the computation using finite difference or matrix logarithm methods. Y1 - 2020 U6 - https://doi.org/10.1137/20M1333006 VL - 19 IS - 2 SP - 758 EP - 774 PB - SIAM ER - TY - THES A1 - Venkatareddy, Narendra Lagumaddepalli T1 - Revealing secrets of mussel-glue mimetic peptides - From advanced NMR to computational process modelling Y1 - 2020 ER - TY - THES A1 - Eshtewy, Neveen Ali Salem T1 - Mathematical Modeling of Metabolic-Genetic Networks Y1 - 2020 ER - TY - JOUR A1 - Öttinger, Hans Christian A1 - Montefusco, Alberto A1 - Peletier, Mark A. T1 - A Framework of Nonequilibrium Statistical Mechanics. I. Role and Types of Fluctuations JF - Journal of Non-Equilibrium Thermodynamics N2 - Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized representation of microscopic details. We consider fluctuation-enhanced equations associated with Markov processes and elaborate the general recipes for evaluating dynamic material properties, which characterize force-flux constitutive laws, by statistical mechanics. Markov processes with continuous trajectories are conveniently characterized by stochastic differential equations and lead to Green–Kubo-type formulas for dynamic material properties. Markov processes with discontinuous jumps include transitions over energy barriers with the rates calculated by Kramers. We describe a unified approach to Markovian fluctuations and demonstrate how the appropriate type of fluctuations (continuous versus discontinuous) is reflected in the mathematical structure of the phenomenological equations. Y1 - 2021 U6 - https://doi.org/10.1515/jnet-2020-0068 VL - 46 IS - 1 SP - 1 EP - 13 PB - De Gruyter ER - TY - JOUR A1 - Montefusco, Alberto A1 - Peletier, Mark A. A1 - Öttinger, Hans Christian T1 - A Framework of Nonequilibrium Statistical Mechanics. II. Coarse-Graining JF - Journal of Non-Equilibrium Thermodynamics N2 - For a given thermodynamic system, and a given choice of coarse-grained state variables, the knowledge of a force-flux constitutive law is the basis for any nonequilibrium modeling. In the first paper of this series we established how, by a generalization of the classical fluctuation-dissipation theorem (FDT), the structure of a constitutive law is directly related to the distribution of the fluctuations of the state variables. When these fluctuations can be expressed in terms of diffusion processes, one may use Green–Kubo-type coarse-graining schemes to find the constitutive laws. In this paper we propose a coarse-graining method that is valid when the fluctuations are described by means of general Markov processes, which include diffusions as a special case. We prove the success of the method by numerically computing the constitutive law for a simple chemical reaction A⇄B. Furthermore, we show that, for such a system, one cannot find a consistent constitutive law by any Green–Kubo-like scheme. Y1 - 2021 U6 - https://doi.org/10.1515/jnet-2020-0069 VL - 46 IS - 1 SP - 15 EP - 33 PB - De Gruyter ER - TY - JOUR A1 - Sunkara, Vikram A1 - Heinz, Gitta A. A1 - Heinrich, Frederik F. A1 - Durek, Pawel A1 - Mobasheri, Ali A1 - Mashreghi, Mir-Farzin A1 - Lang, Annemarie T1 - Combining segmental bulk- and single-cell RNA-sequencing to define the chondrocyte gene expression signature in the murine knee joint JF - bioarxiv (Accepted in Osteoarthr. Cartil.) Y1 - 2020 U6 - https://doi.org/10.1101/2020.06.13.148056 ER - TY - JOUR A1 - Lang, Annemarie A1 - Helfmeier, Sarah A1 - Stefanowski, Jonathan A1 - Kuppe, Aditi A1 - Sunkara, Vikram A1 - Pfeiffenberger, Moritz A1 - Wolter, Angelique A1 - Damerau, Alexandra A1 - Hemmati-Sadeghi, Shabnam A1 - Ringe, Jochen A1 - Haag, Rainer A1 - Hauser, Anja E. A1 - Löhning, Max A1 - Perka, Carsten A1 - Duda, Georg A1 - Hoff, Paula A1 - Schmidt-Bleek, Katharina A1 - Gaber, Timo A1 - Buttgereit, Frank T1 - HIF-stabilization prevents delayed fracture healing JF - bioarxiv Y1 - 2020 U6 - https://doi.org/10.1101/2020.07.02.182832 ER - TY - JOUR A1 - Laydon, Daniel J. A1 - Sunkara, Vikram A1 - Boelen, Lies A1 - Bangham, Charles R. M. A1 - Asquith, Becca T1 - The relative contributions of infectious and mitotic spread to HTLV-1 persistence JF - PLOS Computational Biology Y1 - 2020 U6 - https://doi.org/10.1371/journal.pcbi.1007470 ER - TY - JOUR A1 - Schiela, Anton A1 - Stöcklein, Matthias A1 - Weiser, Martin T1 - A primal dual projection algorithm for efficient constraint preconditioning JF - SIAM Journal on Scientific Computing N2 - We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and analysed as a gradient method on a quotient space, the given problem can be solved by computing sulutions for a sequence of constrained surrogate problems, projections onto the feasible subspaces, and Lagrange multiplier updates. As a major application we consider a class of optimization problems with PDEs, where PDP can be applied together with a projected cg method using a block triangular constraint preconditioner. Numerical experiments show reliable and competitive performance for an optimal control problem in elasticity. Y1 - 2021 U6 - https://doi.org/10.1137/20M1380739 VL - 43 IS - 6 SP - A4095 EP - A4120 ER - TY - JOUR A1 - Mielke, Alexander A1 - Montefusco, Alberto A1 - Peletier, Mark A. T1 - Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence JF - Continuum Mechanics and Thermodynamics N2 - This paper revolves around a subtle distinction between two concepts: passing to the limit in a family of gradient systems, on one hand, and deriving effective kinetic relations on the other. The two concepts are strongly related, and in many examples they even appear to be the same. Our main contributions are to show that they are different, to show that well-known techniques developed for the former may give incorrect results for the latter, and to introduce new tools to remedy this. The approach is based on the Energy-Dissipation Principle that provides a variational formulation to gradient-flow equations that allows one to apply techniques from Γ-convergence of functional on states and functionals on trajectories. Y1 - 2021 U6 - https://doi.org/10.1007/s00161-020-00932-x VL - 33 SP - 611 EP - 637 PB - Springer ER - TY - THES A1 - Santiago, Xavier Garcia T1 - Numerical methods for shape optimization of photonic nanostructures Y1 - 2021 U6 - https://doi.org/10.5445/IR/1000131006 ER - TY - JOUR A1 - Ramos Leite, Tiago A1 - Zschiedrich, Lin A1 - Kizilkaya, Orhan A1 - McPeak, Kevin M. T1 - Resonant Plasmonic–Biomolecular Chiral Interactions in the Far-Ultraviolet: Enantiomeric Discrimination of sub-10 nm Amino Acid Films JF - Nano Lett. Y1 - 2022 UR - https://digitalcommons.lsu.edu/chem_engineering_pubs/34/ U6 - https://doi.org/10.1021/acs.nanolett.2c01724 VL - 22 SP - 7343 ER - TY - JOUR A1 - Rej, Sourav A1 - Santiago, Eva Yazmin A1 - Baturina, Olga A1 - Zhang, Yu A1 - Burger, Sven A1 - Kment, Stepan A1 - Govorov, Alexander O. A1 - Naldoni, Alberto T1 - Colloidal Titanium Nitride Nanobars for Broadband Inexpensive Plasmonics and Photochemistry from Visible to Mid-IR Wavelengths JF - Nano Energy Y1 - 2022 U6 - https://doi.org/10.1016/j.nanoen.2022.107989 VL - 104 SP - 107989 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 - GEN A1 - Rickert, Lucas A1 - Betz, Fridtjof A1 - Plock, Matthias A1 - Burger, Sven A1 - Heindel, Tobias T1 - Data publication for "High-performance designs for fiber-pigtailed quantum-light sources based on quantum dots in electrically-controlled circular Bragg gratings" T2 - Zenodo Y1 - 2022 U6 - https://doi.org/10.5281/zenodo.7360516 SP - 7360516 ER - TY - JOUR A1 - Gorgulla, Christoph A1 - Jayaraj, Abhilash A1 - Fackeldey, Konstantin A1 - Arthanari, Haribabu T1 - Emerging frontiers in virtual drug discovery: From quantum mechanical methods to deep learning approaches JF - Current Opinion in Chemical Biology N2 - Virtual screening-based approaches to discover initial hit and lead compounds have the potential to reduce both the cost and time of early drug discovery stages, as well as to find inhibitors for even challenging target sites such as protein–protein interfaces. Here in this review, we provide an overview of the progress that has been made in virtual screening methodology and technology on multiple fronts in recent years. The advent of ultra-large virtual screens, in which hundreds of millions to billions of compounds are screened, has proven to be a powerful approach to discover highly potent hit compounds. However, these developments are just the tip of the iceberg, with new technologies and methods emerging to propel the field forward. Examples include novel machine-learning approaches, which can reduce the computational costs of virtual screening dramatically, while progress in quantum-mechanical approaches can increase the accuracy of predictions of various small molecule properties. Y1 - 2022 U6 - https://doi.org/10.1016/j.cbpa.2022.102156 VL - 69 SP - 102156 EP - 102156-12 ER - TY - GEN 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 N2 - Our theoretical study concerns an urea-urease-based pH oscillator 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 limit cycle, which controls the dynamics for giant vesicles and dominates the strongly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, amenable to analytic treatments, and show that the accuracy of predictions, including the period of oscillations, is highly sensitive to the choice of the 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 accurate description of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms. T3 - ZIB-Report - 22-21 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88179 SN - 1438-0064 ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Köppl, Jonas A1 - Djurdjevac, Ana T1 - Feedback Loops in Opinion Dynamics of Agent-Based Models with Multiplicative Noise JF - Entropy N2 - We introduce an agent-based model for co-evolving opinions and social dynamics, under the influence of multiplicative noise. In this model, every agent is characterized by a position in a social space and a continuous opinion state variable. Agents’ movements are governed by the positions and opinions of other agents and similarly, the opinion dynamics are influenced by agents’ spatial proximity and their opinion similarity. Using numerical simulations and formal analyses, we study this feedback loop between opinion dynamics and the mobility of agents in a social space. We investigate the behaviour of this ABM in different regimes and explore the influence of various factors on the appearance of emerging phenomena such as group formation and opinion consensus. We study the empirical distribution, and, in the limit of infinite number of agents, we derive a corresponding reduced model given by a partial differential equation (PDE). Finally, using numerical examples, we show that a resulting PDE model is a good approximation of the original ABM. Y1 - 2022 U6 - https://doi.org/10.3390/e24101352 VL - 24(10) 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 - Schneider, Philipp-Immanuel A1 - Zschiedrich, Lin A1 - Hammerschmidt, Martin A1 - Kuen, Lilli A1 - Sekulic, Ivan A1 - Kluge, Julien A1 - Leykauf, Bastian A1 - Krutzik, Markus A1 - Burger, Sven T1 - Boosting quantum optics experiments with Bayesian optimization T2 - Proc. SPIE Y1 - 2022 U6 - https://doi.org/10.1117/12.2632419 VL - 12227 SP - 122270F ER - TY - CHAP A1 - Krüger, Jan A1 - Manley, Phillip A1 - Zschiedrich, Lin A1 - Hammerschmidt, Martin A1 - Schneider, Philipp-Immanuel A1 - Köning, Rainer A1 - Bodermann, Bernd T1 - Untersuchung des Schwingungseinflusses auf gemessene Punktspreizfunktionen in der optischen Mikroskopie T2 - Proc. DGaO Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0287-2022-P005-6 SP - P5 ER - TY - JOUR A1 - Bopp, Julian M. A1 - Plock, Matthias A1 - Turan, Tim A1 - Pieplow, Gregor A1 - Burger, Sven A1 - Schröder, Tim T1 - Sawfish Photonic Crystal Cavity for Near-Unity Emitter-to-Fiber Interfacing in Quantum Network Applications JF - Adv. Opt. Mater. Y1 - 2024 U6 - https://doi.org/10.1002/adom.202301286 VL - 12 SP - 2301286 ER - TY - CHAP A1 - Manley, Phillip A1 - Krüger, Jan A1 - Zschiedrich, Lin A1 - Hammerschmidt, Martin A1 - Bodermann, Bernd A1 - Köning, Rainer A1 - Schneider, Philipp-Immanuel T1 - Elementary, my dear Zernike: model order reduction for accelerating optical dimensional microscopy T2 - EPJ Web Conf. Y1 - 2022 U6 - https://doi.org/10.1051/epjconf/202226610010 VL - 266 SP - 10010 ER - TY - JOUR A1 - Betz, Fridtjof A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Binkowski, Felix T1 - Efficient rational approximation of optical response functions with the AAA algorithm JF - Laser Photonics Rev. Y1 - 2024 U6 - https://doi.org/10.1002/lpor.202400584 VL - 18 SP - 2400584 ER - TY - GEN A1 - Betz, Fridtjof A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Binkowski, Felix T1 - Source code and simulation results: Efficient rational approximation of optical response functions with the AAA algorithm T2 - Zenodo Y1 - 2024 U6 - https://doi.org/10.5281/zenodo.10853692 SP - doi: 10.5281/zenodo.10853692 ER - TY - JOUR A1 - Mukherjee, Deshabrato A1 - Kertész, Krisztián A1 - Zolnai, Zsolt A1 - Kovács, Zoltán A1 - Deák, András A1 - Pálinkás, András A1 - Osváth, Zoltán A1 - Olasz, Dániel A1 - Romanenko, Alekszej A1 - Fried, Miklós A1 - Burger, Sven A1 - Sáfrán, György A1 - Petrik, Peter T1 - Optimized Sensing on Gold Nanoparticles Created by Graded-Layer Magnetron Sputtering and Annealing JF - Sens. Actuators B Chem. Y1 - 2025 U6 - https://doi.org/10.1016/j.snb.2024.136875 VL - 425 SP - 136875 ER - TY - JOUR A1 - Betz, Fridtjof A1 - Binkowski, Felix A1 - Kuen, Lilli A1 - Burger, Sven T1 - Version 2 — RPExpand: Software for Riesz projection expansion of resonance phenomena JF - SoftwareX Y1 - 2024 U6 - https://doi.org/10.1016/j.softx.2024.101694 VL - 26 SP - 101694 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 - JOUR A1 - Plock, Matthias A1 - Binkowski, Felix A1 - Zschiedrich, Lin A1 - Schneider, Phillip-Immanuel A1 - Burger, Sven T1 - Fabrication uncertainty guided design optimization of a photonic crystal cavity by using Gaussian processes JF - J. Opt. Soc. Am. B Y1 - 2024 U6 - https://doi.org/10.1364/JOSAB.505767 VL - 41 SP - 850 ER - TY - GEN A1 - Plock, Matthias A1 - Binkowski, Felix A1 - Zschiedrich, Lin A1 - Schneider, Phillip-Immanuel A1 - Burger, Sven T1 - Research data for "Fabrication uncertainty guided design optimization of a photonic crystal cavity by using Gaussian processes" T2 - Zenodo Y1 - 2024 U6 - https://doi.org/10.5281/zenodo.8131611 SP - doi: 10.5281/zenodo.8131611 ER - TY - GEN A1 - Musial, Anna A1 - Sek, Grzegorz A1 - Schneider, Philipp-Immanuel A1 - Reitzenstein, Stephan T1 - Fiber-coupled solid-state-based single-photon sources T2 - Specialty Optical Fibers Y1 - 2024 U6 - https://doi.org/10.1016/B978-0-443-18495-6.00004-4 SP - 345 EP - 384 PB - Woodhead Publishing ER - TY - JOUR A1 - Kuen, Lilli A1 - Löffler, Lorenz A1 - Tsarapkin, Aleksei A1 - Zschiedrich, Lin A1 - Feichtner, Thorsten A1 - Burger, Sven A1 - Höflich, Katja T1 - Chiral and directional optical emission from a dipole source coupled to a helical plasmonic antenna JF - Appl. Phys. Lett. Y1 - 2024 U6 - https://doi.org/10.1063/5.0201748 VL - 124 SP - 231102 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 - CHAP A1 - Steyer, Joshua A1 - Chegini, Fatemeh A1 - Starý, Tomas A1 - Potse, Mark A1 - Weiser, Martin A1 - Loewe, Axel T1 - Electrograms in a Cardiac Cell-by-Cell Model T2 - Workshop Biosignals 2024 N2 - Cardiac electrograms are an important tool to study the spread of excitation waves inside the heart, which in turn underlie muscle contraction. Electrograms can be used to analyse the dynamics of these waves, e.g. in fibrotic tissue. In computational models, these analyses can be done with greater detail than during minimally invasive in vivo procedures. Whilst homogenised models have been used to study electrogram genesis, such analyses have not yet been done in cellularly resolved models. Such high resolution may be required to develop a thorough understanding of the mechanisms behind abnormal excitation patterns leading to arrhythmias. In this study, we derived electrograms from an excitation propagation simulation in the Extracellular, Membrane, Intracellular (EMI) model, which represents these three domains explicitly in the mesh. We studied the effects of the microstructural excitation dynamics on electrogram genesis and morphology. We found that electrograms are sensitive to the myocyte alignment and connectivity, which translates into micro-fractionations in the electrograms. Y1 - 2024 U6 - https://doi.org/10.47952/gro-publ-194 ER - TY - JOUR A1 - Steudle, Gesine A1 - Winkelmann, Stefanie A1 - Fürst, Steffen A1 - Wolf, Sarah T1 - Understanding Memory Mechanisms in Socio-Technical Systems: the Case of an Agent-based Mobility Model JF - Advances in Complex Systems N2 - This paper explores memory mechanisms in complex socio-technical systems, using a mobility demand model as an example case. We simplified a large-scale agent-based mobility model into a Markov process and discover that the mobility decision process is non-Markovian. This is due to its dependence on the system’s history, including social structure and local infrastructure, which evolve based on prior mobility decisions. To make the process Markovian, we extend the state space by incorporating two history-dependent components. Although our model is a very much reduced version of the original one, it remains too complex for the application of usual analytic methods. Instead, we employ simulations to examine the functionalities of the two history-dependent components. We think that the structure of the analyzed stochastic process is exemplary for many socio-technical, -economic, -ecological systems. Additionally, it exhibits analogies with the framework of extended evolution, which has previously been used to study cultural evolution. Y1 - 2024 U6 - https://doi.org/10.1142/S0219525924400034 VL - 27 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 - Binkowski, Felix A1 - Kullig, Julius A1 - Betz, Fridtjof A1 - Zschiedrich, Lin A1 - Walther, Andrea A1 - Wiersig, Jan A1 - Burger, Sven T1 - Computing eigenfrequency sensitivities near exceptional points JF - Phys. Rev. Research Y1 - 2024 U6 - https://doi.org/10.1103/PhysRevResearch.6.023148 VL - 6 SP - 023148 ER - TY - GEN A1 - Binkowski, Felix A1 - Kullig, Julius A1 - Betz, Fridtjof A1 - Zschiedrich, Lin A1 - Walther, Andrea A1 - Wiersig, Jan A1 - Burger, Sven T1 - Source code and simulation results: Computing eigenfrequency sensitivities near exceptional points T2 - Zenodo Y1 - 2024 U6 - https://doi.org/10.5281/zenodo.10715639 SP - doi: 10.5281/zenodo.10715639 ER - TY - JOUR A1 - Kostré, Margarita A1 - Sunkara, Vikram A1 - Schütte, Christof A1 - Djurdjevac Conrad, Natasa T1 - Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia JF - Applied Network Science N2 - 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. KW - mesoscale spreading process KW - network inference KW - time-evolving network KW - romanization spreading KW - scarce data Y1 - 2022 U6 - https://doi.org/10.1007/s41109-022-00492-w VL - 7 PB - Springer Nature ER - TY - CHAP A1 - Rickert, Lucas A1 - Gao, Timm A1 - Urban, Felix A1 - Große, Jan A1 - Srocka, Nicole A1 - Rodt, Sven A1 - Musial, Anna A1 - Zolnacz, Kinga A1 - Mergo, Pawel A1 - Dybka, Kamil A1 - Urbanczyk, Waclaw A1 - Sek, Grzegorz A1 - Burger, Sven A1 - Reitzenstein, Stephan A1 - Heindel, Tobias T1 - A Plug&Play Telecom-Wavelength Single-Photon Source for Quantum Key Distribution T2 - Quantum 2.0 Y1 - 2022 U6 - https://doi.org/10.1364/QUANTUM.2022.QTu4C.6 SP - QTu4C.6 ER - TY - GEN A1 - Plock, Matthias A1 - Andrle, Kas A1 - Burger, Sven A1 - Schneider, Philipp-Immanuel T1 - Research data and example scripts for the paper "Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction" T2 - Zenodo Y1 - 2022 U6 - https://doi.org/10.5281/zenodo.6359594 ER - TY - GEN A1 - Binkowski, Felix A1 - Betz, Fridtjof A1 - Hammerschmidt, Martin A1 - Schneider, Philipp-Immanuel A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Source code and simulation data for Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators T2 - Zenodo Y1 - 2022 U6 - https://doi.org/10.5281/zenodo.6614951 ER - TY - GEN A1 - Kostré, Margarita A1 - Sunkara, Vikram A1 - Schütte, Christof A1 - Djurdjevac Conrad, Nataša T1 - Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia N2 - 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. T3 - ZIB-Report - 22-10 KW - mesoscale spreading process, network inference, time-evolving network, romanization spreading, scarce data Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86764 SN - 1438-0064 ER - TY - JOUR A1 - Schneider, Philipp-Immanuel A1 - Manley, Phillip A1 - Krüger, Jan A1 - Zschiedrich, Lin A1 - Köning, Rainer A1 - Bodermann, Bernd A1 - Burger, Sven T1 - Reconstructing phase aberrations for high-precision dimensional microscopy JF - Proc. SPIE Y1 - 2022 U6 - https://doi.org/10.1117/12.2620762 VL - 12137 SP - 121370I ER - TY - CHAP A1 - Jäger, Klaus A1 - Sutter, Johannes A1 - Tockhorn, Philipp A1 - Hammerschmidt, Martin A1 - Schneider, Philipp-Immanuel A1 - Albrecht, Steve A1 - Becker, Christiane T1 - Improving perovskite/silicon tandem solar cells with optical simulations T2 - Proc. SPIE Y1 - 2022 U6 - https://doi.org/10.1117/12.2621255 VL - PC12150 SP - PC1215001 ER - TY - JOUR A1 - Avalos-Ovando, Oscar A1 - Santiago, Eva Yazmin A1 - Movsesyan, Artur A1 - Kong, Xiang-Tian A1 - Yu, Peng A1 - Besteiro, Lucas V. A1 - Khosravi Khorashad, Larousse A1 - Okamoto, Hiromi A1 - Slocik, Joseph M. A1 - Correa-Duarte, Miguel A1 - Comesana-Hermo, Miguel A1 - Liedl, Tim A1 - Markovich, Gil A1 - Burger, Sven A1 - Govorov, Alexander O. T1 - Chiral Bioinspired Plasmonics: A Paradigm Shift for Optical Activity and Photochemistry JF - ACS Photon. Y1 - 2022 U6 - https://doi.org/10.1021/acsphotonics.2c00445 VL - 9 SP - 2219 ER - TY - JOUR A1 - Bremer, Lucas A1 - Jimenez, Carlos A1 - Thiele, Simon A1 - Weber, Ksenia A1 - Huber, Tobias A1 - Rodt, Sven A1 - Herkommer, Alois A1 - Burger, Sven A1 - Höfling, Sven A1 - Giessen, Harald A1 - Reitzenstein, Stephan T1 - Numerical optimization of single-mode fiber- coupled single-photon sources based on semiconductor quantum dots JF - Opt. Express Y1 - 2022 U6 - https://doi.org/10.1364/OE.456777 VL - 30 SP - 15913 ER - TY - JOUR A1 - Dass, Mihir A1 - Kuen, Lilli A1 - Posnjak, Gregor A1 - Burger, Sven A1 - Liedl, Tim T1 - Visible wavelength spectral tuning of absorption and circular dichroism of DNA-assembled Au/Ag core-shell nanorod assemblies JF - Mater. Adv. Y1 - 2022 U6 - https://doi.org/10.1039/D1MA01211H VL - 3 SP - 3438 ER - TY - JOUR A1 - Plock, Matthias A1 - Andrle, Kas A1 - Burger, Sven A1 - Schneider, Philipp-Immanuel T1 - Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction JF - Adv. Theory Simul. Y1 - 2022 U6 - https://doi.org/10.1002/adts.202200112 VL - 5 SP - 2200112 ER - TY - JOUR A1 - Volkova, Kseniia A1 - Heupel, Julia A1 - Trofimov, Sergei A1 - Betz, Fridtjof A1 - Colom, Rémi A1 - MacQueen, Rowan W. A1 - Akhundzada, Sapida A1 - Reginka, Meike A1 - Ehresmann, Arno A1 - Reithmeier, Johann Peter A1 - Burger, Sven A1 - Popov, Cyril A1 - Naydenov, Boris T1 - Optical and Spin Properties of NV Center Ensembles in Diamond Nano-Pillars JF - Nanomaterials Y1 - 2022 U6 - https://doi.org/10.3390/nano12091516 VL - 12 SP - 1516 ER - TY - JOUR A1 - Wang, Yujing A1 - Vannucci, Luca A1 - Burger, Sven A1 - Gregersen, Niels T1 - Near-unity efficiency in ridge waveguide-based, on-chip single-photon sources JF - Mater. Quantum Technol. Y1 - 2022 U6 - https://doi.org/10.1088/2633-4356/aca8e8 VL - 2 SP - 045004 ER - TY - JOUR A1 - Lopez-Fraguas, Eduardo A1 - Binkowski, Felix A1 - Burger, Sven A1 - Hagedorn, Sylvia A1 - Garcia-Camara, Braulio A1 - Vergaz, Ricardo A1 - Becker, Christiane A1 - Manley, Phillip T1 - Tripling the light extraction efficiency of a deep ultraviolet LED using a nanostructured p-contact JF - Sci. Rep. Y1 - 2022 U6 - https://doi.org/10.1038/s41598-022-15499-7 VL - 12 SP - 11480 ER - TY - GEN A1 - Betz, Fridtjof A1 - Colom, Remi A1 - Burger, Sven A1 - Naydenov, Boris T1 - Scripts for quantifying the effect of diamond nano-pillars on the fluorescence of NV centers T2 - Zenodo Y1 - 2022 U6 - https://doi.org/10.5281/zenodo.6558815 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 - JOUR A1 - Binkowski, Felix A1 - Betz, Fridtjof A1 - Hammerschmidt, Martin A1 - Schneider, Philipp-Immanuel A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators JF - Commun. Phys. Y1 - 2022 U6 - https://doi.org/10.1038/s42005-022-00977-1 VL - 5 SP - 202 ER - TY - JOUR A1 - Tockhorn, Philipp A1 - Sutter, Johannes A1 - Cruz, Alexandros A1 - Wagner, Philipp A1 - Jäger, Klaus A1 - Yoo, Danbi A1 - Lang, Felix A1 - Grischek, Max A1 - Li, Bor A1 - Li, Jinzhao A1 - Shargaieva, Oleksandra A1 - Unger, Eva A1 - Al-Ashouri, Amran A1 - Köhnen, Eike A1 - Stolterfoth, Martin A1 - Neher, Dieter A1 - Schlatmann, Rutger A1 - Rech, Bernd A1 - Stannowski, Bernd A1 - Albrecht, Steve A1 - Becker, Christiane T1 - Nano-optical designs for high-efficiency monolithic perovskite–silicon tandem solar cells JF - Nat. Nanotechnol. Y1 - 2022 U6 - https://doi.org/10.1038/s41565-022-01228-8 VL - 17 SP - 1214 ER - TY - JOUR A1 - Movsesyan, Artur A1 - Santiago, Eva Yazmin A1 - Burger, Sven A1 - Correa-Duarte, Miguel A1 - Besteiro, Lucas V. A1 - Wang, Zhiming A1 - Govorov, Alexander O. T1 - Plasmonic nanocrystals with complex shapes for photocatalysis and growth: Contrasting anisotropic hot-electron generation with the photothermal effect JF - Adv. Opt. Mater. Y1 - 2022 U6 - https://doi.org/10.1002/adom.202102663 VL - 10 SP - 2102663 ER - TY - GEN A1 - Colom, Remi A1 - Binkowski, Felix A1 - Betz, Fridtjof A1 - Kivshar, Yuri A1 - Burger, Sven T1 - Source code and simulation results for nanoantennas supporting an enhanced Purcell factor due to interfering resonances T2 - Zenodo Y1 - 2022 U6 - https://doi.org/10.5281/zenodo.6565850 ER - TY - JOUR A1 - Klus, Stefan A1 - Djurdjevac Conrad, Natasa T1 - Koopman-based spectral clustering of directed and time-evolving graphs JF - Journal of Nonlinear Science N2 - 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. Y1 - 2022 U6 - https://doi.org/10.1007/s00332-022-09863-0 VL - 33 ER - TY - JOUR A1 - Tillmann, Peter A1 - Jäger, Klaus A1 - Karsenti, Asher A1 - Kreinin, Lev A1 - Becker, Christiane T1 - Model-Chain Validation for Estimating the Energy Yield of Bifacial Perovskite/Silicon Tandem Solar Cells JF - Sol. RRL Y1 - 2022 U6 - https://doi.org/10.1002/solr.202200079 VL - 6 SP - 2200079 ER - TY - JOUR A1 - Engel, Maximilian A1 - Olicón-Méndez, Guillermo A1 - Wehlitz, Nathalie A1 - Winkelmann, Stefanie T1 - Synchronization and random attractors in reaction jump processes JF - Journal of Dynamics and Differential Equations N2 - 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. Y1 - 2024 U6 - https://doi.org/10.1007/s10884-023-10345-4 ER - TY - GEN A1 - Sagnol, Guillaume A1 - Hege, Hans-Christian A1 - Weiser, Martin T1 - Using sparse kernels to design computer experiments with tunable precision N2 - Statistical methods to design computer experiments usually rely on a Gaussian process (GP) surrogate model, and typically aim at selecting design points (combinations of algorithmic and model parameters) that minimize the average prediction variance, or maximize the prediction accuracy for the hyperparameters of the GP surrogate. In many applications, experiments have a tunable precision, in the sense that one software parameter controls the tradeoff between accuracy and computing time (e.g., mesh size in FEM simulations or number of Monte-Carlo samples). We formulate the problem of allocating a budget of computing time over a finite set of candidate points for the goals mentioned above. This is a continuous optimization problem, which is moreover convex whenever the tradeoff function accuracy vs. computing time is concave. On the other hand, using non-concave weight functions can help to identify sparse designs. In addition, using sparse kernel approximations drastically reduce the cost per iteration of the multiplicative weights updates that can be used to solve this problem. T3 - ZIB-Report - 16-33 KW - Optimal design of computer experiments KW - Sparse kernels KW - Gaussian Process Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-59605 SN - 1438-0064 ER - TY - GEN A1 - Witzig, Jakob A1 - Beckenbach, Isabel A1 - Eifler, Leon A1 - Fackeldey, Konstantin A1 - Gleixner, Ambros A1 - Grever, Andreas A1 - Weber, Marcus T1 - Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes N2 - In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst. T3 - ZIB-Report - 16-39 KW - Non-reversible Markov Processes KW - NESS KW - Mixed-Integer Programming KW - Markov State Models Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-60353 SN - 1438-0064 ER - TY - JOUR A1 - Witzig, Jakob A1 - Beckenbach, Isabel A1 - Eifler, Leon A1 - Fackeldey, Konstantin A1 - Gleixner, Ambros A1 - Grever, Andreas A1 - Weber, Marcus T1 - Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes JF - Multiscale Modeling and Simulation N2 - In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst. KW - Markov State Models KW - NESS KW - Non-reversible Markov Processes KW - Mixed-Integer Programming Y1 - 2018 U6 - https://doi.org/10.1137/16M1091162 SN - 1438-0064 VL - 16 IS - 1 SP - 248 EP - 265 ER - TY - BOOK ED - Deuflhard, Peter ED - Grötschel, Martin ED - Hömberg, Dietmar ED - Horst, Ulrich ED - Kramer, Jürg ED - Mehrmann, Volker ED - Polthier, Konrad ED - Schmidt, Frank ED - Schütte, Christof ED - Skutella, Martin ED - Sprekels, Jürgen T1 - MATHEON - Mathematics for Key Technologies Y1 - 2014 SN - 978-3-03719-137-8 U6 - https://doi.org/10.4171/137 VL - 1 PB - European Mathematical Society 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 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - A Discrete-Continuous Algorithm for Free Flight Planning JF - Algorithms N2 - 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. KW - shortest path KW - flight planning KW - free flight KW - discrete-continuous algorithm KW - optimal control KW - discrete optimization Y1 - 2020 U6 - https://doi.org/10.3390/a14010004 SN - 1438-0064 VL - 14 IS - 1 SP - 4 PB - MDPI ER - TY - JOUR A1 - Widler, Valeria A1 - Kaminska, Barbara A1 - Martins, Andre C. R. A1 - Puga-Gonzalez, Ivan T1 - An Investigation into the Causal Mechanism of Political Opinion Dynamics: A Model of Hierarchical Coarse-Graining with Community-Bounded Social Influence JF - Computational Social Science of Social Cohesion and Polarization N2 - 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. Y1 - 2026 U6 - https://doi.org/10.1007/978-3-032-01373-6_10 SP - 225 EP - 256 PB - Springer, Cham. ET - Computational Social Science of Social Cohesion and Polarization ER - TY - JOUR A1 - Carderera, Alejandro A1 - Pokutta, Sebastian A1 - Schütte, Christof A1 - Weiser, Martin T1 - An efficient first-order conditional gradient algorithm in data-driven sparse identification of nonlinear dynamics to solve sparse recovery problems under noise JF - Journal of Computational and Applied Mathematics N2 - 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. Y1 - 2025 U6 - https://doi.org/10.1016/j.cam.2025.116675 VL - 470 ER - TY - THES A1 - Villani, Paolo T1 - Regression Techniques for Surrogate Modelling in Bayesian Inverse Problems N2 - 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. Y1 - 2025 ER - TY - JOUR A1 - Sikeler, Christoph A1 - Kempter, Susanne A1 - Sekulic, Ivan A1 - Burger, Sven A1 - Liedl, Tim T1 - Chiral Plasmonic Crystals Self-Assembled by DNA Origami JF - J. Phys. Chem. C Y1 - 2025 U6 - https://doi.org/10.1021/acs.jpcc.4c08768 VL - 129 IS - 10 SP - 5116 EP - 5121 ER - TY - GEN A1 - Zhang, Wei A1 - Schütte, Christof T1 - Reliable approximation of long relaxation timescales in molecular dynamics N2 - 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. T3 - ZIB-Report - 17-19 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63718 SN - 1438-0064 ER - TY - JOUR A1 - Andrés Arcones, Daniel A1 - Weiser, Martin A1 - Koutsourelakis, Phaedon-Stelios A1 - Unger, Jörg F. T1 - Embedded Model Form Uncertainty Quantification with Measurement Noise for Bayesian Model Calibration JF - Data-Centric Engineering N2 - 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. Y1 - 2026 U6 - https://doi.org/10.1017/dce.2025.10035 VL - 7 ER - TY - JOUR A1 - Lelièvre, Tony A1 - Zhang, Wei T1 - Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates JF - Multiscale Modeling and Simulation N2 - Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Lelièvre, 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. Lelièvre, 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. Y1 - 2018 U6 - https://doi.org/10.1137/18M1186034 IS - 17 SP - 1019 EP - 1051 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Schütte, Christof A1 - Zhang, Wei T1 - Jarzynski's equality, fluctuation theorems, and variance reduction: Mathematical analysis and numerical algorithms JF - Journal of Statistical Physics N2 - In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski's equality. Y1 - 2018 U6 - https://doi.org/10.1007/s10955-019-02286-4 VL - 175 IS - 6 SP - 1214 EP - 1261 ER - TY - JOUR A1 - Zhang, Wei T1 - Some new results on relative entropy production, time reversal, and optimal control of time-inhomogeneous diffusion processes JF - Journal of Mathematical Physics N2 - This paper studies time-inhomogeneous nonequilibrium diffusion processes, including both Brownian dynamics and Langevin dynamics. We derive upper bounds of the relative entropy production of the time-inhomogeneous process with respect to the transient invariant probability measures. We also study the time reversal of the reverse process in Crooks' fluctuation theorem. We show that the time reversal of the reverse process coincides with the optimally controlled forward process that leads to zero variance importance sampling estimator based on Jarzynski's equality. Y1 - 2021 U6 - https://doi.org/10.1063/5.0038740 VL - 62 IS - 4 ER - TY - JOUR A1 - Lelievre, Tony A1 - Stoltz, Gabriel A1 - Zhang, Wei T1 - Multiple projection MCMC algorithms on submanifolds JF - IMA Journal of Numerical Analysis N2 - We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for this generalization is that the numerical solvers used to project proposed moves to the submanifold of interest may find several solutions. We show that the new algorithms indeed sample the target probability measure correctly, thanks to some carefully enforced reversibility property. We demonstrate the interest of the new MCMC algorithms on illustrative numerical examples. Y1 - 2022 U6 - https://doi.org/10.1093/imanum/drac006 ER - TY - JOUR A1 - Zhang, Wei A1 - Li, Tiejun A1 - Schütte, Christof T1 - Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks JF - Journal of Computational Physics N2 - In this paper, we consider the eigenvalue PDE problem of the infinitesimal generators of metastable diffusion processes. We propose a numerical algorithm based on training artificial neural networks for solving the leading eigenvalues and eigenfunctions of such high-dimensional eigenvalue problem. The algorithm is useful in understanding the dynamical behaviors of metastable processes on large timescales. We demonstrate the capability of our algorithm on a high-dimensional model problem, and on the simple molecular system alanine dipeptide. Y1 - 2021 U6 - https://doi.org/10.1016/j.jcp.2022.111377 VL - 465 ER - TY - JOUR A1 - Zhang, Wei A1 - Klus, Stefan A1 - Conrad, Tim A1 - Schütte, Christof T1 - Learning chemical reaction networks from trajectory data JF - SIAM Journal on Applied Dynamical Systems (SIADS) N2 - We develop a data-driven method to learn chemical reaction networks from trajectory data. Modeling the reaction system as a continuous-time Markov chain and assuming the system is fully observed,our method learns the propensity functions of the system with predetermined basis functions by maximizing the likelihood function of the trajectory data under l^1 sparse regularization. We demonstrate our method with numerical examples using synthetic data and carry out an asymptotic analysis of the proposed learning procedure in the infinite-data limit. Y1 - 2019 U6 - https://doi.org/10.1137/19M1265880 VL - 18 IS - 4 SP - 2000 EP - 2046 ER - TY - JOUR A1 - Zhao, Yue A1 - Zhang, Wei A1 - Li, Tiejun T1 - EPR-Net: Constructing non-equilibrium potential landscape via a variational force projection formulation JF - National Science Review N2 - We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state (NESS) systems. EPR-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product space. Remarkably, our loss function has an intimate connection with the steady entropy production rate (EPR), enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness, and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an 8D limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics. Y1 - 2024 U6 - https://doi.org/10.1093/nsr/nwae052 VL - 11 IS - 7 ER - TY - JOUR A1 - Akhyar, Fatima-Zahrae A1 - Zhang, Wei A1 - Stoltz, Gabriel A1 - Schütte, Christof T1 - Generative modeling of conditional probability distributions on the level-sets of collective variables N2 - Given a probability distribution $\mu$ in $\mathbb{R}^d$ represented by data, we study in this paper the generative modeling of its conditional probability distributions on the level-sets of a collective variable $\xi: \mathbb{R}^d \rightarrow \mathbb{R}^k$, where $1 \le k