TY - JOUR A1 - Plöntzke, Julia A1 - Berg, Mascha A1 - Ehrig, Rainald A1 - Leonhard-Marek, Sabine A1 - Müller, Kerstin-Elisabeth A1 - Röblitz, Susanna T1 - Model Based Exploration of Hypokalemia in Dairy Cows JF - Scientific Reports N2 - Hypokalemia, characterized by too low serum potassium levels, is a severe mineral disorder which can be life threatening. It is increasingly diagnosed in veterinarian healthcare and a topic of ongoing research. In this paper, we explore the different originating conditions of hypokalemia: reduced potassium intake, increased excretion, acid-base disturbances, or increased insulin, by using a dynamic mathematical model for potassium balance in non-lactating and lactating cows. Simulations are compared with literature. The results give insights into the network dynamics and point to scenarios on which experimental effort should be focused. Application of mathematical models can assist in experimental planning as well as the reduction, refinement and replacement of animal experiments. Y1 - 2022 U6 - https://doi.org/10.1038/s41598-022-22596-0 VL - 12, 19781 ER - TY - GEN A1 - Schneck, Jakob A1 - Weiser, Martin A1 - Wende, Florian T1 - Impact of mixed precision and storage layout on additive Schwarz smoothers N2 - The growing discrepancy between CPU computing power and memory bandwidth drives more and more numerical algorithms into a bandwidth- bound regime. One example is the overlapping Schwarz smoother, a highly effective building block for iterative multigrid solution of elliptic equations with higher order finite elements. Two options of reducing the required memory bandwidth are sparsity exploiting storage layouts and representing matrix entries with reduced precision in floating point or fixed point format. We investigate the impact of several options on storage demand and contraction rate, both analytically in the context of subspace correction methods and numerically at an example of solid mechanics. Both perspectives agree on the favourite scheme: fixed point representation of Cholesky factors in nested dissection storage. T3 - ZIB-Report - 18-62 KW - higher order finite elements KW - mixed precision KW - overlapping Schwarz smoother Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71305 SN - 1438-0064 ER - TY - JOUR A1 - Binkowski, Felix A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - A Riesz-projection-based method for nonlinear eigenvalue problems JF - J. Comput. Phys. Y1 - 2020 U6 - https://doi.org/10.1016/j.jcp.2020.109678 VL - 419 SP - 109678 ER - TY - GEN A1 - Oates, Chris A1 - Cockayne, Jon A1 - Prangle, Dennis A1 - Sullivan, T. J. A1 - Girolami, Mark ED - Hickernell, F. J. ED - Kritzer, P. T1 - Optimality criteria for probabilistic numerical methods T2 - Multivariate Algorithms and Information-Based Complexity N2 - It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that the decision-theoretic framework is neither appropriate nor sufficient. To this end, we consider an alternative optimality criterion from Bayesian experimental design and study its implied optimal information in the numerical context. This information is demonstrated to differ, in general, from the information that would be used in an average-case-optimal numerical method. The explicit connection to Bayesian experimental design suggests several distinct regimes in which optimal probabilistic numerical methods can be developed. Y1 - 2020 U6 - https://doi.org/10.1515/9783110635461-005 VL - 27 SP - 65 EP - 88 PB - De Gruyter ER - TY - JOUR A1 - Kersting, Hans A1 - Sullivan, T. J. A1 - Hennig, Philipp T1 - Convergence rates of Gaussian ODE filters JF - Statistics and Computing Y1 - 2020 U6 - https://doi.org/10.1007/s11222-020-09972-4 VL - 30 SP - 1791 EP - 1816 PB - Springer CY - Statistics and Computing ER - TY - JOUR A1 - Stoop, Ralph L. A1 - Straube, Arthur A1 - Johansen, Tom H. A1 - Tierno, Pietro T1 - Collective directional locking of colloidal monolayers on a periodic substrate JF - Phys. Rev. Lett. N2 - We investigate the directional locking effects that arise when a monolayer of paramagnetic colloidal particles is driven across a triangular lattice of magnetic bubbles. We use an external rotating magnetic field to generate a two-dimensional traveling wave ratchet forcing the transport of particles along a direction that intersects two crystallographic axes of the lattice. We find that, while single particles show no preferred direction, collective effects induce transversal current and directional locking at high density via a spontaneous symmetry breaking. The colloidal current may be polarized via an additional bias field that makes one transport direction energetically preferred. Y1 - 2020 U6 - https://doi.org/10.1103/PhysRevLett.124.058002 VL - 124 SP - 058002 ER - TY - JOUR A1 - Lie, Han Cheng A1 - Sullivan, T. J. A1 - Teckentrup, Aretha T1 - Error bounds for some approximate posterior measures in Bayesian inference JF - Numerical Mathematics and Advanced Applications ENUMATH 2019 Y1 - 2020 U6 - https://doi.org/10.1007/978-3-030-55874-1_26 SP - 275 EP - 283 PB - Springer ER - TY - JOUR A1 - Khorashad, Larousse Khosravi A1 - Besteiro, Lucas V. A1 - Correa-Duarte, Miguel A1 - Burger, Sven A1 - Wang, Zhiming M. A1 - Govorov, Alexander O. T1 - Hot electrons generated in chiral plasmonic nanocrystals as a mechanism for surface photochemistry and chiral growth JF - J. Am. Chem. Soc. Y1 - 2020 U6 - https://doi.org/10.1021/jacs.9b11124 VL - 142 SP - 4193 ER - TY - JOUR A1 - Werdehausen, Daniel A1 - Burger, Sven A1 - Staude, Isabelle A1 - Pertsch, Thomas A1 - Decker, Manuel T1 - General design formalism for highly efficient flat optics for broadband applications JF - Opt. Express Y1 - 2020 U6 - https://doi.org/10.1364/OE.386573 VL - 28 SP - 6452 ER - TY - JOUR A1 - Pflüger, Mika A1 - Kline, R. Joseph A1 - Fernández Herrero, Analia A1 - Hammerschmidt, Martin A1 - Soltwisch, Victor A1 - Krumrey, Michael T1 - Extracting dimensional parameters of gratings produced with self-aligned multiple patterning using grazing-incidence small-angle x-ray scattering JF - J. Micro Nanolithogr. MEMS MOEMS Y1 - 2020 U6 - https://doi.org/10.1117/1.JMM.19.1.014001 VL - 19 SP - 014001 ER - TY - JOUR A1 - Gutsche, Philipp A1 - Santiago, Xavier Garcia A1 - Schneider, Philipp-Immanuel A1 - McPeak, Kevin A1 - Nieto-Vesperinas, Manuel A1 - Burger, Sven T1 - Role of Geometric Shape in Chiral Optics JF - Symmetry Y1 - 2020 U6 - https://doi.org/10.3390/sym12010158 VL - 12 SP - 158 ER - TY - JOUR A1 - Klebanov, Ilja A1 - Sikorski, Alexander A1 - Schütte, Christof A1 - Röblitz, Susanna T1 - Objective priors in the empirical Bayes framework JF - Scandinavian Journal of Statistics N2 - When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the nonparametric case, the maximum likelihood estimate is known to overfit the data, an issue that is commonly tackled by regularization. However, the majority of regularizations are ad hoc choices which lack invariance under reparametrization of the model and result in inconsistent estimates for equivalent models. We introduce a nonparametric, transformation-invariant estimator for the prior distribution. Being defined in terms of the missing information similar to the reference prior, it can be seen as an extension of the latter to the data-driven setting. This implies a natural interpretation as a trade-off between choosing the least informative prior and incorporating the information provided by the data, a symbiosis between the objective and empirical Bayes methodologies. Y1 - 2021 U6 - https://doi.org/10.1111/sjos.12485 VL - 48 IS - 4 SP - 1212 EP - 1233 PB - Wiley Online Library ER - TY - JOUR A1 - Klebanov, Ilja A1 - Schuster, Ingmar A1 - Sullivan, T. J. T1 - A rigorous theory of conditional mean embeddings JF - SIAM Journal on Mathematics of Data Science Y1 - 2020 U6 - https://doi.org/10.1137/19M1305069 VL - 2 IS - 3 SP - 583 EP - 606 ER - TY - CHAP A1 - Kantner, Markus A1 - Höhne, Theresa A1 - Koprucki, Thomas A1 - Burger, Sven A1 - Wünsche, Hans-Jürgen A1 - Schmidt, Frank A1 - Mielke, Alexander A1 - Bandelow, Uwe ED - Kneissl, Michael ED - Knorr, Andreas ED - Reitzenstein, Stephan ED - Hoffmann, Axel T1 - Multi-dimensional modeling and simulation of semiconductor nanophotonic devices T2 - Semiconductor Nanophotonics Y1 - 2020 U6 - https://doi.org/10.1007/978-3-030-35656-9_7 VL - 194 SP - 241 EP - 283 PB - Springer CY - Cham ER - TY - JOUR A1 - Tillmann, Peter A1 - Jäger, Klaus A1 - Becker, Christiane T1 - Minimising levelised cost of electricity of bifacial solar panel arrays using Bayesian optimisation JF - Sustain. Energy Fuels Y1 - 2020 U6 - https://doi.org/10.1039/C9SE00750D VL - 4 SP - 254 ER - TY - JOUR A1 - Hammerschmidt, Martin A1 - Döpking, Sandra A1 - Burger, Sven A1 - Matera, Sebastian T1 - Field Heterogeneities and Their Impact on Photocatalysis: Combining Optical and Kinetic Monte Carlo Simulations on the Nanoscale JF - J. Phys. Chem. C Y1 - 2020 U6 - https://doi.org/10.1021/acs.jpcc.9b11469 VL - 124 SP - 3177 ER - TY - JOUR A1 - Möller, Jan A1 - Isbilir, Ali A1 - Sungkaworn, Titiwat A1 - Osberg, Brenda A1 - Karathanasis, Christos A1 - Sunkara, Vikram A1 - Grushevsky, Eugene O A1 - Bock, Andreas A1 - Annibale, Paolo A1 - Heilemann, Mike A1 - Schütte, Christof A1 - Lohse, Martin J. T1 - Single molecule mu-opioid receptor membrane-dynamics reveal agonist-specific dimer formation with super-resolved precision JF - Nature Chemical Biology Y1 - 2020 U6 - https://doi.org/10.1038/s41589-020-0566-1 VL - 16 SP - 946 EP - 954 ER - TY - JOUR A1 - Klus, Stefan A1 - Nüske, Feliks A1 - Peitz, Sebastian A1 - Niemann, Jan-Hendrik A1 - Clementi, Cecilia A1 - Schütte, Christof T1 - Data-driven approximation of the Koopman generator: Model reduction, system identification, and control JF - Physica D: Nonlinear Phenomena Y1 - 2020 U6 - https://doi.org/10.1016/j.physd.2020.132416 VL - 406 ER - TY - JOUR A1 - Manley, Phillip A1 - Walde, Sebastian A1 - Hagedorn, Sylvia A1 - Hammerschmidt, Martin A1 - Burger, Sven A1 - Becker, Christiane T1 - Nanopatterned Sapphire Substrates in Deep-UV LEDs: Is there an Optical Benefit? JF - Opt. Express Y1 - 2020 U6 - https://doi.org/10.1364/OE.379438 VL - 28 SP - 3619 ER - TY - BOOK A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - Stochastic Dynamics in Computational Biology T3 - Frontiers in Applied Dynamical Systems: Reviews and Tutorials Y1 - 2020 SN - 978-3-030-62386-9 U6 - https://doi.org/10.1007/978-3-030-62387-6 VL - 8 PB - Springer International Publishing ER - TY - JOUR A1 - Omari, Mohamed A1 - Lange, Alexander A1 - Plöntzke, Julia A1 - Röblitz, Susanna T1 - Model-based exploration of the impact of glucose metabolism on the estrous cycle dynamics in dairy cows JF - Biology Direct Y1 - 2019 U6 - https://doi.org/10.1186/s13062-019-0256-7 VL - 15 ER - TY - JOUR A1 - Becker, Fabian A1 - Djurdjevac Conrad, Natasa A1 - Eser, Raphael A. A1 - Helfmann, Luzie A1 - Schütt, Brigitta A1 - Schütte, Christof A1 - Zonker, Johannes T1 - The Furnace and the Goat—A spatio-temporal model of the fuelwood requirement for iron metallurgy on Elba Island, 4th century BCE to 2nd century CE JF - PLOS ONE Y1 - 2020 UR - https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0241133 U6 - https://doi.org/10.1371/journal.pone.0241133 VL - 15 SP - 1 EP - 37 PB - Public Library of Science ER - TY - JOUR A1 - Götschel, Sebastian A1 - Schiela, Anton A1 - Weiser, Martin T1 - Kaskade 7 - a Flexible Finite Element Toolbox JF - Computers and Mathematics with Applications N2 - Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of partial differential equations, aimed at supporting application-oriented research in numerical analysis and scientific computing. The library is written in C++ and is based on the \textsc{Dune} interface. The code is independent of spatial dimension and works with different grid managers. An important feature is the mix-and-match approach to discretizing systems of PDEs with different ansatz and test spaces for all variables. We describe the mathematical concepts behind the library as well as its structure, illustrating its use at several examples on the way. Y1 - 2021 U6 - https://doi.org/10.1016/j.camwa.2020.02.011 VL - 81 SP - 444 EP - 458 ER - TY - JOUR A1 - Jäger, Klaus A1 - Tillmann, Peter A1 - Becker, Christiane T1 - Detailed illumination model for bifacial solar cells JF - Opt. Express Y1 - 2020 U6 - https://doi.org/10.1364/OE.383570 VL - 28 SP - 4751 ER - TY - JOUR A1 - Feis, Joshua A1 - Beutel, Dominik A1 - Köpfler, Julian A1 - Santiago, Xavier Garcia A1 - Rockstuhl, Carsten A1 - Wegener, Martin A1 - Fernandez-Corbaton, Ivan T1 - Helicity-Preserving Optical Cavity Modes for Enhanced Sensing of Chiral Molecules JF - Phys. Rev. Lett. Y1 - 2020 U6 - https://doi.org/10.1103/PhysRevLett.124.033201 VL - 124 SP - 033201 ER - TY - JOUR A1 - Werdehausen, Daniel A1 - Burger, Sven A1 - Staude, Isabelle A1 - Pertsch, Thomas A1 - Decker, Manuel T1 - Flat optics in high numerical aperture broadband imaging systems JF - J. Opt. Y1 - 2020 U6 - https://doi.org/10.1088/2040-8986/ab8ea2 VL - 22 SP - 065607 ER - TY - JOUR A1 - Farchmin, Nando A1 - Hammerschmidt, Martin A1 - Schneider, Philipp-Immanuel A1 - Wurm, Matthias A1 - Bodermann, Bernd A1 - Bär, Markus A1 - Heidenreich, Sebastian T1 - Efficient Bayesian inversion for shape reconstruction of lithography masks JF - J. Micro/Nanolith. MEMS MOEMS Y1 - 2020 U6 - https://doi.org/10.1117/1.JMM.19.2.024001 VL - 19 SP - 024001 ER - TY - JOUR A1 - Binkowski, Felix A1 - Betz, Fridtjof A1 - Colom, Rémi A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Quasinormal mode expansion of optical far-field quantities JF - Phys. Rev. B Y1 - 2020 U6 - https://doi.org/10.1103/PhysRevB.102.035432 VL - 102 SP - 035432 ER - TY - JOUR A1 - Musiał, Anna A1 - Żołnacz, Kinga A1 - Srocka, Nicole A1 - Kravets, Oleh A1 - Große, Jan A1 - Olszewski, Jacek A1 - Poturaj, Krzysztof A1 - Wojcik, Grzegorz A1 - Mergo, Paweł A1 - Kamil, Dybka A1 - Dyrkacz, Mariusz A1 - Dlubek, Michal A1 - Lauritsen, Kristian A1 - Bülter, Andreas A1 - Schneider, Philipp-Immanuel A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Rodt, Sven A1 - Urbanczyk, Wacław A1 - Sek, Grzegorz A1 - Reitzenstein, Stephan T1 - Plug&play fibre-coupled 73 kHz single-photon source operating in the telecom O-band JF - Adv. Quantum Technol. Y1 - 2020 U6 - https://doi.org/10.1002/qute.202000018 VL - 3 SP - 2000018 ER - TY - JOUR A1 - Colom, Rémi A1 - Stout, Brian A1 - Bonod, Nicolas T1 - Modal Expansion of the Impulse Response Function for Predicting the Time Dynamics of Open Optical Cavities JF - arXiv Y1 - 2020 ER - TY - THES A1 - Wulkow, Hanna T1 - Regularization of Elliptic Partial Differential Equations using Neural Networks N2 - This thesis presents a method for interpolating data using a neural network. The data is sparse and perturbed and is used as training data for a small neural network. For severely perturbed data, the network does not manage to find a smooth interpolation. But as the data resembles the solution to the one-dimensional and time-independent heat equation, the weak form of this PDE and subsequently its functional can be written down. If the functional is minimized, a solution to the weak form of the heat equation is found. The functional is now added to the traditional loss function of a neural network, the mean squared error between the network prediction and the given data, in order to smooth out fluctuations and interpolate between distanced grid points. This way, the network minimizes both the mean squared error and the functional, resulting in a smoother curve that can be used to predict u(x) for any grid point x. KW - elliptic partial differential equations KW - neural networks Y1 - 2020 ER - TY - GEN A1 - Bittracher, Andreas A1 - Schütte, Christof ED - Junge, Oliver ED - Schütze, O. ED - Froyland, Gary ED - Ober-Blobaum, S. ED - Padberg-Gehle, E. T1 - A weak characterization of slow variables in stochastic dynamical systems T2 - Advances in Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday Y1 - 2020 SN - 978-3-030-51264-4 U6 - https://doi.org/10.1007/978-3-030-51264-4_6 VL - 304 SP - 132 EP - 150 PB - Springer International ER - TY - GEN A1 - Mollenhauer, Mattes A1 - Schuster, Ingmar A1 - Klus, Stefan A1 - Schütte, Christof ED - Junge, Oliver ED - Schütze, O. ED - Froyland, Gary ED - Ober-Blobaum, S. ED - Padberg-Gehle, K. T1 - Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces T2 - Advances om Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on his 60th birthday Y1 - 2020 SN - 978-3-030-51264-4 U6 - https://doi.org/10.1007/978-3-030-51264-4_5 VL - 304 SP - 109 EP - 131 PB - Springer International ER - TY - CHAP A1 - Rodt, Sven A1 - Schneider, Philipp-Immanuel A1 - Zschiedrich, Lin A1 - Heindel, Tobias A1 - Bounouar, Samir A1 - Kantner, Markus A1 - Koprucki, Thomas A1 - Bandelow, Uwe A1 - Burger, Sven A1 - Reitzenstein, Stephan ED - Kneissl, Michael ED - Knorr, Andreas ED - Reitzenstein, Stephan ED - Hoffmann, Axel T1 - Deterministic Quantum Devices for Optical Quantum Communication T2 - Semiconductor Nanophotonics Y1 - 2020 U6 - https://doi.org/10.1007/978-3-030-35656-9_8 VL - 194 SP - 285 EP - 359 PB - Springer CY - Cham ER - TY - JOUR A1 - Gorgulla, Christoph A1 - Boeszoermnyi, Andras A1 - Wang, Zi-Fu A1 - Fischer, Patrick D. A1 - Coote, Paul A1 - Das, Krishna M. Padmanabha A1 - Malets, Yehor S. A1 - Radchenko, Dmytro S. A1 - Moroz, Yurii A1 - Scott, David A. A1 - Fackeldey, Konstantin A1 - Hoffmann, Moritz A1 - Iavniuk, Iryna A1 - Wagner, Gerhard A1 - Arthanari, Haribabu T1 - An open-source drug discovery platform enables ultra-large virtual screens JF - Nature N2 - On average, an approved drug today costs $2-3 billion and takes over ten years to develop1. In part, this is due to expensive and time-consuming wet-lab experiments, poor initial hit compounds, and the high attrition rates in the (pre-)clinical phases. Structure-based virtual screening (SBVS) has the potential to mitigate these problems. With SBVS, the quality of the hits improves with the number of compounds screened2. However, despite the fact that large compound databases exist, the ability to carry out large-scale SBVSs on computer clusters in an accessible, efficient, and flexible manner has remained elusive. Here we designed VirtualFlow, a highly automated and versatile open-source platform with perfect scaling behaviour that is able to prepare and efficiently screen ultra-large ligand libraries of compounds. VirtualFlow is able to use a variety of the most powerful docking programs. Using VirtualFlow, we have prepared the largest and freely available ready-to-dock ligand library available, with over 1.4 billion commercially available molecules. To demonstrate the power of VirtualFlow, we screened over 1 billion compounds and discovered a small molecule inhibitor (iKeap1) that engages KEAP1 with nanomolar affinity (Kd = 114 nM) and disrupts the interaction between KEAP1 and the transcription factor NRF2. We also identified a set of structurally diverse molecules that bind to KEAP1 with submicromolar affinity. This illustrates the potential of VirtualFlow to access vast regions of the chemical space and identify binders with high affinity for target proteins. Y1 - 2020 U6 - https://doi.org/https://doi.org/10.1038/s41586-020-2117-z VL - 580 SP - 663 EP - 668 PB - Springer Nature ER - TY - JOUR A1 - Helfmann, Luzie A1 - Ribera Borrell, Enric A1 - Schütte, Christof A1 - Koltai, Peter T1 - Extending Transition Path Theory: Periodically Driven and Finite-Time Dynamics JF - Journal of Nonlinear Science Y1 - 2020 U6 - https://doi.org/https://doi.org/10.1007/s00332-020-09652-7 VL - 30 SP - 3321 EP - 3366 ER - TY - JOUR A1 - Niemann, Jan-Hendrik A1 - Winkelmann, Stefanie A1 - Wolf, Sarah A1 - Schütte, Christof T1 - Agent-based modeling: Population limits and large timescales JF - Chaos: An Interdisciplinary Journal of Nonlinear Science N2 - Modeling, simulation and analysis of interacting agent systems is a broad field of research, with existing approaches reaching from informal descriptions of interaction dynamics to more formal, mathematical models. In this paper, we study agent-based models (ABMs) given as continuous-time stochastic processes and their pathwise approximation by ordinary and stochastic differential equations (ODEs and SDEs, respectively) for medium to large populations. By means of an appropriately adapted transfer operator approach we study the behavior of the ABM process on long time scales. We show that, under certain conditions, the transfer operator approach allows to bridge the gap between the pathwise results for large populations on finite timescales, i.e., the SDE limit model, and approaches built to study dynamical behavior on long time scales like large deviation theory. The latter provides a rigorous analysis of rare events including the associated asymptotic rates on timescales that scale exponentially with the population size. We demonstrate that it is possible to reveal metastable structures and timescales of rare events of the ABM process by finite-length trajectories of the SDE process for large enough populations. This approach has the potential to drastically reduce computational effort for the analysis of ABMs. Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-77309 SN - 1438-0064 VL - 31 IS - 3 ER - TY - THES A1 - Baumann, Felix T1 - Impact of Contact Surfaces on the Death Estimation N2 - The determination of time of death is one of the central tasks in forensic medicine. A standard method of time of death estimation elies on matching temperature measurements of the corpse with a post-mortem cooling model. In addition to widely used empirical post-mortem models, modelling based on a precise mathematical simulation of the cooling process have been gaining popularity. The simulation based cooling models and the resulting time of death estimates dependon a large variety of parameters. These include hermal properties for different body tissue types, environmental conditions such as temperature and air flow, and the presence of clothing and coverings. In this thesis we focus on a specific arameter - the contact between corpse and underground - and investigate its influence on the time of death estimation. Resulting we aim to answer the question whether it is necessary to consider contact mechanics in the underlying mathematical cooling model. KW - time of death estimation KW - contact mechanics KW - heat equation KW - inverse problems Y1 - 2020 ER - TY - JOUR A1 - Temp, Julia A1 - Labuz, Dominika A1 - Negrete, Roger A1 - Sunkara, Vikram A1 - Machelska, Halina T1 - Pain and knee damage in male and female mice in the medial meniscal transection-induced osteoarthritis JF - Osteoarthritis and Cartilage Y1 - 2019 U6 - https://doi.org/10.1016/j.joca.2019.11.003 ER - TY - THES A1 - Semler, Phillip T1 - Mixed finite elements in cloth simulation N2 - This master thesis investigates the use and behaviour of a mixed finite element formulation for the simulation of garments. The garment is modelled as an isotropic shell and is related to its mid-surface by energetic degeneration. Based on this, an energy functional is constructed, which contains the deformation and the mid-surface vector as degree of freedom. It is then shown why this problem does not correspond to a saddle point problem, but to a non-convex energy minimization. The implementation of the energy minimization takes place with the ZIB-internal FE framework Kaskade7.4, whereby a geometric linear and different geometric non-linear problems are examined, whereby for a selected, non-linear example a comparison is made with an existing implementation on basis of Morley elements. The further evaluations include the analysis of the quantitative and qualitative results, the used solution method, the behaviour of the system energy as well as the used CPU time. KW - cloth simulation KW - shell elements KW - mixed finite elements Y1 - 2020 ER - TY - CHAP A1 - Krause, Rolf A1 - Weiser, Martin T1 - Multilevel augmented Lagrangian solvers for overconstrained contact formulations T2 - ESAIM: ProcS N2 - Multigrid methods for two-body contact problems are mostly based on special mortar discretizations, nonlinear Gauss-Seidel solvers, and solution-adapted coarse grid spaces. Their high computational efficiency comes at the cost of a complex implementation and a nonsymmetric master-slave discretization of the nonpenetration condition. Here we investigate an alternative symmetric and overconstrained segment-to-segment contact formulation that allows for a simple implementation based on standard multigrid and a symmetric treatment of contact boundaries, but leads to nonunique multipliers. For the solution of the arising quadratic programs, we propose augmented Lagrangian multigrid with overlapping block Gauss-Seidel smoothers. Approximation and convergence properties are studied numerically at standard test problems. Y1 - 2021 U6 - https://doi.org/10.1051/proc/202171175 VL - 71 SP - 175 EP - 184 ER - TY - GEN A1 - Musiał, Anna A1 - Żołnacz, Kinga A1 - Srocka, Nicole A1 - Kravets, Oleh A1 - Große, Jan A1 - Olszewski, Jacek A1 - Poturaj, Krzysztof A1 - Wojcik, Grzegorz A1 - Mergo, Paweł A1 - Dybka, Kamil A1 - Dyrkacz, Mariusz A1 - Dlubek, Michal A1 - Lauritsen, Kristian A1 - Bülter, Andreas A1 - Schneider, Philipp-Immanuel A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Rodt, Sven A1 - Urbanczyk, Wacław A1 - Sek, Grzegorz A1 - Reitzenstein, Stephan T1 - Front Cover: Plug&Play Fiber‐Coupled 73 kHz Single‐Photon Source Operating in the Telecom O‐Band (Adv. Quantum Technol. 6/2020) T2 - Adv. Quantum Technol. Y1 - 2020 U6 - https://doi.org/10.1002/qute.202070061 VL - 3 SP - 2070061 ER - TY - JOUR A1 - Martens, Kevin A1 - Binkowski, Felix A1 - Nguyen, Linh A1 - Hu, Li A1 - Govorov, Alexander O. A1 - Burger, Sven A1 - Liedl, Tim T1 - Long- and Short-Ranged Chiral Interactions in DNA Assembled Plasmonic Chains JF - Nat. Commun. Y1 - 2021 U6 - https://doi.org/10.1038/s41467-021-22289-8 VL - 12 SP - 2025 ER - TY - JOUR A1 - Gorgulla, Christoph A1 - Fackeldey, Konstantin A1 - Wagner, Gerhard A1 - Arthanari, Haribabu T1 - Accounting of Receptor Flexibility in Ultra-Large Virtual Screens with VirtualFlow Using a Grey Wolf Optimization Method JF - Supercomputing Frontiers and Innovations N2 - Structure-based virtual screening approaches have the ability to dramatically reduce the time and costs associated to the discovery of new drug candidates. Studies have shown that the true hit rate of virtual screenings improves with the scale of the screened ligand libraries. Therefore, we have recently developed an open source drug discovery platform (VirtualFlow), which is able to routinely carry out ultra-large virtual screenings. One of the primary challenges of molecular docking is the circumstance when the protein is highly dynamic or when the structure of the protein cannot be captured by a static pose. To accommodate protein dynamics, we report the extension of VirtualFlow to allow the docking of ligands using a grey wolf optimization algorithm using the docking program GWOVina, which substantially improves the quality and efficiency of flexible receptor docking compared to AutoDock Vina. We demonstrate the linear scaling behavior of VirtualFlow utilizing GWOVina up to 128 000 CPUs. The newly supported docking method will be valuable for drug discovery projects in which protein dynamics and flexibility play a significant role. Y1 - 2020 U6 - https://doi.org/10.14529/jsfi200301 VL - 7 IS - 3 SP - 4 EP - 12 ER - TY - JOUR A1 - Kostre, Margarita A1 - Schütte, Christof A1 - Noé, Frank A1 - del Razo Sarmina, Mauricio T1 - Coupling Particle-Based Reaction-Diffusion Simulations with Reservoirs Mediated by Reaction-Diffusion PDEs JF - Multiscale Modeling & Simulation N2 - Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small to be relevant for life processes. Alternatively, particle-based reaction-diffusion models are currently the most accurate and computationally feasible approach at these scales. Their efficiency lies in modeling entire molecules as particles that can diffuse and interact with each other. In this work, we develop modeling and numerical schemes for particle-based reaction-diffusion in an open setting, where the reservoirs are mediated by reaction-diffusion PDEs. We derive two important theoretical results. The first one is the mean-field for open systems of diffusing particles; the second one is the mean-field for a particle-based reaction-diffusion system with second-order reactions. We employ these two results to develop a numerical scheme that consistently couples particle-based reaction-diffusion processes with reaction-diffusion PDEs. This allows modeling open biochemical systems in contact with reservoirs that are time-dependent and spatially inhomogeneous, as in many relevant real-world applications. Y1 - 2021 U6 - https://doi.org/10.1137/20M1352739 VL - 19 IS - 4 SP - 1659 EP - 1683 PB - Society for Industrial and Applied Mathematics ER - TY - GEN A1 - Bittracher, Andreas A1 - Schütte, Christof T1 - A probabilistic algorithm for aggregating vastly undersampled large Markov chains N2 - Model reduction of large Markov chains is an essential step in a wide array of techniques for understanding complex systems and for efficiently learning structures from high-dimensional data. We present a novel aggregation algorithm for compressing such chains that exploits a specific low-rank structure in the transition matrix which, e.g., is present in metastable systems, among others. It enables the recovery of the aggregates from a vastly undersampled transition matrix which in practical applications may gain a speedup of several orders of mag- nitude over methods that require the full transition matrix. Moreover, we show that the new technique is robust under perturbation of the transition matrix. The practical applicability of the new method is demonstrated by identifying a reduced model for the large-scale traffic flow patterns from real-world taxi trip data. T3 - ZIB-Report - 20-21 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78688 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/7587 SN - 1438-0064 ER - TY - JOUR A1 - Pakhomov, Anton A1 - Löchner, Franz A1 - Zschiedrich, Lin A1 - Saravi, Sina A1 - Hammerschmidt, Martin A1 - Burger, Sven A1 - Pertsch, Thomas A1 - Setzpfand, Frank T1 - Far-field polarization signatures of surface optical nonlinearity in noncentrosymmetric semiconductors JF - Sci. Rep. Y1 - 2020 U6 - https://doi.org/10.1038/s41598-020-67186-0 VL - 10 SP - 10545 ER - TY - JOUR A1 - Werdehausen, Daniel A1 - Santiago, Xavier Garcia A1 - Burger, Sven A1 - Staude, Isabelle A1 - Pertsch, Thomas A1 - Rockstuhl, Carsten A1 - Decker, Manuel T1 - Modeling Optical Materials at the Single Scatterer Level: The Transition from Homogeneous to Heterogeneous Materials JF - Adv. Theory Simul. Y1 - 2020 U6 - https://doi.org/10.1002/adts.202000192 VL - 3 SP - 2000192 ER - TY - JOUR A1 - Boltz, Horst-Holger A1 - Sirbu, Alexei A1 - Stelzer, Nina A1 - Lohse, Martin J. A1 - Schütte, Christof A1 - Annibale, Paolo T1 - Quantitative spectroscopy of single molecule interaction times JF - Optic Letters N2 - Single molecule fluorescence tracking provides information at nanometer-scale and millisecond-temporal resolution about the dynamics and interaction of individual molecules in a biological environment. While the dynamic behavior of isolated molecules can be characterized well, the quantitative insight is more limited when interactions between two indistinguishable molecules occur. We address this aspect by developing a theoretical foundation for a spectroscopy of interaction times, i.e., the inference of interaction from imaging data. A non-trivial crossover between a power law to an exponential behavior of the distribution of the interaction times is highlighted, together with the dependence of the exponential term upon the microscopic reaction affinity. Our approach is validated with simulated and experimental datasets. Y1 - 2021 U6 - https://doi.org/10.1364/OL.413030 VL - 46 IS - 7 SP - 1538 EP - 1541 ER - TY - JOUR A1 - Villatoro, José A1 - Zühlke, Martin A1 - Riebe, Daniel A1 - Beitz, Toralf A1 - Weber, Marcus A1 - Löhmannsröben, Hans-Gerd T1 - Sub-ambient pressure IR-MALDI ion mobility spectrometer for the determination of low and high field mobilities JF - Analytical and Bioanalytical Chemistry N2 - A new ion mobility (IM) spectrometer, enabling mobility measurements in the pressure range between 5 and 500 mbar and in the reduced field strength range E/N of 5–90 Td, was developed and characterized. Reduced mobility (K0) values were studied under low E/N (constant value) as well as high E/N (deviation from low field K0) for a series of molecular ions in nitrogen. Infrared matrix-assisted laser desorption ionization (IR-MALDI) was used in two configurations: a source working at atmospheric pressure (AP) and, for the first time, an IR-MALDI source working with a liquid (aqueous) matrix at sub-ambient/reduced pressure (RP). The influence of RP on IR-MALDI was examined and new insights into the dispersion process were gained. This enabled the optimization of the IM spectrometer for best analytical performance. While ion desolvation is less efficient at RP, the transport of ions is more efficient, leading to intensity enhancement and an increased number of oligomer ions. When deciding between AP and RP IR-MALDI, a trade-off between intensity and resolving power has to be considered. Here, the low field mobility of peptide ions was first measured and compared with reference values from ESI-IM spectrometry (at AP) as well as collision cross sections obtained from molecular dynamics simulations. The second application was the determination of the reduced mobility of various substituted ammonium ions as a function of E/N in nitrogen. The mobility is constant up to a threshold at high E/N. Beyond this threshold, mobility increases were observed. This behavior can be explained by the loss of hydrated water molecules. Y1 - 2020 U6 - https://doi.org/10.1007/s00216-020-02735-0 VL - 412 SP - 5247 EP - 5260 ER - TY - JOUR A1 - Rabben, Robert Julian A1 - Ray, Sourav A1 - Weber, Marcus T1 - ISOKANN: Invariant subspaces of Koopman operators learned by a neural network JF - The Journal of Chemical Physics N2 - The problem of determining the rate of rare events in dynamical systems is quite well-known but still difficult to solve. Recent attempts to overcome this problem exploit the fact that dynamic systems can be represented by a linear operator, such as the Koopman operator. Mathematically, the rare event problem comes down to the difficulty in finding invariant subspaces of these Koopman operators K. In this article, we describe a method to learn basis functions of invariant subspaces using an artificial neural Network. Y1 - 2020 U6 - https://doi.org/10.1063/5.0015132 VL - 153 IS - 11 SP - 114109 ER - TY - GEN A1 - Sunkara, Vikram A1 - Raharinirina, N. Alexia A1 - Peppert, Felix A1 - von Kleist, Max A1 - Schütte, Christof T1 - Inferring Gene Regulatory Networks from Single Cell RNA-seq Temporal Snapshot Data Requires Higher Order Moments N2 - Due to the increase in accessibility and robustness of sequencing technology, single cell RNA-seq (scRNA-seq) data has become abundant. The technology has made significant contributions to discovering novel phenotypes and heterogeneities of cells. Recently, there has been a push for using single-- or multiple scRNA-seq snapshots to infer the underlying gene regulatory networks (GRNs) steering the cells' biological functions. To date, this aspiration remains unrealised. In this paper, we took a bottom-up approach and curated a stochastic two gene interaction model capturing the dynamics of a complete system of genes, mRNAs, and proteins. In the model, the regulation was placed upstream from the mRNA on the gene level. We then inferred the underlying regulatory interactions from only the observation of the mRNA population through~time. We could detect signatures of the regulation by combining information of the mean, covariance, and the skewness of the mRNA counts through time. We also saw that reordering the observations using pseudo-time did not conserve the covariance and skewness of the true time course. The underlying GRN could be captured consistently when we fitted the moments up to degree three; however, this required a computationally expensive non-linear least squares minimisation solver. There are still major numerical challenges to overcome for inference of GRNs from scRNA-seq data. These challenges entail finding informative summary statistics of the data which capture the critical regulatory information. Furthermore, the statistics have to evolve linearly or piece-wise linearly through time to achieve computational feasibility and scalability. T3 - ZIB-Report - 20-25 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-79664 SN - 1438-0064 ER - TY - JOUR A1 - Klebanov, Ilja A1 - Sprungk, Björn A1 - Sullivan, T. J. T1 - The linear conditional expectation in Hilbert space JF - Bernoulli Y1 - 2021 U6 - https://doi.org/10.3150/20-BEJ1308 VL - 27 IS - 4 SP - 2299 EP - 2299 ER -