@misc{SchneckWeiserWende2019, author = {Schneck, Jakob and Weiser, Martin and Wende, Florian}, title = {Impact of mixed precision and storage layout on additive Schwarz smoothers}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71305}, year = {2019}, abstract = {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.}, language = {en} } @article{BinkowskiZschiedrichBurger2020, author = {Binkowski, Felix and Zschiedrich, Lin and Burger, Sven}, title = {A Riesz-projection-based method for nonlinear eigenvalue problems}, volume = {419}, journal = {J. Comput. Phys.}, arxiv = {http://arxiv.org/abs/1811.11624}, doi = {10.1016/j.jcp.2020.109678}, pages = {109678}, year = {2020}, language = {en} } @misc{OatesCockaynePrangleetal.2020, author = {Oates, Chris and Cockayne, Jon and Prangle, Dennis and Sullivan, T. J. and Girolami, Mark}, title = {Optimality criteria for probabilistic numerical methods}, volume = {27}, journal = {Multivariate Algorithms and Information-Based Complexity}, editor = {Hickernell, F. J. and Kritzer, P.}, publisher = {De Gruyter}, arxiv = {http://arxiv.org/abs/1901.04326}, doi = {10.1515/9783110635461-005}, pages = {65 -- 88}, year = {2020}, abstract = {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.}, language = {en} } @article{KerstingSullivanHennig2020, author = {Kersting, Hans and Sullivan, T. J. and Hennig, Philipp}, title = {Convergence rates of Gaussian ODE filters}, volume = {30}, journal = {Statistics and Computing}, publisher = {Springer}, address = {Statistics and Computing}, arxiv = {http://arxiv.org/abs/1807.09737}, doi = {10.1007/s11222-020-09972-4}, pages = {1791 -- 1816}, year = {2020}, language = {en} } @article{StoopStraubeJohansenetal.2020, author = {Stoop, Ralph L. and Straube, Arthur and Johansen, Tom H. and Tierno, Pietro}, title = {Collective directional locking of colloidal monolayers on a periodic substrate}, volume = {124}, journal = {Phys. Rev. Lett.}, doi = {10.1103/PhysRevLett.124.058002}, pages = {058002}, year = {2020}, abstract = {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.}, language = {en} } @article{LieSullivanTeckentrup2021, author = {Lie, Han Cheng and Sullivan, T. J. and Teckentrup, Aretha}, title = {Error bounds for some approximate posterior measures in Bayesian inference}, journal = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, publisher = {Springer}, arxiv = {http://arxiv.org/abs/1911.05669}, doi = {10.1007/978-3-030-55874-1_26}, pages = {275 -- 283}, year = {2021}, language = {en} } @article{KhorashadBesteiroCorreaDuarteetal.2020, author = {Khorashad, Larousse Khosravi and Besteiro, Lucas V. and Correa-Duarte, Miguel and Burger, Sven and Wang, Zhiming M. and Govorov, Alexander O.}, title = {Hot electrons generated in chiral plasmonic nanocrystals as a mechanism for surface photochemistry and chiral growth}, volume = {142}, journal = {J. Am. Chem. Soc.}, doi = {10.1021/jacs.9b11124}, pages = {4193}, year = {2020}, language = {en} } @article{WerdehausenBurgerStaudeetal.2020, author = {Werdehausen, Daniel and Burger, Sven and Staude, Isabelle and Pertsch, Thomas and Decker, Manuel}, title = {General design formalism for highly efficient flat optics for broadband applications}, volume = {28}, journal = {Opt. Express}, doi = {10.1364/OE.386573}, pages = {6452}, year = {2020}, language = {en} } @article{PfluegerKlineFernandezHerreroetal.2020, author = {Pfl{\"u}ger, Mika and Kline, R. Joseph and Fern{\´a}ndez Herrero, Analia and Hammerschmidt, Martin and Soltwisch, Victor and Krumrey, Michael}, title = {Extracting dimensional parameters of gratings produced with self-aligned multiple patterning using grazing-incidence small-angle x-ray scattering}, volume = {19}, journal = {J. Micro Nanolithogr. MEMS MOEMS}, arxiv = {http://arxiv.org/abs/1910.08532}, doi = {10.1117/1.JMM.19.1.014001}, pages = {014001}, year = {2020}, language = {en} } @article{GutscheSantiagoSchneideretal.2020, author = {Gutsche, Philipp and Santiago, Xavier Garcia and Schneider, Philipp-Immanuel and McPeak, Kevin and Nieto-Vesperinas, Manuel and Burger, Sven}, title = {Role of Geometric Shape in Chiral Optics}, volume = {12}, journal = {Symmetry}, arxiv = {http://arxiv.org/abs/1808.01855}, doi = {10.3390/sym12010158}, pages = {158}, year = {2020}, language = {en} } @article{KlebanovSikorskiSchuetteetal.2021, author = {Klebanov, Ilja and Sikorski, Alexander and Sch{\"u}tte, Christof and R{\"o}blitz, Susanna}, title = {Objective priors in the empirical Bayes framework}, volume = {48}, journal = {Scandinavian Journal of Statistics}, number = {4}, publisher = {Wiley Online Library}, doi = {10.1111/sjos.12485}, pages = {1212 -- 1233}, year = {2021}, abstract = {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.}, language = {en} } @article{KlebanovSchusterSullivan2020, author = {Klebanov, Ilja and Schuster, Ingmar and Sullivan, T. J.}, title = {A rigorous theory of conditional mean embeddings}, volume = {2}, journal = {SIAM Journal on Mathematics of Data Science}, number = {3}, arxiv = {http://arxiv.org/abs/1912.00671}, doi = {10.1137/19M1305069}, pages = {583 -- 606}, year = {2020}, language = {en} } @incollection{KantnerHoehneKopruckietal.2020, author = {Kantner, Markus and H{\"o}hne, Theresa and Koprucki, Thomas and Burger, Sven and W{\"u}nsche, Hans-J{\"u}rgen and Schmidt, Frank and Mielke, Alexander and Bandelow, Uwe}, title = {Multi-dimensional modeling and simulation of semiconductor nanophotonic devices}, volume = {194}, booktitle = {Semiconductor Nanophotonics}, editor = {Kneissl, Michael and Knorr, Andreas and Reitzenstein, Stephan and Hoffmann, Axel}, publisher = {Springer}, address = {Cham}, doi = {10.1007/978-3-030-35656-9_7}, pages = {241 -- 283}, year = {2020}, language = {en} } @article{TillmannJaegerBecker2020, author = {Tillmann, Peter and J{\"a}ger, Klaus and Becker, Christiane}, title = {Minimising levelised cost of electricity of bifacial solar panel arrays using Bayesian optimisation}, volume = {4}, journal = {Sustain. Energy Fuels}, doi = {10.1039/C9SE00750D}, pages = {254}, year = {2020}, language = {en} } @article{HammerschmidtDoepkingBurgeretal.2020, author = {Hammerschmidt, Martin and D{\"o}pking, Sandra and Burger, Sven and Matera, Sebastian}, title = {Field Heterogeneities and Their Impact on Photocatalysis: Combining Optical and Kinetic Monte Carlo Simulations on the Nanoscale}, volume = {124}, journal = {J. Phys. Chem. C}, doi = {10.1021/acs.jpcc.9b11469}, pages = {3177}, year = {2020}, language = {en} } @article{MoellerIsbilirSungkawornetal.2020, author = {M{\"o}ller, Jan and Isbilir, Ali and Sungkaworn, Titiwat and Osberg, Brenda and Karathanasis, Christos and Sunkara, Vikram and Grushevsky, Eugene O and Bock, Andreas and Annibale, Paolo and Heilemann, Mike and Sch{\"u}tte, Christof and Lohse, Martin J.}, title = {Single molecule mu-opioid receptor membrane-dynamics reveal agonist-specific dimer formation with super-resolved precision}, volume = {16}, journal = {Nature Chemical Biology}, doi = {10.1038/s41589-020-0566-1}, pages = {946 -- 954}, year = {2020}, language = {en} } @article{KlusNueskePeitzetal.2020, author = {Klus, Stefan and N{\"u}ske, Feliks and Peitz, Sebastian and Niemann, Jan-Hendrik and Clementi, Cecilia and Sch{\"u}tte, Christof}, title = {Data-driven approximation of the Koopman generator: Model reduction, system identification, and control}, volume = {406}, journal = {Physica D: Nonlinear Phenomena}, doi = {10.1016/j.physd.2020.132416}, year = {2020}, language = {en} } @article{ManleyWaldeHagedornetal.2020, author = {Manley, Phillip and Walde, Sebastian and Hagedorn, Sylvia and Hammerschmidt, Martin and Burger, Sven and Becker, Christiane}, title = {Nanopatterned Sapphire Substrates in Deep-UV LEDs: Is there an Optical Benefit?}, volume = {28}, journal = {Opt. Express}, doi = {10.1364/OE.379438}, pages = {3619}, year = {2020}, language = {en} } @book{WinkelmannSchuette2020, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {Stochastic Dynamics in Computational Biology}, volume = {8}, journal = {Frontiers in Applied Dynamical Systems: Reviews and Tutorials}, publisher = {Springer International Publishing}, isbn = {978-3-030-62386-9}, doi = {10.1007/978-3-030-62387-6}, year = {2020}, language = {en} } @article{OmariLangePloentzkeetal.2020, author = {Omari, Mohamed and Lange, Alexander and Pl{\"o}ntzke, Julia and R{\"o}blitz, Susanna}, title = {Model-based exploration of the impact of glucose metabolism on the estrous cycle dynamics in dairy cows}, volume = {15}, journal = {Biology Direct}, doi = {10.1186/s13062-019-0256-7}, year = {2020}, language = {en} } @article{BeckerDjurdjevacConradEseretal.2020, author = {Becker, Fabian and Djurdjevac Conrad, Natasa and Eser, Raphael A. and Helfmann, Luzie and Sch{\"u}tt, Brigitta and Sch{\"u}tte, Christof and Zonker, Johannes}, title = {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}, volume = {15}, journal = {PLOS ONE}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0241133}, pages = {1 -- 37}, year = {2020}, language = {en} } @article{GoetschelSchielaWeiser2021, author = {G{\"o}tschel, Sebastian and Schiela, Anton and Weiser, Martin}, title = {Kaskade 7 - a Flexible Finite Element Toolbox}, volume = {81}, journal = {Computers and Mathematics with Applications}, doi = {10.1016/j.camwa.2020.02.011}, pages = {444 -- 458}, year = {2021}, abstract = {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.}, language = {en} }