@article{KlebanovSikorskiSchuetteetal., author = {Klebanov, Ilja and Sikorski, Alexander and Sch{\"u}tte, Christof and R{\"o}blitz, Susanna}, title = {Objective priors in the empirical Bayes framework}, series = {Scandinavian Journal of Statistics}, volume = {48}, journal = {Scandinavian Journal of Statistics}, number = {4}, publisher = {Wiley Online Library}, doi = {10.1111/sjos.12485}, pages = {1212 -- 1233}, 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{KostreSchuetteNoeetal.2021, author = {Kostre, Margarita and Sch{\"u}tte, Christof and No{\´e}, Frank and del Razo Sarmina, Mauricio}, title = {Coupling Particle-Based Reaction-Diffusion Simulations with Reservoirs Mediated by Reaction-Diffusion PDEs}, series = {Multiscale Modeling \& Simulation}, volume = {19}, journal = {Multiscale Modeling \& Simulation}, number = {4}, publisher = {Society for Industrial and Applied Mathematics}, doi = {10.1137/20M1352739}, pages = {1659 -- 1683}, year = {2021}, abstract = {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.}, language = {en} } @article{PakhomovLoechnerZschiedrichetal., author = {Pakhomov, Anton and L{\"o}chner, Franz and Zschiedrich, Lin and Saravi, Sina and Hammerschmidt, Martin and Burger, Sven and Pertsch, Thomas and Setzpfand, Frank}, title = {Far-field polarization signatures of surface optical nonlinearity in noncentrosymmetric semiconductors}, series = {Sci. Rep.}, volume = {10}, journal = {Sci. Rep.}, doi = {10.1038/s41598-020-67186-0}, pages = {10545}, language = {en} } @article{WeberFischerDamerauetal., author = {Weber, Marie-Christin and Fischer, Lisa and Damerau, Alexandra and Ponomarev, Igor and Pfeiffenberger, Moritz and Gaber, Timo and G{\"o}tschel, Sebastian and Lang, Jens and R{\"o}blitz, Susanna and Buttgereit, Frank and Ehrig, Rainald and Lang, Annemarie}, title = {Macroscale mesenchymal condensation to study cytokine-driven cellular and matrix-related changes during cartilage degradation}, series = {Biofabrication}, volume = {12}, journal = {Biofabrication}, number = {4}, doi = {10.1088/1758-5090/aba08f}, abstract = {Understanding the pathophysiological processes of cartilage degradation requires adequate model systems to develop therapeutic strategies towards osteoarthritis (OA). Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific disease aspects. This study aimed to combine in vitro and in silico modeling based on a tissue-engineering approach using mesenchymal condensation to mimic cytokine-induced cellular and matrix-related changes during cartilage degradation. Thus, scaffold-free cartilage-like constructs (SFCCs) were produced based on self-organization of mesenchymal stromal cells (mesenchymal condensation) and i) characterized regarding their cellular and matrix composition or secondly ii) treated with interleukin-1β (IL-1β) and tumor necrosis factor α (TNFα) for 3 weeks to simulate OA-related matrix degradation. In addition, an existing mathematical model based on partial differential equations was optimized and transferred to the underlying settings to simulate distribution of IL-1β, type II collagen degradation and cell number reduction. By combining in vitro and in silico methods, we aim to develop a valid, efficient alternative approach to examine and predict disease progression and effects of new therapeutics.}, language = {en} } @article{ShiEvlyukhinReinhardtetal., author = {Shi, Liping and Evlyukhin, Andrey B. and Reinhardt, Carsten and Babushkin, Ihar and Zenin, Vladimir A. and Burger, Sven and Malureanu, Radu and Chichkov, Boris N. and Morgner, Uwe and Kovacev, Milutin}, title = {Progressive Self-Boosting Anapole-Enhanced Deep-Ultraviolet Third Harmonic During Few-Cycle Laser Radiation}, series = {ACS Photonics}, volume = {7}, journal = {ACS Photonics}, doi = {10.1021/acsphotonics.0c00753}, pages = {1655}, language = {en} } @article{BinkowskiBetzColometal., author = {Binkowski, Felix and Betz, Fridtjof and Colom, R{\´e}mi and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven}, title = {Quasinormal mode expansion of optical far-field quantities}, series = {Phys. Rev. B}, volume = {102}, journal = {Phys. Rev. B}, doi = {10.1103/PhysRevB.102.035432}, pages = {035432}, language = {en} } @article{MusiałŻołnaczSrockaetal., author = {Musiał, Anna and Żołnacz, Kinga and Srocka, Nicole and Kravets, Oleh and Große, Jan and Olszewski, Jacek and Poturaj, Krzysztof and Wojcik, Grzegorz and Mergo, Paweł and Kamil, Dybka and Dyrkacz, Mariusz and Dlubek, Michal and Lauritsen, Kristian and B{\"u}lter, Andreas and Schneider, Philipp-Immanuel and Zschiedrich, Lin and Burger, Sven and Rodt, Sven and Urbanczyk, Wacław and Sek, Grzegorz and Reitzenstein, Stephan}, title = {Plug\&play fibre-coupled 73 kHz single-photon source operating in the telecom O-band}, series = {Adv. Quantum Technol.}, volume = {3}, journal = {Adv. Quantum Technol.}, doi = {10.1002/qute.202000018}, pages = {2000018}, language = {en} } @article{ColomStoutBonod, author = {Colom, R{\´e}mi and Stout, Brian and Bonod, Nicolas}, title = {Modal Expansion of the Impulse Response Function for Predicting the Time Dynamics of Open Optical Cavities}, series = {arXiv}, journal = {arXiv}, language = {en} } @incollection{RodtSchneiderZschiedrichetal., author = {Rodt, Sven and Schneider, Philipp-Immanuel and Zschiedrich, Lin and Heindel, Tobias and Bounouar, Samir and Kantner, Markus and Koprucki, Thomas and Bandelow, Uwe and Burger, Sven and Reitzenstein, Stephan}, title = {Deterministic Quantum Devices for Optical Quantum Communication}, series = {Semiconductor Nanophotonics}, 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_8}, pages = {285 -- 359}, language = {en} } @article{SiefkeHurtadoDickmannetal., author = {Siefke, Thomas and Hurtado, Carol and Dickmann, Johannes and Dickmann, Walter and K{\"a}seberg, Tim and Meyer, Jan and Burger, Sven and Zeitner, Uwe and Bodermann, Bernd and Kroker, Stefanie}, title = {Quasi-bound states in the continuum for deep subwavelength structural information retrieval for DUV nano-optical polarizers}, series = {Opt. Express}, volume = {28}, journal = {Opt. Express}, doi = {10.1364/OE.396044}, pages = {23122}, language = {en} } @article{TockhornSutterColometal., author = {Tockhorn, Philipp and Sutter, Johannes and Colom, R{\´e}mi and Kegelmann, Lukas and Al-Ashouri, Amran and Roß, Marcel and J{\"a}ger, Klaus and Unold, Thomas and Burger, Sven and Albrecht, Steve and Becker, Christiane}, title = {Improved Quantum Efficiency by Advanced Light Management in Nanotextured Solution-Processed Perovskite Solar Cells}, series = {ACS Photonics}, volume = {7}, journal = {ACS Photonics}, doi = {10.1021/acsphotonics.0c00935}, pages = {2589}, language = {en} } @article{FeisBeutelKoepfleretal., author = {Feis, Joshua and Beutel, Dominik and K{\"o}pfler, Julian and Santiago, Xavier Garcia and Rockstuhl, Carsten and Wegener, Martin and Fernandez-Corbaton, Ivan}, title = {Helicity-Preserving Optical Cavity Modes for Enhanced Sensing of Chiral Molecules}, series = {Phys. Rev. Lett.}, volume = {124}, journal = {Phys. Rev. Lett.}, doi = {10.1103/PhysRevLett.124.033201}, pages = {033201}, language = {en} } @article{WerdehausenBurgerStaudeetal., author = {Werdehausen, Daniel and Burger, Sven and Staude, Isabelle and Pertsch, Thomas and Decker, Manuel}, title = {Flat optics in high numerical aperture broadband imaging systems}, series = {J. Opt.}, volume = {22}, journal = {J. Opt.}, doi = {10.1088/2040-8986/ab8ea2}, pages = {065607}, language = {en} } @article{FarchminHammerschmidtSchneideretal., author = {Farchmin, Nando and Hammerschmidt, Martin and Schneider, Philipp-Immanuel and Wurm, Matthias and Bodermann, Bernd and B{\"a}r, Markus and Heidenreich, Sebastian}, title = {Efficient Bayesian inversion for shape reconstruction of lithography masks}, series = {J. Micro/Nanolith. MEMS MOEMS}, volume = {19}, journal = {J. Micro/Nanolith. MEMS MOEMS}, doi = {10.1117/1.JMM.19.2.024001}, pages = {024001}, language = {en} } @article{MrowińskiSchnauberKaganskiyetal., author = {Mrowiński, Paweł and Schnauber, Peter and Kaganskiy, Arsenty and Schall, Johannes and Burger, Sven and Rodt, Sven and Reitzenstein, Stephan}, title = {Directional single-photon emission from deterministic quantum dot waveguide structures}, series = {Phys. Status Solidi RRL}, volume = {14}, journal = {Phys. Status Solidi RRL}, doi = {10.1002/pssr.202000115}, pages = {2000115}, language = {en} } @article{StraubeKowalikNetzetal., author = {Straube, Arthur and Kowalik, Bartosz G. and Netz, Roland R. and H{\"o}fling, Felix}, title = {Rapid onset of molecular friction in liquids bridging between the atomistic and hydrodynamic pictures}, series = {Commun. Phys.}, volume = {3}, journal = {Commun. Phys.}, publisher = {Nature}, doi = {10.1038/s42005-020-0389-0}, pages = {126}, abstract = {Friction in liquids arises from conservative forces between molecules and atoms. Although the hydrodynamics at the nanoscale is subject of intense research and despite the enormous interest in the non-Markovian dynamics of single molecules and solutes, the onset of friction from the atomistic scale so far could not be demonstrated. Here, we fill this gap based on frequency-resolved friction data from high-precision simulations of three prototypical liquids, including water. Combining with theory, we show that friction in liquids emerges abruptly at a characteristic frequency, beyond which viscous liquids appear as non-dissipative, elastic solids. Concomitantly, the molecules experience Brownian forces that display persistent correlations. A critical test of the generalised Stokes-Einstein relation, mapping the friction of single molecules to the visco-elastic response of the macroscopic sample, disproves the relation for Newtonian fluids, but substantiates it exemplarily for water and a moderately supercooled liquid. The employed approach is suitable to yield insights into vitrification mechanisms and the intriguing mechanical properties of soft materials.}, language = {en} } @article{TempLabuzNegreteetal., author = {Temp, Julia and Labuz, Dominika and Negrete, Roger and Sunkara, Vikram and Machelska, Halina}, title = {Pain and knee damage in male and female mice in the medial meniscal transection-induced osteoarthritis}, series = {Osteoarthritis and Cartilage}, journal = {Osteoarthritis and Cartilage}, doi = {10.1016/j.joca.2019.11.003}, language = {en} } @misc{Semler, type = {Master Thesis}, author = {Semler, Phillip}, title = {Mixed finite elements in cloth simulation}, pages = {116}, abstract = {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.}, language = {en} } @misc{Wulkow, type = {Master Thesis}, author = {Wulkow, Hanna}, title = {Regularization of Elliptic Partial Differential Equations using Neural Networks}, pages = {63}, abstract = {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.}, language = {en} } @inproceedings{KrauseWeiser, author = {Krause, Rolf and Weiser, Martin}, title = {Multilevel augmented Lagrangian solvers for overconstrained contact formulations}, series = {ESAIM: ProcS}, volume = {71}, booktitle = {ESAIM: ProcS}, doi = {10.1051/proc/202171175}, pages = {175 -- 184}, abstract = {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.}, language = {en} } @article{KlebanovSchusterSullivan, author = {Klebanov, Ilja and Schuster, Ingmar and Sullivan, T. J.}, title = {A rigorous theory of conditional mean embeddings}, series = {SIAM Journal on Mathematics of Data Science}, volume = {2}, journal = {SIAM Journal on Mathematics of Data Science}, number = {3}, doi = {10.1137/19M1305069}, pages = {583 -- 606}, language = {en} } @incollection{KantnerHoehneKopruckietal., 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}, series = {Semiconductor Nanophotonics}, 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}, language = {en} } @article{HammerschmidtDoepkingBurgeretal., 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}, series = {J. Phys. Chem. C}, volume = {124}, journal = {J. Phys. Chem. C}, doi = {10.1021/acs.jpcc.9b11469}, pages = {3177}, language = {en} } @article{BeckerDjurdjevacConradEseretal., 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}, series = {PLOS ONE}, volume = {15}, journal = {PLOS ONE}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0241133}, pages = {1 -- 37}, language = {en} } @article{ManleyWaldeHagedornetal., 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?}, series = {Opt. Express}, volume = {28}, journal = {Opt. Express}, doi = {10.1364/OE.379438}, pages = {3619}, language = {en} } @article{OmariLangePloentzkeetal.2019, 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}, series = {Biology Direct}, volume = {15}, journal = {Biology Direct}, doi = {10.1186/s13062-019-0256-7}, year = {2019}, language = {en} } @misc{BeckerJaegerBurger, author = {Becker, Christiane and J{\"a}ger, Klaus and Burger, Sven}, title = {Nanophotonics for Solar Energy}, series = {Sol. Energy Mater. Sol. Cells}, volume = {221}, journal = {Sol. Energy Mater. Sol. Cells}, doi = {10.1016/j.solmat.2020.110916}, pages = {110916}, language = {en} } @article{KlebanovSchuster, author = {Klebanov, Ilja and Schuster, Ingmar}, title = {Markov Chain Importance Sampling - a highly efficient estimator for MCMC}, series = {Journal of Computational and Graphical Statistics}, journal = {Journal of Computational and Graphical Statistics}, doi = {10.1080/10618600.2020.1826953}, abstract = {Markov chain (MC) algorithms are ubiquitous in machine learning and statistics and many other disciplines. Typically, these algorithms can be formulated as acceptance rejection methods. In this work we present a novel estimator applicable to these methods, dubbed Markov chain importance sampling (MCIS), which efficiently makes use of rejected proposals. For the unadjusted Langevin algorithm, it provides a novel way of correcting the discretization error. Our estimator satisfies a central limit theorem and improves on error per CPU cycle, often to a large extent. As a by-product it enables estimating the normalizing constant, an important quantity in Bayesian machine learning and statistics.}, language = {en} } @article{ScottSantiagoBeuteletal., author = {Scott, Philip and Santiago, Xavier Garcia and Beutel, Dominik and Rockstuhl, Carsten and Wegener, Martin and Fernandez-Corbaton, Ivan}, title = {On enhanced sensing of chiral molecules in optical cavities}, series = {Appl. Phys. Rev.}, volume = {7}, journal = {Appl. Phys. Rev.}, doi = {10.1063/5.0025006}, pages = {041413}, language = {en} } @article{delRazoDibakSchuetteetal., author = {del Razo, Mauricio J. and Dibak, Manuel and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics}, series = {The Journal of Chemical Physics}, volume = {155}, journal = {The Journal of Chemical Physics}, number = {12}, doi = {10.1063/5.0060314}, language = {en} } @article{JaegerSutterHammerschmidtetal., author = {J{\"a}ger, Klaus and Sutter, Johannes and Hammerschmidt, Martin and Schneider, Philipp-Immanuel and Becker, Christiane}, title = {Prospects of light management in perovskite/silicon tandem solar cells}, series = {Nanophotonics}, volume = {10}, journal = {Nanophotonics}, doi = {10.1515/nanoph-2020-0674}, pages = {1991}, language = {en} } @article{PakhomovHammerschmidtBurgeretal., author = {Pakhomov, Anton V. and Hammerschmidt, Martin and Burger, Sven and Pertsch, Thomas and Setzpfand, Frank}, title = {Modeling of surface-induced second-harmonic generation from multilayer structures by the transfer matrix method}, series = {Opt. Express}, volume = {29}, journal = {Opt. Express}, doi = {10.1364/OE.417066}, pages = {9098}, language = {en} } @article{BinkowskiWuLalanneetal., author = {Binkowski, Felix and Wu, Tong and Lalanne, Philippe and Burger, Sven and Govorov, Alexander O.}, title = {Hot Electron Generation through Near-Field Excitation of Plasmonic Nanoresonators}, series = {ACS Photonics}, volume = {8}, journal = {ACS Photonics}, doi = {10.1021/acsphotonics.1c00231}, pages = {1243}, language = {en} } @phdthesis{Santiago, author = {Santiago, Xavier Garcia}, title = {Numerical methods for shape optimization of photonic nanostructures}, organization = {Karlsruher Institut f{\"u}r Technologie}, doi = {10.5445/IR/1000131006}, language = {en} } @article{AndrleHoenickeGwaltetal., author = {Andrle, Anna and H{\"o}nicke, Philipp and Gwalt, Grzegorz and Schneider, Philipp-Immanuel and Kayser, Yves and Siewert, Frank and Soltwisch, Victor}, title = {GIXRF and machine learning as metrological tools for shape and element sensitive reconstructions of periodic nanostructures}, series = {Proc. SPIE}, volume = {11611}, journal = {Proc. SPIE}, doi = {10.1117/12.2586082}, pages = {116110R}, language = {en} } @article{ManleySegantiniAhibozetal., author = {Manley, Phillip and Segantini, Michele and Ahiboz, Doguscan and Hammerschmidt, Martin and Arnaoutakis, Georgios and MacQueen, Rowan W. and Burger, Sven and Becker, Christiane}, title = {Double-layer metasurface for enhanced photon up-conversion}, series = {APL Photon.}, volume = {6}, journal = {APL Photon.}, doi = {10.1063/5.0040839}, pages = {036103}, language = {en} } @article{LiuZhouWangetal., author = {Liu, Yongtao and Zhou, Zhiguang and Wang, Fan and Kewes, G{\"u}nter and Wen, Shihui and Burger, Sven and Wakiani, Majid Ebrahimi and Xi, Peng and Yang, Jiong and Yang, Xusan and Benson, Oliver and Jin, Dayong}, title = {Axial localization and tracking of self-interference nanoparticles by lateral point spread functions}, series = {Nat. Commun.}, volume = {12}, journal = {Nat. Commun.}, doi = {10.1038/s41467-021-22283-0}, pages = {2019}, language = {en} } @article{VillatoroZuehlkeRiebeetal., author = {Villatoro, Jos{\´e} and Z{\"u}hlke, Martin and Riebe, Daniel and Beitz, Toralf and Weber, Marcus and L{\"o}hmannsr{\"o}ben, Hans-Gerd}, title = {Sub-ambient pressure IR-MALDI ion mobility spectrometer for the determination of low and high field mobilities}, series = {Analytical and Bioanalytical Chemistry}, volume = {412}, journal = {Analytical and Bioanalytical Chemistry}, doi = {10.1007/s00216-020-02735-0}, pages = {5247 -- 5260}, abstract = {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.}, language = {en} } @article{KlebanovSprungkSullivan, author = {Klebanov, Ilja and Sprungk, Bj{\"o}rn and Sullivan, T. J.}, title = {The linear conditional expectation in Hilbert space}, series = {Bernoulli}, volume = {27}, journal = {Bernoulli}, number = {4}, doi = {10.3150/20-BEJ1308}, pages = {2299 -- 2299}, language = {en} } @article{MironBeronVeraHelfmannetal., author = {Miron, Philippe and Beron-Vera, Francisco and Helfmann, Luzie and Koltai, P{\´e}ter}, title = {Transition paths of marine debris and the stability of the garbage patches}, series = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, volume = {31}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, number = {3}, doi = {https://doi.org/10.1063/5.0030535}, abstract = {We used transition path theory (TPT) to infer "reactive" pathways of floating marine debris trajectories. The TPT analysis was applied on a pollution-aware time-homogeneous Markov chain model constructed from trajectories produced by satellite-tracked undrogued buoys from the NOAA Global Drifter Program. The latter involved coping with the openness of the system in physical space, which further required an adaptation of the standard TPT setting. Directly connecting pollution sources along coastlines with garbage patches of varied strengths, the unveiled reactive pollution routes represent alternative targets for ocean cleanup efforts. Among our specific findings we highlight: constraining a highly probable pollution source for the Great Pacific Garbage Patch; characterizing the weakness of the Indian Ocean gyre as a trap for plastic waste; and unveiling a tendency of the subtropical gyres to export garbage toward the coastlines rather than to other gyres in the event of anomalously intense winds.}, language = {en} } @article{FischerEhrigSchaeferetal., author = {Fischer, Sophie and Ehrig, Rainald and Sch{\"a}fer, Stefan and Tronci, Enrico and Mancini, Toni and Egli, Marcel and Ille, Fabian and Kr{\"u}ger, Tillmann H. C. and Leeners, Brigitte and R{\"o}blitz, Susanna}, title = {Mathematical Modelling and Simulation Provides Evidence for New Strategies of Ovarian Stimulation}, series = {Frontiers in Endocrinology}, volume = {12}, journal = {Frontiers in Endocrinology}, doi = {10.3389/fendo.2021.613048}, abstract = {New approaches to ovarian stimulation protocols, such as luteal start, random start or double stimulation, allow for flexibility in ovarian stimulation at different phases of the menstrual cycle which is especially useful when time for assisted reproductive technology is limited, e.g. for emergency fertility preservation in cancer patients. It has been proposed that the success of these methods is based on the continuous growth of multiple cohorts ("waves") of follicles throughout the menstrual cycle which leads to the availability of ovarian follicles for ovarian controlled stimulation at several time points. Though several preliminary studies have been published, their scientific evidence has not been considered as being strong enough to integrate these results into routine clinical practice. This work aims at adding further scientific evidence about the efficiency of variable-start protocols and underpinning the theory of follicular waves by using mathematical modelling and numerical simulations. For this purpose, we have modified and coupled two previously published models, one describing the time course of hormones and one describing competitive follicular growth in a normal menstrual cycle. The coupled model is used to test stimulation protocols in silico. Simulation results show the occurrence of follicles in a wave-like manner during a normal menstrual cycle and qualitatively predict the outcome of ovarian stimulation initiated at different time points of the menstrual cycle.}, language = {en} } @misc{MusiałŻołnaczSrockaetal., author = {Musiał, Anna and Żołnacz, Kinga and Srocka, Nicole and Kravets, Oleh and Große, Jan and Olszewski, Jacek and Poturaj, Krzysztof and Wojcik, Grzegorz and Mergo, Paweł and Dybka, Kamil and Dyrkacz, Mariusz and Dlubek, Michal and Lauritsen, Kristian and B{\"u}lter, Andreas and Schneider, Philipp-Immanuel and Zschiedrich, Lin and Burger, Sven and Rodt, Sven and Urbanczyk, Wacław and Sek, Grzegorz and Reitzenstein, Stephan}, title = {Front Cover: Plug\&Play Fiber-Coupled 73 kHz Single-Photon Source Operating in the Telecom O-Band (Adv. Quantum Technol. 6/2020)}, series = {Adv. Quantum Technol.}, volume = {3}, journal = {Adv. Quantum Technol.}, doi = {10.1002/qute.202070061}, pages = {2070061}, language = {en} } @article{MartensBinkowskiNguyenetal., author = {Martens, Kevin and Binkowski, Felix and Nguyen, Linh and Hu, Li and Govorov, Alexander O. and Burger, Sven and Liedl, Tim}, title = {Long- and Short-Ranged Chiral Interactions in DNA Assembled Plasmonic Chains}, series = {Nat. Commun.}, volume = {12}, journal = {Nat. Commun.}, doi = {10.1038/s41467-021-22289-8}, pages = {2025}, language = {en} } @article{BonnetAkianSavinetal., author = {Bonnet, Luc and Akian, Jean-Luc and Savin, {\´E}ric and Sullivan, T. J.}, title = {Adaptive reconstruction of imperfectly-observed monotone functions, with applications to uncertainty quantification}, series = {Algorithms}, volume = {13}, journal = {Algorithms}, number = {8}, doi = {10.3390/a13080196}, pages = {196}, abstract = {Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued functions. While this problem is similar to the classical statistical problem of isotonic regression, the optimisation setting alters several characteristics of the problem and opens natural algorithmic possibilities. We present our algorithm, establish sufficient conditions for convergence of the reconstruction to the ground truth, and apply the method to synthetic test cases and a real-world example of uncertainty quantification for aerodynamic design.}, language = {en} } @article{WuerthManleyVoigtetal., author = {W{\"u}rth, Christian and Manley, Phillip and Voigt, Robert and Ahiboz, Doguscan and Becker, Christiane and Resch-Genger, Ute}, title = {Metasurface enhanced sensitized photon upconversion: towards highly efficient low power upconversion applications and nano-scale E-field sensors}, series = {Nano Lett.}, volume = {20}, journal = {Nano Lett.}, doi = {10.1021/acs.nanolett.0c02548}, pages = {6682}, language = {en} } @inproceedings{BinkowskiBetzColometal., author = {Binkowski, Felix and Betz, Fridtjof and Colom, R{\´e}mi and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven}, title = {Modal expansion of optical far-field quantities using quasinormal modes}, series = {EPJ Web Conf.}, volume = {238}, booktitle = {EPJ Web Conf.}, doi = {10.1051/epjconf/202023805007}, pages = {05007}, language = {en} } @inproceedings{ColomBinkowskiBetzetal., author = {Colom, R{\´e}mi and Binkowski, Felix and Betz, Fridtjof and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven}, title = {Quasi-normal mode expansion as a tool for the design of nanophotonic devices}, series = {EPJ Web Conf.}, volume = {238}, booktitle = {EPJ Web Conf.}, doi = {10.1051/epjconf/202023805008}, pages = {05008}, language = {en} } @misc{Betz, type = {Master Thesis}, author = {Betz, Fridtjof}, title = {Investigation and application of contour integral methods for resonance expansion in nanophotonics}, language = {en} } @article{SantiagoBurgerRockstuhletal., author = {Santiago, Xavier Garcia and Burger, Sven and Rockstuhl, Carsten and Schneider, Philipp-Immanuel}, title = {Bayesian optimization with improved scalability and derivative information for efficient design of nanophotonic structures}, series = {J. Light. Technol.}, volume = {39}, journal = {J. Light. Technol.}, doi = {10.1109/JLT.2020.3023450}, pages = {167}, language = {en} } @article{WerdehausenSantiagoBurgeretal., author = {Werdehausen, Daniel and Santiago, Xavier Garcia and Burger, Sven and Staude, Isabelle and Pertsch, Thomas and Rockstuhl, Carsten and Decker, Manuel}, title = {Modeling Optical Materials at the Single Scatterer Level: The Transition from Homogeneous to Heterogeneous Materials}, series = {Adv. Theory Simul.}, volume = {3}, journal = {Adv. Theory Simul.}, doi = {10.1002/adts.202000192}, pages = {2000192}, language = {en} } @book{DeuflhardWeiser, author = {Deuflhard, Peter and Weiser, Martin}, title = {Numerische Mathematik 3. Adaptive L{\"o}sung partieller Differentialgleichungen}, edition = {2}, publisher = {de Gruyter}, isbn = {978-3-11-069168-9}, doi = {10.1515/9783110689655}, pages = {456}, language = {de} } @article{SikorskiWeberSchuette, author = {Sikorski, Alexander and Weber, Marcus and Sch{\"u}tte, Christof}, title = {The Augmented Jump Chain}, series = {Advanced Theory and Simulations}, volume = {4}, journal = {Advanced Theory and Simulations}, number = {4}, publisher = {Wiley-VCH}, doi = {10.1002/adts.202000274}, abstract = {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.}, language = {en} } @phdthesis{Venkatareddy, author = {Venkatareddy, Narendra Lagumaddepalli}, title = {Revealing secrets of mussel-glue mimetic peptides - From advanced NMR to computational process modelling}, language = {en} } @phdthesis{Eshtewy, author = {Eshtewy, Neveen Ali Salem}, title = {Mathematical Modeling of Metabolic-Genetic Networks}, language = {en} } @article{LaydonSunkaraBoelenetal., author = {Laydon, Daniel J. and Sunkara, Vikram and Boelen, Lies and Bangham, Charles R. M. and Asquith, Becca}, title = {The relative contributions of infectious and mitotic spread to HTLV-1 persistence}, series = {PLOS Computational Biology}, journal = {PLOS Computational Biology}, doi = {10.1371/journal.pcbi.1007470}, language = {en} } @article{SunkaraHeinzHeinrichetal., author = {Sunkara, Vikram and Heinz, Gitta A. and Heinrich, Frederik F. and Durek, Pawel and Mobasheri, Ali and Mashreghi, Mir-Farzin and Lang, Annemarie}, title = {Combining segmental bulk- and single-cell RNA-sequencing to define the chondrocyte gene expression signature in the murine knee joint}, series = {bioarxiv (Accepted in Osteoarthr. Cartil.)}, journal = {bioarxiv (Accepted in Osteoarthr. Cartil.)}, doi = {10.1101/2020.06.13.148056}, language = {en} } @article{HelfmannDjurdjevacConradDjurdjevacetal., author = {Helfmann, Luzie and Djurdjevac Conrad, Natasa and Djurdjevac, Ana and Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {From interacting agents to density-based modeling with stochastic PDEs}, series = {Communications in Applied Mathematics and Computational Science}, volume = {16}, journal = {Communications in Applied Mathematics and Computational Science}, number = {1}, doi = {10.2140/camcos.2021.16.1}, pages = {1 -- 32}, abstract = {Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models.}, language = {en} } @article{BinkowskiZschiedrichBurger, author = {Binkowski, Felix and Zschiedrich, Lin and Burger, Sven}, title = {A Riesz-projection-based method for nonlinear eigenvalue problems}, series = {J. Comput. Phys.}, volume = {419}, journal = {J. Comput. Phys.}, doi = {10.1016/j.jcp.2020.109678}, pages = {109678}, language = {en} } @misc{OatesCockaynePrangleetal., author = {Oates, Chris and Cockayne, Jon and Prangle, Dennis and Sullivan, T. J. and Girolami, Mark}, title = {Optimality criteria for probabilistic numerical methods}, series = {Multivariate Algorithms and Information-Based Complexity}, volume = {27}, journal = {Multivariate Algorithms and Information-Based Complexity}, editor = {Hickernell, F. J. and Kritzer, P.}, publisher = {De Gruyter}, doi = {10.1515/9783110635461-005}, pages = {65 -- 88}, 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{KerstingSullivanHennig, author = {Kersting, Hans and Sullivan, T. J. and Hennig, Philipp}, title = {Convergence rates of Gaussian ODE filters}, series = {Statistics and Computing}, volume = {30}, journal = {Statistics and Computing}, publisher = {Springer}, address = {Statistics and Computing}, doi = {10.1007/s11222-020-09972-4}, pages = {1791 -- 1816}, language = {en} } @article{PfluegerKlineFernandezHerreroetal., 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}, series = {J. Micro Nanolithogr. MEMS MOEMS}, volume = {19}, journal = {J. Micro Nanolithogr. MEMS MOEMS}, doi = {10.1117/1.JMM.19.1.014001}, pages = {014001}, language = {en} } @article{StoopStraubeJohansenetal., 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}, series = {Phys. Rev. Lett.}, volume = {124}, journal = {Phys. Rev. Lett.}, doi = {10.1103/PhysRevLett.124.058002}, pages = {058002}, 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{LieSullivanTeckentrup2020, author = {Lie, Han Cheng and Sullivan, T. J. and Teckentrup, Aretha}, title = {Error bounds for some approximate posterior measures in Bayesian inference}, series = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, journal = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, publisher = {Springer}, doi = {10.1007/978-3-030-55874-1_26}, pages = {275 -- 283}, year = {2020}, language = {en} } @article{KhorashadBesteiroCorreaDuarteetal., 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}, series = {J. Am. Chem. Soc.}, volume = {142}, journal = {J. Am. Chem. Soc.}, doi = {10.1021/jacs.9b11124}, pages = {4193}, language = {en} } @article{WerdehausenBurgerStaudeetal., 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}, series = {Opt. Express}, volume = {28}, journal = {Opt. Express}, doi = {10.1364/OE.386573}, pages = {6452}, language = {en} } @article{GoetschelSchielaWeiser, author = {G{\"o}tschel, Sebastian and Schiela, Anton and Weiser, Martin}, title = {Kaskade 7 - a Flexible Finite Element Toolbox}, series = {Computers and Mathematics with Applications}, volume = {81}, journal = {Computers and Mathematics with Applications}, doi = {10.1016/j.camwa.2020.02.011}, pages = {444 -- 458}, 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} } @article{GutscheSantiagoSchneideretal., 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}, series = {Symmetry}, volume = {12}, journal = {Symmetry}, doi = {10.3390/sym12010158}, pages = {158}, language = {en} } @phdthesis{Pakhomov, author = {Pakhomov, Anton}, title = {Efficient modeling and optimization of surface second-harmonic generation from nanophotonic components}, doi = {10.22032/dbt.49369}, language = {en} } @misc{PfluegerKlineFernandezHerreroetal., author = {Pfl{\"u}ger, Mika and Kline, R Joseph and Fern{\´a}ndez Herrero, Anal{\´i}a 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 [Source Code]}, doi = {10.24433/CO.0953516.v2}, language = {en} } @misc{JaegerSutterSchneideretal., author = {J{\"a}ger, Klaus and Sutter, Johannes and Schneider, Philipp-Immanuel and Hammerschmidt, Martin and Becker, Christiane}, title = {Optical simulations of nanotextured perovskite/silicon tandem solar cell}, series = {HZB Data Service}, journal = {HZB Data Service}, doi = {10.5442/ND000005}, language = {en} } @article{PlockBurgerSchneider, author = {Plock, Matthias and Burger, Sven and Schneider, Philipp-Immanuel}, title = {Recent advances in Bayesian optimization with applications to parameter reconstruction in optical nano-metrology}, series = {Proc. SPIE}, volume = {11783}, journal = {Proc. SPIE}, doi = {10.1117/12.2592266}, pages = {117830J}, language = {en} } @article{GaoRickertUrbanetal., author = {Gao, Timm and Rickert, Lucas and Urban, Felix and Große, Jan and Srocka, Nicole and Rodt, Sven and Musial, Anna and Zolnacz, Kinga and Mergo, Pawel and Dybka, Kamil and Urbanczyk, Waclaw and Sek, Grzegorz and Burger, Sven and Reitzenstein, Stephan and Heindel, Tobias}, title = {A quantum key distribution testbed using a plug\&play telecom-wavelength single-photon source}, series = {Appl. Phys. Rev.}, volume = {9}, journal = {Appl. Phys. Rev.}, doi = {10.1063/5.0070966}, pages = {011412}, language = {en} } @article{TorunSchneiderHammerschmidtetal., author = {Torun, Cem G{\"u}ney and Schneider, Philipp-Immanuel and Hammerschmidt, Martin and Burger, Sven and Munns, Joseph H.D. and Schr{\"o}der, Tim}, title = {Optimized diamond inverted nanocones for enhanced color center to fiber coupling}, series = {Appl. Phys. Lett.}, volume = {118}, journal = {Appl. Phys. Lett.}, doi = {10.1063/5.0050338}, pages = {234002}, language = {en} } @article{VolkovaHeupelTrofimovetal., author = {Volkova, Kseniia and Heupel, Julia and Trofimov, Sergei and Betz, Fridtjof and Colom, R{\´e}mi and MacQueen, Rowan W. and Akhundzada, Sapida and Reginka, Meike and Ehresmann, Arno and Reithmeier, Johann Peter and Burger, Sven and Popov, Cyril and Naydenov, Boris}, title = {Optical and Spin Properties of NV Center Ensembles in Diamond Nano-Pillars}, series = {Nanomaterials}, volume = {12}, journal = {Nanomaterials}, doi = {10.3390/nano12091516}, pages = {1516}, language = {en} } @article{AndrleHoenickeGwaltetal., author = {Andrle, Anna and H{\"o}nicke, Philipp and Gwalt, Grzegorz and Schneider, Philipp-Immanuel and Kayser, Yves and Siewert, Frank and Soltwisch, Victor}, title = {Shape- and Element-Sensitive Reconstruction of Periodic Nanostructures with Grazing Incidence X-ray Fluorescence Analysis and Machine Learning}, series = {Nanomaterials}, volume = {11}, journal = {Nanomaterials}, doi = {10.3390/nano11071647}, pages = {1647}, language = {en} } @article{BremerJimenezThieleetal., author = {Bremer, Lucas and Jimenez, Carlos and Thiele, Simon and Weber, Ksenia and Huber, Tobias and Rodt, Sven and Herkommer, Alois and Burger, Sven and H{\"o}fling, Sven and Giessen, Harald and Reitzenstein, Stephan}, title = {Numerical optimization of single-mode fiber- coupled single-photon sources based on semiconductor quantum dots}, series = {Opt. Express}, volume = {30}, journal = {Opt. Express}, doi = {10.1364/OE.456777}, pages = {15913}, language = {en} } @article{DassKuenPosnjaketal., author = {Dass, Mihir and Kuen, Lilli and Posnjak, Gregor and Burger, Sven and Liedl, Tim}, title = {Visible wavelength spectral tuning of absorption and circular dichroism of DNA-assembled Au/Ag core-shell nanorod assemblies}, series = {Mater. Adv.}, volume = {3}, journal = {Mater. Adv.}, doi = {10.1039/D1MA01211H}, pages = {3438}, language = {en} } @article{AhibozAndresenManleyetal., author = {Ahiboz, Doguscan and Andresen, Elina and Manley, Phillip and Resch-Genger, Ute and W{\"u}rth, Christian and Becker, Christiane}, title = {Metasurface-Enhanced Photon Upconversion upon 1550 nm Excitation}, series = {Adv. Opt. Mater.}, volume = {9}, journal = {Adv. Opt. Mater.}, doi = {10.1002/adom.202101285}, pages = {2101285}, language = {en} } @inproceedings{SchneiderGarciaSantiagoWiegandetal., author = {Schneider, Philipp-Immanuel and Garcia-Santiago, Xavier and Wiegand, Benjamin and Anton, Oliver and Krutzik, Markus and Rockstuhl, Carsten and Burger, Sven}, title = {Advances in Bayesian optimization for photonics and quantum atom optics applications}, series = {OSA Advanced Photonics Congress}, booktitle = {OSA Advanced Photonics Congress}, doi = {10.1364/IPRSN.2021.JTh1E.2}, pages = {JTh1E.2}, language = {en} } @article{AyanbayevKlebanovLieetal., author = {Ayanbayev, Birzhan and Klebanov, Ilja and Lie, Han Cheng and Sullivan, T. J.}, title = {Γ-convergence of Onsager-Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems}, series = {Inverse Problems}, volume = {38}, journal = {Inverse Problems}, number = {2}, doi = {10.1088/1361-6420/ac3f81}, pages = {32}, language = {en} } @article{AyanbayevKlebanovLieetal., author = {Ayanbayev, Birzhan and Klebanov, Ilja and Lie, Han Cheng and Sullivan, T. J.}, title = {Γ-convergence of Onsager-Machlup functionals: II. Infinite product measures on Banach spaces}, series = {Inverse Problems}, volume = {38}, journal = {Inverse Problems}, number = {2}, doi = {10.1088/1361-6420/ac3f82}, pages = {35}, language = {en} } @article{TiernoJohansenStraube, author = {Tierno, Pietro and Johansen, Tom H. and Straube, Arthur}, title = {Thermally active nanoparticle clusters enslaved by engineered domain wall traps}, series = {Nature Commun.}, volume = {12}, journal = {Nature Commun.}, doi = {10.1038/s41467-021-25931-7}, pages = {5813}, abstract = {The stable assembly of fluctuating nanoparticle clusters on a surface represents a technological challenge of widespread interest for both fundamental and applied research. Here we demonstrate a technique to stably confine in two dimensions clusters of interacting nanoparticles via size-tunable, virtual magnetic traps. We use cylindrical Bloch walls arranged to form a triangular lattice of ferromagnetic domains within an epitaxially grown ferrite garnet film. At each domain, the magnetic stray field generates an effective harmonic potential with a field tunable stifness. The experiments are combined with theory to show that the magnetic confinement is effectively harmonic and pairwise interactions are of dipolar nature, leading to central, strictly repulsive forces. For clusters of magnetic nanoparticles, the stationary collective states arise from the competition between repulsion, confinement and the tendency to fill the central potential well. Using a numerical simulation model as a quantitative map between the experiment and theory we explore the field-induced crystallization process for larger clusters and unveil the existence of three different dynamical regimes. The present method provides a model platform for investigations of the collective phenomena emerging when strongly confined nanoparticle clusters are forced to move in an idealized, harmonic-like potential.}, language = {en} } @misc{ColomBinkowskiBetzetal., author = {Colom, Remi and Binkowski, Felix and Betz, Fridtjof and Kivshar, Yuri and Burger, Sven}, title = {Source code and simulation results for nanoantennas supporting an enhanced Purcell factor due to interfering resonances}, series = {Zenodo}, journal = {Zenodo}, doi = {10.5281/zenodo.6565850}, language = {en} } @article{GarciaSantiagoHammerschmidtSachsetal., author = {Garcia Santiago, Xavier and Hammerschmidt, Martin and Sachs, Johannes and Burger, Sven and Kwon, Hyunah and Kn{\"o}ller, Marvin and Arens, Tilo and Fischer, Peer and Fernandez-Corbaton, Ivan and Rockstuhl, Carsten}, title = {Toward maximally electromagnetically chiral scatterers at optical frequencies}, series = {ACS Photonics}, volume = {9}, journal = {ACS Photonics}, doi = {10.1021/acsphotonics.1c01887}, pages = {1954}, language = {en} } @article{StoutColomBonodetal., author = {Stout, Brian and Colom, Remi and Bonod, Nicolas and McPhedran, Ross C}, title = {Spectral expansions of open and dispersive optical systems: Gaussian regularization and convergence}, series = {New J. Phys.}, volume = {23}, journal = {New J. Phys.}, doi = {10.1088/1367-2630/ac10a6}, pages = {083004}, language = {en} } @inproceedings{RickertGaoUrbanetal., author = {Rickert, Lucas and Gao, Timm and Urban, Felix and Große, Jan and Srocka, Nicole and Rodt, Sven and Musial, Anna and Zolnacz, Kinga and Mergo, Pawel and Dybka, Kamil and Urbanczyk, Waclaw and Sek, Grzegorz and Burger, Sven and Reitzenstein, Stephan and Tobias, Heindel}, title = {A Quantum Key Distribution Testbed Using Plug\&Play Telecom-Wavelength Single-Photons}, series = {Quantum Information and Measurement VI}, booktitle = {Quantum Information and Measurement VI}, doi = {10.1364/QIM.2021.M2C.1}, pages = {M2C.1}, language = {en} } @misc{BetzBinkowskiBurger, author = {Betz, Fridtjof and Binkowski, Felix and Burger, Sven}, title = {RPExpand: Software for Riesz projection expansion of resonance phenomena [Source Code]}, doi = {10.24433/CO.2372084.v1}, language = {de} } @article{WuArrivaultDurufleetal., author = {Wu, Tong and Arrivault, Denis and Durufl{\´e}, Marc and Gras, Alexandre and Binkowski, Felix and Burger, Sven and Yan, Wei and Lalanne, Philippe}, title = {Efficient hybrid method for the modal analysis of optical microcavities and nanoresonators}, series = {J. Opt. Soc. Am. A}, volume = {38}, journal = {J. Opt. Soc. Am. A}, doi = {10.1364/JOSAA.428224}, pages = {1224}, language = {en} } @article{BetzBinkowskiBurger, author = {Betz, Fridtjof and Binkowski, Felix and Burger, Sven}, title = {RPExpand: Software for Riesz projection expansion of resonance phenomena}, series = {SoftwareX}, volume = {15}, journal = {SoftwareX}, doi = {10.1016/j.softx.2021.100763}, pages = {100763}, language = {en} } @article{NegrinMonteceloMovsesyanGaoetal., author = {Negrin-Montecelo, Yoel and Movsesyan, Artur and Gao, Jie and Burger, Sven and Wang, Zhiming and Nlate, Sylvain and Pouget, Emilie and Oda, Reiko and Comesana-Hermo, Miguel and Govorov, Alexander O. and Correa-Duarte, Miguel}, title = {Chiral Generation of Hot Carriers for Polarization-Sensitive Plasmonic Photocatalysis with Hybrid Nanostructures}, series = {J. Am. Chem. Soc.}, volume = {144}, journal = {J. Am. Chem. Soc.}, doi = {10.1021/jacs.1c10526}, pages = {1663}, language = {en} } @article{WangCockayneChkrebtiietal., author = {Wang, Junyang and Cockayne, Jon and Chkrebtii, Oksana and Sullivan, T. J. and Oates, Chris}, title = {Bayesian numerical methods for nonlinear partial differential equations}, series = {Statistics and Computing}, volume = {31}, journal = {Statistics and Computing}, number = {5}, doi = {10.1007/s11222-021-10030-w}, language = {en} } @inproceedings{SchnauberSchallBounouaretal., author = {Schnauber, Peter and Schall, Johannes and Bounouar, Samir and Srinivasan, Kartik and Davanco, Marcelo and Song, Jin-Dong and Burger, Sven and Rodt, Sven and Reitzenstein, Stephan}, title = {Deterministically fabricated quantum dot - waveguide systems for on-chip quantum optics}, series = {Proc. SPIE}, volume = {11806}, booktitle = {Proc. SPIE}, doi = {10.1117/12.2596042}, pages = {118060G}, language = {en} } @inproceedings{PerevoznikBoseBurgeretal., author = {Perevoznik, Dmitrii and Bose, Surajit and Burger, Sven and Demircan, Ayhan and Morgner, Uwe}, title = {Writing Photonic Components in Polymers Using Femtosecond Pulses}, series = {Conference on Lasers and Electro-Optics (CLEO)}, booktitle = {Conference on Lasers and Electro-Optics (CLEO)}, doi = {10.1364/CLEO_AT.2021.ATh4P.4}, pages = {ATh4P.4}, language = {en} } @article{MovsesyanSantiagoBurgeretal., author = {Movsesyan, Artur and Santiago, Eva Yazmin and Burger, Sven and Correa-Duarte, Miguel and Besteiro, Lucas V. and Wang, Zhiming and Govorov, Alexander O.}, title = {Plasmonic nanocrystals with complex shapes for photocatalysis and growth: Contrasting anisotropic hot-electron generation with the photothermal effect}, series = {Adv. Opt. Mater.}, volume = {10}, journal = {Adv. Opt. Mater.}, doi = {10.1002/adom.202102663}, pages = {2102663}, language = {en} } @inproceedings{MusialZolnaczSrockaetal., author = {Musial, Anna and Zolnacz, Kinga and Srocka, Nicole and Kravets, Oleh and Große, Jan and Schneider, Philipp-Immanuel and Olszewski, Jacek and Poturaj, Krzystof and Wojcik, Grzegorz and Mergo, Pawel and Dybka, Kamil and Dyrkacz, Mariusz and Dlubek, Michal and Rodt, Sven and Burger, Sven and Zschiedrich, Lin and Urbanczyk, Waclaw and Sek, Grzegorz and Reitzenstein, Stephan}, title = {Stand-alone quantum dot-based single-photon source operating at telecommunication wavelengths}, series = {10th International Conference on Spontaneous Coherence in Excitonic Systems ICSCE10}, booktitle = {10th International Conference on Spontaneous Coherence in Excitonic Systems ICSCE10}, pages = {39}, language = {en} } @phdthesis{Moldenhauer, author = {Moldenhauer, Marian}, title = {Adaptive Algorithms in Optimization under PDE Constraints}, pages = {106}, abstract = {In this thesis, adaptive algorithms in optimization under PDE constraints have been inves- tigated. In its application, the aim of optimization is to increase the longevity of implants, namely the hip joint implant, and in doing so to minimize stress shielding and simultaneously minimize the influence of locally high stresses, that, above a threshold value, are malign to the bone structure. Under the constraint of the equilibrium of forces, describing an elastodynamic setup, coupled with a contact inequality condition, a computationally expensive problem formulation is given. The first step to make the solution of the given problem possible and efficient was to change over to the spatial equilibrium equation, thus rendering an elastostatic setup. Subsequently the intrinsically dynamic motions - trajectories in the load domain - were converted to the static setup. Thus, the trajectories are marginalized to the load domain and characterized with probability distributions. Therefore the solving of the PDE constraint, the contact problem, is simplified. Yet in the whole optimization process, the solving of the PDE, the spatial equilibrium equation together with the contact condition has the most expensive contribution still and hence needed further reduction. This was achieved by application of Kriging interpolation to the load responses of the integrated distribution of stress difference and the maximum stresses. The interpolation of the two response surfaces only needs comparatively few PDE solves to set up the models. Moreover, the Kriging models can be adaptively extended by sequentially adding sample-response pairs. For this the Kriging inherent variance is used to estimate ideal new sample locations with maximum variance values. In doing so, the overall interpolation variance and therefore the interpolation error is reduced. For the integration of the integrated stress differences and penalty values on the relative high dimensional load domain Monte Carlo integration was implemented, averting the curse of dimension. Here, the motion's probability distribution combined with patient specific data of motion frequencies is taken advantage of, making obsolete the use of the otherwise necessary importance sampling. Throughout the optimization, the FE-discretization error and the subsequently attached errors entering the solution process via PDE discretization and approximative solving of the PDE, Kriging interpolation and Monte Carlo integration need to decrease. While the FE-discretization error and the solution of the elastostatic contact problem were assumed precise enough, numerics showed, that the interpolation and integration errors can be controlled by adaptive refinement of the respective methods. For this purpose comparable error quantities for the particular algorithms were introduced and effectively put to use. For the implant position's optimization, the derivative of the objective function was derived using the implicit function theorem. As the FE-discretization changes with implant position modifications big enough, a special line search had to be used to deal with the discontinuities in the objective function. The interplay and performance of the subalgorithms was demonstrated numerically on a reduced 2D setup of a hip joint with and without the implant. Consequently the load domain and the control variable were also limited to the 2D case.}, language = {en} } @inproceedings{PerevoznikBoseBurgeretal., author = {Perevoznik, Dmitrii and Bose, Surajit and Burger, Sven and Demircan, Ayhan and Morgner, Uwe}, title = {Photonic components in polymers made by femtosecond pulses}, series = {Conference on Lasers and Electro-Optics Europe \& European Quantum Electronics Conference (CLEO/Europe-EQEC)}, booktitle = {Conference on Lasers and Electro-Optics Europe \& European Quantum Electronics Conference (CLEO/Europe-EQEC)}, doi = {10.1109/CLEO/Europe-EQEC52157.2021.9541906}, pages = {1}, language = {en} } @article{LueckeNueske, author = {L{\"u}cke, Marvin and N{\"u}ske, Feliks}, title = {tgEDMD: Approximation of the Kolmogorov Operator in Tensor Train Format}, series = {Journal of Nonlinear Science}, volume = {32}, journal = {Journal of Nonlinear Science}, doi = {10.1007/s00332-022-09801-0}, abstract = {Extracting information about dynamical systems from models learned off simulation data has become an increasingly important research topic in the natural and engineering sciences. Modeling the Koopman operator semigroup has played a central role in this context. As the approximation quality of any such model critically depends on the basis set, recent work has focused on deriving data-efficient representations of the Koopman operator in low-rank tensor formats, enabling the use of powerful model classes while avoiding over-fitting. On the other hand, detailed information about the system at hand can be extracted from models for the infinitesimal generator, also called Kolmogorov backward operator for stochastic differential equations. In this work, we present a data-driven method to efficiently approximate the generator using the tensor train (TT) format. The centerpiece of the method is a TT representation of the tensor of generator evaluations at all data sites. We analyze consistency and complexity of the method, present extensions to practically relevant settings, and demonstrate its applicability to benchmark numerical examples.}, language = {en} } @article{TockhornSutterCruzetal., author = {Tockhorn, Philipp and Sutter, Johannes and Cruz, Alexandros and Wagner, Philipp and J{\"a}ger, Klaus and Yoo, Danbi and Lang, Felix and Grischek, Max and Li, Bor and Li, Jinzhao and Shargaieva, Oleksandra and Unger, Eva and Al-Ashouri, Amran and K{\"o}hnen, Eike and Stolterfoth, Martin and Neher, Dieter and Schlatmann, Rutger and Rech, Bernd and Stannowski, Bernd and Albrecht, Steve and Becker, Christiane}, title = {Nano-optical designs for high-efficiency monolithic perovskite-silicon tandem solar cells}, series = {Nat. Nanotechnol.}, volume = {17}, journal = {Nat. Nanotechnol.}, doi = {10.1038/s41565-022-01228-8}, pages = {1214}, language = {en} } @article{MoellerIsbilirSungkawornetal., 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}, series = {Nature Chemical Biology}, volume = {16}, journal = {Nature Chemical Biology}, doi = {10.1038/s41589-020-0566-1}, pages = {946 -- 954}, language = {en} } @misc{MollenhauerSchusterKlusetal., author = {Mollenhauer, Mattes and Schuster, Ingmar and Klus, Stefan and Sch{\"u}tte, Christof}, title = {Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces}, series = {Advances om Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on his 60th birthday}, volume = {304}, journal = {Advances om Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on his 60th birthday}, editor = {Junge, Oliver and Sch{\"u}tze, O. and Froyland, Gary and Ober-Blobaum, S. and Padberg-Gehle, K.}, publisher = {Springer International}, isbn = {978-3-030-51264-4}, doi = {10.1007/978-3-030-51264-4_5}, pages = {109 -- 131}, language = {en} } @misc{BittracherSchuette, author = {Bittracher, Andreas and Sch{\"u}tte, Christof}, title = {A weak characterization of slow variables in stochastic dynamical systems}, series = {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}, volume = {304}, journal = {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}, editor = {Junge, Oliver and Sch{\"u}tze, O. and Froyland, Gary and Ober-Blobaum, S. and Padberg-Gehle, E.}, publisher = {Springer International}, isbn = {978-3-030-51264-4}, doi = {10.1007/978-3-030-51264-4_6}, pages = {132 -- 150}, language = {en} } @article{BittracherMoschnerKokschetal., author = {Bittracher, Andreas and Moschner, Johann and Koksch, Beate and Netz, Roland and Sch{\"u}tte, Christof}, title = {Exploring the locking stage of NFGAILS amyloid fibrillation via transition manifold analysis}, series = {The European Physical Journal B}, volume = {94}, journal = {The European Physical Journal B}, doi = {10.1140/epjb/s10051-021-00200-0}, language = {en} } @article{SechiFackeldeyChewleetal.2022, author = {Sechi, Renata and Fackeldey, Konstantin and Chewle, Surahit and Weber, Marcus}, title = {SepFree NMF: A Toolbox for Analyzing the Kinetics of Sequential Spectroscopic Data}, series = {Algorithms}, volume = {15}, journal = {Algorithms}, number = {9}, doi = {10.3390/a15090297}, pages = {297}, year = {2022}, abstract = {This work addresses the problem of determining the number of components from sequential spectroscopic data analyzed by non-negative matrix factorization without separability assumption (SepFree NMF). These data are stored in a matrix M of dimension "measured times" versus "measured wavenumbers" and can be decomposed to obtain the spectral fingerprints of the states and their evolution over time. SepFree NMF assumes a memoryless (Markovian) process to underline the dynamics and decomposes M so that M=WH, with W representing the components' fingerprints and H their kinetics. However, the rank of this decomposition (i.e., the number of physical states in the process) has to be guessed from pre-existing knowledge on the observed process. We propose a measure for determining the number of components with the computation of the minimal memory effect resulting from the decomposition; by quantifying how much the obtained factorization is deviating from the Markovian property, we are able to score factorizations of a different number of components. In this way, we estimate the number of different entities which contribute to the observed system, and we can extract kinetic information without knowing the characteristic spectra of the single components. This manuscript provides the mathematical background as well as an analysis of computer generated and experimental sequentially measured Raman spectra.}, language = {en} } @article{BauerWeberDiehlWieseneckeretal., author = {Bauer, Wolfgang and Weber, Marcus and Diehl-Wiesenecker, Eva and Galtung, Noa and Prpic, Monika and Somasundaram, Rajan and Tauber, Rudolf and Schwenk, Jochen and Micke, Patrick and Kappert, Kai}, title = {Plasma Proteome Fingerprints Reveal Distinctiveness and Clinical Outcome of SARS-CoV-2 Infection}, series = {Viruses}, volume = {13}, journal = {Viruses}, number = {12}, doi = {10.3390/v13122456}, pages = {2456}, abstract = {We evaluated how plasma proteomic signatures in patients with suspected COVID-19 can unravel the pathophysiology, and determine kinetics and clinical outcome of the infection. We identified distinct plasma proteins linked to the presence and course of COVID-19. These plasma proteomic findings may translate to a protein fingerprint, helping to assist clinical management decisions.}, language = {en} } @article{MollenhauerKlusSchuetteetal., author = {Mollenhauer, Mattes and Klus, Stefan and Sch{\"u}tte, Christof and Koltai, P{\´e}ter}, title = {Kernel Autocovariance Operators of Stationary Processes: Estimation and Convergence}, series = {Journal of Machine Learning Research}, volume = {23}, journal = {Journal of Machine Learning Research}, number = {327}, pages = {1 -- 34}, abstract = {We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the process under various conditions. In particular, we examine ergodic and strongly mixing processes and obtain several asymptotic results as well as finite sample error bounds. We provide applications of our theory in terms of consistency results for kernel PCA with dependent data and the conditional mean embedding of transition probabilities. Finally, we use our approach to examine the nonparametric estimation of Markov transition operators and highlight how our theory can give a consistency analysis for a large family of spectral analysis methods including kernel-based dynamic mode decomposition.}, language = {en} } @book{Reuter, author = {Reuter, Bernhard}, title = {Generalisierte Markov-Modellierung}, publisher = {Springer Spektrum, Wiesbaden}, isbn = {978-3-658-29711-4}, doi = {10.1007/978-3-658-29712-1}, abstract = {Markov State Models (MSM) sind der Goldstandard zur Modellierung biomolekularer Dynamik, da sie die Identifizierung und Analyse metastabiler Zust{\"a}nde erm{\"o}glichen. Die robuste Perron-Cluster-Cluster-Analyse (PCCA+) ist ein verbreiteter Spectral-Clustering-Algorithmus, der f{\"u}r das Clustering hochdimensionaler MSM verwendet wird. Da die PCCA+ auf reversible Prozesse beschr{\"a}nkt ist, wird sie zur Generalisierten PCCA+ (G-PCCA) verallgemeinert, die geeignet ist, nichtreversible Prozesse aufzukl{\"a}ren. Bernhard Reuter untersucht hier mittels G-PCCA die nichtthermischen Auswirkungen von Mikrowellen auf die Proteindynamik. Dazu f{\"u}hrt er molekulardynamische Nichtgleichgewichtssimulationen des Amyloid-β-(1-40)-Peptids durch und modelliert diese.}, language = {de} } @book{WinkelmannSchuette, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {Stochastic Dynamics in Computational Biology}, series = {Frontiers in Applied Dynamical Systems: Reviews and Tutorials}, 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}, language = {en} } @misc{BittracherSchuette, author = {Bittracher, Andreas and Sch{\"u}tte, Christof}, title = {A probabilistic algorithm for aggregating vastly undersampled large Markov chains}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78688}, abstract = {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.}, language = {en} } @inproceedings{RichterBerner, author = {Richter, Lorenz and Berner, Julius}, title = {Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning}, series = {Proceedings of the 39th International Conference on Machine Learning, PMLR}, volume = {162}, booktitle = {Proceedings of the 39th International Conference on Machine Learning, PMLR}, pages = {18649 -- 18666}, abstract = {The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations based on associated stochastic differential equations (SDEs), which allow the minimization of corresponding losses using gradient-based optimization methods. In respective numerical implementations it is therefore crucial to rely on adequate gradient estimators that exhibit low variance in order to reach convergence accurately and swiftly. In this article, we rigorously investigate corresponding numerical aspects that appear in the context of linear Kolmogorov PDEs. In particular, we systematically compare existing deep learning approaches and provide theoretical explanations for their performances. Subsequently, we suggest novel methods that can be shown to be more robust both theoretically and numerically, leading to substantial performance improvements.}, language = {en} } @inproceedings{BernerRichterUllrich, author = {Berner, Julius and Richter, Lorenz and Ullrich, Karen}, title = {An optimal control perspective on diffusion-based generative modeling}, series = {NeurIPS 2022 Workshop on Score-Based Methods}, booktitle = {NeurIPS 2022 Workshop on Score-Based Methods}, abstract = {We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs) such as recently developed diffusion probabilistic models. In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals. This perspective allows to transfer methods from optimal control theory to generative modeling. First, we show that the evidence lower bound is a direct consequence of the well-known verification theorem from control theory. Further, we develop a novel diffusion-based method for sampling from unnormalized densities -- a problem frequently occurring in statistics and computational sciences.}, language = {en} } @misc{ReidelbachWeber, author = {Reidelbach, Marco and Weber, Marcus}, title = {MaRDI - The mathematical Research Data Initiative}, series = {Aktionstag Forschungsdaten}, journal = {Aktionstag Forschungsdaten}, doi = {10.5281/zenodo.7397588}, language = {en} } @article{AlhaddadFoerstnerGrothetal., author = {Alhaddad, Samer and F{\"o}rstner, Jens and Groth, Stefan and Gr{\"u}newald, Daniel and Grynko, Yevgen and Hannig, Frank and Kenter, Tobias and Pfreundt, F.J. and Plessl, Christian and Schotte, Merlind and Steinke, Thomas and Teich, J. and Weiser, Martin and Wende, Florian}, title = {The HighPerMeshes Framework for Numerical Algorithms on Unstructured Grids}, series = {Concurrency and Computation: Practice and Experience}, volume = {34}, journal = {Concurrency and Computation: Practice and Experience}, number = {14}, doi = {10.1002/cpe.6616}, abstract = {Solving PDEs on unstructured grids is a cornerstone of engineering and scientific computing. Heterogeneous parallel platforms, including CPUs, GPUs, and FPGAs, enable energy-efficient and computationally demanding simulations. In this article, we introduce the HPM C++-embedded DSL that bridges the abstraction gap between the mathematical formulation of mesh-based algorithms for PDE problems on the one hand and an increasing number of heterogeneous platforms with their different programming models on the other hand. Thus, the HPM DSL aims at higher productivity in the code development process for multiple target platforms. We introduce the concepts as well as the basic structure of the HPM DSL, and demonstrate its usage with three examples. The mapping of the abstract algorithmic description onto parallel hardware, including distributed memory compute clusters, is presented. A code generator and a matching back end allow the acceleration of HPM code with GPUs. Finally, the achievable performance and scalability are demonstrated for different example problems.}, language = {en} } @article{LelievreStoltzZhang2020, author = {Lelievre, Tony and Stoltz, Gabriel and Zhang, Wei}, title = {Multiple projection MCMC algorithms on submanifolds}, series = {IMA Journal of Numerical Analysis}, journal = {IMA Journal of Numerical Analysis}, doi = {10.1093/imanum/drac006}, year = {2020}, abstract = {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.}, language = {en} } @article{ZhangLiSchuette2021, author = {Zhang, Wei and Li, Tiejun and Sch{\"u}tte, Christof}, title = {Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks}, series = {Journal of Computational Physics}, volume = {465}, journal = {Journal of Computational Physics}, doi = {10.1016/j.jcp.2022.111377}, year = {2021}, abstract = {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.}, language = {en} } @misc{SchneckWeiserWende, 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}, 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{AlhaddadFoerstnerGrothetal., author = {Alhaddad, Samer and F{\"o}rstner, Jens and Groth, Stefan and Gr{\"u}newald, Daniel and Grynko, Yevgen and Hannig, Frank and Kenter, Tobias and Pfreundt, Franz-Josef and Plessl, Christian and Schotte, Merlind and Steinke, Thomas and Teich, J{\"u}rgen and Weiser, Martin and Wende, Florian}, title = {HighPerMeshes - A Domain-Specific Language for Numerical Algorithms on Unstructured Grids}, series = {Euro-Par 2020: Parallel Processing Workshops.}, journal = {Euro-Par 2020: Parallel Processing Workshops.}, publisher = {Springer}, doi = {10.1007/978-3-030-71593-9_15}, pages = {185 -- 196}, abstract = {Solving partial differential equations on unstructured grids is a cornerstone of engineering and scientific computing. Nowadays, heterogeneous parallel platforms with CPUs, GPUs, and FPGAs enable energy-efficient and computationally demanding simulations. We developed the HighPerMeshes C++-embedded Domain-Specific Language (DSL) for bridging the abstraction gap between the mathematical and algorithmic formulation of mesh-based algorithms for PDE problems on the one hand and an increasing number of heterogeneous platforms with their different parallel programming and runtime models on the other hand. Thus, the HighPerMeshes DSL aims at higher productivity in the code development process for multiple target platforms. We introduce the concepts as well as the basic structure of the HighPer-Meshes DSL, and demonstrate its usage with three examples, a Poisson and monodomain problem, respectively, solved by the continuous finite element method, and the discontinuous Galerkin method for Maxwell's equation. The mapping of the abstract algorithmic description onto parallel hardware, including distributed memory compute clusters is presented. Finally, the achievable performance and scalability are demonstrated for a typical example problem on a multi-core CPU cluster.}, language = {en} } @article{DonatiWeberKeller, author = {Donati, Luca and Weber, Marcus and Keller, Bettina G.}, title = {A review of Girsanov Reweighting and of Square Root Approximation for building molecular Markov State Models}, series = {Journal of Mathematical Physics}, volume = {63}, journal = {Journal of Mathematical Physics}, number = {12}, publisher = {AIP Publishing}, doi = {10.1063/5.0127227}, pages = {123306-1 -- 123306-21}, abstract = {Dynamical reweighting methods permit to estimate kinetic observables of a stochastic process governed by a target potential U(x) from trajectories that have been generated at a different potential V(x). In this article, we present Girsanov reweighting and Square Root Approximation (SqRA): the first method reweights path probabilities exploiting the Girsanov theorem and can be applied to Markov State Models (MSMs) to reweight transition probabilities; the second method was originally developed to discretize the Fokker-Planck operator into a transition rate matrix, but here we implement it into a reweighting scheme for transition rates. We begin by reviewing the theoretical background of the methods, then present two applications relevant to Molecular Dynamics (MD), highlighting their strengths and weaknesses.}, language = {en} } @article{FernandesChaowdharySalehetal., author = {Fernandes, Rita and Chaowdhary, Suvrat and Saleh, Noureldin and Mikula, Natalia and Kanevche, Katerina and Berlepsch, Hans and Hosogi, Naoki and Heberle, Joachim and Weber, Marcus and B{\"o}ttcher, Christoph and Koksch, Beate}, title = {Cyanine Dye Coupling Mediates Self-assembly of a pH Sensitive Peptide into Novel 3D Architectures}, series = {Angewandte Chemie}, volume = {61}, journal = {Angewandte Chemie}, number = {48}, pages = {e202208647}, abstract = {A conjugated Cy5 dye-peptide system reveals the formation of two novel and structurally distinct supramolecular assemblies with photo-physical characteristics of H-type dimers or tetramers, respectively. The molecular ultrastructures are triggered by the complementary interplay of mutual chromophore coupling and pH induced changes in the peptide charge pattern.}, language = {en} } @misc{Rabben, type = {Master Thesis}, author = {Rabben, Robert Julian}, title = {Ein holistischer Ansatz zur Analyse molekularer Konformationen auf der Basis von ISOKANN}, language = {de} } @article{BergPloentzkeSiebertetal., author = {Berg, Mascha and Pl{\"o}ntzke, Julia and Siebert, Heike and R{\"o}blitz, Susanna}, title = {Modelling Oscillatory Patterns in the Bovine Estrous Cycle with Boolean Delay Equations}, series = {Bulletin of Mathematical Biology}, volume = {83}, journal = {Bulletin of Mathematical Biology}, number = {121}, doi = {10.1007/s11538-021-00942-z}, pages = {1 -- 25}, abstract = {Boolean delay equations (BDEs), with their relatively simple and intuitive mode of modelling, have been used in many research areas including, for example, climate dynamics and earthquake propagation. Their application to biological systems has been scarce and limited to the molecular level. Here, we derive and present two BDE models. One is directly derived from a previously published ordinary differential equation (ODE) model for the bovine estrous cycle, whereas the second model includes a modification of a particular biological mechanism. We not only compare the simulation results from the BDE models with the trajectories of the ODE model, but also validate the BDE models with two additional numerical experiments. One experiment induces a switch in the oscillatory pattern upon changes in the model parameters, and the other simulates the administration of a hormone that is known to shift the estrous cycle in time. The models presented here are the first BDE models for hormonal oscillators, and the first BDE models for drug administration. Even though automatic parameter estimation still remains challenging, our results support the role of BDEs as a framework for the systematic modelling of complex biological oscillators.}, language = {en} } @article{SchneiderManleyKruegeretal., author = {Schneider, Philipp-Immanuel and Manley, Phillip and Kr{\"u}ger, Jan and Zschiedrich, Lin and K{\"o}ning, Rainer and Bodermann, Bernd and Burger, Sven}, title = {Reconstructing phase aberrations for high-precision dimensional microscopy}, series = {Proc. SPIE}, volume = {12137}, journal = {Proc. SPIE}, doi = {10.1117/12.2620762}, pages = {121370I}, language = {en} } @inproceedings{JaegerSutterTockhornetal., author = {J{\"a}ger, Klaus and Sutter, Johannes and Tockhorn, Philipp and Hammerschmidt, Martin and Schneider, Philipp-Immanuel and Albrecht, Steve and Becker, Christiane}, title = {Improving perovskite/silicon tandem solar cells with optical simulations}, series = {Proc. SPIE}, volume = {PC12150}, booktitle = {Proc. SPIE}, doi = {10.1117/12.2621255}, pages = {PC1215001}, language = {en} } @article{AvalosOvandoSantiagoMovsesyanetal., author = {Avalos-Ovando, Oscar and Santiago, Eva Yazmin and Movsesyan, Artur and Kong, Xiang-Tian and Yu, Peng and Besteiro, Lucas V. and Khosravi Khorashad, Larousse and Okamoto, Hiromi and Slocik, Joseph M. and Correa-Duarte, Miguel and Comesana-Hermo, Miguel and Liedl, Tim and Markovich, Gil and Burger, Sven and Govorov, Alexander O.}, title = {Chiral Bioinspired Plasmonics: A Paradigm Shift for Optical Activity and Photochemistry}, series = {ACS Photon.}, volume = {9}, journal = {ACS Photon.}, doi = {10.1021/acsphotonics.2c00445}, pages = {2219}, language = {en} } @inproceedings{AhibozAndresenManleyetal., author = {Ahiboz, Doguscan and Andresen, Elina and Manley, Phillip and Resch Genger, Ute and W{\"u}rth, Christian and Becker, Christiane}, title = {Enhanced Photon Upconversion Using Erbium-Doped Nanoparticles Interacting with Silicon Metasurfaces}, series = {IEEE 48th Photovoltaic Specialists Conference (PVSC)}, booktitle = {IEEE 48th Photovoltaic Specialists Conference (PVSC)}, doi = {10.1109/PVSC43889.2021.9518495}, pages = {2008 -- 2010}, language = {en} } @inproceedings{CheginiKopanicakovaWeiseretal., author = {Chegini, Fatemeh and Kopanicakova, Alena and Weiser, Martin and Krause, Rolf}, title = {Quantitative Analysis of Nonlinear MultifidelityOptimization for Inverse Electrophysiology}, series = {Domain Decomposition Methods in Science and Engineering XXVI}, booktitle = {Domain Decomposition Methods in Science and Engineering XXVI}, publisher = {Springer}, pages = {65 -- 76}, abstract = {The electric conductivity of cardiac tissue determines excitation propagation and is important for quantifying ischemia and scar tissue and for building personalized models. Estimating conductivity distributions from endocardial mapping data is a challenging inverse problem due to the computational complexity of the monodomain equation, which describes the cardiac excitation. For computing a maximum posterior estimate, we investigate different optimization approaches based on adjoint gradient computation: steepest descent, limited memory BFGS, and recursive multilevel trust region methods, which are using mesh hierarchies or heterogeneous model hierarchies. We compare overall performance, asymptotic convergence rate, and pre-asymptotic progress on selected examples in order to assess the benefit of our multifidelity acceleration.}, language = {en} } @article{BinkowskiBetzHammerschmidtetal., author = {Binkowski, Felix and Betz, Fridtjof and Hammerschmidt, Martin and Schneider, Philipp-Immanuel and Zschiedrich, Lin and Burger, Sven}, title = {Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators}, series = {Commun. Phys.}, volume = {5}, journal = {Commun. Phys.}, doi = {10.1038/s42005-022-00977-1}, pages = {202}, language = {en} } @article{WinkelmannZonkerSchuetteetal., author = {Winkelmann, Stefanie and Zonker, Johannes and Sch{\"u}tte, Christof and Djurdjevac Conrad, Natasa}, title = {Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading}, series = {Mathematical Biosciences}, volume = {336}, journal = {Mathematical Biosciences}, publisher = {Elsevier}, doi = {10.1016/j.mbs.2021.108619}, abstract = {Agent based models (ABMs) are a useful tool for modeling spatio-temporal population dynamics, where many details can be included in the model description. Their computational cost though is very high and for stochastic ABMs a lot of individual simulations are required to sample quantities of interest. Especially, large numbers of agents render the sampling infeasible. Model reduction to a metapopulation model leads to a significant gain in computational efficiency, while preserving important dynamical properties. Based on a precise mathematical description of spatio-temporal ABMs, we present two different metapopulation approaches (stochastic and piecewise deterministic) and discuss the approximation steps between the different models within this framework. Especially, we show how the stochastic metapopulation model results from a Galerkin projection of the underlying ABM onto a finite-dimensional ansatz space. Finally, we utilize our modeling framework to provide a conceptual model for the spreading of COVID-19 that can be scaled to real-world scenarios.}, language = {en} } @article{PlockAndrleBurgeretal., author = {Plock, Matthias and Andrle, Kas and Burger, Sven and Schneider, Philipp-Immanuel}, title = {Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction}, series = {Adv. Theory Simul.}, volume = {5}, journal = {Adv. Theory Simul.}, doi = {10.1002/adts.202200112}, pages = {2200112}, language = {en} } @article{MartensFunckSantiagoetal., author = {Martens, Kevin and Funck, Timon and Santiago, Eva Y. and Govorov, Alexander O. and Burger, Sven and Liedl, Tim}, title = {Onset of Chirality in Plasmonic Meta-Molecules and Dielectric Coupling}, series = {ACS Nano}, volume = {16}, journal = {ACS Nano}, doi = {10.1021/acsnano.2c04729}, pages = {16143}, language = {en} } @article{FischerHolzhausenRoeblitz, author = {Fischer-Holzhausen, Sophie and R{\"o}blitz, Susanna}, title = {Hormonal regulation of ovarian follicle growth in humans: Model-based exploration of cycle variability and parameter sensitivities}, series = {Journal of Theoretical Biology}, journal = {Journal of Theoretical Biology}, doi = {https://doi.org/10.1016/j.jtbi.2022.111150}, abstract = {We present a modelling and simulation framework for the dynamics of ovarian follicles and key hormones along the hypothalamic-pituitary-gonadal axis throughout consecutive human menstrual cycles. All simulation results (hormone concentrations and ovarian follicle sizes) are in biological units and can easily be compared to clinical data. The model takes into account variability in follicles' response to stimulating hormones, which introduces variability between cycles. The growth of ovarian follicles in waves is an emergent property in our model simulations and further supports the hypothesis that follicular waves are also present in humans. We use Approximate Bayesian Computation and cluster analysis to construct a population of virtual subjects and to study parameter distributions and sensitivities. The model can be used to compare and optimize treatment protocols for ovarian hyperstimulation, thus potentially forming the integral part of a clinical decision support system in reproductive endocrinology.}, language = {en} } @article{KruegerLeenersTroncietal., author = {Kr{\"u}ger, Tillmann and Leeners, Brigitte and Tronci, Enrico and Mancini, Toni and Ille, Fabian and Egli, Marcel and Engler, Harald and R{\"o}blitz, Susanna and Frieling, Helge and Sinke, Christopher and Jahn, Kirsten}, title = {The androgen system across the menstrual cycle: Hormonal, (epi-)genetic and psychometric alterations}, series = {Physiology and Behavior}, journal = {Physiology and Behavior}, doi = {https://doi.org/10.1016/j.physbeh.2022.114034}, language = {en} } @inproceedings{DhanakotiMaddocksWeiser, author = {Dhanakoti, Siva Prasad Chakri and Maddocks, John and Weiser, Martin}, title = {Navigation of Concentric Tube Continuum Robots using Optimal Control}, series = {Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics}, booktitle = {Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics}, doi = {10.5220/0011271000003271}, pages = {146 -- 154}, abstract = {Recently developed Concentric Tube Continuum Robots (CTCRs) are widely exploited in, for example in minimally invasive surgeries which involve navigating inside narrow body cavities close to sensitive regions. These CTCRs can be controlled by extending and rotating the tubes in order to reach a target point or perform some task. The robot must deviate as little as possible from this narrow space and avoid damaging neighbouring tissue. We consider \emph{open-loop} optimal control of CTCRs parameterized over pseudo-time, primarily aiming at minimizing the robot's working volume during its motion. External loads acting on the system like tip loads or contact with tissues are not considered here. We also discussed the inclusion of tip's orientation in the optimal framework to perform some tasks. We recall a quaternion-based formulation of the robot configuration, discuss discretization, develop optimization objectives addressing different criteria, and investigate their impact on robot path planning for several numerical examples. This optimal framework can be applied to any backbone based continuum robots.}, language = {en} } @article{ColomBinkowskiBetzetal., author = {Colom, Remi and Binkowski, Felix and Betz, Fridtjof and Kivshar, Yuri and Burger, Sven}, title = {Enhanced Purcell factor for nanoantennas supporting interfering resonances}, series = {Phys. Rev. Research}, volume = {4}, journal = {Phys. Rev. Research}, doi = {10.1103/PhysRevResearch.4.023189}, pages = {023189}, language = {en} } @article{FischerHolzhausenRoeblitz, author = {Fischer-Holzhausen, Sophie and R{\"o}blitz, Susanna}, title = {Mathematical modelling of follicular growth and ovarian stimulation}, series = {Current Opinion in Endocrine and Metabolic Research}, journal = {Current Opinion in Endocrine and Metabolic Research}, doi = {https://doi.org/10.1016/j.coemr.2022.100385}, language = {en} } @article{StraubeWinkelmannSchuetteetal., author = {Straube, Arthur and Winkelmann, Stefanie and Sch{\"u}tte, Christof and H{\"o}fling, Felix}, title = {Stochastic pH oscillations in a model of the urea-urease reaction confined to lipid vesicles}, series = {J. Phys. Chem. Lett.}, volume = {12}, journal = {J. Phys. Chem. Lett.}, doi = {10.1021/acs.jpclett.1c03016}, pages = {9888 -- 9893}, abstract = {The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We numerically study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules. For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller. The mean period, however, is found to be remarkably robust for vesicle sizes down to approximately 200 nm, but the periodicity of the rhythm is gradually destroyed for smaller vesicles. The observed oscillations are explained as a canard-like limit cycle that differs from the wide class of conventional feedback oscillators.}, language = {en} } @article{Djurdjevac, author = {Djurdjevac, Ana}, title = {Linear Parabolic Problems in Random Moving Domains}, volume = {9}, number = {2}, doi = {https://doi.org/10.1137/19M1284889}, pages = {848 -- 879}, abstract = {We consider linear parabolic equations on a random non-cylindrical domain. Utilizing the domain mapping method, we write the problem as a partial differential equation with random coefficients on a cylindrical deterministic domain. Exploiting the deterministic results concerning equations on non-cylindrical domains, we state the necessary assumptions about the velocity filed and in addition, about the flow transformation that this field generates. In this paper we consider both cases, the uniformly bounded with respect to the sample and log-normal type transformation. In addition, we give an explicit example of a log-normal type transformation and prove that it does not satisfy the uniformly bounded condition. We define a general framework for considering linear parabolic problems on random non-cylindrical domains. As the first example, we consider the heat equation on a random tube domain and prove its well-posedness. Moreover, as the other example we consider the parabolic Stokes equation which illustrates the case when it is not enough just to study the plain-back transformation of the function, but instead to consider for example the Piola type transformation, in order to keep the divergence free property.}, language = {en} } @article{DjurdjevacGraeserHerbert, author = {Djurdjevac, Ana and Gr{\"a}ser, Carsten and Herbert, Philip J.}, title = {Non-stationary incompressible linear fluid equations in a moving domain}, series = {arXiv}, journal = {arXiv}, abstract = {This article considers non-stationary incompressible linear fluid equations in a moving domain. We demonstrate the existence and uniqueness of an appropriate weak formulation of the problem by making use of the theory of time-dependent Bochner spaces. It is not possible to directly apply established evolving Hilbert space theory due to the incompressibility constraint. After we have established the well-posedness, we derive and analyse a time discretisation of the system.}, language = {en} } @article{CheginiKopanicakovaKrauseetal., author = {Chegini, Fatemeh and Kopanicakova, Alena and Krause, Rolf and Weiser, Martin}, title = {Efficient Identification of Scars using Heterogeneous Model Hierarchies}, series = {EP Europace}, volume = {23}, journal = {EP Europace}, doi = {10.1093/europace/euaa402}, pages = {i113 -- i122}, abstract = {Aims. Detection and quantification of myocardial scars are helpful both for diagnosis of heart diseases and for building personalized simulation models. Scar tissue is generally charac­terized by a different conduction of electrical excitation. We aim at estimating conductivity-related parameters from endocardial mapping data, in particular the conductivity tensor. Solving this inverse problem requires computationally expensive monodomain simulations on fine discretizations. Therefore, we aim at accelerating the estimation using a multilevel method combining electrophysiology models of different complexity, namely the mono­domain and the eikonal model. Methods. Distributed parameter estimation is performed by minimizing the misfit between simulated and measured electrical activity on the endocardial surface, subject to the mono­domain model and regularization, leading to a constrained optimization problem. We formulate this optimization problem, including the modeling of scar tissue and different regularizations, and design an efficient iterative solver. We consider monodomain grid hierarchies and monodomain-eikonal model hierarchies in a recursive multilevel trust-region method. Results. From several numerical examples, both the efficiency of the method and the estimation quality, depending on the data, are investigated. The multilevel solver is significantly faster than a comparable single level solver. Endocardial mapping data of realistic density appears to be just sufficient to provide quantitatively reasonable estimates of location, size, and shape of scars close to the endocardial surface. Conclusion. In several situations, scar reconstruction based on eikonal and monodomain models differ significantly, suggesting the use of the more accurate but more expensive monodomain model for this purpose. Still, eikonal models can be utilized to accelerate the computations considerably, enabling the use of complex electrophysiology models for estimating myocardial scars from endocardial mapping data.}, language = {en} } @misc{SchuetteKlusHartmann, author = {Sch{\"u}tte, Christof and Klus, Stefan and Hartmann, Carsten}, title = {Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-88637}, abstract = {One of the main challenges in molecular dynamics is overcoming the "timescale barrier", a phrase used to describe that in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, not even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based techniques that have emerged from dynamical systems theory, numerical mathematics, and machine learning over the last two decades. We will focus on how transfer operators can be used to approximate the dynamical behavior on long timescales, review the introduction of this approach into molecular dynamics, and outline the respective theory as well as the algorithmic development from the early numerics-based methods, via variational reformulations, to modern data-based techniques utilizing and improving concepts from machine learning. Furthermore, its relation to rare event simulation techniques will be explained, revealing a broad equivalence of variational principles for long-time quantities in MD. The article will mainly take a mathematical perspective and will leave the application to real-world molecular systems to the more than 1000 research articles already written on this subject.}, language = {en} } @article{BoltzSirbuStelzeretal., author = {Boltz, Horst-Holger and Sirbu, Alexei and Stelzer, Nina and de Lanerolle, Primal and Winkelmann, Stefanie and Annibale, Paolo}, title = {The Impact of Membrane Protein Diffusion on GPCR Signaling}, series = {Cells}, volume = {11}, journal = {Cells}, number = {10}, doi = {10.3390/cells11101660}, pages = {1660}, abstract = {Spatiotemporal signal shaping in G protein-coupled receptor (GPCR) signaling is now a well-established and accepted notion to explain how signaling specificity can be achieved by a superfamily sharing only a handful of downstream second messengers. Dozens of Gs-coupled GPCR signals ultimately converge on the production of cAMP, a ubiquitous second messenger. This idea is almost always framed in terms of local concentrations, the differences in which are maintained by means of spatial separation. However, given the dynamic nature of the reaction-diffusion processes at hand, the dynamics, in particular the local diffusional properties of the receptors and their cognate G proteins, are also important. By combining some first principle considerations, simulated data, and experimental data of the receptors diffusing on the membranes of living cells, we offer a short perspective on the modulatory role of local membrane diffusion in regulating GPCR-mediated cell signaling. Our analysis points to a diffusion-limited regime where the effective production rate of activated G protein scales linearly with the receptor-G protein complex's relative diffusion rate and to an interesting role played by the membrane geometry in modulating the efficiency of coupling}, language = {en} } @article{BoltzKurchanLiu2020, author = {Boltz, Horst-Holger and Kurchan, Jorge and Liu, Andrea J.}, title = {Fluctuation distributions of energy minima in complex landscapes}, series = {Physical Review Research}, volume = {3}, journal = {Physical Review Research}, number = {1}, doi = {10.1103/PhysRevResearch.3.013061}, pages = {013061}, year = {2020}, abstract = {We discuss the properties of the distributions of energies of minima obtained by gradient descent in complex energy landscapes. We find strikingly similar phenomenology across several prototypical models. We particularly focus on the distribution of energies of minima in the analytically well-understood p-spin-interaction spin-glass model. We numerically find non-Gaussian distributions that resemble the Tracy-Widom distributions often found in problems of random correlated variables, and nontrivial finite-size scaling. Based on this, we propose a picture of gradient-descent dynamics that highlights the importance of a first-passage process in the eigenvalues of the Hessian. This picture provides a concrete link to problems in which the Tracy-Widom distribution is established. Aspects of this first-passage view of gradient-descent dynamics are generic for nonconvex complex landscapes, rationalizing the commonality that we find across models.}, language = {en} } @article{BoltzSirbuStelzeretal., author = {Boltz, Horst-Holger and Sirbu, Alexei and Stelzer, Nina and Lohse, Martin J. and Sch{\"u}tte, Christof and Annibale, Paolo}, title = {Quantitative spectroscopy of single molecule interaction times}, series = {Optic Letters}, volume = {46}, journal = {Optic Letters}, number = {7}, doi = {10.1364/OL.413030}, pages = {1538 -- 1541}, abstract = {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.}, language = {en} } @article{HeidaSikorskiWeber, author = {Heida, Martin and Sikorski, Alexander and Weber, Marcus}, title = {Consistency and order 1 convergence of cell-centered finite volume discretizations of degenerate elliptic problems in any space dimension}, series = {SIAM Journal on Numerical Analysis}, journal = {SIAM Journal on Numerical Analysis}, doi = {10.20347/WIAS.PREPRINT.2913}, abstract = {We study consistency of cell-centered finite difference methods for elliptic equations with degenerate coefficients in any space dimension \$d \geq 2\$. This results in order of convergence estimates in the natural weighted energy norm and in the weighted discrete \$L^2\$-norm on admissible meshes. The cells of meshes under consideration may be very irregular in size. We particularly allow the size of certain cells to remain bounded from below even in the asymptotic limit. For uniform meshes we show that the order of convergence is at least 1 in the energy semi-norm, provided the discrete and continuous solutions exist and the continuous solution has \$H^2\$ regularity.}, language = {en} } @phdthesis{Chegini, author = {Chegini, Fatemeh}, title = {Multilevel optimization algorithm for Inverse Problem in Electrocardiography}, abstract = {The electric conductivity of cardiac tissue determines excitation propagation and is vital for quantifying ischemia and scar tissue and building personalized models. As scar tissue is generally characterized by different conduction of electrical excitation, we aim to estimate conductivity-related parameters in mathematical excitation models from endocardial mapping data, particularly the anisotropic conductivity tensor in the monodomain equation, which describes the cardiac excitation. Yet, estimating the distributed and anisotropic conductivity tensors reliably and efficiently from endocardial mapping data or electrocardiograms is a challenging inverse problem due to the computational complexity of the monodomain equation; Many expensive high-resolution computations for the monodomain equation on very fine space and time discretizations are involved. Thus, we aim at building an efficient multilevel method for accelerating the estimation procedure combining electrophysiology models of different complex- ity, which uses a computationally cheap eikonal model in addition to the more accurate monodomain model. Distributed parameter estimation, well-known as an ill-posed inverse problem, can be performed by minimizing the misfit between simulated and measured electrical activity on the endocardial surface subject to the monodomain model and some regularization, leading to a partial differential equation constrained optimization problem. We formulate this optimization problem, including scar tissue modeling and different regularizations, and design an efficient iterative solver. To this aim, we consider monodomain grid hi- erarchies, monodomain-eikonal model hierarchies, and the combination of both hierarchies in a recursive multilevel trust-region (RMTR) method. On the one hand, both the trust region method's estimation quality and efficiency, independent of the data, are investigated from several numerical exam- ples. Endocardial mapping data of realistic density appears to be sufficient to provide quantitatively reasonable estimates of the location, size, and shape of scars close to the endocardial surface. In several situations, scar reconstruction based on eikonal and monodomain models differ significantly, suggesting the use of the more involved monodomain model for this purpose. Moreover, Eikonal models can accelerate the computations considerably, enabling the use of complex electrophysiology models for estimating myocardial scars from endocardial mapping data. In many situations, eikonal models approximate monodomain models well but are orders of magnitude faster to solve. Thus, eikonal models can utilize them to provide an RMTR acceleration with negligible overhead per iteration, resulting in a practical approach to estimating myocardial scars from endocardial mapping data. In addition, the multilevel solver is faster than a comparable single-level solver. On the other hand, we investigate different optimization approaches based on adjoint gradient computation for computing a maximum posterior estimate: steepest descent, limited memory BFGS, and recursive multilevel trust region methods using mesh hierarchies or heterogeneous model hierarchies. We compare overall performance, asymptotic convergence rate, and pre-asymptotic progress on selected examples in order to assess the benefit of our multifidelity acceleration.}, language = {en} } @article{PloentzkeBergEhrigetal., author = {Pl{\"o}ntzke, Julia and Berg, Mascha and Ehrig, Rainald and Leonhard-Marek, Sabine and M{\"u}ller, Kerstin-Elisabeth and R{\"o}blitz, Susanna}, title = {Model Based Exploration of Hypokalemia in Dairy Cows}, series = {Scientific Reports}, volume = {12, 19781}, journal = {Scientific Reports}, doi = {10.1038/s41598-022-22596-0}, abstract = {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.}, language = {en} } @article{ReidelbachBaiZoellneretal., author = {Reidelbach, Marco and Bai, Mei and Z{\"o}llner, Martin Sebastian and Schneeberger, Michaela and Kubicek, Katharina and Kirchberg, Henning and Bressler, Christian and Thorwart, Michael and Herrmann, Carmen}, title = {Solvent dynamics of aqueous halides before and after photoionization}, series = {Journal of Physical Chemistry}, journal = {Journal of Physical Chemistry}, language = {en} } @inproceedings{WeiserChegini, author = {Weiser, Martin and Chegini, Fatemeh}, title = {Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods}, series = {CMBE22 - 7th International Conference on Computational \& Mathematical Biomedical Engineering}, booktitle = {CMBE22 - 7th International Conference on Computational \& Mathematical Biomedical Engineering}, pages = {528 -- 531}, abstract = {The highly localized dynamics of cardiac electrophysiology models call for adaptive simulation methods. Unfortunately, the overhead incurred by classical mesh adaptivity turns out to outweigh the performance improvements achieved by reducing the problem size. Here, we explore a different approach to adaptivity based on algebraic degree of freedom subset selection during spectral deferred correction sweeps, which realizes a kind of multirate higher order integration. Numerical experience indicates a significant performance increase compared to uniform simulations.}, language = {en} } @inproceedings{MukherjeeKalasBurgeretal., author = {Mukherjee, Deshabrato and Kalas, Benj{\´a}min and Burger, Sven and S{\´a}fr{\´a}n, Gy{\"o}rgy and Ser{\´e}nyi, Mikl{\´o}s and Fried, Mikl{\´o}s and Petrik, P{\´e}ter}, title = {Nanostructures for in-situ surface-enhanced Kretschmann-Raether ellipsometry}, series = {Proc. SPIE}, volume = {12428}, booktitle = {Proc. SPIE}, doi = {10.1117/12.2649080}, pages = {124280S}, language = {en} } @article{BetzBinkowskiHammerschmidtetal., author = {Betz, Fridtjof and Binkowski, Felix and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven}, title = {Resonance expansion of quadratic quantities with regularized quasinormal modes}, series = {Phys. Status Solidi A}, volume = {220}, journal = {Phys. Status Solidi A}, doi = {10.1002/pssa.202200892}, pages = {2200892}, language = {en} } @inproceedings{BinkowskiBetzColometal., author = {Binkowski, Felix and Betz, Fridtjof and Colom, Remi and Hammerschmidt, Martin and Schneider, Philipp-Immanuel and Zschiedrich, Lin and Burger, Sven}, title = {Contour integral methods for resonance phenomena in nano-optics}, series = {The 11th International Conference on Metamaterials, Photonic Crystals and Plasmonics (META 2021)}, booktitle = {The 11th International Conference on Metamaterials, Photonic Crystals and Plasmonics (META 2021)}, editor = {Zouhdi, S. and Pawlak, D. and Kudelski, A.}, issn = {2429-1390}, pages = {523}, language = {en} } @misc{RickertBetzPlocketal., author = {Rickert, Lucas and Betz, Fridtjof and Plock, Matthias and Burger, Sven and Heindel, Tobias}, title = {Data publication for "High-performance designs for fiber-pigtailed quantum-light sources based on quantum dots in electrically-controlled circular Bragg gratings"}, series = {Zenodo}, journal = {Zenodo}, doi = {10.5281/zenodo.7360516}, pages = {7360516}, language = {en} } @misc{BetzBinkowskiHammerschmidtetal., author = {Betz, Fridtjof and Binkowski, Felix and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven}, title = {Source code and simulation results for computing resonance expansions of quadratic quantities with regularized quasinormal modes}, series = {Zenodo}, journal = {Zenodo}, doi = {10.5281/zenodo.7376556}, language = {en} } @article{BenSoltaneColomStoutetal., author = {Ben Soltane, Isam and Colom, R{\´e}mi and Stout, Brian and Bonod, Nicolas}, title = {Derivation of the Transient and Steady Optical States from the Poles of the S-Matrix}, series = {Laser Photon. Rev.}, volume = {17}, journal = {Laser Photon. Rev.}, doi = {10.1002/lpor.202200141}, pages = {2200141}, language = {en} } @article{ChewleEmmerlingWeber, author = {Chewle, Surahit and Emmerling, Franziska and Weber, Marcus}, title = {Effect of choice of solvent on crystallization pathway of Paracetamol: An experimental and theoretical case study}, series = {Crystals}, volume = {10}, journal = {Crystals}, number = {12}, doi = {10.3390/cryst10121107}, pages = {1107}, abstract = {The choice of solvents influences crystalline solid formed during the crystallization of active pharmaceutical ingredients (API). The underlying effects are not always well understood because of the complexity of the systems. Theoretical models are often insufficient to describe this phenomenon. In this study, the crystallization behavior of the model drug paracetamol in different solvents was studied based on experimental and molecular dynamics data. The crystallization process was followed in situ using time-resolved Raman spectroscopy. Molecular dynamics with simulated annealing algorithm was used for an atomistic understanding of the underlying processes. The experimental and theoretical data indicate that paracetamol molecules adopt a particular geometry in a given solvent predefining the crystallization of certain polymorphs.}, language = {en} } @article{LopezFraguasBinkowskiBurgeretal., author = {Lopez-Fraguas, Eduardo and Binkowski, Felix and Burger, Sven and Hagedorn, Sylvia and Garcia-Camara, Braulio and Vergaz, Ricardo and Becker, Christiane and Manley, Phillip}, title = {Tripling the light extraction efficiency of a deep ultraviolet LED using a nanostructured p-contact}, series = {Sci. Rep.}, volume = {12}, journal = {Sci. Rep.}, doi = {10.1038/s41598-022-15499-7}, pages = {11480}, language = {en} } @article{WangVannucciBurgeretal., author = {Wang, Yujing and Vannucci, Luca and Burger, Sven and Gregersen, Niels}, title = {Near-unity efficiency in ridge waveguide-based, on-chip single-photon sources}, series = {Mater. Quantum Technol.}, volume = {2}, journal = {Mater. Quantum Technol.}, doi = {10.1088/2633-4356/aca8e8}, pages = {045004}, language = {en} } @article{RamosLeiteZschiedrichKizilkayaetal., author = {Ramos Leite, Tiago and Zschiedrich, Lin and Kizilkaya, Orhan and McPeak, Kevin M.}, title = {Resonant Plasmonic-Biomolecular Chiral Interactions in the Far-Ultraviolet: Enantiomeric Discrimination of sub-10 nm Amino Acid Films}, series = {Nano Lett.}, volume = {22}, journal = {Nano Lett.}, doi = {10.1021/acs.nanolett.2c01724}, pages = {7343}, language = {en} } @article{RejSantiagoBaturinaetal., author = {Rej, Sourav and Santiago, Eva Yazmin and Baturina, Olga and Zhang, Yu and Burger, Sven and Kment, Stepan and Govorov, Alexander O. and Naldoni, Alberto}, title = {Colloidal Titanium Nitride Nanobars for Broadband Inexpensive Plasmonics and Photochemistry from Visible to Mid-IR Wavelengths}, series = {Nano Energy}, volume = {104}, journal = {Nano Energy}, doi = {10.1016/j.nanoen.2022.107989}, pages = {107989}, language = {en} } @misc{BinkowskiBetzHammerschmidtetal., author = {Binkowski, Felix and Betz, Fridtjof and Hammerschmidt, Martin and Schneider, Philipp-Immanuel and Zschiedrich, Lin and Burger, Sven}, title = {Source code and simulation data for Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators}, series = {Zenodo}, journal = {Zenodo}, doi = {10.5281/zenodo.6614951}, language = {en} } @misc{PlockAndrleBurgeretal., author = {Plock, Matthias and Andrle, Kas and Burger, Sven and Schneider, Philipp-Immanuel}, title = {Research data and example scripts for the paper "Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction"}, series = {Zenodo}, journal = {Zenodo}, doi = {10.5281/zenodo.6359594}, language = {en} } @misc{BetzColomBurgeretal., author = {Betz, Fridtjof and Colom, Remi and Burger, Sven and Naydenov, Boris}, title = {Scripts for quantifying the effect of diamond nano-pillars on the fluorescence of NV centers}, series = {Zenodo}, journal = {Zenodo}, doi = {10.5281/zenodo.6558815}, language = {en} } @misc{Mathew, type = {Master Thesis}, author = {Mathew, Maria}, title = {Numerical treatment of radiative heat transfer on cooling process}, pages = {53}, abstract = {This thesis examines how taking into account surface to surface radiation impacts the cooling process in general. We formulate the non local bound- ary condition after introducing the general setting for the cooling model. In section 3, the mathematical description of the radiative heat transfer is dis- cussed. We cover the implementation of the radiative matrix in section 4, which is followed by a brief explanation of the radiative matrix's structure and several techniques to dealing with the accompanying challenges. We investigate the importance of radiative heat transport by applying the given approach to a two-dimensional geometry and computing the ensuing cooling curves. We compare the findings of our computation to those ac- quired from experiment conducted and find that they are extremely similar. There is a considerable difference (of about 35\%) in the time of cooling of the surface where there is a possibility of influence of radiation from the second surface to that of the surface with no influence at all. Although it is possible to infer that heat convection plays a role in the total result, this has yet to be proved. However, one can clearly see the significance of the surface to surface radiative heat transfer on these parts confirming the research question posed at the begining. The effect of the surface to surface radiative heat transfer has an influence on the resulting cooling time and should be considered in the model.}, language = {en} } @misc{WeiserChegini, author = {Weiser, Martin and Chegini, Fatemeh}, title = {Higher-order time integration using spectral deferred correction method (SDC) in a cell by cell discretization of cardiac excitation}, doi = {10.35097/716}, abstract = {This C++ code implements a cell-by-cell model of cardiac excitation using a piecewise-continuous finite element discretization and spectral deferred correction time stepping. The code is based on the Kaskade 7 finite element toolbox and forms a prototype for the µCarp code to be implemented in the Microcard project.}, language = {en} } @article{BittracherMollenhauerKoltaietal., author = {Bittracher, Andreas and Mollenhauer, Mattes and Koltai, P{\´e}ter and Sch{\"u}tte, Christof}, title = {Optimal Reaction Coordinates: Variational Characterization and Sparse Computation}, series = {Multiscale Modelling \& Simulation}, volume = {21}, journal = {Multiscale Modelling \& Simulation}, number = {2}, doi = {10.1137/21M1448367}, pages = {449 -- 488}, abstract = {Reaction coordinates (RCs) are indicators of hidden, low-dimensional mechanisms that govern the long-term behavior of high-dimensional stochastic processes. We present a novel and general variational characterization of optimal RCs and provide conditions for their existence. Optimal RCs are minimizers of a certain loss function, and reduced models based on them guarantee a good approximation of the statistical long-term properties of the original high-dimensional process. We show that for slow-fast systems, metastable systems, and other systems with known good RCs, the novel theory reproduces previous insight. Remarkably, for reversible systems, the numerical effort required to evaluate the loss function scales only with the variability of the underlying, low-dimensional mechanism, and not with that of the full system. The theory provided lays the foundation for an efficient and data-sparse computation of RCs via modern machine learning techniques.}, language = {en} } @article{RickertBetzPlocketal., author = {Rickert, Lucas and Betz, Fridtjof and Plock, Matthias and Burger, Sven and Heindel, Tobias}, title = {High-performance designs for fiber-pigtailed quantum-light sources based on quantum dots in electrically-controlled circular Bragg gratings}, series = {Opt. Express}, volume = {31}, journal = {Opt. Express}, doi = {10.1364/OE.486060}, pages = {14750}, language = {en} } @article{CardereraPokuttaSchuetteetal., author = {Carderera, Alejandro and Pokutta, Sebastian and Sch{\"u}tte, Christof and Weiser, Martin}, title = {CINDy: Conditional gradient-based Identification of Non-linear Dynamics - Noise-robust recovery}, series = {Journal of Computational and Applied Mathematics}, journal = {Journal of Computational and Applied Mathematics}, abstract = {Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the potential to transform data-rich fields where well-established dynamical models remain unknown. This work contributes to the recent trend in data-driven sparse identification of nonlinear dynamics of finding the best sparse fit to observational data in a large library of potential nonlinear models. We propose an efficient first-order Conditional Gradient algorithm for solving the underlying optimization problem. In comparison to the most prominent alternative algorithms, the new algorithm shows significantly improved performance on several essential issues like sparsity-induction, structure-preservation, noise robustness, and sample efficiency. We demonstrate these advantages on several dynamics from the field of synchronization, particle dynamics, and enzyme chemistry.}, language = {en} } @article{WolfFuerstGeigesetal., author = {Wolf, Sarah and F{\"u}rst, Steffen and Geiges, Andreas and Laublichler, Manfred and Mielke, Jahel and Steudle, Gesine and Winter, Konstantin and Jaeger, Carlo}, title = {The Decision Theatre Triangle for societal challenges - an example case and research needs}, series = {Journal of Cleaner Production}, volume = {394}, journal = {Journal of Cleaner Production}, doi = {10.1016/j.jclepro.2023.136299}, pages = {136299}, abstract = {Tackling societal challenges relating to sustainability requires both an understanding of the underlying complex socio-ecological systems and participation of scientists as well as relevant stakeholders, such as practice experts, decision makers, and citizens. This paper introduces the Decision Theatre Triangle, a method which combines empirical information, mathematical modelling and simulation, and a format for dialogue between scientists and stakeholders. While it builds on previous Decision Theatre work, the new structuring into these three elements emphasizes what is needed for setting up a Decision Theatre for a given challenge. Based on experience with a specific example - sustainable mobility in Germany - it is argued that agent-based models are particularly suitable for Decision Theatres and that the method is useful not only for decision support but also for science communication and co-creation of a deeper knowledge of the system under discussion. As a step towards facilitating a broader use of the Decision Theatre Triangle method, the paper then sketches research needs for each of its three elements, with a focus on mathematical modelling and simulation.}, language = {en} } @inproceedings{BinkowskiBetzHammerschmidtetal., author = {Binkowski, Felix and Betz, Fridtjof and Hammerschmidt, Martin and Schneider, Philipp-Immanuel and Zschiedrich, Lin and Burger, Sven}, title = {Numerical methods for the investigation of resonances in nanophotonics}, series = {The 12th International Conference on Metamaterials, Photonic Crystals and Plasmonics (META 2022)}, booktitle = {The 12th International Conference on Metamaterials, Photonic Crystals and Plasmonics (META 2022)}, editor = {Zouhdi, S.}, issn = {2429-1390}, pages = {247}, language = {en} } @inproceedings{TockhornSutterCruzetal., author = {Tockhorn, Philipp and Sutter, Johannes and Cruz, Alexandros and Wagner, Philipp and J{\"a}ger, Klaus and Yoo, Danbi and Lang, Felix and Grischek, Max and Li, Bor and Al-Ashouri, Amran and K{\"o}hnen, Eike and Stolterfoht, Martin and Neher, Dieter and Schlatmann, Rutger and Rech, Bernd and Stannowski, Bernd and Albrecht, Steve and Becker, Christiane}, title = {Nanooptically Enhanced Perovskite/Silicon Tandem Solar Cells with 29.80\% Power Conversion Efficiency}, series = {OSA Adv. Photonics}, booktitle = {OSA Adv. Photonics}, doi = {10.1364/NOMA.2022.JTu4H.2}, pages = {JTu4H.2}, language = {en} } @inproceedings{RickertGaoUrbanetal., author = {Rickert, Lucas and Gao, Timm and Urban, Felix and Große, Jan and Srocka, Nicole and Rodt, Sven and Musial, Anna and Zolnacz, Kinga and Mergo, Pawel and Dybka, Kamil and Urbanczyk, Waclaw and Sek, Grzegorz and Burger, Sven and Reitzenstein, Stephan and Heindel, Tobias}, title = {A Plug\&Play Telecom-Wavelength Single-Photon Source for Quantum Key Distribution}, series = {Quantum 2.0}, booktitle = {Quantum 2.0}, doi = {10.1364/QUANTUM.2022.QTu4C.6}, pages = {QTu4C.6}, language = {en} } @inproceedings{MovsesyanSantiagoBurgeretal., author = {Movsesyan, Artur and Santiago, Eva Yazmin and Burger, Sven and Correa-Duarte, Miguel and Besteiro, Lucas V. and Wang, Zhiming and Govorov, Alexander O.}, title = {The anisotropy of hot carriers' spatial distribution contrasts the isotropy of photothermal effects in complex and small plasmonic nanocrystals with complex shapes}, series = {The 12th International Conference on Metamaterials, Photonic Crystals and Plasmonics (META 2022)}, booktitle = {The 12th International Conference on Metamaterials, Photonic Crystals and Plasmonics (META 2022)}, editor = {Zouhdi, S.}, issn = {2429-1390}, pages = {285}, language = {en} } @inproceedings{KruegerManleyZschiedrichetal., author = {Kr{\"u}ger, Jan and Manley, Phillip and Zschiedrich, Lin and Hammerschmidt, Martin and Schneider, Philipp-Immanuel and K{\"o}ning, Rainer and Bodermann, Bernd}, title = {Untersuchung des Schwingungseinflusses auf gemessene Punktspreizfunktionen in der optischen Mikroskopie}, series = {Proc. DGaO}, booktitle = {Proc. DGaO}, url = {http://nbn-resolving.de/urn:nbn:de:0287-2022-P005-6}, pages = {P5}, language = {en} } @inproceedings{ManleyKruegerZschiedrichetal., author = {Manley, Phillip and Kr{\"u}ger, Jan and Zschiedrich, Lin and Hammerschmidt, Martin and Bodermann, Bernd and K{\"o}ning, Rainer and Schneider, Philipp-Immanuel}, title = {Elementary, my dear Zernike: model order reduction for accelerating optical dimensional microscopy}, series = {EPJ Web Conf.}, volume = {266}, booktitle = {EPJ Web Conf.}, doi = {10.1051/epjconf/202226610010}, pages = {10010}, language = {en} } @article{DonatiKeller, author = {Donati, Luca and Keller, Bettina G.}, title = {Girsanov reweighting for metadynamics simulations}, series = {The Journal of Chemical Physics}, volume = {149}, journal = {The Journal of Chemical Physics}, number = {7}, doi = {10.1063/1.5027728}, pages = {072335}, abstract = {Metadynamics is a computational method to explore the phase space of a molecular system. Gaussian functions are added along relevant coordinates on the fly during a molecular-dynamics simulation to force the system to escape from minima in the potential energy function. The dynamics in the resulting trajectory are however unphysical and cannot be used directly to estimate dynamical properties of the system. Girsanov reweighting is a recent method used to construct the Markov State Model (MSM) of a system subjected to an external perturbation. With the combination of these two techniques—metadynamics/Girsanov-reweighting—the unphysical dynamics in a metadynamics simulation can be reweighted to obtain the MSM of the unbiased system. We demonstrate the method on a one-dimensional diffusion process, alanine dipeptide, and the hexapeptide Val-Gly-Val-Ala-Pro-Gly (VGVAPG). The results are in excellent agreement with the MSMs obtained from direct unbiased simulations of these systems. We also apply metadynamics/Girsanov-reweighting to a β-hairpin peptide, whose dynamics is too slow to efficiently explore its phase space by direct simulation}, language = {en} } @incollection{KellerAleksićDonati, author = {Keller, Bettina G. and Aleksić, Stevan and Donati, Luca}, title = {Markov State Models in Drug Design}, series = {Biomolecular Simulations in Structure-Based Drug Discovery}, booktitle = {Biomolecular Simulations in Structure-Based Drug Discovery}, publisher = {Wiley-Interscience, Weinheim}, isbn = {1865-0562}, doi = {10.1002/9783527806836.ch4}, pages = {67 -- 86}, abstract = {This chapter explains the different ways in which Markov State Models (MSMs) can be helpful in structure-based drug design. MSMs are constructed from the time series of molecular dynamics (MD), which can be generated by classical MD simulations. Several features of the MSMs can be utilized for rational drug design. The discretization of a validated MSM is particularly suited to extract meaningful representatives from the conformational ensemble, because the discretization yields a small number of microstates and mirrors the features of the free energy landscape. Long-lived conformations consist of a set of microstates which show high transition rates within the set and low transition rates to microstates outside of the set. The Bayesian agglomerative clustering engine (BACE) algorithm uses the observed transition counts to extract long-lived conformations from an MSM. By iteratively merging microstates according to the Bayes factor and recalculating the Bayes-factor matrix, the algorithm yields an aggregation of the microstates into long-lived conformations.}, language = {en} } @article{HassanDonatiStensitzkietal., author = {Hassan, Irtaza and Donati, Luca and Stensitzki, Till and Keller, Bettina G and Heyne, Karsten and Imhof, Petra}, title = {The vibrational spectrum of the hydrated alanine-leucine peptide in the amide region from IR experiments and first principles calculations}, series = {Chemical Physics Letters}, volume = {698}, journal = {Chemical Physics Letters}, doi = {10.1016/j.cplett.2018.03.026}, pages = {227 -- 233}, abstract = {We have combined infrared (IR) experiments with molecular dynamics (MD) simulations in solution at finite temperature to analyse the vibrational signature of the small floppy peptide Alanine-Leucine. IR spectra computed from first-principles MD simulations exhibit no distinct differences between conformational clusters of -helix or -sheet-like folds with different orientations of the bulky leucine side chain. All computed spectra show two prominent bands, in good agreement with the experiment, that are assigned to the stretch vibrations of the carbonyl and carboxyl group, respectively. Variations in band widths and exact maxima are likely due to small fluctuations in the backbone torsion angles.}, language = {en} } @article{BetzBinkowskiHammerschmidtetal., author = {Betz, Fridtjof and Binkowski, Felix and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven}, title = {Cover Picture: Resonance Expansion of Quadratic Quantities with Regularized Quasinormal Modes}, series = {Phys. Status Solidi A}, volume = {220}, journal = {Phys. Status Solidi A}, doi = {10.1002/pssa.202370013}, pages = {2370013}, language = {en} } @article{WulkowKoltaiSchuette, author = {Wulkow, Niklas and Koltai, P{\´e}ter and Sch{\"u}tte, Christof}, title = {Memory-Based Reduced Modelling and Data-Based Estimation of Opinion Spreading}, series = {Journal of Nonlinear Science}, volume = {31}, journal = {Journal of Nonlinear Science}, doi = {10.1007/s00332-020-09673-2}, abstract = {We investigate opinion dynamics based on an agent-based model and are interested in predicting the evolution of the percentages of the entire agent population that share an opinion. Since these opinion percentages can be seen as an aggregated observation of the full system state, the individual opinions of each agent, we view this in the framework of the Mori-Zwanzig projection formalism. More specifically, we show how to estimate a nonlinear autoregressive model (NAR) with memory from data given by a time series of opinion percentages, and discuss its prediction capacities for various specific topologies of the agent interaction network. We demonstrate that the inclusion of memory terms significantly improves the prediction quality on examples with different network topologies.}, language = {en} } @article{DriesenElKhatibWulkowetal., author = {Driesen, Joshua and El-Khatib, Ziad and Wulkow, Niklas and Joblin, Mitchell and Vasileva, Iskriyana and Gl{\"u}cker, Andreas and Kruspel, Valentin and Vogel, Catherine}, title = {Data-Powered Positive Deviance during the SARS-CoV-2 Pandemic—An Ecological Pilot Study of German Districts}, series = {International Journal of Environmental Research and Public Health}, volume = {18}, journal = {International Journal of Environmental Research and Public Health}, number = {9765}, doi = {https://doi.org/10.3390/ijerph18189765}, pages = {1 -- 29}, abstract = {We introduced the mixed-methods Data-Powered Positive Deviance (DPPD) framework as a potential addition to the set of tools used to search for effective response strategies against the SARS-CoV-2 pandemic. For this purpose, we conducted a DPPD study in the context of the early stages of the German SARS-CoV-2 pandemic. We used a framework of scalable quantitative methods to identify positively deviant German districts that is novel in the scientific literature on DPPD, and subsequently employed qualitative methods to identify factors that might have contributed to their comparatively successful reduction of the forward transmission rate. Our qualitative analysis suggests that quick, proactive, decisive, and flexible/pragmatic actions, the willingness to take risks and deviate from standard procedures, good information flows both in terms of data collection and public communication, alongside the utilization of social network effects were deemed highly important by the interviewed districts. Our study design with its small qualitative sample constitutes an exploratory and illustrative effort and hence does not allow for a clear causal link to be established. Thus, the results cannot necessarily be extrapolated to other districts as is. However, the findings indicate areas for further research to assess these strategies' effectiveness in a broader study setting. We conclude by stressing DPPD's strengths regarding replicability, scalability, adaptability, as well asits focus on local solutions, which make it a promising framework to be applied in various contexts,e.g., in the context of the Global South.}, language = {en} } @article{DonatiWeberKeller, author = {Donati, Luca and Weber, Marcus and Keller, Bettina G.}, title = {Markov models from the square root approximation of the Fokker-Planck equation: calculating the grid-dependent flux}, series = {Journal of Physics: Condensed Matter}, volume = {33}, journal = {Journal of Physics: Condensed Matter}, number = {11}, doi = {10.1088/1361-648X/abd5f7}, pages = {115902}, abstract = {Molecular dynamics (MD) are extremely complex, yet understanding the slow components of their dynamics is essential to understanding their macroscopic properties. To achieve this, one models the MD as a stochastic process and analyses the dominant eigenfunctions of the associated Fokker-Planck operator, or of closely related transfer operators. So far, the calculation of the discretized operators requires extensive MD simulations. The square-root approximation of the Fokker-Planck equation is a method to calculate transition rates as a ratio of the Boltzmann densities of neighboring grid cells times a flux, and can in principle be calculated without a simulation. In a previous work we still used MD simulations to determine the flux. Here, we propose several methods to calculate the exact or approximate flux for various grid types, and thus estimate the rate matrix without a simulation. Using model potentials we test computational efficiency of the methods, and the accuracy with which they reproduce the dominant eigenfunctions and eigenvalues. For these model potentials, rate matrices with up to \$\mathcal{O}\left(1{0}^{6}\right)\$ states can be obtained within seconds on a single high-performance compute server if regular grids are used.}, language = {en} } @article{DonatiWeber, author = {Donati, Luca and Weber, Marcus}, title = {Assessing transition rates as functions of environmental variables}, series = {The Journal of Chemical Physics}, volume = {157}, journal = {The Journal of Chemical Physics}, number = {22}, publisher = {AIP Publishing}, doi = {10.1063/5.0109555}, pages = {224103-1 -- 224103-14}, abstract = {We present a method to estimate the transition rates of molecular systems under different environmental conditions which cause the formation or the breaking of bonds and require the sampling of the Grand Canonical Ensemble. For this purpose, we model the molecular system in terms of probable "scenarios", governed by different potential energy functions, which are separately sampled by classical MD simulations. Reweighting the canonical distribution of each scenario according to specific environmental variables, we estimate the grand canonical distribution, then we use the Square Root Approximation (SqRA) method to discretize the Fokker-Planck operator into a rate matrix and the robust Perron Cluster Cluster Analysis (PCCA+) method to coarse-grain the kinetic model. This permits to efficiently estimate the transition rates of conformational states as functions of environmental variables, for example, the local pH at a cell membrane. In this work we formalize the theoretical framework of the procedure and we present a numerical experiment comparing the results with those provided by a constant-pH method based on non-equilibrium Molecular Dynamics Monte Carlo simulations. The method is relevant for the development of new drug design strategies which take into account how the cellular environment influences biochemical processes.}, language = {en} } @article{KieningerDonatiKeller, author = {Kieninger, Stefanie and Donati, Luca and Keller, Bettina G.}, title = {Dynamical reweighting methods for Markov models}, series = {Current Opinion in Structural Biology}, volume = {61}, journal = {Current Opinion in Structural Biology}, doi = {10.1016/j.sbi.2019.12.018}, pages = {124 -- 131}, abstract = {Conformational dynamics is essential to biomolecular processes. Markov State Models (MSMs) are widely used to elucidate dynamic properties of molecular systems from unbiased Molecular Dynamics (MD). However, the implementation of reweighting schemes for MSMs to analyze biased simulations is still at an early stage of development. Several dynamical reweighing approaches have been proposed, which can be classified as approaches based on (i) Kramers rate theory, (ii) rescaling of the probability density flux, (iii) reweighting by formulating a likelihood function, (iv) path reweighting. We present the state-of-the-art and discuss the methodological differences of these methods, their limitations and recent applications.}, language = {en} } @misc{TernesBauerBraueretal., author = {Ternes, Thomas and Bauer, Karl-Heinz and Brauer, Frank and Drewes, J{\"u}rgen and Jewell, Kevin and Joss, Adriano and Oehlmann, J{\"o}rg and Radtke, Michael and Schulte-Oehlmann, Ulrike and Schwartz, Thomas and Seel, Peter and V{\"o}lker, Jeanette and Weber, Lilo and Weber, Marcus}, title = {Handlungsempfehlung zur integrativen Bewertung der weitergehenden Abwasserbehandlung von kommunalen Kl{\"a}ranlagen}, series = {DWA-Themen}, volume = {T1/2023}, journal = {DWA-Themen}, publisher = {DWA}, abstract = {Der DWA-Themenband beschreibt ein Konzept zur weitergehenden Abwasserbehandlung f{\"u}r die Bewertung von Aufbereitungsverfahren, sowohl in einer Pilotphase zur Auswahl von Verfahrensoptionen als auch f{\"u}r die Bewertung großtechnischer Anlagen. Emissionsseitig basiert das Konzept auf bereits regulatorisch definierten Parametern wie anorganischen Stickstoff-Verbindungen oder Phosphat sowie auf neuen noch nicht in der Abwasserverordnung regulierten Parametern. Die immissionsseitige Betrachtung erfolgt auf Basis der rechtlich durch die Europ{\"a}ische Wasserrahmenrichtlinie und andere Anforderungen bindenden Instrumente. Hierf{\"u}r werden spezifische Vorgehensweisen vorgeschlagen. Anhand zweier ausgew{\"a}hlter Praxisbeispiele wird deutlich, dass es zur Bewertung der Verfahrensoptionen an einem Standort dienlich ist, ausgew{\"a}hlte Reduktionen bzw. Entfernungen von Stoffen, Organismen und Effekten zu bestimmen.}, language = {de} } @inproceedings{GanderKrauseWeiseretal., author = {Gander, Lia and Krause, Rolf and Weiser, Martin and Costabal, Francisco and Pezzuto, Simone}, title = {On the Accuracy of Eikonal Approximations in Cardiac Electrophysiology in the Presence of Fibrosis}, series = {Functional Imaging and Modeling of the Heart. FIMH 2023.}, volume = {13958}, booktitle = {Functional Imaging and Modeling of the Heart. FIMH 2023.}, publisher = {Springer, Cham}, doi = {10.1007/978-3-031-35302-4_14}, abstract = {Fibrotic tissue is one of the main risk factors for cardiac arrhythmias. It is therefore a key component in computational studies. In this work, we compare the monodomain equation to two eikonal models for cardiac electrophysiology in the presence of fibrosis. We show that discontinuities in the conductivity field, due to the presence of fibrosis, introduce a delay in the activation times. The monodomain equation and eikonal-diffusion model correctly capture these delays, contrarily to the classical eikonal equation. Importantly, a coarse space discretization of the monodomain equation amplifies these delays, even after accounting for numerical error in conduction velocity. The numerical discretization may also introduce artificial conduction blocks and hence increase propagation complexity. Therefore, some care is required when comparing eikonal models to the discretized monodomain equation.}, language = {en} } @article{ErnstSchuetteSigristetal., author = {Ernst, Ariane and Sch{\"u}tte, Christof and Sigrist, Stephan and Winkelmann, Stefanie}, title = {Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics}, series = {Mathematical Biosciences}, volume = {343}, journal = {Mathematical Biosciences}, doi = {10.1016/j.mbs.2021.108760}, abstract = {Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact first- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the filtered signal's second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to efficiently compare different spatial coarse graining approaches for a specific model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a filtered stochastic signal.}, language = {en} } @misc{ErnstSchuetteSigristetal., author = {Ernst, Ariane and Sch{\"u}tte, Christof and Sigrist, Stephan and Winkelmann, Stefanie}, title = {Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics}, issn = {1438-0064}, doi = {10.1016/j.mbs.2021.108760}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-82674}, abstract = {Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact first- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the filtered signal's second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to efficiently compare different spatial coarse graining approaches for a specific model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a filtered stochastic signal.}, language = {en} } @article{RoehlWeberFackeldey, author = {R{\"o}hl, Susanne and Weber, Marcus and Fackeldey, Konstantin}, title = {Computing the minimal rebinding effect for non-reversible processes}, series = {Multiscale Modeling and Simulation}, volume = {19}, journal = {Multiscale Modeling and Simulation}, number = {1}, doi = {https://doi.org/10.1137/20M1334966}, pages = {460 -- 477}, abstract = {The aim of this paper is to investigate the rebinding effect, a phenomenon describing a "short-time memory" which can occur when projecting a Markov process onto a smaller state space. For guaranteeing a correct mapping by the Markov State Model, we assume a fuzzy clustering in terms of membership functions, assigning degrees of membership to each state. The macro states are represented by the membership functions and may be overlapping. The magnitude of this overlap is a measure for the strength of the rebinding effect, caused by the projection and stabilizing the system. A minimal bound for the rebinding effect included in a given system is computed as the solution of an optimization problem. Based on membership functions chosen as a linear combination of Schur vectors, this generalized approach includes reversible as well as non-reversible processes.}, language = {en} } @article{GorgullaDasLeighetal., author = {Gorgulla, Christoph and Das, Krishna M. Padmanabha and Leigh, Kendra E and Cespugli, Marco and Fischer, Patrick D. and Wang, Zi-Fu and Tesseyre, Guilhem and Pandita, Shreya and Shnapir, Alex and Calderaio, Anthony and Hutcheson, Colin and Gechev, Minko and Rose, Alexander and Lewis, Noam and Yaffe, Erez and Luxenburg, Roni and Herce, Henry D. and Durmaz, Vedat and Halazonetis, Thanos D. and Fackeldey, Konstantin and Patten, Justin J. and Chuprina, Alexander and Dziuba, Igor and Plekhova, Alla and Moroz, Yurii and Radchenko, Dmytro and Tarkhanova, Olga and Yavnyuk, Irina and Gruber, Christian C. and Yust, Ryan and Payne, Dave and N{\"a}{\"a}r, Anders M. and Namchuk, Mark N. and Davey, Robert A. and Wagner, Gerhard and Kinney, Jamie and Arthanari, Haribabu}, title = {A Multi-Pronged Approach Targeting SARS-CoV-2 Proteins Using Ultra-Large Virtual Screening}, series = {iScience}, volume = {24}, journal = {iScience}, number = {2}, publisher = {CellPress}, doi = {10.26434/chemrxiv.12682316}, pages = {102021}, abstract = {Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), previously known as 2019 novel coronavirus (2019-nCoV), has spread rapidly across the globe, creating an unparalleled global health burden and spurring a deepening economic crisis. As of July 7th, 2020, almost seven months into the outbreak, there are no approved vaccines and few treatments available. Developing drugs that target multiple points in the viral life cycle could serve as a strategy to tackle the current as well as future coronavirus pandemics. Here we leverage the power of our recently developed in silico screening platform, VirtualFlow, to identify inhibitors that target SARS-CoV-2. VirtualFlow is able to efficiently harness the power of computing clusters and cloud-based computing platforms to carry out ultra-large scale virtual screens. In this unprecedented structure-based multi-target virtual screening campaign, we have used VirtualFlow to screen an average of approximately 1 billion molecules against each of 40 different target sites on 17 different potential viral and host targets in the cloud. In addition to targeting the active sites of viral enzymes, we also target critical auxiliary sites such as functionally important protein-protein interaction interfaces. This multi-target approach not only increases the likelihood of finding a potent inhibitor, but could also help identify a collection of anti-coronavirus drugs that would retain efficacy in the face of viral mutation. Drugs belonging to different regimen classes could be combined to develop possible combination therapies, and top hits that bind at highly conserved sites would be potential candidates for further development as coronavirus drugs. Here, we present the top 200 in silico hits for each target site. While in-house experimental validation of some of these compounds is currently underway, we want to make this array of potential inhibitor candidates available to researchers worldwide in consideration of the pressing need for fast-tracked drug development.}, language = {en} } @article{GorgullaBoeszoermnyiWangetal., author = {Gorgulla, Christoph and Boeszoermnyi, Andras and Wang, Zi-Fu and Fischer, Patrick D. and Coote, Paul and Das, Krishna M. Padmanabha and Malets, Yehor S. and Radchenko, Dmytro S. and Moroz, Yurii and Scott, David A. and Fackeldey, Konstantin and Hoffmann, Moritz and Iavniuk, Iryna and Wagner, Gerhard and Arthanari, Haribabu}, title = {An open-source drug discovery platform enables ultra-large virtual screens}, series = {Nature}, volume = {580}, journal = {Nature}, publisher = {Springer Nature}, doi = {https://doi.org/10.1038/s41586-020-2117-z}, pages = {663 -- 668}, abstract = {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.}, language = {en} } @article{GorgullaCınaroğluFischeretal., author = {Gorgulla, Christoph and {\c{C}}{\i}naroğlu, S{\"u}leyman and Fischer, Patrick D. and Fackeldey, Konstantin and Wagner, Gerhard and Arthanari, Haribabu}, title = {VirtualFlow Ants—Ultra-Large Virtual Screenings with Artificial Intelligence Driven Docking Algorithm Based on Ant Colony Optimization}, series = {Special Issue Artificial Intelligence \& Deep Learning Approaches for Structural Bioinformatics}, volume = {22}, journal = {Special Issue Artificial Intelligence \& Deep Learning Approaches for Structural Bioinformatics}, number = {11}, doi = {https://doi.org/10.3390/ijms22115807}, pages = {5807}, abstract = {The docking program PLANTS, which is based on ant colony optimization (ACO) algorithm, has many advanced features for molecular docking. Among them are multiple scoring functions, the possibility to model explicit displaceable water molecules, and the inclusion of experimental constraints. Here, we add support of PLANTS to VirtualFlow (VirtualFlow Ants), which adds a valuable method for primary virtual screenings and rescoring procedures. Furthermore, we have added support of ligand libraries in the MOL2 format, as well as on the fly conversion of ligand libraries which are in the PDBQT format to the MOL2 format to endow VirtualFlow Ants with an increased flexibility regarding the ligand libraries. The on the fly conversion is carried out with Open Babel and the program SPORES. We applied VirtualFlow Ants to a test system involving KEAP1 on the Google Cloud up to 128,000 CPUs, and the observed scaling behavior is approximately linear. Furthermore, we have adjusted several central docking parameters of PLANTS (such as the speed parameter or the number of ants) and screened 10 million compounds for each of the 10 resulting docking scenarios. We analyzed their docking scores and average docking times, which are key factors in virtual screenings. The possibility of carrying out ultra-large virtual screening with PLANTS via VirtualFlow Ants opens new avenues in computational drug discovery.}, language = {en} } @article{GorgullaFackeldeyWagneretal., author = {Gorgulla, Christoph and Fackeldey, Konstantin and Wagner, Gerhard and Arthanari, Haribabu}, title = {Accounting of Receptor Flexibility in Ultra-Large Virtual Screens with VirtualFlow Using a Grey Wolf Optimization Method}, series = {Supercomputing Frontiers and Innovations}, volume = {7}, journal = {Supercomputing Frontiers and Innovations}, number = {3}, doi = {10.14529/jsfi200301}, pages = {4 -- 12}, abstract = {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.}, language = {en} } @article{FackeldeyRoehmNiknejadetal., author = {Fackeldey, Konstantin and R{\"o}hm, Jonas and Niknejad, Amir and Chewle, Surahit and Weber, Marcus}, title = {Analyzing Raman Spectral Data without Separabiliy Assumption}, series = {Journal of Mathematical Chemistry}, volume = {3}, journal = {Journal of Mathematical Chemistry}, number = {59}, publisher = {Springer}, doi = {10.1007/s10910-020-01201-7}, pages = {575 -- 596}, abstract = {Raman spectroscopy is a well established tool for the analysis of vibration spectra, which then allow for the determination of individual substances in a chemical sample, or for their phase transitions. In the Time-Resolved-Raman-Sprectroscopy the vibration spectra of a chemical sample are recorded sequentially over a time interval, such that conclusions for intermediate products (transients) can be drawn within a chemical process. The observed data-matrix M from a Raman spectroscopy can be regarded as a matrix product of two unknown matrices W and H, where the first is representing the contribution of the spectra and the latter represents the chemical spectra. One approach for obtaining W and H is the non-negative matrix factorization. We propose a novel approach, which does not need the commonly used separability assumption. The performance of this approach is shown on a real world chemical example.}, language = {en} } @article{FackeldeyOsterSallandtetal., author = {Fackeldey, Konstantin and Oster, Mathias and Sallandt, Leon and Schneider, Reinhold}, title = {Approximative Policy Iteration for Exit Time Feedback Control Problems driven by Stochastic Differential Equations using Tensor Train format}, series = {SIAM Journal on Multiscale Modeling and Simulation}, volume = {20}, journal = {SIAM Journal on Multiscale Modeling and Simulation}, number = {1}, doi = {10.1137/20M1372500}, pages = {379 -- 403}, abstract = {We consider a stochastic optimal exit time feedback control problem. The Bellman equation is solved approximatively via the Policy Iteration algorithm on a polynomial ansatz space by a sequence of linear equations. As high degree multi-polynomials are needed, the corresponding equations suffer from the curse of dimensionality even in moderate dimensions. We employ tensor-train methods to account for this problem. The approximation process within the Policy Iteration is done via a Least-Squares ansatz and the integration is done via Monte-Carlo methods. Numerical evidences are given for the (multi dimensional) double well potential and a three-hole potential.}, language = {en} } @article{ErlekamZumbansenWeber, author = {Erlekam, Franziska and Zumbansen, Maximilian and Weber, Marcus}, title = {Parameter estimation on multivalent ITC data sets}, series = {Scientific Reports}, volume = {12}, journal = {Scientific Reports}, doi = {10.1038/s41598-022-17188-x}, pages = {13402}, abstract = {The Wiseman fitting can be used to extract binding parameters from ITC data sets, such as heat of binding, number of binding sites, and the overall dissociation rate. The classical Wiseman fitting assumes a direct binding process and neglects the possibility of intermediate binding steps. In principle, it only provides thermodynamic information and not the kinetics of the process. In this article we show that a concentration dependent dissociation constant could possibly stem from intermediate binding steps. The mathematical form of this dependency can be exploited with the aid of the Robust Perron Cluster Cluster Analysis method. Our proposed extension of the Wiseman fitting rationalizes the concentration dependency, and can probably also be used to determine the kinetic parameters of intermediate binding steps of a multivalent binding process. The novelty of this paper is to assume that the binding rate varies per titration step due to the change of the ligand concentration and to use this information in the Wiseman fitting. We do not claim to produce the most accurate values of the binding parameters, we rather present a novel method of how to approach multivalent bindings from a different angle.}, language = {en} } @article{GelssKlusSchusteretal., author = {Gelss, Patrick and Klus, Stefan and Schuster, Ingmar and Sch{\"u}tte, Christof}, title = {Feature space approximation for kernel-based supervised learning}, series = {Knowledge-Based Sytems}, volume = {221}, journal = {Knowledge-Based Sytems}, publisher = {Elsevier}, doi = {https://doi.org/10.1016/j.knosys.2021.106935}, language = {en} } @misc{Baumann, type = {Master Thesis}, author = {Baumann, Felix}, title = {Impact of Contact Surfaces on the Death Estimation}, pages = {69}, abstract = {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.}, language = {en} } @article{LangHelfmeierStefanowskietal., author = {Lang, Annemarie and Helfmeier, Sarah and Stefanowski, Jonathan and Kuppe, Aditi and Sunkara, Vikram and Pfeiffenberger, Moritz and Wolter, Angelique and Damerau, Alexandra and Hemmati-Sadeghi, Shabnam and Ringe, Jochen and Haag, Rainer and Hauser, Anja E. and L{\"o}hning, Max and Perka, Carsten and Duda, Georg and Hoff, Paula and Schmidt-Bleek, Katharina and Gaber, Timo and Buttgereit, Frank}, title = {HIF-stabilization prevents delayed fracture healing}, series = {bioarxiv}, journal = {bioarxiv}, doi = {10.1101/2020.07.02.182832}, language = {en} } @misc{SunkaraRaharinirinaPeppertetal., author = {Sunkara, Vikram and Raharinirina, N. Alexia and Peppert, Felix and von Kleist, Max and Sch{\"u}tte, Christof}, title = {Inferring Gene Regulatory Networks from Single Cell RNA-seq Temporal Snapshot Data Requires Higher Order Moments}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-79664}, abstract = {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.}, language = {en} } @article{BorndoerferDaneckerWeiser, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Error Bounds for Discrete-Continuous Free Flight Trajectory Optimization}, series = {Journal of Optimization Theory and Applications}, volume = {198}, journal = {Journal of Optimization Theory and Applications}, doi = {10.1007/s10957-023-02264-7}, pages = {830 -- 856}, abstract = {Flight planning, the computation of optimal routes in view of flight time and fuel consumption under given weather conditions, is traditionally done by finding globally shortest paths in a predefined airway network. Free flight trajectories, not restricted to a network, have the potential to reduce the costs significantly, and can be computed using locally convergent continuous optimal control methods. Hybrid methods that start with a discrete global search and refine with a fast continuous local optimization combine the best properties of both approaches, but rely on a good switchover, which requires error estimates for discrete paths relative to continuous trajectories. Based on vertex density and local complete connectivity, we derive localized and a priori bounds for the flight time of discrete paths relative to the optimal continuous trajectory, and illustrate their properties on a set of benchmark problems. It turns out that localization improves the error bound by four orders of magnitude, but still leaves ample opportunities for tighter bounds using a posteriori error estimators.}, language = {en} } @misc{BorndoerferDaneckerWeiser, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {A Discrete-Continuous Algorithm for Free Flight Planning}, issn = {1438-0064}, doi = {10.3390/a14010004}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81343}, abstract = {We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach.}, language = {en} } @article{RaharinirinaAcevedoTrejosMerico, author = {Raharinirina, N. Alexia and Acevedo-Trejos, Esteban and Merico, Agostino}, title = {Modelling the acclimation capacity of coral reefs to a warming ocean}, series = {PLOS COMPUTATIONAL BIOLOGY}, journal = {PLOS COMPUTATIONAL BIOLOGY}, doi = {10.1371/journal.pcbi.1010099}, abstract = {The symbiotic relationship between corals and photosynthetic algae is the foundation of coral reef ecosystems. This relationship breaks down, leading to coral death, when sea temperature exceeds the thermal tolerance of the coral-algae complex. While acclimation via phenotypic plasticity at the organismal level is an important mechanism for corals to cope with global warming, community-based shifts in response to acclimating capacities may give valuable indications about the future of corals at a regional scale. Reliable regional-scale predictions, however, are hampered by uncertainties on the speed with which coral communities will be able to acclimate. Here we present a trait-based, acclimation dynamics model, which we use in combination with observational data, to provide a first, crude estimate of the speed of coral acclimation at the community level and to investigate the effects of different global warming scenarios on three iconic reef ecosystems of the tropics: Great Barrier Reef, South East Asia, and Caribbean. The model predicts that coral acclimation may confer some level of protection by delaying the decline of some reefs such as the Great Barrier Reef. However, the current rates of acclimation will not be sufficient to rescue corals from global warming. Based on our estimates of coral acclimation capacities, the model results suggest substantial declines in coral abundances in all three regions, ranging from 12\% to 55\%, depending on the region and on the climate change scenario considered. Our results highlight the importance and urgency of precise assessments and quantitative estimates, for example through laboratory experiments, of the natural acclimation capacity of corals and of the speed with which corals may be able to acclimate to global warming.}, language = {en} } @inproceedings{BorndoerferDaneckerWeiser, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization}, series = {22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)}, volume = {106}, booktitle = {22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)}, doi = {10.4230/OASIcs.ATMOS.2022.2}, pages = {1 -- 13}, abstract = {We present an efficient algorithm that finds a globally optimal solution to the 2D Free Flight Trajectory Optimization Problem (aka Zermelo Navigation Problem) up to arbitrary precision in finite time. The algorithm combines a discrete and a continuous optimization phase. In the discrete phase, a set of candidate paths that densely covers the trajectory space is created on a directed auxiliary graph. Then Yen's algorithm provides a promising set of discrete candidate paths which subsequently undergo a locally convergent refinement stage. Provided that the auxiliary graph is sufficiently dense, the method finds a path that lies within the convex domain around the global minimizer. From this starting point, the second stage will converge rapidly to the optimum. The density of the auxiliary graph depends solely on the wind field, and not on the accuracy of the solution, such that the method inherits the superior asymptotic convergence properties of the optimal control stage.}, language = {en} } @article{RaharinirinaFackeldeyWeber, author = {Raharinirina, N. Alexia and Fackeldey, Konstantin and Weber, Marcus}, title = {Qualitative Euclidean embedding of Disjoint Sets of Points}, abstract = {We consider two disjoint sets of points with a distance metric, or a proximity function, associated with each set. If each set can be separately embedded into separate Euclidean spaces, then we provide sufficient conditions for the two sets to be jointly embedded in one Euclidean space. In this joint Euclidean embedding, the distances between the points are generated by a specific relation-preserving function. Consequently, the mutual distances between two points of the same set are specific qualitative transformations of their mutual distances in their original space; the pairwise distances between the points of different sets can be constructed from an arbitrary proximity function (might require scaling).}, language = {en} } @article{MontefuscoSharmaTse, author = {Montefusco, Alberto and Sharma, Upanshu and Tse, Oliver}, title = {Fourier-Cattaneo equation: stochastic origin, variational formulation, and asymptotic limits}, abstract = {We introduce a variational structure for the Fourier-Cattaneo (FC) system which is a second-order hyperbolic system. This variational structure is inspired by the large-deviation rate functional for the Kac process which is closely linked to the FC system. Using this variational formulation we introduce appropriate solution concepts for the FC equation and prove an a priori estimate which connects this variational structure to an appropriate Lyapunov function and Fisher information, the so-called FIR inequality. Finally, we use this formulation and estimate to study the diffusive and hyperbolic limits for the FC system.}, language = {en} } @article{MontefuscoPeletierOettinger, author = {Montefusco, Alberto and Peletier, Mark A. and {\"O}ttinger, Hans Christian}, title = {A Framework of Nonequilibrium Statistical Mechanics. II. Coarse-Graining}, series = {Journal of Non-Equilibrium Thermodynamics}, volume = {46}, journal = {Journal of Non-Equilibrium Thermodynamics}, number = {1}, publisher = {De Gruyter}, doi = {10.1515/jnet-2020-0069}, pages = {15 -- 33}, abstract = {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.}, language = {en} } @article{MielkeMontefuscoPeletier, author = {Mielke, Alexander and Montefusco, Alberto and Peletier, Mark A.}, title = {Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence}, series = {Continuum Mechanics and Thermodynamics}, volume = {33}, journal = {Continuum Mechanics and Thermodynamics}, publisher = {Springer}, doi = {10.1007/s00161-020-00932-x}, pages = {611 -- 637}, abstract = {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.}, language = {en} } @article{BorndoerferDaneckerWeiser2020, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {A Discrete-Continuous Algorithm for Free Flight Planning}, series = {Algorithms}, volume = {14}, journal = {Algorithms}, number = {1}, publisher = {MDPI}, issn = {1438-0064}, doi = {10.3390/a14010004}, pages = {4}, year = {2020}, abstract = {We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach.}, language = {en} } @misc{RaharinirinaWeberBirketal., author = {Raharinirina, N. Alexia and Weber, Marcus and Birk, Ralph and Fackeldey, Konstantin and Klasse, Sarah M. and Richter, Tonio Sebastian}, title = {Different Tools and Results for Correspondence Analysis}, doi = {10.12752/8257}, abstract = {This is a list of codes generated from ancient egyptian texts. The codes are used for a correspondence analysis (CA). Codes and CA software are available from the linked webpage.}, language = {en} } @misc{BorndoerferDaneckerWeiser, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Newton's Method for Global Free Flight Trajectory Optimization}, doi = {10.12752/8987}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-89876}, abstract = {Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case.}, language = {en} } @article{OettingerMontefuscoPeletier, author = {{\"O}ttinger, Hans Christian and Montefusco, Alberto and Peletier, Mark A.}, title = {A Framework of Nonequilibrium Statistical Mechanics. I. Role and Types of Fluctuations}, series = {Journal of Non-Equilibrium Thermodynamics}, volume = {46}, journal = {Journal of Non-Equilibrium Thermodynamics}, number = {1}, publisher = {De Gruyter}, doi = {10.1515/jnet-2020-0068}, pages = {1 -- 13}, abstract = {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.}, language = {en} } @article{HuynhCheginiPavarinoetal., author = {Huynh, Ngoc and Chegini, Fatemeh and Pavarino, Luca and Weiser, Martin and Scacchi, Simone}, title = {Convergence analysis of BDDC preconditioners for hybrid DG discretizations of the cardiac cell-by-cell model}, series = {SIAM Journal on Scientific Computing}, volume = {45}, journal = {SIAM Journal on Scientific Computing}, number = {6}, pages = {A2836 -- A2857}, abstract = {A Balancing Domain Decomposition by Constraints (BDDC) preconditioner is constructed and analyzed for the solution of hybrid Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models. The latter are different from the classical Bidomain and Monodomain cardiac models based on homogenized descriptions of the cardiac tissue at the macroscopic level, and therefore they allow the representation of individual cardiac cells, cell aggregates, damaged tissues and nonuniform distributions of ion channels on the cell membrane. The resulting discrete cell-by-cell models have discontinuous global solutions across the cell boundaries, hence the proposed BDDC preconditioner is based on appropriate dual and primal spaces with additional constraints which transfer information between cells (subdomains) without influencing the overall discontinuity of the global solution. A scalable convergence rate bound is proved for the resulting BDDC cell-by-cell preconditioned operator, while numerical tests validate this bound and investigate its dependence on the discretization parameters.}, language = {en} } @misc{Sikorski, author = {Sikorski, Alexander}, title = {VoronoiGraph.jl}, doi = {10.5281/zenodo.6417636}, abstract = {This Package implements a variation of the Voronoi Graph Traversal algorithm by Polianskii and Pokorny [1]. It constructs a Voronoi Diagram from a set of points by performing a random walk on the graph of the vertices of the diagram. Unlike many other Voronoi implementations this algorithm is not limited to 2 or 3 dimensions and promises good performance even in higher dimensions.}, language = {en} } @article{PeppertvonKleistSchuetteetal., author = {Peppert, Felix and von Kleist, Max and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {On the Sufficient Condition for Solving the Gap-Filling Problem Using Deep Convolutional Neural Networks}, series = {IEEE Transactions on Neural Networks and Learning Systems}, volume = {33}, journal = {IEEE Transactions on Neural Networks and Learning Systems}, number = {11}, doi = {10.1109/TNNLS.2021.3072746}, pages = {6194 -- 6205}, abstract = {Deep convolutional neural networks (DCNNs) are routinely used for image segmentation of biomedical data sets to obtain quantitative measurements of cellular structures like tissues. These cellular structures often contain gaps in their boundaries, leading to poor segmentation performance when using DCNNs like the U-Net. The gaps can usually be corrected by post-hoc computer vision (CV) steps, which are specific to the data set and require a disproportionate amount of work. As DCNNs are Universal Function Approximators, it is conceivable that the corrections should be obsolete by selecting the appropriate architecture for the DCNN. In this article, we present a novel theoretical framework for the gap-filling problem in DCNNs that allows the selection of architecture to circumvent the CV steps. Combining information-theoretic measures of the data set with a fundamental property of DCNNs, the size of their receptive field, allows us to formulate statements about the solvability of the gap-filling problem independent of the specifics of model training. In particular, we obtain mathematical proof showing that the maximum proficiency of filling a gap by a DCNN is achieved if its receptive field is larger than the gap length. We then demonstrate the consequence of this result using numerical experiments on a synthetic and real data set and compare the gap-filling ability of the ubiquitous U-Net architecture with variable depths. Our code is available at https://github.com/ai-biology/dcnn-gap-filling.}, language = {en} } @article{WulkowTelgmannHungenbergetal., author = {Wulkow, Niklas and Telgmann, Regina and Hungenberg, Klaus-Dieter and Sch{\"u}tte, Christof and Wulkow, Michael}, title = {Deterministic and Stochastic Parameter Estimation for Polymer Reaction Kinetics I: Theory and Simple Examples}, series = {Macromolecular Theory and Simulations}, volume = {30}, journal = {Macromolecular Theory and Simulations}, doi = {10.1002/mats.202100017}, abstract = {Two different approaches to parameter estimation (PE) in the context of polymerization are introduced, refined, combined, and applied. The first is classical PE where one is interested in finding parameters which minimize the distance between the output of a chemical model and experimental data. The second is Bayesian PE allowing for quantifying parameter uncertainty caused by experimental measurement error and model imperfection. Based on detailed descriptions of motivation, theoretical background, and methodological aspects for both approaches, their relation are outlined. The main aim of this article is to show how the two approaches complement each other and can be used together to generate strong information gain regarding the model and its parameters. Both approaches and their interplay in application to polymerization reaction systems are illustrated. This is the first part in a two-article series on parameter estimation for polymer reaction kinetics with a focus on theory and methodology while in the second part a more complex example will be considered.}, language = {en} } @article{HungenbergSchwedeWulkowetal., author = {Hungenberg, Klaus-Dieter and Schwede, Christian and Wulkow, Michael and Wulkow, Niklas}, title = {Determination of reactivity ratios for acrylic acid and its dimer from classical parameter estimation and Bayesian approach}, series = {Canadian Journal of Chemical Engineering}, journal = {Canadian Journal of Chemical Engineering}, doi = {https://doi.org/10.1002/cjce.24330}, pages = {1 -- 10}, abstract = {The reactivity ratios of acrylic acid (AA, M1) and its dimer beta-acroyloxypropionic acid (diAA, M2) are determined from cumulative copolymerization data by two different methods: classical parameter estimation (PE) by minimizing the objective function and a Bayesian analysis. Classical PE gives r1 =0.74 and r2 = 1.23 at the minimum of the residual. From the Bayesian analysis, the probability distribution of the parameter sets is obtained, revealing the existence of parameter sets with rather the same probability. The influence of the number of data and the size of the measurement error are discussed.}, language = {en} } @book{TernesBauerBraueretal., author = {Ternes, Thomas and Bauer, Karl-Heinz and Brauer, Frank and Drewes, J{\"o}rg and Joss, Adriano and Hiller, Georg and Jewell, Kevin and Oehlmann, J{\"o}rg and Radke, Michael and Schulte-Oehlmann, Ulrike and Schwartz, Thomas and Seel, Peter and V{\"o}lker, Jeanette and Weber, Lilo and Weber, Marcus}, title = {Handlungsempfehlung zur integrativen Bewertung der weitergehenden Abwasserbehandlung von kommunalen Kl{\"a}ranlagen}, volume = {T1/2023}, editor = {Wilhelm, Christian}, publisher = {DWA / GDCh}, isbn = {978-3-96862-563-8}, abstract = {Das vorliegende Statuspapier beschreibt ein Konzept zur weitergehenden Abwasserbehandlung f{\"u}r die Bewertung von Aufbereitungsverfahren, sowohl in einer Pilotphase zur Auswahl von Verfah- rensoptionen als auch f{\"u}r die Bewertung großtechnischer Anlagen.}, language = {de} } @article{ColomMikheevaAchourietal., author = {Colom, Remi and Mikheeva, Elena and Achouri, Karim and Zuniga-Perez, Jesus and Bonod, Nicolas and Martin, Olivier J. F. and Burger, Sven and Genevet, Patrice}, title = {Crossing of the branch cut: the topological origin of a universal 2π-phase retardation in non-Hermitian metasurfaces}, series = {Laser Photonics Rev.}, volume = {17}, journal = {Laser Photonics Rev.}, doi = {10.1002/lpor.202200976}, pages = {2200976}, language = {en} } @inproceedings{ZinkEkteraiMartinetal., author = {Zink, Christof and Ekterai, Michael and Martin, Dominik and Clemens, William and Maennel, Angela and Mundinger, Konrad and Richter, Lorenz and Crump, Paul and Knigge, Andrea}, title = {Deep-learning-based visual inspection of facets and p-sides for efficient quality control of diode lasers}, series = {High-Power Diode Laser Technology XXI}, volume = {12403}, booktitle = {High-Power Diode Laser Technology XXI}, publisher = {SPIE}, doi = {10.1117/12.2648691}, pages = {94 -- 112}, abstract = {The optical inspection of the surfaces of diode lasers, especially the p-sides and facets, is an essential part of the quality control in the laser fabrication procedure. With reliable, fast, and flexible optical inspection processes, it is possible to identify and eliminate defects, accelerate device selection, reduce production costs, and shorten the cycle time for product development. Due to a vast range of rapidly changing designs, structures, and coatings, however, it is impossible to realize a practical inspection with conventional software. In this work, we therefore suggest a deep learning based defect detection algorithm that builds on a Faster Regional Convolutional Neural Network (Faster R-CNN) as a core component. While for related, more general object detection problems, the application of such models is straightforward, it turns out that our task exhibits some additional challenges. On the one hand, a sophisticated pre- and postprocessing of the data has to be deployed to make the application of the deep learning model feasible. On the other hand, we find that creating labeled training data is not a trivial task in our scenario, and one has to be extra careful with model evaluation. We can demonstrate in multiple empirical assessments that our algorithm can detect defects in diode lasers accurately and reliably in most cases. We analyze the results of our production-ready pipeline in detail, discuss its limitations and provide some proposals for further improvements.}, language = {en} } @article{WeilandtBehlingGoncalvesetal., author = {Weilandt, Frank and Behling, Robert and Goncalves, Romulo and Madadi, Arash and Richter, Lorenz and Sanona, Tiago and Spengler, Daniel and Welsch, Jona}, title = {Early Crop Classification via Multi-Modal Satellite Data Fusion and Temporal Attention}, series = {Remote Sensing}, volume = {15}, journal = {Remote Sensing}, number = {3}, doi = {10.3390/rs15030799}, pages = {799}, abstract = {In this article, we propose a deep learning-based algorithm for the classification of crop types from Sentinel-1 and Sentinel-2 time series data which is based on the celebrated transformer architecture. Crucially, we enable our algorithm to do early classification, i.e., predict crop types at arbitrary time points early in the year with a single trained model (progressive intra-season classification). Such early season predictions are of practical relevance for instance for yield forecasts or the modeling of agricultural water balances, therefore being important for the public as well as the private sector. Furthermore, we improve the mechanism of combining different data sources for the prediction task, allowing for both optical and radar data as inputs (multi-modal data fusion) without the need for temporal interpolation. We can demonstrate the effectiveness of our approach on an extensive data set from three federal states of Germany reaching an average F1 score of 0.92 using data of a complete growing season to predict the eight most important crop types and an F1 score above 0.8 when doing early classification at least one month before harvest time. In carefully chosen experiments, we can show that our model generalizes well in time and space.}, language = {en} } @article{NueskenRichter, author = {N{\"u}sken, Nikolas and Richter, Lorenz}, title = {Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems}, series = {Journal of Machine Learning}, volume = {2}, journal = {Journal of Machine Learning}, number = {1}, doi = {0.4208/jml.220416}, pages = {31 -- 64}, abstract = {Solving high-dimensional partial differential equations is a recurrent challenge in economics, science and engineering. In recent years, a great number of computational approaches have been developed, most of them relying on a combination of Monte Carlo sampling and deep learning based approximation. For elliptic and parabolic problems, existing methods can broadly be classified into those resting on reformulations in terms of backward stochastic differential equations (BSDEs) and those aiming to minimize a regression-type L2-error (physics-informed neural networks, PINNs). In this paper, we review the literature and suggest a methodology based on the novel diffusion loss that interpolates between BSDEs and PINNs. Our contribution opens the door towards a unified understanding of numerical approaches for high-dimensional PDEs, as well as for implementations that combine the strengths of BSDEs and PINNs. The diffusion loss furthermore bears close similarities to (least squares) temporal difference objectives found in reinforcement learning. We also discuss eigenvalue problems and perform extensive numerical studies, including calculations of the ground state for nonlinear Schr ¨odinger operators and committor functions relevant in molecular dynamics.}, language = {en} } @misc{BinkowskiBetzColometal., author = {Binkowski, Felix and Betz, Fridtjof and Colom, Remi and Genevet, Patrice and Burger, Sven}, title = {Source code and simulation results: Poles and zeros of electromagnetic quantities in photonic systems}, series = {Zenodo}, journal = {Zenodo}, doi = {10.5281/zenodo.8063931}, pages = {8063931}, language = {en} } @article{BennerBurgerGoeddekeetal., author = {Benner, Peter and Burger, Michael and G{\"o}ddeke, Dominik and G{\"o}rgen, Christiane and Himpe, Christian and Heiland, Jan and Koprucki, Thomas and Ohlberger, Mario and Rave, Stephan and Reidelbach, Marco and Saak, Jens and Sch{\"o}bel, Anita and Tabelow, Karsten and Weber, Marcus}, title = {Die mathematische Forschungsdateninitiative in der NFDI: MaRDI (Mathematical Research Data Initiative)}, series = {GAMM Rundbrief}, journal = {GAMM Rundbrief}, number = {1}, pages = {40 -- 43}, language = {de} } @article{CvetkovicConradLie, author = {Cvetkovic, Nada and Conrad, Tim and Lie, Han Cheng}, title = {A Convergent Discretisation Method for Transition Path Theory for Diffusion Processes}, series = {Multiscale Modeling \& Simulation}, volume = {19}, journal = {Multiscale Modeling \& Simulation}, number = {1}, publisher = {Society for Industrial and Applied Mathematics}, doi = {10.1137/20M1329354}, pages = {242 -- 266}, language = {en} } @phdthesis{Helfmann, author = {Helfmann, Luzie}, title = {Non-stationary Transition Path Theory with applications to tipping and agent-based models}, doi = {http://dx.doi.org/10.17169/refubium-35374}, abstract = {The interesting dynamical regimes in agent-based models (ABMs) of social dynamics are the transient dynamics leading to metastable or absorbing states, and the transition paths between metastable states possibly caused by external influences. In this thesis, we are particularly interested in the pathways of rare and critical transitions such as the tipping of the public opinion in a population or the forming of social movements. For a detailed quantitative analysis of these transition paths, we consider the agent-based models as Markov chains and employ Transition Path Theory. Since ABMs are usually not considered in stationarity and possibly even forced, we generalize Transition Path Theory to time-dependent dynamics, for example on finite-time intervals or with periodically varying transition probabilities. We also specifically consider the case of dynamics with absorbing states and show how the transitions prior to absorption can be studied. These generalizations can also be useful in other application domains such as for studying tipping in climate models or transitions in molecular models with external stimuli. Another obstacle when analysing the dynamics of agent-based models is the large number of agents resulting in a high-dimensional state space for the model. However, the emergent dynamics of the ABM usually has significantly fewer degrees of freedom and many symmetries enabling a model reduction. On the example of two stationary ABMs we demonstrate how a long model simulation can be employed to find a lower-dimensional parametrization of the state space using a manifold learning algorithm called Diffusion Maps. In the considered models, agents adapt their binary behaviour to the local neighbourhood. When the interaction network consists of several densely connected communities, the dynamics result in a largely coherent behaviour in each community. The low-dimensional structure of the state space is therefore a hypercube. The corners represent metastable states with coherent agent behaviour in each group and the edges correspond to transition paths where agents in a community change their behaviour through a chain reaction. Finally, we can apply Transition Path Theory to the effective dynamics in the reduced space to reveal, for example, the dominant transition paths or the agents that are most indicative of an impending tipping event.}, language = {en} } @incollection{HartmannRichter, author = {Hartmann, Carsten and Richter, Lorenz}, title = {Transgressing the Boundaries: Towards a Rigorous Understanding of Deep Learning and Its (Non )Robustness}, series = {AI - Limits and Prospects of Artificial Intelligence}, volume = {4}, booktitle = {AI - Limits and Prospects of Artificial Intelligence}, editor = {Klimczak, Peter and Petersen, Christer}, publisher = {transcript Verlag}, doi = {10.1515/9783839457320}, pages = {43 -- 82}, abstract = {The recent advances in machine learning in various fields of applications can be largely attributed to the rise of deep learning (DL) methods and architectures. Despite being a key technology behind autonomous cars, image processing, speech recognition, etc., a notorious problem remains the lack of theoretical understanding of DL and related interpretability and (adversarial) robustness issues. Understanding the specifics of DL, as compared to, say, other forms of nonlinear regression methods or statistical learning, is interesting from a mathematical perspective, but at the same time it is of crucial importance in practice: treating neural networks as mere black boxes might be sufficient in certain cases, but many applications require waterproof performance guarantees and a deeper understanding of what could go wrong and why it could go wrong. It is probably fair to say that, despite being mathematically well founded as a method to approximate complicated functions, DL is mostly still more like modern alchemy that is firmly in the hands of engineers and computer scientists. Nevertheless, it is evident that certain specifics of DL that could explain its success in applications demands systematic mathematical approaches. In this work, we review robustness issues of DL and particularly bridge concerns and attempts from approximation theory to statistical learning theory. Further, we review Bayesian Deep Learning as a means for uncertainty quantification and rigorous explainability.}, language = {en} } @article{HelfmannHeitzigKoltaietal., author = {Helfmann, Luzie and Heitzig, Jobst and Koltai, P{\´e}ter and Kurths, J{\"u}rgen and Sch{\"u}tte, Christof}, title = {Statistical analysis of tipping pathways in agent-based models}, series = {Eur. Phys. J. Spec. Top.}, volume = {230}, journal = {Eur. Phys. J. Spec. Top.}, doi = {10.1140/epjs/s11734-021-00191-0}, pages = {3249 -- 3271}, abstract = {Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals on the microscopic scale can lead to emergent dynamics on the macroscopic scale, for instance a sudden shift of majority opinion or behavior. Here we are introducing a methodology for studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations. Due to a large number of interacting individuals, agent-based models are high-dimensional, though usually a lower-dimensional structure of the emerging collective behaviour exists. We therefore apply Diffusion Maps, a non-linear dimension reduction technique, to reveal the intrinsic low-dimensional structure. We characterize the tipping behaviour by means of Transition Path Theory, which helps gaining a statistical understanding of the tipping paths such as their distribution, flux and rate. By systematically studying two agent-based models that exhibit a multitude of tipping pathways and cascading effects, we illustrate the practicability of our approach.}, language = {en} } @article{QuerRiberaBorrell2023, author = {Quer, Jannes and Ribera Borrell, Enric}, title = {Connecting Stochastic Optimal Control and Reinforcement Learning}, series = {Journal of Mathematical Physics}, journal = {Journal of Mathematical Physics}, year = {2023}, abstract = {In this article we study the connection of stochastic optimal control and reinforcement learning. Our main motivation is an importance sampling application to rare events sampling which can be reformulated as an optimal control problem. By using a parameterized approach the optimal control problem turns into a stochastic optimization problem which still presents some open questions regarding how to tackle the scalability to high-dimensional problems and how to deal with the intrinsic metastability of the system. With the aim to explore new methods we connect the optimal control problem to reinforcement learning since both share the same underlying framework namely a Markov decision process (MDP). We show how the MDP can be formulated for the optimal control problem. Furthermore, we discuss how the stochastic optimal control problem can be interpreted in a reinforcement learning framework. At the end of the article we present the application of two different reinforcement learning algorithms to the optimal control problem and compare the advantages and disadvantages of the two algorithms.}, language = {en} } @article{SechiWeberHeyne, author = {Sechi, Renata and Weber, Marcus and Heyne, Karsten}, title = {MSM building and projection for the analysis of time-resolved spectra}, series = {Proceedings in Applied Mathematics and Mechanics}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {21}, doi = {https://doi.org/10.1002/pamm.202100102}, url = {http://nbn-resolving.de/https://onlinelibrary.wiley.com/doi/10.1002/pamm.202100102}, pages = {e202100102}, abstract = {Understanding the kinetics between the components of time-resolved spectra is a crucial step in the study of photo-activatedprocesses. However, modeling the kinetics requires usually some a priori knowledge about the system. In our approach, webuild a Markov State Model (MSM) from the spectral data, and obtain a Koopman transition matrix K(t). With genPCCA,an invariant subspace projection, we project the process into its metastable components. The result of the application of gen-PCCA is a transition matrix Kc(t), from which we can read the transition probability between the metastable components of the reaction. We discuss the application of this analysis method to the transient absorption spectrum of brominated Al-corrole}, language = {en} } @article{SechiSikorskiWeber2020, author = {Sechi, Renata and Sikorski, Alexander and Weber, Marcus}, title = {Estimation of the Koopman Generator by Newton's Extrapolation}, series = {Multiscale Modeling and Simulation}, volume = {19}, journal = {Multiscale Modeling and Simulation}, number = {2}, publisher = {SIAM}, doi = {10.1137/20M1333006}, pages = {758 -- 774}, year = {2020}, abstract = {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.}, language = {en} } @inproceedings{BoppPlockTuranetal., author = {Bopp, Julian M. and Plock, Matthias and Turan, Tim and Pieplow, Gregor and Burger, Sven and Schr{\"o}der, Tim}, title = {'Sawfish' Spin-Photon Interface for Near-Unity Emitter-to-Waveguide Coupling}, series = {Conference on Lasers and Electro-Optics (CLEO)}, booktitle = {Conference on Lasers and Electro-Optics (CLEO)}, doi = {10.1364/CLEO_SI.2023.SF1O.6}, pages = {SF1O.6}, language = {en} } @article{PlockHammerschmidtBurgeretal., author = {Plock, Matthias and Hammerschmidt, Martin and Burger, Sven and Schneider, Philipp-Immanuel and Sch{\"u}tte, Christof}, title = {Impact Study of Numerical Discretization Accuracy on Parameter Reconstructions and Model Parameter Distributions}, series = {Metrologia}, volume = {60}, journal = {Metrologia}, doi = {10.1088/1681-7575/ace4cd}, pages = {054001}, abstract = {In optical nano metrology numerical models are used widely for parameter reconstructions. Using the Bayesian target vector optimization method we fit a finite element numerical model to a Grazing Incidence x-ray fluorescence data set in order to obtain the geometrical parameters of a nano structured line grating. Gaussian process, stochastic machine learning surrogate models, were trained during the reconstruction and afterwards sampled with a Markov chain Monte Carlo sampler to determine the distribution of the reconstructed model parameters. The numerical discretization parameters of the used finite element model impact the numerical discretization error of the forward model. We investigated the impact of the polynomial order of the finite element ansatz functions on the reconstructed parameters as well as on the model parameter distributions. We showed that such a convergence study allows to determine numerical parameters which allows for efficient and accurate reconstruction results.}, language = {en} } @inproceedings{PlockBurgerSchneider, author = {Plock, Matthias and Burger, Sven and Schneider, Philipp-Immanuel}, title = {Efficient reconstruction of model parameters using Bayesian target-vector optimization}, series = {Proc. SPIE}, volume = {PC12619}, booktitle = {Proc. SPIE}, doi = {10.1117/12.2673590}, pages = {PC1261905}, language = {en} } @inproceedings{ManleyKruegerBodermannetal., author = {Manley, Phillip and Kr{\"u}ger, Jan and Bodermann, Bernd and K{\"o}ning, Rainer and Heinrich, Andreas and Eder, Christian and Goehnermeier, Aksel and Zeiser, Ulrike and Hammerschmidt, Martin and Zschiedrich, Lin and Schneider, Philipp-Immanuel}, title = {Efficient simulation of microscopic imaging for reconstruction of nanostructures}, series = {Proc. SPIE}, volume = {PC12619}, booktitle = {Proc. SPIE}, doi = {10.1117/12.2673077}, pages = {PC126190B}, language = {en} } @inproceedings{KruegerBodermannKoeningetal., author = {Kr{\"u}ger, Jan and Bodermann, Bernd and K{\"o}ning, Rainer and Manley, Phillip and Zschiedrich, Lin and Schneider, Philipp-Immanuel and Heinrich, Andreas and Eder, Christian and Zeiser, Ulrike and Goehnermeier, Aksel}, title = {On aberration retrieval for optical microscopes in length metrology}, series = {Proc. SPIE}, volume = {PC12619}, booktitle = {Proc. SPIE}, doi = {10.1117/12.2672294}, pages = {PC126190A}, language = {en} } @article{SchneckWeiserWende, author = {Schneck, Jakob and Weiser, Martin and Wende, Florian}, title = {Impact of mixed precision and storage layout on additive Schwarz smoothers}, series = {Numerical Linear Algebra with Applications}, volume = {28}, journal = {Numerical Linear Algebra with Applications}, number = {4}, doi = {10.1002/nla.2366}, 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{SchielaStoeckleinWeiser, author = {Schiela, Anton and St{\"o}cklein, Matthias and Weiser, Martin}, title = {A primal dual projection algorithm for efficient constraint preconditioning}, series = {SIAM Journal on Scientific Computing}, volume = {43}, journal = {SIAM Journal on Scientific Computing}, number = {6}, doi = {10.1137/20M1380739}, pages = {A4095 -- A4120}, abstract = {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.}, language = {en} } @inproceedings{HammerschmidtZschiedrichSiaudinyteetal., author = {Hammerschmidt, Martin and Zschiedrich, Lin and Siaudinyt{\´e}, Lauryna and Manley, Phillip and Schneider, Philipp-Immanuel and Burger, Sven}, title = {Forward simulation of coherent beams on grating structures for coherent scatterometry}, series = {Proc. SPIE}, volume = {PC12619}, booktitle = {Proc. SPIE}, doi = {10.1117/12.2673231}, pages = {PC1261907}, language = {en} } @article{MikheevaColomAchourietal., author = {Mikheeva, Elena and Colom, R{\´e}mi and Achouri, Karim and Overvig, Adam and Binkowski, Felix and Duboz, Jean-Yves and Cueff, S{\´e}bastien and Fan, Shanhui and Burger, Sven and Al{\`u}, Andrea and Genevet, Patrice}, title = {Asymmetric phase modulation with light with parity-symmetry broken metasurfaces}, series = {Optica}, volume = {10}, journal = {Optica}, doi = {10.1364/OPTICA.495681}, pages = {1287}, language = {en} } @article{HelfmannRiberaBorrellSchuetteetal., author = {Helfmann, Luzie and Ribera Borrell, Enric and Sch{\"u}tte, Christof and Koltai, Peter}, title = {Extending Transition Path Theory: Periodically Driven and Finite-Time Dynamics}, series = {Journal of Nonlinear Science}, volume = {30}, journal = {Journal of Nonlinear Science}, doi = {https://doi.org/10.1007/s00332-020-09652-7}, pages = {3321 -- 3366}, language = {en} } @inproceedings{ChaukairSchuetteSunkara, author = {Chaukair, Mustafa and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {On the Activation Space of ReLU Equipped Deep Neural Networks}, series = {Procedia Computer Science}, volume = {222}, booktitle = {Procedia Computer Science}, doi = {10.1016/j.procs.2023.08.200}, pages = {624 -- 635}, abstract = {Modern Deep Neural Networks are getting wider and deeper in their architecture design. However, with an increasing number of parameters the decision mechanisms becomes more opaque. Therefore, there is a need for understanding the structures arising in the hidden layers of deep neural networks. In this work, we present a new mathematical framework for describing the canonical polyhedral decomposition in the input space, and in addition, we introduce the notions of collapsing- and preserving patches, pertinent to understanding the forward map and the activation space they induce. The activation space can be seen as the output of a layer and, in the particular case of ReLU activations, we prove that this output has the structure of a polyhedral complex.}, language = {en} } @inproceedings{KuenBetzBinkowskietal., author = {Kuen, Lilli and Betz, Fridtjof and Binkowski, Felix and Schneider, Philipp-Immanuel and Hammerschmidt, Martin and Heermeier, Niels and Rodt, Sven and Reitzenstein, Stephan and Burger, Sven}, title = {Applying a Riesz-projection-based contour integral eigenvalue solver to compute resonance modes of a VCSEL}, series = {Proc. SPIE}, volume = {12575}, booktitle = {Proc. SPIE}, doi = {10.1117/12.2665490}, pages = {125750J}, language = {en} } @misc{RiberaBorrellQuerRichteretal., author = {Ribera Borrell, Enric and Quer, Jannes and Richter, Lorenz and Sch{\"u}tte, Christof}, title = {Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics}, issn = {1438-0064}, abstract = {Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings.}, language = {en} } @article{SubramaniamHubigMuggenthaleretal., author = {Subramaniam, Jayant S. and Hubig, Michael and Muggenthaler, Holger and Schenkl, Sebastian and Ullrich, Julia and Pourtier, Gr{\´e}groire and Weiser, Martin and Mall, Gita}, title = {Sensitivity of temperature-based time since death estimation on measurement location}, series = {International Journal of Legal Medicine}, volume = {137}, journal = {International Journal of Legal Medicine}, doi = {10.1007/s00414-023-03040-y}, pages = {1815 -- 1837}, abstract = {Rectal temperature measurement (RTM) from crime scenes is an important parameter for temperature-based time of death estimation (TDE). Various influential variables exist in TDE methods like the uncertainty in thermal and environmental parameters. Although RTM depends in particular on the location of measurement position, this relationship has never been investigated separately. The presented study fills this gap using Finite Element (FE) simulations of body cooling. A manually meshed coarse human FE model and an FE geometry model developed from the CT scan of a male corpse are used for TDE sensitivity analysis. The coarse model is considered with and without a support structure of moist soil. As there is no clear definition of ideal rectal temperature measurement location for TDE, possible variations in RTM location (RTML) are considered based on anatomy and forensic practice. The maximum variation of TDE caused by RTML changes is investigated via FE simulation. Moreover, the influence of ambient temperature, of FE model change and of the models positioning on a wet soil underground are also discussed. As a general outcome, we notice that maximum TDE deviations of up to ca. 2-3 h due to RTML deviations have to be expected. The direction of maximum influence of RTML change on TDE generally was on the line caudal to cranial.}, language = {en} } @article{ChewleWeberEmmerling, author = {Chewle, Surahit and Weber, Marcus and Emmerling, Franziska}, title = {Revealing Kinetics of Paracetamol Crystallization Using Time-Resolved Raman Spectroscopy, Orthogonal Time-Lapse Photography, and Non-Negative Matrix Factorization (OSANO)}, series = {Crystal Growth \& Design}, volume = {23}, journal = {Crystal Growth \& Design}, number = {9}, edition = {Crystal Growth \& Design}, publisher = {American Chemical Society}, doi = {10.1021/acs.cgd.3c00617}, pages = {6737 -- 6746}, abstract = {Crystallization is a complex phenomenon with far-reaching implications for the production and formulation of active pharmaceutical ingredients. Understanding this process is critical for achieving control over key physicochemical properties that can affect, for example, the bioavailability and stability of a drug. In this study, we were able to reveal intricate and diverse dynamics of the formation of metastable intermediates of paracetamol crystallization varying with the choice of solvent. We demonstrate the efficacy of our novel approach utilizing an objective function-based non-negative matrix factorization technique for the analysis of time-resolved Raman spectroscopy data, in conjunction with time-lapse photography. Furthermore, we emphasize the crucial importance of integrating Raman spectroscopy with supplementary experimental instrumentation for the mathematical analysis of the obtained spectra.}, language = {en} } @article{BoethBiesenHollnageletal.2021, author = {Boeth, Heide and Biesen, Robert and Hollnagel, Jeremias and Herrmann, Sandra and Ehrig, Rainald and Pelli, Lorenzo and Taylor, William R. and Duda, Georg and Buttgereit, Frank}, title = {Quantification of morning stiffness to assess disease activity and treatment effects in rheumatoid arthritis}, series = {Rheumatology}, volume = {60}, journal = {Rheumatology}, number = {11}, doi = {10.1093/rheumatology/keab323}, pages = {5282 -- 5291}, year = {2021}, abstract = {Objectives The clinical parameter "morning stiffness" is widely used to assess the status of rheumatoid arthritis (RA), but its accurate quantitative assessment in a clinical setting has not yet been successful. This lack of individual quantification limits both personalized medication and efficacy evaluation in the treatment of RA. Methods We have developed a novel technology to assess passive resistance of the metacarpophalangeal (MCP) III joint (stiffness) and its Passive Range of Motion (PRoM). Within this pilot study, nineteen female postmenopausal RA patients and nine healthy controls were examined in the evening as well as in the morning of the following day. To verify the specificity of the biomechanical quantification, eleven patients with RA were assessed both prior to and ∼3 h after glucocorticoid therapy. Results While the healthy controls showed only minor changes between afternoon and morning, in RA patients mean±SD PRoM decreased significantly by 18 ± 22\% and stiffness increased significantly by 20 ± 18\% in the morning compared with the previous afternoon. We found a significant positive correlation between RA activity and biomechanical measures. Glucocorticoids significantly increased mean PRoM by 16 ± 11\% and reduced mean stiffness by 23 ± 22\%. Conclusion This technology allowed mechanical stiffness to be quantified in MCP joints, and has demonstrated high sensitivity in respect to disease status as well as medication effect in RA patients. Such non-invasive, low risk, and rapid assessment of biomechanical joint stiffness opens a novel avenue for judging therapy efficacy in patients with RA, and potentially also in other non-RA inflammatory joint diseases.}, language = {en} } @article{AlvesEhrigRaffaltetal., author = {Alves, S{\´o}nia and Ehrig, Rainald and Raffalt, Peter C. and Bender, Alwina and Duda, Georg and Agres, Alison N.}, title = {Quantifying Asymmetry in Gait: A Weighted Universal Symmetry Index to Evaluate 3D Ground Reaction Forces}, series = {Frontiers in Bioengineering and Biotechnology}, journal = {Frontiers in Bioengineering and Biotechnology}, abstract = {Though gait asymmetry is used as a metric of functional recovery in clinical rehabilitation, there is no consensus on an ideal method for its evaluation. Various methods have been proposed but are limited in scope, as they can often use only positive signals or discrete values extracted from time-scale data as input. By defining five symmetry axioms, a framework for benchmarking existing methods was established and a new method was described here for the first time: the weighted universal symmetry index (wUSI), which overcomes limitations of other methods. Both existing methods and the wUSI were mathematically compared to each other and in respect to their ability to fulfill the proposed symmetry axioms. Eligible methods that fulfilled these axioms were then applied using both discrete and continuous approaches to ground reaction force (GRF) data collected from healthy gait, both with and without artificially induced asymmetry using a single instrumented elbow crutch. The wUSI with a continuous approach was the only symmetry method capable of determining GRF asymmetries in different walking conditions in all three planes of motion. When used with a continuous approach, the wUSI method was able to detect asymmetries while avoiding artificial inflation, a common problem reported in other methods. In conclusion, the wUSI is proposed as a universal method to quantify three-dimensional GRF asymmetries, which may also be expanded to other biomechanical signals.}, language = {en} } @article{GorgullaJayarajFackeldeyetal., author = {Gorgulla, Christoph and Jayaraj, Abhilash and Fackeldey, Konstantin and Arthanari, Haribabu}, title = {Emerging frontiers in virtual drug discovery: From quantum mechanical methods to deep learning approaches}, series = {Current Opinion in Chemical Biology}, volume = {69}, journal = {Current Opinion in Chemical Biology}, doi = {10.1016/j.cbpa.2022.102156}, pages = {102156 -- 102156-12}, abstract = {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.}, language = {en} } @article{NitzkeFackeldeyVrabec, author = {Nitzke, Isabel and Fackeldey, Konstantin and Vrabec, Jadran}, title = {Long range corrections for inhomogeneous fluids containing a droplet or a bubble}, series = {Molecular Simulation}, journal = {Molecular Simulation}, doi = {https://doi.org/10.1080/08927022.2021.1954639}, pages = {1 -- 14}, abstract = {Long range corrections for molecular simulations of inhomogeneous fluids with a spherical interface are presented. Correction terms for potential energy, force and virial are derived for the monatomic Lennard-Jones fluid. The method is generalised to the Mie potential and arbitrary molecular structures, employing a numerically efficient centre of mass cut-off scheme. The results are validated by a series of droplet simulations for one-centre and two-centre Lennard-Jones fluids with different cut-off radii rc. Systems with rc=8σ provide a check of self-consistence. Further, a system containing a bubble is investigated for the one-centre Lennard-Jones fluid. The equilibrium properties are almost completely independent on the cut-off radius. In comparison with vapour-liquid equilibrium data for systems without a curved interface, all properties show the expected behaviour. Simulation data are used to approximate the surface tension, which is in good agreement with the findings for planar interfaces, thus verifying the present corrections.}, language = {en} } @article{FackeldeyGorgullaWeber, author = {Fackeldey, Konstantin and Gorgulla, Christoph and Weber, Marcus}, title = {Neue Medikamente dank Supercomputern}, series = {Spektrum der Wissenschaft}, journal = {Spektrum der Wissenschaft}, number = {11}, pages = {40 -- 46}, abstract = {Die aktuelle Pandemie verdeutlicht, wie wichtig es ist, rasch geeignete Arzneimittel zu finden. In Computer­simulationen gelingt das erheblich schneller als im Labor. Gegen das Coronavirus ließen sich auf diese Weise bereits Wirkstoffkandidaten identifizieren.}, language = {de} } @article{TillmannBlaesiBurgeretal., author = {Tillmann, Peter and Bl{\"a}si, Benedikt and Burger, Sven and Hammerschmidt, Martin and H{\"o}hn, Oliver and Becker, Christiane and J{\"a}ger, Klaus}, title = {Optimizing metal grating back reflectors for III-V-on-silicon multijunction solar cells}, series = {Opt. Express}, volume = {29}, journal = {Opt. Express}, doi = {10.1364/OE.426761}, pages = {22517}, language = {en} } @article{JaegerTillmannKatzetal., author = {J{\"a}ger, Klaus and Tillmann, Peter and Katz, Eugene A. and Becker, Christiane}, title = {Perovskite/silicon tandem solar cells: Effect of luminescent coupling and bifaciality}, series = {Sol. RRL}, volume = {5}, journal = {Sol. RRL}, doi = {10.1002/solr.202000628}, pages = {2000628}, language = {en} } @inproceedings{JaegerTillmannKatzetal., author = {J{\"a}ger, Klaus and Tillmann, Peter and Katz, Eugene A. and Becker, Christiane}, title = {Simulating bifacial perovskite/silicon tandem solar cells in large PV fields}, series = {OSA Advanced Photonics Congress}, booktitle = {OSA Advanced Photonics Congress}, doi = {10.1364/PVLED.2020.PvTh1G.3}, pages = {PvTh1G.3}, language = {en} } @article{TillmannJaegerBecker, 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}, series = {Sustain. Energy Fuels}, volume = {4}, journal = {Sustain. Energy Fuels}, doi = {10.1039/C9SE00750D}, pages = {254}, language = {en} } @article{JaegerTillmannBecker, author = {J{\"a}ger, Klaus and Tillmann, Peter and Becker, Christiane}, title = {Detailed illumination model for bifacial solar cells}, series = {Opt. Express}, volume = {28}, journal = {Opt. Express}, doi = {10.1364/OE.383570}, pages = {4751}, language = {en} } @article{YooTillmannKraussetal., author = {Yoo, Danbi and Tillmann, Peter and Krauss, Tobias and Sutter, Johannes and Harter, Angelika and Trofimov, Sergei and Naydenov, Boris and J{\"a}ger, Klaus and Hauser, Hubert and Becker, Christiane}, title = {Comparative Optical Analysis of Imprinted Nano-, Micro- and Biotextures on Solar Glasses for Increased Energy Yield}, series = {Solar RRL}, volume = {7}, journal = {Solar RRL}, doi = {10.1002/solr.202300071}, pages = {2300071}, language = {en} } @inproceedings{TillmannJaegerKatzetal., author = {Tillmann, Peter and J{\"a}ger, Klaus and Katz, Eugene and Becker, Christiane}, title = {Relaxed current-matching constraints by bifacial operation and luminescent coupling in perovskite/silicon tandem solar cells}, series = {2021 IEEE 48th Photovoltaic Specialists Conference (PVSC)}, booktitle = {2021 IEEE 48th Photovoltaic Specialists Conference (PVSC)}, doi = {10.1109/PVSC43889.2021.9518891}, pages = {1086}, language = {en} } @article{TillmannJaegerKarsentietal., author = {Tillmann, Peter and J{\"a}ger, Klaus and Karsenti, Asher and Kreinin, Lev and Becker, Christiane}, title = {Model-Chain Validation for Estimating the Energy Yield of Bifacial Perovskite/Silicon Tandem Solar Cells}, series = {Sol. RRL}, volume = {6}, journal = {Sol. RRL}, doi = {10.1002/solr.202200079}, pages = {2200079}, language = {en} } @article{Schweigart, author = {Schweigart, Fleur}, title = {KARTHAGO, TUNESIEN Datengesteuerte Modellierung des Romanisierungsprozesses in Nordafrika}, series = {e-Forschungsberichte des Deutschen Arch{\"a}ologischen Instituts. Berlin: Deutsches Arch{\"a}ologisches Institut, Zentrale.}, volume = {Fasc. 1}, journal = {e-Forschungsberichte des Deutschen Arch{\"a}ologischen Instituts. Berlin: Deutsches Arch{\"a}ologisches Institut, Zentrale.}, doi = {https://doi.org/10.34780/d469-84h2}, language = {de} } @masterthesis{Chemnitz, type = {Bachelor Thesis}, author = {Chemnitz, Robin}, title = {Spectral Coarse-Graining of SIS Dynamics on Networks}, language = {en} } @article{SchuetteKlusHartmann, author = {Sch{\"u}tte, Christof and Klus, Stefan and Hartmann, Carsten}, title = {Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning}, series = {Acta Numerica}, volume = {32}, journal = {Acta Numerica}, doi = {10.1017/S0962492923000016}, pages = {517 -- 673}, abstract = {One of the main challenges in molecular dynamics is overcoming the 'timescale barrier': in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based techniques that have emerged from dynamical systems theory, numerical mathematics and machine learning over the last two decades. We will focus on how transfer operators can be used to approximate the dynamical behaviour on long timescales, review the introduction of this approach into molecular dynamics, and outline the respective theory, as well as the algorithmic development, from the early numerics-based methods, via variational reformulations, to modern data-based techniques utilizing and improving concepts from machine learning. Furthermore, its relation to rare event simulation techniques will be explained, revealing a broad equivalence of variational principles for long-time quantities in molecular dynamics. The article will mainly take a mathematical perspective and will leave the application to real-world molecular systems to the more than 1000 research articles already written on this subject.}, language = {en} } @phdthesis{Tillmann, author = {Tillmann, Peter}, title = {Optimizing bifacial tandem solar cells for realistic operation conditions}, doi = {10.17169/refubium-39571}, language = {en} } @article{DonatiHartmannKeller, author = {Donati, Luca and Hartmann, Carsten and Keller, Bettina G.}, title = {Girsanov reweighting for path ensembles and Markov state models}, series = {The Journal of Chemical Physics}, volume = {146}, journal = {The Journal of Chemical Physics}, number = {24}, doi = {10.1063/1.4989474}, pages = {244112}, abstract = {The sensitivity of molecular dynamics on changes in the potential energy function plays an important role in understanding the dynamics and function of complex molecules. We present a method to obtain path ensemble averages of a perturbed dynamics from a set of paths generated by a reference dynamics. It is based on the concept of path probability measure and the Girsanov theorem, a result from stochastic analysis to estimate a change of measure of a path ensemble. Since Markov state models (MSMs) of the molecular dynamics can be formulated as a combined phase-space and path ensemble average, the method can be extended to reweight MSMs by combining it with a reweighting of the Boltzmann distribution. We demonstrate how to efficiently implement the Girsanov reweighting in a molecular dynamics simulation program by calculating parts of the reweighting factor "on the fly" during the simulation, and we benchmark the method on test systems ranging from a two-dimensional diffusion process and an artificial many-body system to alanine dipeptide and valine dipeptide in implicit and explicit water. The method can be used to study the sensitivity of molecular dynamics on external perturbations as well as to reweight trajectories generated by enhanced sampling schemes to the original dynamics.}, language = {en} } @article{BoegeFritzeGoergenetal., author = {Boege, Tobias and Fritze, Ren{\´e} and G{\"o}rgen, Christiane and Hanselmann, Jeroen and Iglezakis, Dorothea and Kastner, Lars and Koprucki, Thomas and Krause, Tabea and Lehrenfeld, Christoph and Polla, Silvia and Reidelbach, Marco and Riedel, Christian and Saak, Jens and Schembera, Bj{\"o}rn and Tabelow, Karsten and Weber, Marcus}, title = {Research-Data Management Planning in the German Mathematical Community}, series = {Eur. Math. Soc. Mag.}, volume = {130}, journal = {Eur. Math. Soc. Mag.}, doi = {10.4171/mag/152}, pages = {40 -- 47}, abstract = {In this paper we discuss the notion of research data for the field of mathematics and report on the status quo of research-data management and planning. A number of decentralized approaches are presented and compared to needs and challenges faced in three use cases from different mathematical subdisciplines. We highlight the importance of tailoring research-data management plans to mathematicians' research processes and discuss their usage all along the data life cycle.}, language = {en} } @phdthesis{Zonker, author = {Zonker, Johannes}, title = {Coarse Graining of Agent-Based Models and Spatio-Temporal Modeling of Spreading Processes}, language = {en} } @article{BeronVeraOlascoagaHelfmannetal., author = {Beron-Vera, Francisco Javier and Olascoaga, Maria Josefina and Helfmann, Luzie and Miron, Philippe}, title = {Sampling-Dependent Transition Paths of Iceland-Scotland Overflow Water}, series = {Journal of Physical Oceanography}, volume = {53}, journal = {Journal of Physical Oceanography}, number = {4}, doi = {10.1175/JPO-D-22-0172.1}, pages = {1151 -- 1160}, abstract = {In this note, we apply Transition Path Theory (TPT) from Markov chains to shed light on the problem of Iceland-Scotland Overflow Water (ISOW) equatorward export. A recent analysis of observed trajectories of submerged floats demanded revision of the traditional abyssal circulation theory, which postulates that ISOW should steadily flow along a deep boundary current (DBC) around the subpolar North Atlantic prior to exiting it. The TPT analyses carried out here allow to focus the attention on the portions of flow from the origin of ISOW to the region where ISOW exits the subpolar North Atlantic and suggest that insufficient sampling may be biasing the aforementioned demand. The analyses, appropriately adapted to represent a continuous input of ISOW, are carried out on three time-homogeneous Markov chains modeling the ISOW flow. One is constructed using a high number of simulated trajectories homogeneously covering the flow domain. The other two use much fewer trajectories which heterogeneously cover the domain. The trajectories in the latter two chains are observed trajectories or simulated trajectories subsampled at the observed frequency. While the densely sampled chain supports a well-defined DBC, the more heterogeneously sampled chains do not, irrespective of whether observed or simulated trajectories are used. Studying the sampling sensitivity of the Markov chains, we can give recommendations for enlarging the existing float dataset to improve the significance of conclusions about time-asymptotic aspects of the ISOW circulation.}, language = {en} } @inproceedings{SekuliĉSchneiderAntonetal., author = {Sekuliĉ, Ivan and Schneider, Philipp-Immanuel and Anton, Oliver and Da Ros, Elisa and Henderson, Victoria and Krutzik, Markus}, title = {Efficient machine-learning approach to optimize trapped cold atom ensembles for quantum memory applications}, series = {Proc. SPIE}, volume = {12740}, booktitle = {Proc. SPIE}, doi = {10.1117/12.2684406}, pages = {127400F}, language = {en} } @inproceedings{SchneiderZschiedrichHammerschmidtetal., author = {Schneider, Philipp-Immanuel and Zschiedrich, Lin and Hammerschmidt, Martin and Kuen, Lilli and Sekuliĉ, Ivan and Kluge, Julien and Leykauf, Bastian and Krutzik, Markus and Burger, Sven}, title = {Boosting quantum optics experiments with Bayesian optimization}, series = {Proc. SPIE}, volume = {12227}, booktitle = {Proc. SPIE}, doi = {10.1117/12.2632419}, pages = {122270F}, language = {en} } @misc{ColomMikheevaAchourietal., author = {Colom, R{\´e}mi and Mikheeva, Elena and Achouri, Karim and Zuniga-Perez, Jesus and Bonod, Nicolas and Martin, Olivier J.F. and Burger, Sven and Genevet, Patrice}, title = {Crossing of the Branch Cut: The Topological Origin of a Universal 2π-Phase Retardation in Non-Hermitian Metasurfaces (Laser Photonics Rev. 17(6)/2023)}, series = {Laser Photonics Rev.}, volume = {17}, journal = {Laser Photonics Rev.}, doi = {10.1002/lpor.202370029}, pages = {2370029}, language = {en} } @phdthesis{Binkowski, author = {Binkowski, Felix}, title = {Riesz-projection-based methods for the numerical simulation of resonance phenomena in nanophotonics}, doi = {10.17169/refubium-41230}, language = {en} } @inproceedings{JaegerBerwigKurpiersetal., author = {J{\"a}ger, Klaus and Berwig, Sebastian and Kurpiers, Jona and Yang, Fengjiu and Tockhorn, Philipp and Albrecht, Steve and Becker, Christiane}, title = {Optical Simulations of Perovskite/Perovskite Tandem Solar Cells}, series = {Integrated Photonics Research, Silicon and Nanophotonics}, booktitle = {Integrated Photonics Research, Silicon and Nanophotonics}, doi = {10.1364/IPRSN.2023.JM4D.3}, pages = {JM4D.3}, language = {en} } @article{ErnstFalkenhagenWinkelmann, author = {Ernst, Ariane and Falkenhagen, Undine and Winkelmann, Stefanie}, title = {Model reduction for calcium-induced vesicle fusion dynamics}, series = {Proceedings in Applied Mathematics \& Mechanics}, volume = {23}, journal = {Proceedings in Applied Mathematics \& Mechanics}, number = {4}, doi = {10.1002/pamm.202300184}, abstract = {In this work, we adapt an established model for the Ca2+-induced fusion dynamics of synaptic vesicles and employ a lumping method to reduce its complexity. In the reduced system, sequential Ca2+-binding steps are merged to a single releasable state, while keeping the important dependence of the reaction rates on the local Ca2+ concentration. We examine the feasibility of this model reduction for a representative stimulus train over the physiologically relevant site-channel distances. Our findings show that the approximation error is generally small and exhibits an interesting nonlinear and non-monotonic behavior where it vanishes for very low distances and is insignificant at intermediary distances. Furthermore, we give expressions for the reduced model's reaction rates and suggest that our approach may be used to directly compute effective fusion rates for assessing the validity of a fusion model, thereby circumventing expensive simulations.}, language = {en} } @misc{BorndoerferDaneckerWeiser, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-91309}, abstract = {The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition.}, language = {en} } @misc{BetzBinkowskiBurgeretal., author = {Betz, Fridtjof and Binkowski, Felix and Burger, Sven and Kuen, Lilli}, title = {RPExpand (Version 2.0)}, series = {Zenodo}, journal = {Zenodo}, doi = {10.5281/zenodo.10371002}, pages = {doi: 10.5281/zenodo.10371002}, language = {en} } @misc{BetzBinkowskiBurger, author = {Betz, Fridtjof and Binkowski, Felix and Burger, Sven}, title = {RPExpand (Version 1)}, series = {Zenodo}, journal = {Zenodo}, doi = {10.5281/zenodo.7840116}, pages = {doi: 10.5281/zenodo.7840116}, language = {en} } @article{BirkRaharinirinaFackeldeyetal., author = {Birk, Ralph and Raharinirina, N. Alexia and Fackeldey, Konstantin and Richter, Tonio Sebastian and Weber, Marcus}, title = {Inferring cultural and social processes based on patterns of statistical relationships between Synodal texts}, abstract = {In this paper, we explore the relationship patterns between Ancient Egyptian texts of the corpus ``Synodal decrees'', which are originating between 243 and 185 BCE, during the Ptolemaic period. Particularly, we are interested in analyzing the grammatical features of the different texts. Conventional data analysis methods such as correspondence Analysis are very useful to explore the patterns of statistical interdependence between categories of variables. However, it is based on a PCA-like dimension-reduction method and turned out to be unsuitable for our dataset due to the high dimensionality of our data representations. Additionally, the similarity between pairs of texts and pairs of grammatical features is observed through the distance between their representation, but the degree of association between a particular grammatical feature and a text is not. Here, we applied a qualitative Euclidean embedding method that provides a new Euclidean representation of the categories of variables. This new representation of the categories is constructed in such a way that all the patterns of statistical interdependence, similarity, and association, are seen through the Euclidean distance between them. Nevertheless, the PCA-like dimension-reduction method also performed poorly on our new representation. Therefore, we obtained a two-dimensional visualization using non-linear methods such UMAP or t-SNE. Although these dimension-reduction methods reduced the interpretability of interpoint distances, we were still able to identify important similarity patterns between the Synodal text as well as their association patterns with the grammatical features.}, language = {en} } @article{UllrichWeiserSubramaniametal., author = {Ullrich, Julia and Weiser, Martin and Subramaniam, Jayant and Schenkl, Sebastian and Muggenthaler, Holger and Hubig, Michael and Mall, Gita}, title = {The impact of anatomy variation on temperature based time of death estimation}, series = {International Journal of Legal Medicine}, volume = {137}, journal = {International Journal of Legal Medicine}, doi = {10.1007/s00414-023-03026-w}, pages = {1615 -- 1627}, abstract = {Temperature-based time of death estimation (TTDE) using simulation methods such as the finite element (FE) method promises higher accuracy and broader applicability in nonstandard cooling scenarios than established phenomenological methods. Their accuracy depends crucially on the simulation model to capture the actual situation. The model fidelity in turn hinges on the representation of the corpse's anatomy in form of computational meshes as well as on the thermodynamic parameters. While inaccuracies in anatomy representation due to coarse mesh resolution are known to have a minor impact on the estimated time of death, the sensitivity with respect to larger differences in the anatomy has so far not been studied. We assess this sensitivity by comparing four independently generated and vastly different anatomical models in terms of the estimated time of death in an identical cooling scenario. In order to isolate the impact of shape variation, the models are scaled to a reference size, and the possible impact of measurement location variation is excluded explicitly, which gives a lower bound on the impact of anatomy on the estimated time of death.}, language = {en} } @article{DonatiWeber, author = {Donati, Luca and Weber, Marcus}, title = {Efficient Estimation of Transition Rates as Functions of pH}, series = {Proceedings in Applied Mathematics \& Mechanics}, volume = {23}, journal = {Proceedings in Applied Mathematics \& Mechanics}, doi = {10.1002/pamm.202300264}, abstract = {Extracting the kinetic properties of a system whose dynamics depend on the pH of the environment with which it exchanges energy and atoms requires sampling the Grand Canonical Ensemble. As an alternative, we present a novel strategy that requires simulating only the most recurrent Canonical Ensembles that compose the Grand Canonical Ensemble. The simulations are used to estimate the Gran Canonical distribution for a specific pH value by reweighting and to construct the transition rate matrix by discretizing the Fokker-Planck equation by Square Root Approximation and robust Perron Cluster Cluster Analysis. As an application, we have studied the tripeptide Ala-Asp-Ala.}, language = {en} } @article{OehmeMoewisBoethetal., author = {Oehme, Stephan and Moewis, Philippe and Boeth, Heide and Bartek, Benjamin and Lippert, Annika and von Tycowicz, Christoph and Ehrig, Rainald and Duda, Georg and Jung, Tobias}, title = {PCL insufficient patients with increased translational and rotational passive knee joint laxity have no increased range of anterior-posterior and rotational tibiofemoral motion during level walking}, series = {Scientific Reports}, volume = {12}, journal = {Scientific Reports}, number = {1}, doi = {10.1038/s41598-022-17328-3}, pages = {1 -- 11}, language = {en} } @inproceedings{CheginiFroehlyHuynhetal., author = {Chegini, Fatemeh and Froehly, Algiane and Huynh, Ngoc Mai Monica and Pavarino, Luca and Potse, Mark and Scacchi, Simone and Weiser, Martin}, title = {Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution}, series = {10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023}, booktitle = {10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023}, doi = {10.23967/c.coupled.2023.004}, abstract = {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.}, language = {en} } @article{LueckeHeitzigKoltaietal., author = {L{\"u}cke, Marvin and Heitzig, Jobst and Koltai, P{\´e}ter and Molkethin, Nora and Winkelmann, Stefanie}, title = {Large population limits of Markov processes on random networks}, series = {Stochastic Processes and their Applications}, volume = {166}, journal = {Stochastic Processes and their Applications}, doi = {10.1016/j.spa.2023.09.007}, abstract = {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-R{\´e}nyi 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.}, language = {en} } @inproceedings{SteyerCheginiStaryetal., author = {Steyer, Joshua and Chegini, Fatemeh and Star{\´y}, Tomas and Potse, Mark and Weiser, Martin and Loewe, Axel}, title = {Electrograms in a Cardiac Cell-by-Cell Model}, abstract = {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.}, language = {en} } @article{ErnstUngerSchuetteetal., author = {Ernst, Ariane and Unger, Nathalie and Sch{\"u}tte, Christof and Walter, Alexander and Winkelmann, Stefanie}, title = {Rate-limiting recovery processes in neurotransmission under sustained stimulation}, series = {Mathematical Biosciences}, volume = {362}, journal = {Mathematical Biosciences}, doi = {10.1016/j.mbs.2023.109023}, abstract = {At chemical synapses, an arriving electric signal induces the fusion of vesicles with the presynaptic membrane, thereby releasing neurotransmitters into the synaptic cleft. After a fusion event, both the release site and the vesicle undergo a recovery process before becoming available for reuse again. Of central interest is the question which of the two restoration steps acts as the limiting factor during neurotrans-mission under high-frequency sustained stimulation. In order to investigate this question, we introduce a novel non-linear reaction network which involves explicit recovery steps for both the vesicles and the release sites, and includes the induced time-dependent output current. The associated reaction dynamics are formulated by means of ordinary differential equations (ODEs), as well as via the associated stochastic jump process. While the stochastic jump model describes a single release site, the average over many release sites is close to the ODE solution and shares its periodic structure. The reason for this can be traced back to the insight that recovery dynamics of vesicles and release sites are statistically almost independent. A sensitivity analysis on the recovery rates based on the ODE formulation reveals that neither the vesicle nor the release site recovery step can be identified as the essential rate-limiting step but that the rate- limiting feature changes over the course of stimulation. Under sustained stimulation the dynamics given by the ODEs exhibit transient dynamics leading from an initial depression of the postsynaptic response to an asymptotic periodic orbit, while the individual trajectories of the stochastic jump model lack the oscillatory behavior an asymptotic periodicity of the ODE-solution.}, language = {de} } @article{StraubeWinkelmannHoefling, author = {Straube, Arthur and Winkelmann, Stefanie and H{\"o}fling, Felix}, title = {Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles}, series = {The Journal of Physical Chemistry B}, volume = {127}, journal = {The Journal of Physical Chemistry B}, number = {13}, doi = {10.1021/acs.jpcb.2c09092}, pages = {2955 -- 2967}, abstract = {This theoretical study concerns a pH oscillator based on the urea-urease reaction confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyse the structure of the phase flow and of the limit cycle, which controls the dynamics for giant vesicles and dominates the pronouncedly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, which are amenable to analytic treatments that are complemented by numerical solutions, and obtain the period and amplitude of the oscillations as well as the parameter domain, where oscillatory behavior persists. We show that the accuracy of these predictions is highly sensitive to the employed reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The faithful modeling of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms.}, language = {en} } @article{MontefuscoSchuetteWinkelmann2023, author = {Montefusco, Alberto and Sch{\"u}tte, Christof and Winkelmann, Stefanie}, title = {A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures}, series = {SIAM Journal on Applied Mathematics}, volume = {83}, journal = {SIAM Journal on Applied Mathematics}, number = {2}, doi = {10.1137/22M1488831}, pages = {837 -- 861}, year = {2023}, abstract = {The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit of an infinitely large population, may be described by means of reaction-diffusion partial differential equations. Analyzing and understanding the relation between different mathematical models for reaction-diffusion dynamics is a research topic of steady interest. In this work, we explore a route to the hydrodynamic limit of the RDME which uses gradient structures. Specifically, we elaborate on a method introduced in [J. Maas and A. Mielke, J. Stat. Phys., 181 (2020), pp. 2257-2303] in the context of well-mixed reaction networks by showing that, once it is complemented with an appropriate limit procedure, it can be applied to spatially extended systems with diffusion. Under the assumption of detailed balance, we write down a gradient structure for the RDME and use the method in order to produce a gradient structure for its hydrodynamic limit, namely, for the corresponding RDPDE.}, language = {en} } @article{LueckeLuQuevedo, author = {L{\"u}cke, Marvin and Lu, Jingyi and Quevedo, Daniel E.}, title = {Coding for secrecy in remote state estimation with an adversary}, series = {IEEE Transactions on Automatic Control}, volume = {67}, journal = {IEEE Transactions on Automatic Control}, number = {9}, doi = {10.1109/TAC.2022.3169839}, pages = {4955 -- 4962}, abstract = {We study the problem of remote state estimation in the presence of an eavesdropper. A sensor transmits state information over a packet-dropping link to a legitimate user. This information is randomly overheard by an eavesdropper. To reduce information leakage to the eavesdropper, previous studies have shown that by encoding the estimate with the acknowledgments (Acks), perfect secrecy can be achieved. However, this strategy greatly relies on the accuracy of the Acks and may easily fail if the Acks are compromised by cyberattacks. In this article, we tackle this issue by proposing to switch between sending an encoded state and sending the plain state to stay resilient against fake Acks. Specifically, we assume the Acks to be randomly attacked and derive recursive expressions for the minimum-mean-squared error estimates and error covariance matrices at the legitimate user and at the eavesdropper. Based upon this, we propose a transmission policy that depends on the probability of synchronization. We formulate a partially observable Markov decision process to model the evolution of the synchronization status and derive associated optimal transmission policies. Numerical examples are provided to verify the theoretical results.}, language = {en} } @article{GhysbrechtDonatiKeller, author = {Ghysbrecht, Simon and Donati, Luca and Keller, Bettina G.}, title = {Accuracy of reaction coordinate based rate theories for modelling chemical reactions: insights from the thermal isomerization in retinal}, series = {Submitted to The Journal of Physical Chemistry A}, journal = {Submitted to The Journal of Physical Chemistry A}, abstract = {Modern potential energy surfaces have shifted attention to molecular simulations of chemical reactions. While various methods can estimate rate constants for conformational transitions in molecular dynamics simulations, their applicability to studying chemical reactions remains uncertain due to the high and sharp energy barriers and complex reaction coordinates involved. This study focuses on the thermal cis-trans isomerization in retinal, employing molecular simulations and comparing rate constant estimates based on one-dimensional rate theories with those based on sampling transitions and grid-based models for low-dimensional collective variable spaces. Even though each individual method to estimate the rate passes its quality tests, the rate constant estimates exhibit disparities of up to four orders of magnitude. Rate constant estimates based on one-dimensional reaction coordinates prove challenging to converge, even if the reaction coordinate is optimized. However, consistent estimates of the rate constant are achieved by sampling transitions and by multi-dimensional grid-based models.}, language = {en} } @article{HelfmannConradLorenzSpreenetal., author = {Helfmann, Luzie and Conrad, Natasa Djurdjevac and Lorenz-Spreen, Philipp and Sch{\"u}tte, Christof}, title = {Modelling opinion dynamics under the impact of influencer and media strategies}, series = {Scientific Reports}, volume = {13}, journal = {Scientific Reports}, doi = {10.1038/s41598-023-46187-9}, pages = {19375}, abstract = {Digital communication has made the public discourse considerably more complex, and new actors and strategies have emerged as a result of this seismic shift. Aside from the often-studied interactions among individuals during opinion formation, which have been facilitated on a large scale by social media platforms, the changing role of traditional media and the emerging role of "influencers" are not well understood, and the implications of their engagement strategies arising from the incentive structure of the attention economy even less so. Here we propose a novel opinion dynamics model that accounts for these different roles, namely that media and influencers change their own positions on slower time scales than individuals, while influencers dynamically gain and lose followers. Numerical simulations show the importance of their relative influence in creating qualitatively different opinion formation dynamics: with influencers, fragmented but short-lived clusters emerge, which are then counteracted by more stable media positions. Mean-field approximations by partial differential equations reproduce this dynamic. Based on the mean-field model, we study how strategies of influencers to gain more followers can influence the overall opinion distribution. We show that moving towards extreme positions can be a beneficial strategy for influencers to gain followers. Finally, we demonstrate that optimal control strategies allow other influencers or media to counteract such attempts and prevent further fragmentation of the opinion landscape. Our modelling framework contributes to better understanding the different roles and strategies in the increasingly complex information ecosystem and their impact on public opinion formation.}, language = {en} } @article{BartelsFisikopoulosWeiser, author = {Bartels, Tinko and Fisikopoulos, Vissarion and Weiser, Martin}, title = {Fast Floating-Point Filters for Robust Predicates}, series = {BIT Numerical Mathematics}, volume = {63}, journal = {BIT Numerical Mathematics}, doi = {10.1007/s10543-023-00975-x}, abstract = {Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information systems and computer-aided design. With floating-point arithmetic, these geometric predicates can incur round-off errors that may lead to incorrect results and inconsistencies, causing computations to fail. This issue has been addressed using a combination of exact arithmetic for robustness and floating-point filters to mitigate the computational cost of exact computations. The implementation of exact computations and floating-point filters can be a difficult task, and code generation tools have been proposed to address this. We present a new C++ meta-programming framework for the generation of fast, robust predicates for arbitrary geometric predicates based on polynomial expressions. We combine and extend different approaches to filtering, branch reduction, and overflow avoidance that have previously been proposed. We show examples of how this approach produces correct results for data sets that could lead to incorrect predicate results with naive implementations. Our benchmark results demonstrate that our implementation surpasses state-of-the-art implementations.}, language = {en} } @misc{HelfmannDjurdjevacConradLorenzSpreenetal., author = {Helfmann, Luzie and Djurdjevac Conrad, Natasa and Lorenz-Spreen, Philipp and Sch{\"u}tte, Christof}, title = {Supplementary code for the paper Modelling opinion dynamics under the impact of influencer and media strategies}, doi = {10.12752/9267}, abstract = {This repository contains the Julia code accompanying the paper "Modelling opinion dynamics under the impact of influencer and media strategies", Scientific Reports, Vol.13, p. 19375, 2023.}, language = {en} } @misc{KostreSunkaraSchuetteetal., author = {Kostr{\´e}, Margarita and Sunkara, Vikram and Sch{\"u}tte, Christof and Djurdjevac Conrad, Nataša}, title = {Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-86764}, abstract = {Spreading processes are important drivers of change in social systems. To understand the mechanisms of spreading it is fundamental to have information about the underlying contact network and the dynamical parameters of the process. However, in many real-wold examples, this information is not known and needs to be inferred from data. State-of-the-art spreading inference methods have mostly been applied to modern social systems, as they rely on availability of very detailed data. In this paper we study the inference challenges for historical spreading processes, for which only very fragmented information is available. To cope with this problem, we extend existing network models by formulating a model on a mesoscale with temporal spreading rate. Furthermore, we formulate the respective parameter inference problem for the extended model. We apply our approach to the romanization process of Northern Tunisia, a scarce dataset, and study properties of the inferred time-evolving interregional networks. As a result, we show that (1) optimal solutions consist of very different network structures and spreading rate functions; and that (2) these diverse solutions produce very similar spreading patterns. Finally, we discuss how inferred dominant interregional connections are related to available archaeological traces. Historical networks resulting from our approach can help understanding complex processes of cultural change in ancient times.}, language = {en} } @phdthesis{Chewle, author = {Chewle, Surahit}, title = {Probing effects of organic solvents on paracetamol crystallization using in silico and orthogonal in situ methods}, abstract = {Polymorphism is the property exhibited by many inorganic and organic molecules to crystallize in more than one crystal structure. There is a strong need for understanding the influencing factors on polymorphism, as it is responsible for differences in many physicochemical properties such as stability and solubility. Nearly 80 \% of marketed drugs exhibit polymorphism. In this work, we took the model system of paracetamol to investigate the influence of solvent choice on its polymorphism. Different methods were developed and employed to understand the influence of small organic solvents on the crystallization of paracetamol. Non-equilibrium molecular dynamics simulations with periodic simulated annealing were used as a tool to probe the nature of precursors of the metastable intermediates occurring in the crystallization process. Using this method, it was found that the structures of the building blocks of crystals of paracetamol is governed by solvent-solute interactions. In situ Raman spectroscopy was used with a custom-made acoustic levitator to follow crystallization. This set-up is a reliable method for investigating solvent influence, attenuating heterogeneous nucleation and stabilizing other environmental factors. It was established that as a solvent, ethanol is much stronger than methanol in its effect of driving paracetamol solutions to their crystal form. The time-resolved Raman spectroscopy crystallization data was processed using a newly developed objective function based non-negative matrix factorization method (NMF). An orthogonal time-lapse photography was used in conjunction with NMF to get unique and accurate factors that pertain to the spectra and concentrations of different moieties of paracetamol crystallization existing as latent components in the untreated data.}, language = {en} } @article{KostreSunkaraSchuetteetal.2022, author = {Kostr{\´e}, Margarita and Sunkara, Vikram and Sch{\"u}tte, Christof and Djurdjevac Conrad, Natasa}, title = {Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia}, series = {Applied Network Science}, volume = {7}, journal = {Applied Network Science}, publisher = {Springer Nature}, doi = {10.1007/s41109-022-00492-w}, pages = {18}, year = {2022}, abstract = {Spreading processes are important drivers of change in social systems. To understand the mechanisms of spreading it is fundamental to have information about the underlying contact network and the dynamical parameters of the process. However, in many real-wold examples, this information is not known and needs to be inferred from data. State-of-the-art spreading inference methods have mostly been applied to modern social systems, as they rely on availability of very detailed data. In this paper we study the inference challenges for historical spreading processes, for which only very fragmented information is available. To cope with this problem, we extend existing network models by formulating a model on a mesoscale with temporal spreading rate. Furthermore, we formulate the respective parameter inference problem for the extended model. We apply our approach to the romanization process of Northern Tunisia, a scarce dataset, and study properties of the inferred time-evolving interregional networks. As a result, we show that (1) optimal solutions consist of very different network structures and spreading rate functions; and that (2) these diverse solutions produce very similar spreading patterns. Finally, we discuss how inferred dominant interregional connections are related to available archaeological traces. Historical networks resulting from our approach can help understanding complex processes of cultural change in ancient times.}, language = {en} } @article{DjurdjevacConradKoepplDjurdjevac, author = {Djurdjevac Conrad, Natasa and K{\"o}ppl, Jonas and Djurdjevac, Ana}, title = {Feedback Loops in Opinion Dynamics of Agent-Based Models with Multiplicative Noise}, series = {Entropy}, volume = {24(10)}, journal = {Entropy}, doi = {10.3390/e24101352}, abstract = {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.}, language = {en} } @article{DjurdjevacConradChemnitzKostreetal., author = {Djurdjevac Conrad, Natasa and Chemnitz, Robin and Kostre, Margarita and Schweigart, Fleur and Fless, Friederike and Sch{\"u}tte, Christof and Ducke, Benjamin}, title = {A Mathematical perspective on Romanisation: Modelling the Roman road activation process in ancient Tunisia}, language = {en} } @article{GorgullaNigamKoopetal., author = {Gorgulla, Christoph and Nigam, AkshatKumar and Koop, Matt and Selim {\c{C}}{\i}naroğlu, S{\"u}leyman and Secker, Christopher and Haddadnia, Mohammad and Kumar, Abhishek and Malets, Yehor and Hasson, Alexander and Li, Minkai and Tang, Ming and Levin-Konigsberg, Roni and Radchenko, Dmitry and Kumar, Aditya and Gehev, Minko and Aquilanti, Pierre-Yves and Gabb, Henry and Alhossary, Amr and Wagner, Gerhard and Aspuru-Guzik, Al{\´a}n and Moroz, Yurii S. and Fackeldey, Konstantin and Arthanari, Haribabu}, title = {VirtualFlow 2.0 - The Next Generation Drug Discovery Platform Enabling Adaptive Screens of 69 Billion Molecules}, series = {bioRxiv}, journal = {bioRxiv}, doi = {10.1101/2023.04.25.537981}, language = {en} } @article{FrankSikorskiRoeblitz, author = {Frank, Anna-Simone and Sikorski, Alexander and R{\"o}blitz, Susanna}, title = {Spectral clustering of Markov chain transition matrices with complex eigenvalues}, series = {Journal of Computational and Applied Mathematics}, volume = {444}, journal = {Journal of Computational and Applied Mathematics}, doi = {10.1016/j.cam.2024.115791}, pages = {115791}, abstract = {The Robust Perron Cluster Analysis (PCCA+) has become a popular spectral clustering algorithm for coarse-graining transition matrices of nearly decomposable Markov chains with transition states. Originally developed for reversible Markov chains, the algorithm only worked for transition matrices with real eigenvalues. In this paper, we therefore extend the theoretical framework of PCCA+ to Markov chains with a complex eigen-decomposition. We show that by replacing a complex conjugate pair of eigenvectors by their real and imaginary components, a real representation of the same subspace is obtained, which is suitable for the cluster analysis. We show that our approach leads to the same results as the generalized PCCA+ (GPCCA), which replaces the complex eigen-decomposition by a conceptually more difficult real Schur decomposition. We apply the method on non-reversible Markov chains, including circular chains, and demonstrate its efficiency compared to GPCCA. The experiments are performed in the Matlab programming language and codes are provided.}, language = {de} } @article{ZhangSchuette, author = {Zhang, Wei and Sch{\"u}tte, Christof}, title = {Understanding recent deep-learning techniques for identifying collective variables of molecular dynamics}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {23}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {4}, doi = {10.1002/pamm.202300189}, abstract = {High-dimensional metastable molecular dynamics (MD) can often be characterised by a few features of the system, that is, collective variables (CVs). Thanks to the rapid advance in the area of machine learning and deep learning, various deep learning-based CV identification techniques have been developed in recent years, allowing accurate modelling and efficient simulation of complex molecular systems. In this paper, we look at two different categories of deep learning-based approaches for finding CVs, either by computing leading eigenfunctions of transfer operator associated to the underlying dynamics, or by learning an autoencoder via minimisation of reconstruction error. We present a concise overview of the mathematics behind these two approaches and conduct a comparative numerical study of these two approaches on illustrative examples.}, language = {en} } @article{RaySunkaraSchuetteetal.2020, author = {Ray, Sourav and Sunkara, Vikram and Sch{\"u}tte, Christof and Weber, Marcus}, title = {How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs}, series = {Molecular Simulation}, volume = {46}, journal = {Molecular Simulation}, number = {18}, publisher = {Taylor and Francis}, doi = {10.1080/08927022.2020.1839660}, pages = {1443 -- 1452}, year = {2020}, abstract = {Molecular simulations of ligand-receptor interactions are a computational challenge, especially when their association- ('on'-rate) and dissociation- ('off'-rate) mechanisms are working on vastly differing timescales. One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)-N-phenyl propionamide (NFEPP) in a μ-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab.}, language = {en} } @article{RayFackeldeySteinetal., author = {Ray, Sourav and Fackeldey, Konstantin and Stein, Christoph and Weber, Marcus}, title = {Coarse Grained MD Simulations of Opioid interactions with the µ-opioid receptor and the surrounding lipid membrane}, series = {Biophysica}, volume = {3}, journal = {Biophysica}, number = {2}, doi = {10.3390/biophysica3020017}, pages = {263 -- 275}, abstract = {In our previous studies, a new opioid (NFEPP) was developed to only selectively bind to the 𝜇-opoid receptor (MOR) in inflamed tissue and thus avoid the severe side effects of fentanyl. We know that NFEPP has a reduced binding affinity to MOR in healthy tissue. Inspired by the modelling and simulations performed by Sutcliffe et al., we present our own results of coarse-grained molecular dynamics simulations of fentanyl and NFEPP with regards to their interaction with the 𝜇-opioid receptor embedded within the lipid cell membrane. For technical reasons, we have slightly modified Sutcliffe's parametrisation of opioids. The pH-dependent opioid simulations are of interest because while fentanyl is protonated at the physiological pH, NFEPP is deprotonated due to its lower pKa value than that of fentanyl. Here, we analyse for the first time whether pH changes have an effect on the dynamical behaviour of NFEPP when it is inside the cell membrane. Besides these changes, our analysis shows a possible alternative interaction of NFEPP at pH 7.4 outside the binding region of the MOR. The interaction potential of NFEPP with MOR is also depicted by analysing the provided statistical molecular dynamics simulations with the aid of an eigenvector analysis of a transition rate matrix. In our modelling, we see differences in the XY-diffusion profiles of NFEPP compared with fentanyl in the cell membrane.}, language = {en} } @article{RabbenRayWeber, author = {Rabben, Robert Julian and Ray, Sourav and Weber, Marcus}, title = {ISOKANN: Invariant subspaces of Koopman operators learned by a neural network}, series = {The Journal of Chemical Physics}, volume = {153}, journal = {The Journal of Chemical Physics}, number = {11}, doi = {10.1063/5.0015132}, pages = {114109}, abstract = {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.}, language = {en} } @misc{RayThiesSunkaraetal., author = {Ray, Sourav and Thies, Arne and Sunkara, Vikram and Wulkow, Hanna and Celik, {\"O}zg{\"u}r and Yerg{\"o}z, Fatih and Sch{\"u}tte, Christof and Stein, Christoph and Weber, Marcus and Winkelmann, Stefanie}, title = {Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-82797}, abstract = {Initiated by mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands in normal versus diseased (inflamed) environments, we previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. Uniquely, this design recognised that GPCRs function differently under pathological versus healthy conditions. We now present a novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels associated with parameters of inflamed tissue (pH, radicals). By means of molecular dynamics simulations, we also assessed qualitative changes of the reaction rates due to additional disulfide bridges inside the GPCR binding pocket and used these rates for stochastic simulations of the corresponding reaction jump process. The modelling results were validated with in vitro experiments measuring calcium currents and G-protein activation. We found markedly reduced G-protein dissociation and calcium channel inhibition induced by NFEPP at normal pH, and enhanced constitutive G-protein activation but lower probability of ligand binding with increasing radical concentrations. These results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.}, language = {en} } @misc{RaySunkaraSchuetteetal., author = {Ray, Sourav and Sunkara, Vikram and Sch{\"u}tte, Christof and Weber, Marcus}, title = {How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs}, issn = {1438-0064}, doi = {10.1080/08927022.2020.1839660}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78437}, abstract = {Molecular simulations of ligand-receptor interactions are a computational challenge, especially when their association- (``on''-rate) and dissociation- (``off''-rate) mechanisms are working on vastly differing timescales. In addition, the timescale of the simulations themselves is, in practice, orders of magnitudes smaller than that of the mechanisms; which further adds to the complexity of observing these mechanisms, and of drawing meaningful and significant biological insights from the simulation. One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)- N-phenyl propionamide (NFEPP) in a \$\mu\$-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab, who investigated the influence of pH on the inhibitory constant of fentanyl and NFEPP (Spahn et al. 2017). MD simulations are far more accessible and cost-effective than in vitro and in vivo studies. Especially in the context of the current opioid crisis, MD simulations can aid in unravelling molecular functionality and assist in clinical decision-making; the approaches presented in this paper are a pertinent step forward in this direction.}, language = {en} } @article{PrasadTiwariRayetal., author = {Prasad, Anup K. and Tiwari, Chandni and Ray, Sourav and Holden, Stephanie and Armstrong, David A. and Rosengren, K. Johan and Rodger, Alison and Panwar, Ajay S. and Martin, Lisandra L.}, title = {Secondary Structure Transitions for a Family of Amyloidogenic, Antimircobial Uperin 3 Peptides in Contact with Sodium Dodecyl Sulfate}, series = {ChemPlusChem}, volume = {87}, journal = {ChemPlusChem}, doi = {10.1002/cplu.202100408}, pages = {e202100408}, language = {en} } @misc{PlockBinkowskiZschiedrichetal., author = {Plock, Matthias and Binkowski, Felix and Zschiedrich, Lin and Schneider, Phillip-Immanuel and Burger, Sven}, title = {Research data for "Fabrication uncertainty guided design optimization of a photonic crystal cavity by using Gaussian processes"}, series = {Zenodo}, journal = {Zenodo}, doi = {10.5281/zenodo.8131611}, pages = {doi: 10.5281/zenodo.8131611}, language = {en} } @misc{MusialSekSchneideretal., author = {Musial, Anna and Sek, Grzegorz and Schneider, Philipp-Immanuel and Reitzenstein, Stephan}, title = {Fiber-coupled solid-state-based single-photon sources}, series = {Specialty Optical Fibers}, journal = {Specialty Optical Fibers}, publisher = {Woodhead Publishing}, doi = {10.1016/B978-0-443-18495-6.00004-4}, pages = {345 -- 384}, language = {de} } @misc{BinkowskiKulligBetzetal., author = {Binkowski, Felix and Kullig, Julius and Betz, Fridtjof and Zschiedrich, Lin and Walther, Andrea and Wiersig, Jan and Burger, Sven}, title = {Source code and simulation results: Computing eigenfrequency sensitivities near exceptional points}, series = {Zenodo}, journal = {Zenodo}, doi = {10.5281/zenodo.10715639}, pages = {doi: 10.5281/zenodo.10715639}, language = {en} } @article{CerecedaLopezOstinatoOrtizAmbrizetal., author = {Cereceda-L{\´o}pez, Eric and Ostinato, Mattia and Ortiz-Ambriz, Antonio and Straube, Arthur and Palassini, Matteo and Tierno, Pietro}, title = {Excluded volume induces buckling in optically driven colloidal rings}, series = {Phys. Rev. Research}, volume = {6}, journal = {Phys. Rev. Research}, doi = {10.1103/PhysRevResearch.6.L012044}, pages = {L012044}, abstract = {In our combined experimental, theoretical and numerical work, we study the out of equilibrium deformations in a shrinking ring of optically trapped, interacting colloidal particles. Steerable optical tweezers are used to confine dielectric microparticles along a circle of discrete harmonic potential wells, and to reduce the ring radius at a controlled quench speed. We show that excluded-volume interactions are enough to induce particle sliding from their equilibrium positions and nonequilibrium zigzag roughening of the colloidal structure. Our work unveils the underlying mechanism of interfacial deformation in radially driven microscopic discrete rings.}, language = {en} } @article{DellnitzHuellermeierLueckeetal., author = {Dellnitz, Michael and H{\"u}llermeier, Eyke and L{\"u}cke, Marvin and Ober-Bl{\"o}baum, Sina and Offen, Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, title = {Efficient Time-Stepping for Numerical Integration Using Reinforcement Learning}, series = {SIAM Journal on Scientific Computing}, volume = {45}, journal = {SIAM Journal on Scientific Computing}, number = {2}, doi = {10.1137/21M1412682}, pages = {A579 -- A595}, language = {en} } @article{NiemannWinkelmannWolfetal., author = {Niemann, Jan-Hendrik and Winkelmann, Stefanie and Wolf, Sarah and Sch{\"u}tte, Christof}, title = {Agent-based modeling: Population limits and large timescales}, series = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, volume = {31}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, number = {3}, issn = {1438-0064}, doi = {10.1063/5.0031373}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-77309}, abstract = {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.}, language = {en} } @article{NiemannKlusSchuette, author = {Niemann, Jan-Hendrik and Klus, Stefan and Sch{\"u}tte, Christof}, title = {Data-driven model reduction of agent-based systems using the Koopman generator}, series = {PLOS ONE}, volume = {16}, journal = {PLOS ONE}, number = {5}, doi = {10.1371/journal.pone.0250970}, abstract = {The dynamical behavior of social systems can be described by agent-based models. Although single agents follow easily explainable rules, complex time-evolving patterns emerge due to their interaction. The simulation and analysis of such agent-based models, however, is often prohibitively time-consuming if the number of agents is large. In this paper, we show how Koopman operator theory can be used to derive reduced models of agent-based systems using only simulation or real-world data. Our goal is to learn coarse-grained models and to represent the reduced dynamics by ordinary or stochastic differential equations. The new variables are, for instance, aggregated state variables of the agent-based model, modeling the collective behavior of larger groups or the entire population. Using benchmark problems with known coarse-grained models, we demonstrate that the obtained reduced systems are in good agreement with the analytical results, provided that the numbers of agents is sufficiently large.}, language = {en} } @misc{NiemannSchuetteKlus, author = {Niemann, Jan-Hendrik and Sch{\"u}tte, Christof and Klus, Stefan}, title = {Simulation data: Data-driven model reduction of agent-based systems using the Koopman generator}, series = {PLOS ONE}, volume = {16}, journal = {PLOS ONE}, number = {5}, doi = {http://doi.org/10.5281/zenodo.4522119}, language = {en} } @article{KlusNueskePeitzetal., 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}, series = {Physica D: Nonlinear Phenomena}, volume = {406}, journal = {Physica D: Nonlinear Phenomena}, doi = {10.1016/j.physd.2020.132416}, language = {en} } @phdthesis{Niemann, author = {Niemann, Jan-Hendrik}, title = {Learning Reduced Models for Large-Scale Agent-Based Systems}, doi = {10.17169/refubium-35245}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-refubium-35530-6}, pages = {130}, abstract = {Modeling social systems and studying their dynamical behavior plays an important role in many fields of research. Agent-based modeling provides a high degree of detail into artificial societies by describing the model from the perspective of the agents. The interactions of agents, often characterized by simple rules, lead to complex, time-evolving patterns. Their understanding is of great importance, e.g., for predicting and influencing epidemics. Analysis and simulation, however, often becomes prohibitively time-consuming when the number of agents or the time scale of interest is large. Therefore, this thesis is devoted to learn significantly reduced models of large-scale agent-based systems from simulation data. We show how data-driven methods based on transfer operators can be used to find reduced models represented by ordinary or stochastic differential equations that describe the dynamical behavior of larger groups or entire populations and thus enable the analysis and prediction of agent-based systems. To this end, we first present an extension of EDMD (extended dynamic mode decomposition) called gEDMD to approximate the Koopman generator from data. This method can be used to compute eigenfunctions, eigenvalues, and modes of the generator, as well as for system identification and model reduction of both deterministic and non-deterministic dynamical systems. Secondly, we analyze the long-term behavior of certain agent-based models and their pathwise approximations by stochastic differential equations for large numbers of agents using transfer operators. We show that, under certain conditions, the transfer operator approach connects the pathwise approximations on finite time scales with methods for describing the behavior on possibly exponentially long time scales. As a consequence, we can use the finite-time, pathwise approximations to characterize metastable behavior on long time scales using transfer operators. This can significantly reduce the computational cost. The third part addresses the data-driven model reduction since in many cases no analytical limit models are known or existent. We show how the Koopman operator theory can be used to infer the governing equations of agent-based systems directly from simulation data. Using benchmark problems, we demonstrate that for sufficiently large population sizes the data-driven models agree well with analytical limit equations and, moreover, that the reduced models allow predictions even in cases far from the limit or when no limit equations are known. Lastly, we demonstrate the potential of the presented approach. We present an ansatz for the multi-objective optimization of agent-based systems with the help of data-driven surrogate models based on the Koopman generator. In particular, when limit models are unknown or non-existent, this approach makes multi-objective optimization problems solvable that would otherwise be computationally infeasible due to very expensive objective functions.}, language = {en} } @article{NiemannKlusConradetal., author = {Niemann, Jan-Hendrik and Klus, Stefan and Conrad, Natasa Djurdjevac and Sch{\"u}tte, Christof}, title = {Koopman-Based Surrogate Models for Multi-Objective Optimization of Agent-Based Systems}, series = {Physica D: Nonlinear Phenomena}, volume = {460}, journal = {Physica D: Nonlinear Phenomena}, doi = {https://doi.org/10.1016/j.physd.2024.134052}, pages = {134052}, abstract = {Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics of ABMs, the demand to solve optimization problems to support, for example, decision-making processes naturally arises. Most ABMs, however, are non-deterministic, high-dimensional dynamical systems, so objectives defined in terms of their behavior are computationally expensive. In particular, if the number of agents is large, evaluating the objective functions often becomes prohibitively time-consuming. We consider data-driven reduced models based on the Koopman generator to enable the efficient solution of multi-objective optimization problems involving ABMs. In a first step, we show how to obtain data-driven reduced models of non-deterministic dynamical systems (such as ABMs) that depend on potentially nonlinear control inputs. We then use them in the second step as surrogate models to solve multi-objective optimal control problems. We first illustrate our approach using the example of a voter model, where we compute optimal controls to steer the agents to a predetermined majority, and then using the example of an epidemic ABM, where we compute optimal containment strategies in a prototypical situation. We demonstrate that the surrogate models effectively approximate the Pareto-optimal points of the ABM dynamics by comparing the surrogate-based results with test points, where the objectives are evaluated using the ABM. Our results show that when objectives are defined by the dynamic behavior of ABMs, data-driven surrogate models support or even enable the solution of multi-objective optimization problems.}, language = {en} } @misc{SikorskiSechiHelfmann, author = {Sikorski, Alexander and Sechi, Renata and Helfmann, Luzie}, title = {cmdtools}, doi = {https://doi.org/10.5281/zenodo.4749331}, abstract = {Python implementation of severals tools (PCCA, AJC, SQRA, P/Q estimation) for the analysis of dynamical systems from the transfer operator perspective.}, language = {en} } @article{NiemannUramWolfetal., author = {Niemann, Jan-Hendrik and Uram, Samuel and Wolf, Sarah and Conrad, Natasa Djurdjevac and Weiser, Martin}, title = {Multilevel Optimization for Policy Design with Agent-Based Epidemic Models}, series = {Computational Science}, volume = {77}, journal = {Computational Science}, doi = {10.1016/j.jocs.2024.102242}, pages = {102242}, abstract = {Epidemiological models can not only be used to forecast the course of a pandemic like COVID-19, but also to propose and design non-pharmaceutical interventions such as school and work closing. In general, the design of optimal policies leads to nonlinear optimization problems that can be solved by numerical algorithms. Epidemiological models come in different complexities, ranging from systems of simple ordinary differential equations (ODEs) to complex agent-based models (ABMs). The former allow a fast and straightforward optimization, but are limited in accuracy, detail, and parameterization, while the latter can resolve spreading processes in detail, but are extremely expensive to optimize. We consider policy optimization in a prototypical situation modeled as both ODE and ABM, review numerical optimization approaches, and propose a heterogeneous multilevel approach based on combining a fine-resolution ABM and a coarse ODE model. Numerical experiments, in particular with respect to convergence speed, are given for illustrative examples.}, language = {en} } @article{DonatiFackeldeyWeber2023, author = {Donati, Luca and Fackeldey, Konstantin and Weber, Marcus}, title = {Augmented ant colony algorithm for virtual drug discovery}, series = {Journal of Mathematical Chemistry}, volume = {62}, journal = {Journal of Mathematical Chemistry}, doi = {10.1007/s10910-023-01549-6}, pages = {367 -- 385}, year = {2023}, abstract = {Docking is a fundamental problem in computational biology and drug discovery that seeks to predict a ligand's binding mode and affinity to a target protein. However, the large search space size and the complexity of the underlying physical interactions make docking a challenging task. Here, we review a docking method, based on the ant colony optimization algorithm, that ranks a set of candidate ligands by solving a minimization problem for each ligand individually. In addition, we propose an augmented version that takes into account all energy functions collectively, allowing only one minimization problem to be solved. The results show that our modification outperforms in accuracy and efficiency.}, language = {en} } @misc{StraubeWinkelmannHoefling, author = {Straube, Arthur and Winkelmann, Stefanie and H{\"o}fling, Felix}, title = {Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles}, issn = {1438-0064}, doi = {10.12752/8817}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-88179}, abstract = {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.}, language = {en} } @article{MukherjeeKerteszZolnaietal., author = {Mukherjee, Deshabrato and Kert{\´e}sz, Kriszti{\´a}n and Zolnai, Zsolt and Kov{\´a}cs, Zolt{\´a}n and De{\´a}k, Andr{\´a}s and P{\´a}link{\´a}s, Andr{\´a}s and Osv{\´a}th, Zolt{\´a}n and Olasz, D{\´a}niel and Romanenko, Alekszej and Fried, Mikl{\´o}s and Burger, Sven and S{\´a}fr{\´a}n, Gy{\"o}rgy and Petrik, Peter}, title = {Optimized Sensing on Gold Nanoparticles Created by Graded-Layer Magnetron Sputtering and Annealing}, doi = {10.2139/ssrn.4752470}, language = {en} } @article{BinkowskiBetzColometal., author = {Binkowski, Felix and Betz, Fridtjof and Colom, Remi and Genevet, Patrice and Burger, Sven}, title = {Poles and zeros in non-Hermitian systems: Application to photonics}, series = {Phys. Rev. B}, volume = {109}, journal = {Phys. Rev. B}, doi = {10.1103/PhysRevB.109.045414}, pages = {045414}, language = {en} } @article{BetzBinkowskiKuenetal., author = {Betz, Fridtjof and Binkowski, Felix and Kuen, Lilli and Burger, Sven}, title = {Version 2 — RPExpand: Software for Riesz projection expansion of resonance phenomena}, series = {SoftwareX}, volume = {26}, journal = {SoftwareX}, doi = {10.1016/j.softx.2024.101694}, pages = {101694}, language = {en} } @article{SchimunekSeidlElezetal.2023, author = {Schimunek, Johannes and Seidl, Philipp and Elez, Katarina and Hempel, Tim and Le, Tuan and No{\´e}, Frank and Olsson, Simon and Raich, Llu{\´i}s and Winter, Robin and Gokcan, Hatice and Gusev, Filipp and Gutkin, Evgeny M. and Isayev, Olexandr and Kurnikova, Maria G. and Narangoda, Chamali H. and Zubatyuk, Roman and Bosko, Ivan P. and Furs, Konstantin V. and Karpenko, Anna D. and Kornoushenko, Yury V. and Shuldau, Mikita and Yushkevich, Artsemi and Benabderrahmane, Mohammed B. and Bousquet-Melou, Patrick and Bureau, Ronan and Charton, Beatrice and Cirou, Bertrand C. and Gil, G{\´e}rard and Allen, William J. and Sirimulla, Suman and Watowich, Stanley and Antonopoulos, Nick and Epitropakis, Nikolaos and Krasoulis, Agamemnon and Itsikalis, Vassilis and Theodorakis, Stavros and Kozlovskii, Igor and Maliutin, Anton and Medvedev, Alexander and Popov, Petr and Zaretckii, Mark and Eghbal-Zadeh, Hamid and Halmich, Christina and Hochreiter, Sepp and Mayr, Andreas and Ruch, Peter and Widrich, Michael and Berenger, Francois and Kumar, Ashutosh and Yamanishi, Yoshihiro and Zhang, Kam Y. J. and Bengio, Emmanuel and Bengio, Yoshua and Jain, Moksh J. and Korablyov, Maksym and Liu, Cheng-Hao and Marcou, Gilles and Glaab, Enrico and Barnsley, Kelly and Iyengar, Suhasini M. and Ondrechen, Mary Jo and Haupt, V. Joachim and Kaiser, Florian and Schroeder, Michael and Pugliese, Luisa and Albani, Simone and Athanasiou, Christina and Beccari, Andrea and Carloni, Paolo and D'Arrigo, Giulia and Gianquinto, Eleonora and Goßen, Jonas and Hanke, Anton and Joseph, Benjamin P. and Kokh, Daria B. and Kovachka, Sandra and Manelfi, Candida and Mukherjee, Goutam and Mu{\~n}iz-Chicharro, Abraham and Musiani, Francesco and Nunes-Alves, Ariane and Paiardi, Giulia and Rossetti, Giulia and Sadiq, S. Kashif and Spyrakis, Francesca and Talarico, Carmine and Tsengenes, Alexandros and Wade, Rebecca C. and Copeland, Conner and Gaiser, Jeremiah and Olson, Daniel R. and Roy, Amitava and Venkatraman, Vishwesh and Wheeler, Travis J. and Arthanari, Haribabu and Blaschitz, Klara and Cespugli, Marco and Durmaz, Vedat and Fackeldey, Konstantin and Fischer, Patrick D. and Gorgulla, Christoph and Gruber, Christian and Gruber, Karl and Hetmann, Michael and Kinney, Jamie E. and Padmanabha Das, Krishna M. and Pandita, Shreya and Singh, Amit and Steinkellner, Georg and Tesseyre, Guilhem and Wagner, Gerhard and Wang, Zi-Fu and Yust, Ryan J. and Druzhilovskiy, Dmitry S. and Filimonov, Dmitry A. and Pogodin, Pavel V. and Poroikov, Vladimir and Rudik, Anastassia V. and Stolbov, Leonid A. and Veselovsky, Alexander V. and De Rosa, Maria and De Simone, Giada and Gulotta, Maria R. and Lombino, Jessica and Mekni, Nedra and Perricone, Ugo and Casini, Arturo and Embree, Amanda and Gordon, D. Benjamin and Lei, David and Pratt, Katelin and Voigt, Christopher A. and Chen, Kuang-Yu and Jacob, Yves and Krischuns, Tim and Lafaye, Pierre and Zettor, Agn{\`e}s and Rodr{\´i}guez, M. Luis and White, Kris M. and Fearon, Daren and Von Delft, Frank and Walsh, Martin A. and Horvath, Dragos and Brooks III, Charles L. and Falsafi, Babak and Ford, Bryan and Garc{\´i}a-Sastre, Adolfo and Yup Lee, Sang and Naffakh, Nadia and Varnek, Alexandre and Klambauer, G{\"u}nter and Hermans, Thomas M.}, title = {A community effort in SARS-CoV-2 drug discovery}, series = {Molecular Informatics}, volume = {43}, journal = {Molecular Informatics}, number = {1}, doi = {https://doi.org/10.1002/minf.202300262}, pages = {e202300262}, year = {2023}, language = {en} } @article{SikorskiNiknejadWeberetal., author = {Sikorski, Alexander and Niknejad, Amir and Weber, Marcus and Donati, Luca}, title = {Tensor-SqRA: Modeling the transition rates of interacting molecular systems in terms of potential energies}, series = {Journal of Chemical Physics}, volume = {160}, journal = {Journal of Chemical Physics}, doi = {10.1063/5.0187792}, pages = {104112}, abstract = {Estimating the rate of rare conformational changes in molecular systems is one of the goals of molecular dynamics simulations. In the past few decades, a lot of progress has been done in data-based approaches toward this problem. In contrast, model-based methods, such as the Square Root Approximation (SqRA), directly derive these quantities from the potential energy functions. In this article, we demonstrate how the SqRA formalism naturally blends with the tensor structure obtained by coupling multiple systems, resulting in the tensor-based Square Root Approximation (tSqRA). It enables efficient treatment of high-dimensional systems using the SqRA and provides an algebraic expression of the impact of coupling energies between molecular subsystems. Based on the tSqRA, we also develop the projected rate estimation, a hybrid data-model-based algorithm that efficiently estimates the slowest rates for coupled systems. In addition, we investigate the possibility of integrating low-rank approximations within this framework to maximize the potential of the tSqRA.}, language = {en} } @article{SikorskiRiberaBorrellWeber, author = {Sikorski, Alexander and Ribera Borrell, Enric and Weber, Marcus}, title = {Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN}, series = {Journal of Mathematical Physics}, volume = {65}, journal = {Journal of Mathematical Physics}, doi = {10.1063/5.0140764}, pages = {013502}, abstract = {The dominant eigenfunctions of the Koopman operator characterize the metastabilities and slow-timescale dynamics of stochastic diffusion processes. In the context of molecular dynamics and Markov state modeling, they allow for a description of the location and frequencies of rare transitions, which are hard to obtain by direct simulation alone. In this article, we reformulate the eigenproblem in terms of the ISOKANN framework, an iterative algorithm that learns the eigenfunctions by alternating between short burst simulations and a mixture of machine learning and classical numerics, which naturally leads to a proof of convergence. We furthermore show how the intermediate iterates can be used to reduce the sampling variance by importance sampling and optimal control (enhanced sampling), as well as to select locations for further training (adaptive sampling). We demonstrate the usage of our proposed method in experiments, increasing the approximation accuracy by several orders of magnitude.}, language = {en} } @article{OehmeMoewisBoethetal., author = {Oehme, Stephan and Moewis, Philippe and Boeth, Heide and Bartek, Benjamin and von Tycowicz, Christoph and Ehrig, Rainald and Duda, Georg and Jung, Tobias}, title = {Altered knee kinematics after posterior cruciate single-bundle reconstruction - a comprehensive prospective biomechanical in vivo analysis}, series = {Frontiers in Bioengineering and Biotechnology}, volume = {12}, journal = {Frontiers in Bioengineering and Biotechnology}, doi = {10.3389/fbioe.2024.1322136}, language = {en} } @article{ErbanWinkelmann, author = {Erban, Radek and Winkelmann, Stefanie}, title = {Multi-grid reaction-diffusion master equation: applications to morphogen gradient modelling}, abstract = {The multi-grid reaction-diffusion master equation (mgRDME) provides a generalization of stochastic compartment-based reaction-diffusion modelling described by the standard reaction-diffusion master equation (RDME). By enabling different resolutions on lattices for biochemical species with different diffusion constants, the mgRDME approach improves both accuracy and efficiency of compartment-based reaction-diffusion simulations. The mgRDME framework is examined through its application to morphogen gradient formation in stochastic reaction-diffusion scenarios, using both an analytically tractable first-order reaction network and a model with a second-order reaction. The results obtained by the mgRDME modelling are compared with the standard RDME model and with the (more detailed) particle-based Brownian dynamics simulations. The dependence of error and numerical cost on the compartment sizes is defined and investigated through a multi-objective optimization problem.}, language = {en} } @article{AntonHendersonDaRosetal., author = {Anton, Oliver and Henderson, Victoria A. and Da Ros, Elisa and Sekuliĉ, Ivan and Burger, Sven and Schneider, Philipp-Immanuel and Krutzik, Markus}, title = {Review and experimental benchmarking of machine learning algorithms for efficient optimization of cold atom experiments}, series = {Mach. Learn. Sci. Technol.}, volume = {5}, journal = {Mach. Learn. Sci. Technol.}, doi = {10.1088/2632-2153/ad3cb6}, pages = {025022}, language = {en} } @article{BoppPlockTuranetal., author = {Bopp, Julian M. and Plock, Matthias and Turan, Tim and Pieplow, Gregor and Burger, Sven and Schr{\"o}der, Tim}, title = {Sawfish Photonic Crystal Cavity for Near-Unity Emitter-to-Fiber Interfacing in Quantum Network Applications}, series = {Adv. Opt. Mater.}, volume = {12}, journal = {Adv. Opt. Mater.}, doi = {10.1002/adom.202301286}, pages = {2301286}, language = {en} } @article{MuellerMartinezLahuertaSekuliĉetal., author = {M{\"u}ller, Gabriel and Mart{\´i}nez-Lahuerta, V. J. and Sekuliĉ, Ivan and Burger, Sven and Schneider, Philipp-Immanuel and Gaaloul, Naceur}, title = {Bayesian optimization for state engineering of quantum gases}, series = {arXiv}, journal = {arXiv}, pages = {arXiv:2404.18234}, language = {en} } @article{BinkowskiKulligBetzetal., author = {Binkowski, Felix and Kullig, Julius and Betz, Fridtjof and Zschiedrich, Lin and Walther, Andrea and Wiersig, Jan and Burger, Sven}, title = {Computing eigenfrequency sensitivities near exceptional points}, series = {Phys. Rev. Research}, volume = {6}, journal = {Phys. Rev. Research}, doi = {10.1103/PhysRevResearch.6.023148}, pages = {023148}, language = {en} } @article{KlusDjurdjevacConrad, author = {Klus, Stefan and Djurdjevac Conrad, Natasa}, title = {Koopman-based spectral clustering of directed and time-evolving graphs}, series = {Journal of Nonlinear Science}, volume = {33}, journal = {Journal of Nonlinear Science}, doi = {10.1007/s00332-022-09863-0}, pages = {8}, abstract = {While spectral clustering algorithms for undirected graphs are well established and have been successfully applied to unsupervised machine learning problems ranging from image segmentation and genome sequencing to signal processing and social network analysis, clustering directed graphs remains notoriously difficult. Two of the main challenges are that the eigenvalues and eigenvectors of graph Laplacians associated with directed graphs are in general complex-valued and that there is no universally accepted definition of clusters in directed graphs. We first exploit relationships between the graph Laplacian and transfer operators and in particular between clusters in undirected graphs and metastable sets in stochastic dynamical systems and then use a generalization of the notion of metastability to derive clustering algorithms for directed and time-evolving graphs. The resulting clusters can be interpreted as coherent sets, which play an important role in the analysis of transport and mixing processes in fluid flows.}, language = {en} } @inproceedings{KostreSunkaraDjurdjevacConrad, author = {Kostre, Margarita and Sunkara, Vikram and Djurdjevac Conrad, Natasa}, title = {Inference of historical influence networks}, series = {International Conference on Complex Networks \& Their Applications Proceedings}, booktitle = {International Conference on Complex Networks \& Their Applications Proceedings}, edition = {International Conference on Complex Networks \& Their Applications}, doi = {10.12752/8558}, pages = {110 -- 113}, abstract = {We study the romanization process of northern Africa from 50 BC till 300 AD. Our goal is to infer the communication strength between different subregions, based on the evolution of the status of cities. Herefore, we use the general inverse infection model, that infers the weights of a known underlying network, given observations of the spreading on this network. As infection process we choose the SI metapopulation model, where I stands for a city with a Roman status. To solve the minimization problem we use the particle swarm optimization algorithm with a specific choice of parameters.}, language = {de} } @article{ZonkerPadillaIglesiasDjurdjevacConrad, author = {Zonker, Johannes and Padilla-Iglesias, Cecilia and Djurdjevac Conrad, Natasa}, title = {Insights into drivers of mobility and cultural dynamics of African hunter-gatherers over the past 120 000 years}, series = {Royal Society Open Science}, volume = {10}, journal = {Royal Society Open Science}, number = {11}, doi = {10.1098/rsos.230495}, abstract = {Humans have a unique capacity to innovate, transmit and rely on complex, cumulative culture for survival. While an important body of work has attempted to explore the role of changes in the size and interconnectedness of populations in determining the persistence, diversity and complexity of material culture, results have achieved limited success in explaining the emergence and spatial distribution of cumulative culture over our evolutionary trajectory. Here, we develop a spatio-temporally explicit agent-based model to explore the role of environmentally driven changes in the population dynamics of hunter-gatherer communities in allowing the development, transmission and accumulation of complex culture. By modelling separately demography- and mobility-driven changes in interaction networks, we can assess the extent to which cultural change is driven by different types of population dynamics. We create and validate our model using empirical data from Central Africa spanning 120 000 years. We find that populations would have been able to maintain diverse and elaborate cultural repertoires despite abrupt environmental changes and demographic collapses by preventing isolation through mobility. However, we also reveal that the function of cultural features was also an essential determinant of the effects of environmental or demographic changes on their dynamics. Our work can therefore offer important insights into the role of a foraging lifestyle on the evolution of cumulative culture.}, language = {en} } @article{KlusDjurdjevacConrad, author = {Klus, Stefan and Djurdjevac Conrad, Natasa}, title = {Dynamical systems and complex networks: A Koopman operator perspective}, abstract = {The Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept-representing highly nonlinear dynamical systems by infinite-dimensional linear operators-has been known for a long time, the availability of large data sets and efficient machine learning algorithms for estimating the Koopman operator from data make this framework extremely powerful and popular. Koopman operator theory allows us to gain insights into the characteristic global properties of a system without requiring detailed mathematical models. We will show how these methods can also be used to analyze complex networks and highlight relationships between Koopman operators and graph Laplacians.}, language = {en} } @misc{ZonkerPadillaIglesiasDjurdjevacConrad, author = {Zonker, Johannes and Padilla-Iglesias, Cecilia and Djurdjevac Conrad, Natasa}, title = {Supplementary code and data for Royal Society Open Science Manuscript rsos.230495}, doi = {10.12752/9254}, abstract = {In this repository are all files necessary to run the agent-based model of the paper "Insights into drivers of mobility and cultural dynamics of African hunter-gatherers over the past 120 000 years", Royal Society Open Science, 10(11), 2023.}, language = {en} } @misc{Secker, author = {Secker, Christopher}, title = {Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists (Dataset)}, doi = {10.12752/9622}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-96220}, abstract = {Virtual Screening Dataset for the paper "Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists" by Secker et al. (https://doi.org/10.1186/s13321-023-00746-4)}, language = {en} } @article{SchaibleNouriHoepkenetal., author = {Schaible, Jonas and Nouri, Bijan and H{\"o}pken, Lars and Kotzab, Tim and Loevenich, Matthias and Blum, Niklas and Hammer, Annette and St{\"u}hrenberg, Jonas and J{\"a}ger, Klaus and Becker, Christiane and Wilbert, Stefan}, title = {Application of nowcasting to reduce the impact of irradiance ramps on PV power plants}, series = {EPJ Photovolt.}, volume = {15}, journal = {EPJ Photovolt.}, doi = {10.1051/epjpv/2024009}, pages = {15}, language = {en} } @article{ReidelbachFerrerWeber, author = {Reidelbach, Marco and Ferrer, Eloi and Weber, Marcus}, title = {MaRDMO Plugin}, series = {Proceedings of the Conference on Research Data Infrastructure}, volume = {1}, journal = {Proceedings of the Conference on Research Data Infrastructure}, publisher = {TIB Open Publishing}, issn = {2941-296X}, doi = {10.52825/cordi.v1i.254}, abstract = {MaRDMO, a plugin for the Research Data Management Organiser, was developed in the Mathematical Research Data Initiative to document interdisciplinary workflows using a standardised scheme. Interdisciplinary workflows recorded this way are published directly on the MaRDI portal. In addition, central information is integrated into the MaRDI knowledge graph. Next to the documentation, MaRDMO offers the possibility to retrieve existing interdisciplinary workflows from the MaRDI Knowledge Graph to allow the reproduction of the initial work and to provide scientists with new researchimpulses. Thus, MaRDMO creates a community-driven knowledge loop that could help to overcome the replication crisis.}, language = {en} } @article{BennerDanabalanGoedekkeetal., author = {Benner, Peter and Danabalan, Renita and G{\"o}dekke, Dominik and Kastner, Lars and Krause, Tabea and Mietchen, Daniel and Reidelbach, Marco and Schembera, Bj{\"o}rn and Schubotz, Moritz and Sinn, Rainer and Tabelow, Karsten}, title = {Research Data Management Planning in Mathematics}, doi = {10.5281/zenodo.10018245}, abstract = {Research data are crucial in mathematics and all scientific disciplines, as they form the foundation for empirical evidence, by enabling the validation and reproducibility of scientific findings. Mathematical research data (MathRD) have become vast and complex, and their interdisciplinary potential and abstract nature make them ubiquitous in various scientific fields. The volume of data and the velocity of its creation are rapidly increasing due to advancements in data science and computing power. This complexity extends to other disciplines, resulting in diverse research data and computational models. Thus, proper handling of research data is crucial both within mathematics and for its manifold connections and exchange with other disciplines. The National Research Data Infrastructure (NFDI), funded by the federal and state governments of Germany, consists of discipline-oriented consortia, including the Mathematical Research Data Initiative (MaRDI). MaRDI has been established to develop services, guidelines and outreach measures for all aspects of MathRD, and thus support the mathematical research community. Research data management (RDM) should be an integral component of every scientific project, and is becoming a mandatory component of grants with funding bodies such as the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation). At the core of RDM are the FAIR (Findable, Accessible, Interoperable, and Reusable) principles. This document aims to guide mathematicians and researchers from related disciplines who create RDM plans. It highlights the benefits and opportunities of RDM in mathematics and interdisciplinary studies, showcases examples of diverse MathRD, and suggests technical solutions that meet the requirements of funding agencies with specific examples. The document is regularly updated to reflect the latest developments within the mathematical community represented by MaRDI.}, language = {en} } @article{DiederichsKrauseLemaireetal., author = {Diederichs, Katja and Krause, Celia and Lemaire, Marina and Reidelbach, Marco and Windeck, J{\"u}rgen}, title = {A Vision for Data Management Plans in the NFDI}, doi = {10.5281/zenodo.10570653}, abstract = {At present, data management plans (DMPs) are still often perceived as mere documents for funding agencies providing clarity on how research data will be handled during a funded project, but are not usually actively involved in the processes. However, they contain a great deal of information that can be shared automatically to facilitate active research data management (RDM) by providing metadata to research infrastructures and supporting communication between all involved stakeholders. This position paper brings together a number of ideas developed and collected during interdisciplinary workshops of the Data Management Planning Working Group (infra-dmp), which is part of the section Common Infrastructures of the National Research Data Infrastructure (NFDI) in Germany. We present our vision of a possible future role of DMPs, templates, and tools in the upcoming NFDI service architecture.}, language = {en} } @article{DonatiSchuetteWeber, author = {Donati, Luca and Sch{\"u}tte, Christof and Weber, Marcus}, title = {The Kramers turnover in terms of a macro-state projection on phase space}, series = {Molecular Physics}, journal = {Molecular Physics}, number = {Ciccotti Special Issue (by invitation only)}, publisher = {Taylor \& Francis}, doi = {10.1080/00268976.2024.2356748}, pages = {e2356748}, abstract = {We have investigated how Langevin dynamics is affected by the friction coefficient using the novel algorithm ISOKANN, which combines the transfer operator approach with modern machine learning techniques. ISOKANN describes the dynamics in terms of an invariant subspace projection of the Koopman operator defined in the entire state space, avoiding approximations due to dimensionality reduction and discretization. Our results are consistent with the Kramers turnover and show that in the low and moderate friction regimes, metastable macro-states and transition rates are defined in phase space, not only in position space.}, language = {en} } @article{KuenLoefflerTsarapkinetal., author = {Kuen, Lilli and L{\"o}ffler, Lorenz and Tsarapkin, Aleksei and Zschiedrich, Lin and Feichtner, Thorsten and Burger, Sven and H{\"o}flich, Katja}, title = {Chiral and directional optical emission from a dipole source coupled to a helical plasmonic antenna}, series = {Appl. Phys. Lett.}, volume = {124}, journal = {Appl. Phys. Lett.}, doi = {10.1063/5.0201748}, pages = {231102}, language = {en} } @article{SikorskiRabbenChewleetal., author = {Sikorski, Alexander and Rabben, Robert Julian and Chewle, Surahit and Weber, Marcus}, title = {Capturing the Macroscopic Behaviour of Molecular Dynamics with Membership Functions}, abstract = {Markov processes serve as foundational models in many scientific disciplines, such as molecular dynamics, and their simulation forms a common basis for analysis. While simulations produce useful trajectories, obtaining macroscopic information directly from microstate data presents significant challenges. This paper addresses this gap by introducing the concept of membership functions being the macrostates themselves. We derive equations for the holding times of these macrostates and demonstrate their consistency with the classical definition. Furthermore, we discuss the application of the ISOKANN method for learning these quantities from simulation data. In addition, we present a novel method for extracting transition paths based on the ISOKANN results and demonstrate its efficacy by applying it to simulations of the 𝜇-opioid receptor. With this approach we provide a new perspective on analyzing the macroscopic behaviour of Markov systems.}, language = {en} } @article{ThiesSunkaraRayetal., author = {Thies, Arne and Sunkara, Vikram and Ray, Sourav and Wulkow, Hanna and Celik, M. {\"O}zg{\"u}r and Yerg{\"o}z, Fatih and Sch{\"u}tte, Christof and Stein, Christoph and Weber, Marcus and Winkelmann, Stefanie}, title = {Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design}, series = {Scientific Reports}, volume = {13}, journal = {Scientific Reports}, number = {607}, doi = {10.1038/s41598-023-27699-w}, abstract = {We previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. The design process of NFEPP was based on mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands, recognizing that GPCRs function differently under pathological versus healthy conditions. We now present an additional and novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels and their dependence on parameters of inflamed and healthy tissue (pH, radicals). The model is validated against in vitro experimental data for the ligands NFEPP and fentanyl at different pH values and radical concentrations. We observe markedly reduced binding affinity and calcium channel inhibition for NFEPP at normal pH compared to lower pH, in contrast to the effect of fentanyl. For increasing radical concentrations, we find enhanced constitutive G-protein activation but reduced ligand binding affinity. Assessing the different effects, the results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.}, language = {en} } @article{delRazoWinkelmannKleinetal., author = {del Razo, Mauricio and Winkelmann, Stefanie and Klein, Rupert and H{\"o}fling, Felix}, title = {Chemical diffusion master equation: formulations of reaction-diffusion processes on the molecular level}, series = {Journal of Mathematical Physics}, volume = {64}, journal = {Journal of Mathematical Physics}, number = {1}, doi = {10.1063/5.0129620}, abstract = {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.}, language = {en} } @article{delRazoFroembergStraubeetal., author = {del Razo, Mauricio and Fr{\"o}mberg, Daniela and Straube, Arthur and Sch{\"u}tte, Christof and H{\"o}fling, Felix and Winkelmann, Stefanie}, title = {A probabilistic framework for particle-based reaction-diffusion dynamics using classical Fock space representations}, series = {Letters in Mathematical Physics}, volume = {112}, journal = {Letters in Mathematical Physics}, number = {49}, doi = {10.1007/s11005-022-01539-w}, language = {en} } @article{ErnstAsselineauTillmannetal., author = {Ernst, Marco and Asselineau, Charles-Alexis and Tillmann, Peter and J{\"a}ger, Klaus and Becker, Christiane}, title = {Modelling bifacial irradiance - Step-by-step comparison and validation of view factor and ray tracing models}, series = {Appl. Energy}, volume = {369}, journal = {Appl. Energy}, publisher = {Elsevier BV}, issn = {0306-2619}, doi = {10.1016/j.apenergy.2024.123574}, pages = {123574}, language = {en} } @article{MontefuscoHelfmannOkunolaetal., author = {Montefusco, Alberto and Helfmann, Luzie and Okunola, Toluwani and Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {Partial mean-field model for neurotransmission dynamics}, series = {Mathematical Biosciences}, volume = {369}, journal = {Mathematical Biosciences}, doi = {10.1016/j.mbs.2024.109143}, abstract = {This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the stochastic-spatial particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios.}, language = {en} } @article{LueckeWinkelmannHeitzigetal., author = {L{\"u}cke, Marvin and Winkelmann, Stefanie and Heitzig, Jobst and Molkenthin, Nora and Koltai, P{\´e}ter}, title = {Learning interpretable collective variables for spreading processes on networks}, series = {Physical Review E}, volume = {109}, journal = {Physical Review E}, number = {2}, doi = {10.1103/PhysRevE.109.L022301}, pages = {L022301}, abstract = {Collective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes on networks. The relation between CVs and network measures is not well understood and its derivation typically requires detailed knowledge of both the dynamical system and the network topology. In this Letter, we present a data-driven method for algorithmically learning and understanding CVs for binary-state spreading processes on networks of arbitrary topology. We demonstrate our method using four example networks: the stochastic block model, a ring-shaped graph, a random regular graph, and a scale-free network generated by the Albert-Barab{\´a}si model. Our results deliver evidence for the existence of low-dimensional CVs even in cases that are not yet understood theoretically.}, language = {en} } @article{WeberWeitereAutoren, author = {Weber, Marcus and Weitere Autoren,}, title = {DIN SPEC 2343: {\"U}bertragung von sprachbasierten Daten zwischen K{\"u}nstlichen Intelligenzen - Festlegung von Parametern und Formaten}, series = {Beuth Verlag}, journal = {Beuth Verlag}, editor = {Reichardt, Christine}, abstract = {Dieses Dokument legt Parameter und Formate f{\"u}r die {\"U}bertragung sprachbasierter Daten zwischen verschiedenen KI-{\"O}kosystemen fest.}, language = {de} } @article{TrepteSeckerKostovaetal., author = {Trepte, Philipp and Secker, Christopher and Kostova, Simona and Maseko, Sibusiso B. and Gang Choi, Soon and Blavier, Jeremy and Minia, Igor and Silva Ramos, Eduardo and Cassonnet, Patricia and Golusik, Sabrina and Zenkner, Martina and Beetz, Stephanie and Liebich, Mara J. and Scharek, Nadine and Sch{\"u}tz, Anja and Sperling, Marcel and Lisurek, Michael and Wang, Yang and Spirohn, Kerstin and Hao, Tong and Calderwood, Michael A. and Hill, David E. and Landthaler, Markus and Olivet, Julien and Twizere, Jean-Claude and Vidal, Marc and Wanker, Erich E.}, title = {AI-guided pipeline for protein-protein interaction drug discovery identifies a SARS-CoV-2 inhibitor}, series = {bioRxiv}, journal = {bioRxiv}, doi = {10.1101/2023.06.14.544560}, language = {en} } @misc{BetzHammerschmidtZschiedrichetal., author = {Betz, Fridtjof and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven and Binkowski, Felix}, title = {Source code and simulation results: Efficient rational approximation of optical response functions with the AAA algorithm}, series = {Zenodo}, journal = {Zenodo}, doi = {10.5281/zenodo.10853692}, pages = {doi: 10.5281/zenodo.10853692}, language = {en} } @misc{KuenLoefflerTsarapkinetal., author = {Kuen, Lilli and L{\"o}ffler, Lorenz and Tsarapkin, Aleksei and Zschiedrich, Lin and Feichtner, Thorsten and Burger, Sven and H{\"o}flich, Katja}, title = {Source Code and Simulation Results: Chiral and directional optical emission from a dipole source coupled to a helical plasmonic antenna}, series = {Zenodo}, journal = {Zenodo}, doi = {10.5281/zenodo.10598255}, pages = {doi: 10.5281/zenodo.10598255}, language = {en} } @article{TrepteSeckerOlivetetal., author = {Trepte, Philipp and Secker, Christopher and Olivet, Julien and Blavier, Jeremy and Kostova, Simona and Maseko, Sibusiso B and Minia, Igor and Silva Ramos, Eduardo and Cassonnet, Patricia and Golusik, Sabrina and Zenkner, Martina and Beetz, Stephanie and Liebich, Mara J and Scharek, Nadine and Sch{\"u}tz, Anja and Sperling, Marcel and Lisurek, Michael and Wang, Yang and Spirohn, Kerstin and Hao, Tong and Calderwood, Michael A and Hill, David E and Landthaler, Markus and Choi, Soon Gang and Twizere, Jean-Claude and Vidal, Marc and Wanker, Erich E}, title = {AI-guided pipeline for protein-protein interaction drug discovery identifies a SARS-CoV-2 inhibitor}, series = {Molecular Systems Biology}, volume = {20}, journal = {Molecular Systems Biology}, number = {4}, publisher = {Springer Science and Business Media LLC}, issn = {1744-4292}, doi = {https://doi.org/10.1038/s44320-024-00019-8}, pages = {428 -- 457}, abstract = {Protein-protein interactions (PPIs) offer great opportunities to expand the druggable proteome and therapeutically tackle various diseases, but remain challenging targets for drug discovery. Here, we provide a comprehensive pipeline that combines experimental and computational tools to identify and validate PPI targets and perform early-stage drug discovery. We have developed a machine learning approach that prioritizes interactions by analyzing quantitative data from binary PPI assays or AlphaFold-Multimer predictions. Using the quantitative assay LuTHy together with our machine learning algorithm, we identified high-confidence interactions among SARS-CoV-2 proteins for which we predicted three-dimensional structures using AlphaFold-Multimer. We employed VirtualFlow to target the contact interface of the NSP10-NSP16 SARS-CoV-2 methyltransferase complex by ultra-large virtual drug screening. Thereby, we identified a compound that binds to NSP10 and inhibits its interaction with NSP16, while also disrupting the methyltransferase activity of the complex, and SARS-CoV-2 replication. Overall, this pipeline will help to prioritize PPI targets to accelerate the discovery of early-stage drug candidates targeting protein complexes and pathways.}, language = {en} } @inproceedings{LueckeKoltaiWinkelmannetal., author = {L{\"u}cke, Marvin and Koltai, Peter and Winkelmann, Stefanie and Molkethin, Nora and Heitzig, Jobst}, title = {Discovering collective variable dynamics of agent-based models}, series = {25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022}, booktitle = {25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022}, doi = {https://doi.org/10.15495/EPub_UBT_00006809}, abstract = {Analytical approximations of the macroscopic behavior of agent-based models (e.g. via mean-field theory) often introduce a significant error, especially in the transient phase. For an example model called continuous-time noisy voter model, we use two data-driven approaches to learn the evolution of collective variables instead. The first approach utilizes the SINDy method to approximate the macroscopic dynamics without prior knowledge, but has proven itself to be not particularly robust. The second approach employs an informed learning strategy which includes knowledge about the agent-based model. Both approaches exhibit a considerably smaller error than the conventional analytical approximation.}, language = {en} } @article{SeckerFackeldeyWeberetal., author = {Secker, Christopher and Fackeldey, Konstantin and Weber, Marcus and Ray, Sourav and Gorgulla, Christoph and Sch{\"u}tte, Christof}, title = {Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists}, series = {Journal of Cheminformatics}, volume = {15}, journal = {Journal of Cheminformatics}, doi = {10.1186/s13321-023-00746-4}, abstract = {Opioids are essential pharmaceuticals due to their analgesic properties, however, lethal side effects, addiction, and opioid tolerance are extremely challenging. The development of novel molecules targeting the μ-opioid receptor (MOR) in inflamed, but not in healthy tissue, could significantly reduce these unwanted effects. Finding such novel molecules can be achieved by maximizing the binding affinity to the MOR at acidic pH while minimizing it at neutral pH, thus combining two conflicting objectives. Here, this multi-objective optimal affinity approach is presented, together with a virtual drug discovery pipeline for its practical implementation. When applied to finding pH-specific drug candidates, it combines protonation state-dependent structure and ligand preparation with high-throughput virtual screening. We employ this pipeline to characterize a set of MOR agonists identifying a morphine-like opioid derivative with higher predicted binding affinities to the MOR at low pH compared to neutral pH. Our results also confirm existing experimental evidence that NFEPP, a previously described fentanyl derivative with reduced side effects, and recently reported β-fluorofentanyls and -morphines show an increased specificity for the MOR at acidic pH when compared to fentanyl and morphine. We further applied our approach to screen a >50K ligand library identifying novel molecules with pH-specific predicted binding affinities to the MOR. The presented differential docking pipeline can be applied to perform multi-objective affinity optimization to identify safer and more specific drug candidates at large scale.}, language = {en} } @article{WulkowConradDjurdjevacConradetal., author = {Wulkow, Hanna and Conrad, Tim and Djurdjevac Conrad, Natasa and M{\"u}ller, Sebastian A. and Nagel, Kai and Sch{\"u}tte, Christof}, title = {Prediction of Covid-19 spreading and optimal coordination of counter-measures: From microscopic to macroscopic models to Pareto fronts}, series = {PLOS One}, volume = {16}, journal = {PLOS One}, number = {4}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0249676}, language = {en} } @article{ManleyHammerschmidtZschiedrichetal., author = {Manley, Phillip and Hammerschmidt, Martin and Zschiedrich, Lin and J{\"a}ger, Klaus and Becker, Christiane and Burger, Sven}, title = {Modelling luminescent coupling in multi-junction solar cells: perovskite silicon tandem case study}, series = {Proc. SPIE}, volume = {13014}, journal = {Proc. SPIE}, doi = {10.1117/12.3023941}, pages = {1301404}, language = {en} } @misc{SekuliĉSchneiderHammerschmidtetal., author = {Sekuliĉ, Ivan and Schneider, Philipp-Immanuel and Hammerschmidt, Martin and Burger, Sven}, title = {Machine-learning driven design of metasurfaces: learn the physics and not the objective function}, series = {Proc. SPIE}, volume = {PC13017}, journal = {Proc. SPIE}, doi = {10.1117/12.3022119}, pages = {PC130170X}, language = {en} } @masterthesis{Bena, type = {Bachelor Thesis}, author = {Bena, Noor-Cella}, title = {Finding Rules and Patterns in Egyptological Research Objects using Boolean Polynomial Rings}, pages = {35}, language = {en} } @inproceedings{BeckerBlaesiBurgeretal., author = {Becker, Christiane and Bl{\"a}si, Benedikt and Burger, Sven and Ehrler, Bruno and Gordon, Ivan and Isabella, Olindo and Jaeger, Klaus and Jost, Marko and Manley, Phillip and Mu{\~n}oz, Delfina and Paetzold, Ulrich W. and Sai, Hitoshi and Yablonovitch, Eli}, title = {Optical challenges for terawatt-scale photovoltaics}, series = {Proc. SPIE}, volume = {PC13014}, booktitle = {Proc. SPIE}, publisher = {SPIE}, doi = {10.1117/12.3016415}, pages = {PC1301401}, language = {en} } @inproceedings{SchaibleYooWinartoetal., author = {Schaible, Jonas and Yoo, Danbi and Winarto, Hanifa and Miaskiewicz, Alexandra and Albrecht, Steve and Wessels, Andreas and Bl{\"a}si, Benedikt and Burger, Sven and Jaeger, Klaus and Becker, Christiane}, title = {On aesthetical appearance of colored perovskite solar modules}, series = {Proc. SPIE}, volume = {PC13014}, booktitle = {Proc. SPIE}, publisher = {SPIE}, doi = {10.1117/12.3017427}, pages = {PC1301406}, language = {en} } @article{PlockBinkowskiZschiedrichetal., author = {Plock, Matthias and Binkowski, Felix and Zschiedrich, Lin and Schneider, Phillip-Immanuel and Burger, Sven}, title = {Fabrication uncertainty guided design optimization of a photonic crystal cavity by using Gaussian processes}, series = {J. Opt. Soc. Am. B}, volume = {41}, journal = {J. Opt. Soc. Am. B}, doi = {10.1364/JOSAB.505767}, pages = {850}, language = {en} } @inproceedings{SemlerWeiser, author = {Semler, Phillip and Weiser, Martin}, title = {Adaptive Gradient Enhanced Gaussian Process Surrogates for Inverse Problems}, series = {Proceedings of the MATH+ Thematic Einstein Semester on Mathematical Optimization for Machine Learning}, booktitle = {Proceedings of the MATH+ Thematic Einstein Semester on Mathematical Optimization for Machine Learning}, abstract = {Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a fully adaptive greedy approach to the computational design of experiments problem using gradient-enhanced Gaussian process regression as surrogates. Designs are incrementally defined by solving an optimization problem for accuracy given a certain computational budget. We address not only the choice of evaluation points but also of required simulation accuracy, both of values and gradients of the forward model. Numerical results show a significant reduction of the computational effort compared to just position-adaptive and static designs as well as a clear benefit of including gradient information into the surrogate training.}, language = {en} } @article{LelievrePigeonStoltzetal.2023, author = {Leli{\`e}vre, Tony and Pigeon, Thomas and Stoltz, Gabriel and Zhang, Wei}, title = {Analyzing multimodal probability measures with autoencoders}, series = {J. Phys. Chem. B}, volume = {128}, journal = {J. Phys. Chem. B}, number = {11}, doi = {10.1021/acs.jpcb.3c07075}, pages = {2607 -- 2631}, year = {2023}, abstract = {Finding collective variables to describe some important coarse-grained information on physical systems, in particular metastable states, remains a key issue in molecular dynamics. Recently, machine learning techniques have been intensively used to complement and possibly bypass expert knowledge in order to construct collective variables. Our focus here is on neural network approaches based on autoencoders. We study some relevant mathematical properties of the loss function considered for training autoencoders, and provide physical interpretations based on conditional variances and minimum energy paths. We also consider various extensions in order to better describe physical systems, by incorporating more information on transition states at saddle points, and/or allowing for multiple decoders in order to describe several transition paths. Our results are illustrated on toy two dimensional systems and on alanine dipeptide.}, language = {en} } @article{KruegerManleyBergmannetal., author = {Kr{\"u}ger, Jan and Manley, Phillip and Bergmann, Detlef and K{\"o}ning, Rainer and Bodermann, Bernd and Eder, Christian and Heinrich, Andreas and Schneider, Philipp-Immanuel and Hammerschmidt, Martin and Zschiedrich, Lin and Manske, Eberhard}, title = {Introduction and application of a new approach for model-based optical bidirectional measurements}, series = {Meas. Sci. Technol.}, volume = {35}, journal = {Meas. Sci. Technol.}, number = {8}, doi = {10.1088/1361-6501/ad4b53}, language = {en} } @article{GaskinConradPavliotisetal., author = {Gaskin, Thomas and Conrad, Tim and Pavliotis, Grigorios A. and Sch{\"u}tte, Christof}, title = {Neural parameter calibration and uncertainty quantification for epidemic forecasting}, series = {PLOS ONE}, journal = {PLOS ONE}, abstract = {The recent COVID-19 pandemic has thrown the importance of accurately forecasting contagion dynamics and learning infection parameters into sharp focus. At the same time, effective policy-making requires knowledge of the uncertainty on such predictions, in order, for instance, to be able to ready hospitals and intensive care units for a worst-case scenario without needlessly wasting resources. In this work, we apply a novel and powerful computational method to the problem of learning probability densities on contagion parameters and providing uncertainty quantification for pandemic projections. Using a neural network, we calibrate an ODE model to data of the spread of COVID-19 in Berlin in 2020, achieving both a significantly more accurate calibration and prediction than Markov-Chain Monte Carlo (MCMC)-based sampling schemes. The uncertainties on our predictions provide meaningful confidence intervals e.g. on infection figures and hospitalisation rates, while training and running the neural scheme takes minutes where MCMC takes hours. We show convergence of our method to the true posterior on a simplified SIR model of epidemics, and also demonstrate our method's learning capabilities on a reduced dataset, where a complex model is learned from a small number of compartments for which data is available.}, language = {en} } @article{EngelOliconMendezWehlitzetal., author = {Engel, Maximilian and Olic{\´o}n-M{\´e}ndez, Guillermo and Wehlitz, Nathalie and Winkelmann, Stefanie}, title = {Synchronization and random attractors in reaction jump processes}, series = {Journal of Dynamics and Differential Equations}, journal = {Journal of Dynamics and Differential Equations}, doi = {10.1007/s10884-023-10345-4}, abstract = {This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. Based on Gillespie's stochastic simulation algorithm, a corresponding random dynamical system is formulated in a two-step procedure, at first for the states of the embedded discrete-time Markov chain and then for the augmented Markov chain including random jump times. We uncover a time-shifted synchronization in the sense that—after some initial waiting time—one trajectory exactly replicates another one with a certain time delay. Whether or not such a synchronization behavior occurs depends on the combination of the initial states. We prove this partial time-shifted synchronization for the special setting of a birth-death process by analyzing the corresponding two-point motion of the embedded Markov chain and determine the structure of the associated random attractor. In this context, we also provide general results on existence and form of random attractors for discrete-time, discrete-space random dynamical systems.}, language = {en} } @article{DjurdjevacConradQuangVuNagel, author = {Djurdjevac Conrad, Natasa and Quang Vu, Nhu and Nagel, Soeren}, title = {Co-evolving networks for opinion and social dynamics in agent-based models}, series = {arxiv}, journal = {arxiv}, abstract = {The rise of digital social media has strengthened the coevolution of public opinions and social interactions, that shape social structures and collective outcomes in increasingly complex ways. Existing literature often explores this interplay as a one-directional influence, focusing on how opinions determine social ties within adaptive networks. However, this perspective overlooks the intrinsic dynamics driving social interactions, which can significantly influence how opinions form and evolve. In this work, we address this gap, by introducing the co-evolving opinion and social dynamics using stochastic agent-based models. Agents' mobility in a social space is governed by both their social and opinion similarity with others. Similarly, the dynamics of opinion formation is driven by the opinions of agents in their social vicinity. We analyze the underlying social and opinion interaction networks and explore the mechanisms influencing the appearance of emerging phenomena, like echo chambers and opinion consensus. To illustrate the model's potential for real-world analysis, we apply it to General Social Survey data on political identity and public opinion regarding governmental issues. Our findings highlight the model's strength in capturing the coevolution of social connections and individual opinions over time.}, language = {en} } @article{ZhangSchuette2024, author = {Zhang, Wei and Sch{\"u}tte, Christof}, title = {On finding optimal collective variables for complex systems by minimizing the deviation between effective and full dynamics}, year = {2024}, abstract = {This paper is concerned with collective variables, or reaction coordinates, that map a discrete-in-time Markov process X_n in R^d to a (much) smaller dimension k≪d. We define the effective dynamics under a given collective variable map ξ as the best Markovian representation of X_n under ξ. The novelty of the paper is that it gives strict criteria for selecting optimal collective variables via the properties of the effective dynamics. In particular, we show that the transition density of the effective dynamics of the optimal collective variable solves a relative entropy minimization problem from certain family of densities to the transition density of X_n. We also show that many transfer operator-based data-driven numerical approaches essentially learn quantities of the effective dynamics. Furthermore, we obtain various error estimates for the effective dynamics in approximating dominant timescales / eigenvalues and transition rates of the original process X_n and how optimal collective variables minimize these errors. Our results contribute to the development of theoretical tools for the understanding of complex dynamical systems, e.g. molecular kinetics, on large timescales. These results shed light on the relations among existing data-driven numerical approaches for identifying good collective variables, and they also motivate the development of new methods.}, language = {en} } @article{ZhaoZhangLi, author = {Zhao, Yue and Zhang, Wei and Li, Tiejun}, title = {EPR-Net: Constructing non-equilibrium potential landscape via a variational force projection formulation}, series = {National Science Review}, volume = {11}, journal = {National Science Review}, number = {7}, doi = {10.1093/nsr/nwae052}, abstract = {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.}, language = {en} } @article{NagelHeitzigSchoell, author = {Nagel, Soeren and Heitzig, Jobst and Schoell, Eckehard}, title = {Capital Inequality Induced Business Cycles}, pages = {1 -- 6}, abstract = {In this letter we present a stochastic dynamic model which can explain economic cycles. We show that the macroscopic description yields a complex dynamical landscape consisting of multiple stable fixed points, each corresponding to a split of the population into a large low and a small high income group. The stochastic fluctuations induce switching between the resulting metastable states, and excitation oscillations just below a deterministic bifurcation. The shocks are caused by the decisions of a few agents who have a disproportionate influence over the macroscopic state of the economy due to the unequal distribution of wealth among the population. The fluctuations have a long-term effect on the growth of economic output and lead to business cycle oscillations exhibiting coherence resonance, where the correlation time is controlled by the population size which is inversely proportional to the noise intensity.}, language = {en} } @misc{BoppPlockTuranetal., author = {Bopp, Julian M. and Plock, Matthias and Turan, Tim and Pieplow, Gregor and Burger, Sven and Schr{\"o}der, Tim}, title = {'Sawfish' Photonic Crystal Cavity for Near-Unity Emitter-to-Fiber Interfacing in Quantum Network Applications (Advanced Optical Materials 13/2024)}, series = {Adv. Optical Mater.}, volume = {12}, journal = {Adv. Optical Mater.}, doi = {10.1002/adom.202470046}, pages = {2470046}, language = {en} } @inproceedings{SteyerCheginiPotseetal., author = {Steyer, Joshua and Chegini, Fatemeh and Potse, Mark and Loewe, Axel and Weiser, Martin}, title = {Continuity of Microscopic Cardiac Conduction in a Computational Cell-by-Cell Model}, series = {2023 Computing in Cardiology Conference (CinC)}, volume = {50}, booktitle = {2023 Computing in Cardiology Conference (CinC)}, publisher = {Computing in Cardiology}, issn = {2325-887X}, doi = {10.22489/CinC.2023.385}, abstract = {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.}, language = {en} } @article{SemlerWeiser, author = {Semler, Phillip and Weiser, Martin}, title = {Adaptive Gaussian Process Regression for Efficient Building of Surrogate Models in Inverse Problems}, series = {Inverse Problems}, volume = {39}, journal = {Inverse Problems}, number = {12}, doi = {10.1088/1361-6420/ad0028}, pages = {125003}, abstract = {In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model y with a surrogate model y(s) that can be evaluated quickly leads to a significant speedup. The approximation quality of the surrogate model depends strongly on the number, position, and accuracy of the sample points. With an additional finite computational budget, this leads to a problem of (computer) experimental design. In contrast to the selection of sample points, the trade-off between accuracy and effort has hardly been studied systematically. We therefore propose an adaptive algorithm to find an optimal design in terms of position and accuracy. Pursuing a sequential design by incrementally appending the computational budget leads to a convex and constrained optimization problem. As a surrogate, we construct a Gaussian process regression model. We measure the global approximation error in terms of its impact on the accuracy of the identified parameter and aim for a uniform absolute tolerance, assuming that y(s) is computed by finite element calculations. A priori error estimates and a coarse estimate of computational effort relate the expected improvement of the surrogate model error to computational effort, resulting in the most efficient combination of sample point and evaluation tolerance. We also allow for improving the accuracy of already existing sample points by continuing previously truncated finite element solution procedures.}, language = {en} } @inproceedings{CheginiSteinkeWeiser, author = {Chegini, Fatemeh and Steinke, Thomas and Weiser, Martin}, title = {Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods}, abstract = {The locality of solution features in cardiac electrophysiology simulations calls for adaptive methods. Due to the overhead incurred by established mesh refinement and coarsening, however, such approaches failed in accelerating the computations. Here we investigate a different route to spatial adaptivity that is based on nested subset selection for algebraic degrees of freedom in spectral deferred correction methods. This combination of algebraic adaptivity and iterative solvers for higher order collocation time stepping realizes a multirate integration with minimal overhead. This leads to moderate but significant speedups in both monodomain and cell-by-cell models of cardiac excitation, as demonstrated at four numerical examples.}, language = {en} } @article{HartmannRichter, author = {Hartmann, Carsten and Richter, Lorenz}, title = {Nonasymptotic bounds for suboptimal importance sampling}, series = {SIAM/ASA Journal on Uncertainty Quantification}, volume = {12}, journal = {SIAM/ASA Journal on Uncertainty Quantification}, number = {2}, doi = {10.1137/21M1427760}, pages = {309 -- 346}, abstract = {Importance sampling is a popular variance reduction method for Monte Carlo estimation, where an evident question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically possible, in practice only suboptimal proposal distributions are available and it can often be observed numerically that those can reduce statistical performance significantly, leading to large relative errors and therefore counteracting the original intention. Previous analysis on importance sampling has often focused on asymptotic arguments that work well in a large deviations regime. In this article, we provide lower and upper bounds on the relative error in a nonasymptotic setting. They depend on the deviation of the actual proposal from optimality, and we thus identify potential robustness issues that importance sampling may have, especially in high dimensions. We particularly focus on path sampling problems for diffusion processes with nonvanishing noise, for which generating good proposals comes with additional technical challenges. We provide numerous numerical examples that support our findings and demonstrate the applicability of the derived bounds.}, language = {en} } @inproceedings{AndresArconesWeiserKoutsourelakisetal., author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Faidon-Stelios and Unger, J{\"o}rg F.}, title = {Evaluation of Model Bias Identification Approaches Based on Bayesian Inference and Applications to Digital Twins}, series = {5th ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering}, booktitle = {5th ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering}, pages = {1 -- 15}, abstract = {In recent years, the use of simulation-based digital twins for monitoring and assessment of complex mechanical systems has greatly expanded. Their potential to increase the information obtained from limited data makes them an invaluable tool for a broad range of real-world applications. Nonetheless, there usually exists a discrepancy between the predicted response and the measurements of the system once built. One of the main contributors to this difference in addition to miscalibrated model parameters is the model error. Quantifying this socalled model bias (as well as proper values for the model parameters) is critical for the reliable performance of digital twins. Model bias identification is ultimately an inverse problem where information from measurements is used to update the original model. Bayesian formulations can tackle this task. Including the model bias as a parameter to be inferred enables the use of a Bayesian framework to obtain a probability distribution that represents the uncertainty between the measurements and the model. Simultaneously, this procedure can be combined with a classic parameter updating scheme to account for the trainable parameters in the original model. This study evaluates the effectiveness of different model bias identification approaches based on Bayesian inference methods. This includes more classical approaches such as direct parameter estimation using MCMC in a Bayesian setup, as well as more recent proposals such as stat-FEM or orthogonal Gaussian Processes. Their potential use in digital twins, generalization capabilities, and computational cost is extensively analyzed.}, language = {en} } @article{AndresArconesWeiserKoutsourelakisetal., author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Faidon-Stelios and Unger, J{\"o}rg F.}, title = {A Bayesian Framework for Simulation-based Digital Twins of Bridges}, series = {EUROSTRUCT 2023:European Association on Quality Control of Bridges and Structures: Digital Transformation in Sustainability}, volume = {6}, journal = {EUROSTRUCT 2023:European Association on Quality Control of Bridges and Structures: Digital Transformation in Sustainability}, number = {5}, doi = {10.1002/cepa.2177}, pages = {734 -- 740}, abstract = {Simulation-based digital twins have emerged as a powerful tool for evaluating the mechanical response of bridges. As virtual representations of physical systems, digital twins can provide a wealth of information that complements traditional inspection and monitoring data. By incorporating virtual sensors and predictive maintenance strategies, they have the potential to improve our understanding of the behavior and performance of bridges over time. However, as bridges age and undergo regular loading and extreme events, their structural characteristics change, often differing from the predictions of their initial design. Digital twins must be continuously adapted to reflect these changes. In this article, we present a Bayesian framework for updating simulation-based digital twins in the context of bridges. Our approach integrates information from measurements to account for inaccuracies in the simulation model and quantify uncertainties. Through its implementation and assessment, this work demonstrates the potential for digital twins to provide a reliable and up-to-date representation of bridge behavior, helping to inform decision-making for maintenance and management.}, language = {en} } @article{MaierWeiserConrad, author = {Maier, Kristina and Weiser, Martin and Conrad, Tim}, title = {Hybrid PDE-ODE Models for Efficient Simulation of Infection Spread in Epidemiology}, abstract = {This paper introduces a novel hybrid mathematical modeling approach that effectively couples Partial Differential Equations (PDEs) with Ordinary Differential Equations (ODEs), exemplified through the simulation of epidemiological processes. The hybrid model aims to integrate the spatially detailed representation of disease dynamics provided by PDEs with the computational efficiency of ODEs. In the presented epidemiological use-case, this integration allows for the rapid assessment of public health interventions and the potential impact of infectious diseases across large populations. We discuss the theoretical formulation of the hybrid PDE-ODE model, including the governing equations and boundary conditions. The model's capabilities are demonstrated through detailed simulations of disease spread in synthetic environments and real-world scenarios, specifically focusing on the regions of Lombardy, Italy, and Berlin, Germany. Results indicate that the hybrid model achieves a balance between computational speed and accuracy, making it a valuable tool for policymakers in real-time decision-making and scenario analysis in epidemiology and potentially in other fields requiring similar modeling approaches.}, language = {en} } @article{StraubeHoefling, author = {Straube, Arthur and H{\"o}fling, Felix}, title = {Memory effects in colloidal motion under confinement and driving}, series = {J. Phys. A: Math. Theor.}, volume = {57}, journal = {J. Phys. A: Math. Theor.}, publisher = {IOP Publishing}, issn = {1751-8113}, doi = {10.1088/1751-8121/ad5b2d}, pages = {295003}, abstract = {The transport of individual particles in inhomogeneous environments is complex and exhibits non-Markovian responses. The latter may be quantified by a memory function within the framework of the linear generalised Langevin equation (GLE). Here, we exemplify the implications of steady driving on the memory function of a colloidal model system for Brownian motion in a corrugated potential landscape, specifically, for one-dimensional motion in a sinusoidal potential. To this end, we consider the overdamped limit of the GLE, which is facilitated by separating the memory function into a singular (Markovian) and a regular (non-Markovian) part. Relying on exact solutions for the investigated model, we show that the random force entering the GLE must display a bias far from equilibrium, which corroborates a recent general prediction. Based on data for the mean-square displacement (MSD) obtained from Brownian dynamics simulations, we estimate the memory function for different driving strengths and show that already moderate driving accelerates the decay of the memory function by several orders of magnitude in time. We find that the memory may persist on much longer timescales than expected from the convergence of the MSD to its long-time asymptote. Furthermore, the functional form of the memory function changes from a monotonic decay to a non-monotonic, damped oscillatory behaviour, which can be understood from a competition of confined motion and depinning. Our analysis of the simulation data further reveals a pronounced non-Gaussianity, which questions the Gaussian approximation of the random force entering the GLE.}, language = {en} } @article{AndresArconesWeiserKoutsourelakisetal., author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Faidon-Stelios and Unger, J{\"o}rg F.}, title = {Model bias identification for Bayesian calibration of stochastic digital twins of bridges}, abstract = {Simulation-based digital twins must provide accurate, robust and reliable digital representations of their physical counterparts. Quantifying the uncertainty in their predictions plays, therefore, a key role in making better-informed decisions that impact the actual system. The update of the simulation model based on data must be then carefully implemented. When applied to complex standing structures such as bridges, discrepancies between the computational model and the real system appear as model bias, which hinders the trustworthiness of the digital twin and increases its uncertainty. Classical Bayesian updating approaches aiming to infer the model parameters often fail at compensating for such model bias, leading to overconfident and unreliable predictions. In this paper, two alternative model bias identification approaches are evaluated in the context of their applicability to digital twins of bridges. A modularized version of Kennedy and O'Hagan's approach and another one based on Orthogonal Gaussian Processes are compared with the classical Bayesian inference framework in a set of representative benchmarks. Additionally, two novel extensions are proposed for such models: the inclusion of noise-aware kernels and the introduction of additional variables not present in the computational model through the bias term. The integration of such approaches in the digital twin corrects the predictions, quantifies their uncertainty, estimates noise from unknown physical sources of error and provides further insight into the system by including additional pre-existing information without modifying the computational model.}, language = {en} } @article{SteudleWinkelmannFuerstetal., author = {Steudle, Gesine and Winkelmann, Stefanie and F{\"u}rst, Steffen and Wolf, Sarah}, title = {Understanding Memory Mechanisms in Socio-Technical Systems: the Case of an Agent-based Mobility Model}, series = {Advances in Complex Systems}, volume = {27}, journal = {Advances in Complex Systems}, doi = {10.1142/S0219525924400034}, abstract = {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.}, language = {en} } @article{TrowerDjurdjevacConradKlus, author = {Trower, Maia and Djurdjevac Conrad, Natasa and Klus, Stefan}, title = {Clustering Time-Evolving Networks Using the Dynamic Graph Laplacian}, abstract = {Time-evolving graphs arise frequently when modeling complex dynamical systems such as social networks, traffic flow, and biological processes. Developing techniques to identify and analyze communities in these time-varying graph structures is an important challenge. In this work, we generalize existing spectral clustering algorithms from static to dynamic graphs using canonical correlation analysis (CCA) to capture the temporal evolution of clusters. Based on this extended canonical correlation framework, we define the dynamic graph Laplacian and investigate its spectral properties. We connect these concepts to dynamical systems theory via transfer operators, and illustrate the advantages of our method on benchmark graphs by comparison with existing methods. We show that the dynamic graph Laplacian allows for a clear interpretation of cluster structure evolution over time for directed and undirected graphs.}, language = {en} } @inproceedings{BorndoerferDaneckerWeiser, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization}, series = {23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)}, volume = {115}, booktitle = {23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)}, doi = {10.4230/OASIcs.ATMOS.2023.3}, pages = {3:1 -- 3:6}, abstract = {The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition.}, language = {en} } @article{BetzHammerschmidtZschiedrichetal., author = {Betz, Fridtjof and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven and Binkowski, Felix}, title = {Efficient rational approximation of optical response functions with the AAA algorithm}, series = {Laser Photonics Rev.}, journal = {Laser Photonics Rev.}, doi = {10.1002/lpor.202400584}, pages = {2400584}, language = {en} } @phdthesis{Danecker, author = {Danecker, Fabian}, title = {A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization}, abstract = {This thesis introduces the novel hybrid algorithm DisCOptER for globally optimal flight planning. DisCOptER (Discrete-Continuous Optimization for Enhanced Resolution) com- bines discrete and continuous optimization in a two-stage approach to find optimal trajectories up to arbitrary precision in finite time. In the discrete phase, a directed auxiliary graph is created in order to define a set of candidate paths that densely covers the relevant part of the trajectory space. Then, Yen's algorithm is employed to identify a set of promising candidate paths. These are used as starting points for the subsequent stage in which they are refined with a locally convergent optimal control method. The correctness, accuracy, and complexity of DisCOptER are intricately linked to the choice of the switch-over point, defined by the discretization coarseness. Only a sufficiently dense graph enables the algorithm to find a path within the convex domain surrounding the global minimizer. Initialized with such a path, the second stage rapidly converges to the optimum. Conversely, an excessively dense graph poses the risk of overly costly and redundant computations. The determination of the optimal switch-over point necessitates a profound understanding of the local behavior of the problem, the approximation properties of the graph, and the convergence characteristics of the employed optimal control method. These topics are explored extensively in this thesis. Crucially, the density of the auxiliary graph is solely dependent on the en- vironmental conditions, yet independent of the desired solution accuracy. As a consequence, the algorithm inherits the superior asymptotic convergence properties of the optimal control stage. The practical implications of this computational efficiency are demonstrated in realistic environments, where the DisCOptER algorithm consistently delivers highly accurate globally optimal trajectories with exceptional computational efficiency. This notable improvement upon existing approaches underscores the algorithm's significance. Beyond its technical prowess, the DisCOptER algorithm stands as a valuable tool contributing to the reduction of costs and the overall enhancement of flight operations efficiency.}, language = {en} } @article{SikorskiHeida, author = {Sikorski, Alexander and Heida, Martin}, title = {Voronoi Graph - Improved raycasting and integration schemes for high dimensional Voronoi diagrams}, abstract = {The computation of Voronoi Diagrams, or their dual Delauney triangulations is difficult in high dimensions. In a recent publication Polianskii and Pokorny propose an iterative randomized algorithm facilitating the approximation of Voronoi tesselations in high dimensions. In this paper, we provide an improved vertex search method that is not only exact but even faster than the bisection method that was previously recommended. Building on this we also provide a depth-first graph-traversal algorithm which allows us to compute the entire Voronoi diagram. This enables us to compare the outcomes with those of classical algorithms like qHull, which we either match or marginally beat in terms of computation time. We furthermore show how the raycasting algorithm naturally lends to a Monte Carlo approximation for the volume and boundary integrals of the Voronoi cells, both of which are of importance for finite Volume methods. We compare the Monte-Carlo methods to the exact polygonal integration, as well as a hybrid approximation scheme.}, language = {en} } @article{StraubeHoefling, author = {Straube, Arthur and H{\"o}fling, Felix}, title = {Depinning transition of self-propelled particles}, abstract = {A depinning transition is observed in a variety of contexts when a certain threshold force must be applied to drive a system out of an immobile state. A well-studied example is the depinning of colloidal particles from a corrugated landscape, whereas its active-matter analogue has remained unexplored. We discuss how active noise due to self-propulsion impacts the nature of the transition: it causes a change of the critical exponent from 1/2 for quickly reorienting particles to 3/2 for slowly reorienting ones. In between these analytically tractable limits, the drift velocity exhibits a superexponential behavior as is corroborated by high-precision data. Giant diffusion phenomena occur in the two different regimes. Our predictions appear amenable to experimental tests, lay foundations for insight into the depinning of collective variables in active matter, and are relevant for any system with a saddle-node bifurcation in the presence of a bounded noise.}, language = {en} } @article{BonifaceStraubeTierno, author = {Boniface, Dolachai and Straube, Arthur and Tierno, Pietro}, title = {Photocatalytic magnetic microgyroscopes with activity-tunable precessional dynamics}, abstract = {Magnetic nano/microrotors are passive elements that spin around an axis due to an external rotating field while remaining confined to a close plane. They have been used to date in different applications related to fluid mixing, drug delivery or biomedicine. Here we realize an active version of a magnetic microgyroscope which is simultaneously driven by a photo-activated catalytic reaction and a rotating magnetic field. We investigate the uplift dynamics of this colloidal spinner when it stands up and precesses around its long axis while self-propelling due to the light induced decomposition of hydrogen peroxide in water. By combining experiments with theory, we show that activity emerging from the cooperative action of phoretic and osmotic forces effectively increase the gravitational torque which counteracts the magnetic and viscous ones, and carefully measure its contribution.}, language = {en} } @inproceedings{VillaniUngerWeiser, author = {Villani, Paolo and Unger, J{\"o}rg F. and Weiser, Martin}, title = {Adaptive Gaussian Process Regression for Bayesian inverse problems}, series = {ALGORITMY 2024 Proceedings}, booktitle = {ALGORITMY 2024 Proceedings}, abstract = {We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on optimizing both the positioning and simulation accuracy of training data in order to reduce the computational cost of simulating training data without compromising the fidelity of the posterior distributions of parameters. The method interleaves a goal-oriented active learning algorithm selecting evaluation points and tolerances based on the expected impact on the Kullback-Leibler divergence of surrogated and true posterior with a Markov Chain Monte Carlo sampling of the posterior. The performance benefit of the adaptive approach is demonstrated for two simple test problems.}, language = {en} } @misc{VillaniWeiser, author = {Villani, Paolo and Weiser, Martin}, title = {Adaptive Gaussian process regression for inverse problems. ALGORITMY 2024}, abstract = {This submission contains the code used for the proceedings paper for ALGORITMY 2024, concerning surrogate model-based inverse problems. Version 2 modified plot appearances and fixed some minor typos.}, language = {en} } @article{BorndoerferDaneckerWeiser, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Newton's Method for Global Free Flight Trajectory Optimization}, series = {Operations Research Forum}, volume = {4}, journal = {Operations Research Forum}, doi = {10.1007/s43069-023-00238-z}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-91846}, abstract = {Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case.}, language = {en} } @article{SchemberaWuebbelingKopruckietal., author = {Schembera, Bj{\"o}rn and W{\"u}bbeling, Frank and Koprucki, Thomas and Biedinger, Christine and Reidelbach, Marco and Schmidt, Burkhard and G{\"o}ddeke, Dominik and Fiedler, Jochen}, title = {Building Ontologies and Knowledge Graphs for Mathematics and its Applications}, series = {Proceedings of the Conference on Research Data Infrastructure}, volume = {1}, journal = {Proceedings of the Conference on Research Data Infrastructure}, publisher = {TIB Open Publishing}, issn = {2941-296X}, doi = {10.52825/cordi.v1i.255}, abstract = {Ontologies and knowledge graphs for mathematical algorithms and models are presented, that have been developed by the Mathematical Research Data Initiative. This enables FAIR data handling in mathematics and the applied disciplines. Moreover, challenges of harmonization during the ontology development are discussed.}, language = {en} } @article{WehlitzSadeghiMontefuscoetal., author = {Wehlitz, Nathalie and Sadeghi, Mohsen and Montefusco, Alberto and Sch{\"u}tte, Christof and Pavliotis, Grigorios A. and Winkelmann, Stefanie}, title = {Approximating particle-based clustering dynamics by stochastic PDEs}, abstract = {This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane mediated receptor dynamics on cell surfaces, we formulate a stochastic particle-based model for diffusion and pairwise interaction of particles, leading to intriguing clustering phenomena. Employing numerical simulation and cluster detection methods, we explore the approximation of the particle-based clustering dynamics through mean-field approaches. We find that SPDEs successfully reproduce spatiotemporal clustering dynamics, not only in the initial cluster formation period, but also on longer time scales where the successive merging of clusters cannot be tracked by deterministic mean-field models. The computational efficiency of the SPDE approach allows us to generate extensive statistical data for parameter estimation in a simpler model that uses a Markov jump process to capture the temporal evolution of the cluster number.}, language = {en} } @inproceedings{SchemberaWuebbelingKleikampetal., author = {Schembera, Bj{\"o}rn and W{\"u}bbeling, Frank and Kleikamp, Hendrik and Biedinger, Christine and Fiedler, Jochen and Reidelbach, Marco and Shehu, Aurela and Schmidt, Burkhard and Koprucki, Thomas and Iglezakis, Dotothea and G{\"o}ddeke, Dominik}, title = {Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines}, series = {Metadata and Semantic Research - MTSR 2023}, booktitle = {Metadata and Semantic Research - MTSR 2023}, edition = {Communications in Computer and Information Science}, publisher = {Springer Nature Switzerland}, address = {Cham}, doi = {10.1007/978-3-031-65990-4_14}, pages = {161 -- 168}, abstract = {In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data, the Mathematical Research Data Initiative has developed, merged and implemented ontologies and knowledge graphs. This contributes to making mathematical research data FAIR by introducing semantic technology and documenting the mathematical foundations accordingly. Using the concrete example of microfracture analysis of porous media, it is shown how the knowledge of the underlying mathematical model and the corresponding numerical algorithms for its solution can be represented by the ontologies.}, language = {en} } @inproceedings{ReidelbachSchemberaWeber, author = {Reidelbach, Marco and Schembera, Bj{\"o}rn and Weber, Marcus}, title = {Towards a FAIR Documentation of Workflows and Models in Applied Mathematics}, series = {Mathematical Software - ICMS 2024}, volume = {14749}, booktitle = {Mathematical Software - ICMS 2024}, edition = {Lecture Notes in Computer Science}, publisher = {Springer Nature Switzerland}, address = {Cham}, doi = {10.1007/978-3-031-64529-7_27}, pages = {254 -- 262}, abstract = {Modeling-Simulation-Optimization workflows play a fundamental role in applied mathematics. The Mathematical Research Data Initiative, MaRDI, responded to this by developing a FAIR and machine-interpretable template for a comprehensive documentation of such workflows. MaRDMO, a Plugin for the Research Data Management Organiser, enables scientists from diverse fields to document and publish their workflows on the MaRDI Portal seamlessly using the MaRDI template. Central to these workflows are mathematical models. MaRDI addresses them with the MathModDB ontology, offering a structured formal model description. Here, we showcase the interaction between MaRDMO and the MathModDB Knowledge Graph through an algebraic modeling workflow from the Digital Humanities. This demonstration underscores the versatility of both services beyond their original numerical domain.}, language = {en} } @inproceedings{RichterBerner, author = {Richter, Lorenz and Berner, Julius}, title = {Improved sampling via learned diffusions}, series = {International Conference on Learning Representations 2024}, booktitle = {International Conference on Learning Representations 2024}, abstract = {Recently, a series of papers proposed deep learning-based approaches to sample from unnormalized target densities using controlled diffusion processes. In this work, we identify these approaches as special cases of the Schr{\"o}dinger bridge problem, seeking the most likely stochastic evolution between a given prior distribution and the specified target. We further generalize this framework by introducing a variational formulation based on divergences between path space measures of time-reversed diffusion processes. This abstract perspective leads to practical losses that can be optimized by gradient-based algorithms and includes previous objectives as special cases. At the same time, it allows us to consider divergences other than the reverse Kullback-Leibler divergence that is known to suffer from mode collapse. In particular, we propose the so-called log-variance loss, which exhibits favorable numerical properties and leads to significantly improved performance across all considered approaches.}, language = {en} } @article{RiberaBorrellQuerRichteretal., author = {Ribera Borrell, Enric and Quer, Jannes and Richter, Lorenz and Sch{\"u}tte, Christof}, title = {Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics}, series = {SIAM Journal on Scientific Computing (SISC)}, volume = {89}, journal = {SIAM Journal on Scientific Computing (SISC)}, number = {1}, doi = {10.1137/22M1503464}, abstract = {Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings.}, language = {en} } @article{RichterSallandtNuesken, author = {Richter, Lorenz and Sallandt, Leon and N{\"u}sken, Nikolas}, title = {From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs}, series = {Journal of Machine Learning Research}, journal = {Journal of Machine Learning Research}, abstract = {The numerical approximation of partial differential equations (PDEs) poses formidable challenges in high dimensions since classical grid-based methods suffer from the so-called curse of dimensionality. Recent attempts rely on a combination of Monte Carlo methods and variational formulations, using neural networks for function approximation. Extending previous work (Richter et al., 2021), we argue that tensor trains provide an appealing framework for parabolic PDEs: The combination of reformulations in terms of backward stochastic differential equations and regression-type methods holds the romise of leveraging latent low-rank structures, enabling both compression and efficient computation. Emphasizing a continuous-time viewpoint, we develop iterative schemes, which differ in terms of computational efficiency and robustness. We demonstrate both theoretically and numerically that our methods can achieve a favorable trade-off between accuracy and computational efficiency. While previous methods have been either accurate or fast, we have identified a novel numerical strategy that can often combine both of these aspects.}, language = {en} }