@article{WulkowKoltaiSchuette2021, 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}, volume = {31}, journal = {Journal of Nonlinear Science}, doi = {10.1007/s00332-020-09673-2}, year = {2021}, 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{StraubeKowalikNetzetal.2020, 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}, volume = {3}, journal = {Commun. Phys.}, publisher = {Nature}, doi = {10.1038/s42005-020-0389-0}, pages = {126}, year = {2020}, 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{FischerEhrigSchaeferetal.2021, 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}, volume = {12}, journal = {Frontiers in Endocrinology}, doi = {10.3389/fendo.2021.613048}, year = {2021}, 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} } @article{FackeldeyOsterSallandtetal.2022, 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}, volume = {20}, journal = {SIAM Journal on Multiscale Modeling and Simulation}, number = {1}, arxiv = {http://arxiv.org/abs/2010.04465}, doi = {10.1137/20M1372500}, pages = {379 -- 403}, year = {2022}, 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{HelfmannDjurdjevacConradDjurdjevacetal.2021, 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}, volume = {16}, journal = {Communications in Applied Mathematics and Computational Science}, number = {1}, arxiv = {http://arxiv.org/abs/1905.13525}, doi = {10.2140/camcos.2021.16.1}, pages = {1 -- 32}, year = {2021}, 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{ChewleEmmerlingWeber2020, 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}, volume = {10}, journal = {Crystals}, number = {12}, doi = {10.3390/cryst10121107}, pages = {1107}, year = {2020}, 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{NiemannKlusSchuette2021, 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}, volume = {16}, journal = {PLOS ONE}, number = {5}, arxiv = {http://arxiv.org/abs/2012.07718}, doi = {10.1371/journal.pone.0250970}, year = {2021}, 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{BeckerJaegerBurger2021, author = {Becker, Christiane and J{\"a}ger, Klaus and Burger, Sven}, title = {Nanophotonics for Solar Energy}, volume = {221}, journal = {Sol. Energy Mater. Sol. Cells}, doi = {10.1016/j.solmat.2020.110916}, pages = {110916}, year = {2021}, language = {en} } @article{KlebanovSchuster2020, author = {Klebanov, Ilja and Schuster, Ingmar}, title = {Markov Chain Importance Sampling - a highly efficient estimator for MCMC}, journal = {Journal of Computational and Graphical Statistics}, doi = {10.1080/10618600.2020.1826953}, year = {2020}, 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.2020, 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}, volume = {7}, journal = {Appl. Phys. Rev.}, doi = {10.1063/5.0025006}, pages = {041413}, year = {2020}, language = {en} } @article{SchneckWeiserWende2021, author = {Schneck, Jakob and Weiser, Martin and Wende, Florian}, title = {Impact of mixed precision and storage layout on additive Schwarz smoothers}, volume = {28}, journal = {Numerical Linear Algebra with Applications}, number = {4}, doi = {10.1002/nla.2366}, year = {2021}, 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{WulkowConradDjurdjevacConradetal.2021, 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}, volume = {16}, journal = {PLOS One}, number = {4}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0249676}, year = {2021}, language = {en} } @article{ZimperDjurdjevacHartmannetal.2025, author = {Zimper, Sebastian and Djurdjevac, Ana and Hartmann, Carsten and Sch{\"u}tte, Christof and Conrad, Natasa Djurdjevac}, title = {Mean-field optimal control with stochastic leaders}, arxiv = {http://arxiv.org/abs/2512.19201}, year = {2025}, abstract = {We consider interacting agent systems with a large number of stochastic agents (or particles) influenced by a fixed number of external stochastic lead agents. Such examples arise, for example in models of opinion dynamics, where a small number of leaders (influencers) can steer the behaviour of a large population of followers. In this context, we study a partial mean-field limit where the number of followers tends to infinity, while the number of leaders stays constant. The partial mean-field limit dynamics is then given by a McKean-Vlasov stochastic differential equation (SDE) for the followers, coupled to a controlled It{\^o}-SDE governing the dynamics of the lead agents. For a given cost functional that the lead agents seek to minimise, we show that the unique optimal control of the finite agent system convergences to the optimal control of the limiting system. This establishes that the low-dimensional control of the partial (mean-field) system provides an effective approximation for controlling the high-dimensional finite agent system. In addition, we propose a stochastic gradient descent algorithm that can efficiently approximate the mean-field control. Our theoretical results are illustrated on opinion dynamics model with lead agents, where the control objective is to drive the followers to reach consensus in finite time.}, language = {en} } @article{HartmannJoesterSchuetteetal.2026, author = {Hartmann, Carsten and J{\"o}ster, Annika and Sch{\"u}tte, Christof and Sikorski, Alexander and Weber, Marcus}, title = {Importance sampling of unbounded random stopping times: computing committor functions and exit rates without reweighting}, arxiv = {http://arxiv.org/abs/2601.01489}, year = {2026}, abstract = {Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on average exponentially long compared to the characteristic timescale of the system, with waiting time distributions that have (sub)exponential tails and infinite support. As a result, sampling such rare events can lead to trajectories that can be become arbitrarily long, with not too low probability, which makes the reweighting of such trajectories a real challenge. Here, we discuss rare event simulation by importance sampling from a variational perspective, with a focus on applications in molecular dynamics, in particular the computation of committor functions. The idea is to design importance sampling schemes that (a) reduce the variance of a rare event estimator while controlling the average length of the trajectories and (b) that do not require the reweighting of possibly very long trajectories. In doing so, we study different stochastic control formulations for committor and mean first exit times, which we compare both from a theoretical and a computational point of view, including numerical studies of some benchmark examples.}, language = {en} } @article{GarciaSantiagoHammerschmidtSachsetal.2022, 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}, volume = {9}, journal = {ACS Photonics}, arxiv = {http://arxiv.org/abs/2112.04422}, doi = {10.1021/acsphotonics.1c01887}, pages = {1954}, year = {2022}, language = {en} } @misc{ErnstSchuetteSigristetal.2021, 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}, year = {2021}, 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{ErnstSchuetteSigristetal.2022, 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}, volume = {343}, journal = {Mathematical Biosciences}, doi = {10.1016/j.mbs.2021.108760}, year = {2022}, 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{ThiesSunkaraRayetal.2023, 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}, volume = {13}, journal = {Scientific Reports}, number = {607}, doi = {10.1038/s41598-023-27699-w}, year = {2023}, 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} } @misc{RayThiesSunkaraetal.2021, 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}, year = {2021}, 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} } @phdthesis{Pakhomov2021, author = {Pakhomov, Anton}, title = {Efficient modeling and optimization of surface second-harmonic generation from nanophotonic components}, doi = {10.22032/dbt.49369}, year = {2021}, language = {en} } @article{PrasadTiwariRayetal.2022, 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}, volume = {87}, journal = {ChemPlusChem}, doi = {10.1002/cplu.202100408}, pages = {e202100408}, year = {2022}, language = {en} } @article{BergPloentzkeSiebertetal.2021, 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}, volume = {83}, journal = {Bulletin of Mathematical Biology}, number = {121}, doi = {10.1007/s11538-021-00942-z}, pages = {1 -- 25}, year = {2021}, 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{Djurdjevac2021, 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}, year = {2021}, 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{DjurdjevacGraeserHerbert2021, author = {Djurdjevac, Ana and Gr{\"a}ser, Carsten and Herbert, Philip J.}, title = {Non-stationary incompressible linear fluid equations in a moving domain}, journal = {arXiv}, arxiv = {http://arxiv.org/abs/2106.08312}, year = {2021}, 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{ColomMikheevaAchourietal.2023, 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}, volume = {17}, journal = {Laser Photonics Rev.}, arxiv = {http://arxiv.org/abs/2202.05632}, doi = {10.1002/lpor.202200976}, pages = {2200976}, year = {2023}, 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}, volume = {83}, journal = {SIAM Journal on Applied Mathematics}, number = {2}, arxiv = {http://arxiv.org/abs/2201.02613}, 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{DellnitzHuellermeierLueckeetal.2023, 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}, volume = {45}, journal = {SIAM Journal on Scientific Computing}, number = {2}, doi = {10.1137/21M1412682}, pages = {A579 -- A595}, year = {2023}, language = {en} } @article{PeppertvonKleistSchuetteetal.2022, 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}, volume = {33}, journal = {IEEE Transactions on Neural Networks and Learning Systems}, number = {11}, doi = {10.1109/TNNLS.2021.3072746}, pages = {6194 -- 6205}, year = {2022}, 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{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}, 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} } @misc{PfluegerKlineFernandezHerreroetal.2020, 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}, year = {2020}, language = {en} } @article{GaoRickertUrbanetal.2022, 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}, volume = {9}, journal = {Appl. Phys. Rev.}, arxiv = {http://arxiv.org/abs/2105.03473}, doi = {10.1063/5.0070966}, pages = {011412}, year = {2022}, language = {en} } @article{TorunSchneiderHammerschmidtetal.2021, 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}, volume = {118}, journal = {Appl. Phys. Lett.}, arxiv = {http://arxiv.org/abs/2105.13333}, doi = {10.1063/5.0050338}, pages = {234002}, year = {2021}, language = {en} } @article{GorgullaCınaroğluFischeretal.2021, 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}, volume = {22}, journal = {Special Issue Artificial Intelligence \& Deep Learning Approaches for Structural Bioinformatics}, number = {11}, doi = {https://doi.org/10.3390/ijms22115807}, pages = {5807}, year = {2021}, 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{AhibozAndresenManleyetal.2021, 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}, volume = {9}, journal = {Adv. Opt. Mater.}, doi = {10.1002/adom.202101285}, pages = {2101285}, year = {2021}, language = {en} } @article{MartensFunckSantiagoetal.2022, 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}, volume = {16}, journal = {ACS Nano}, arxiv = {http://arxiv.org/abs/2110.06689}, doi = {10.1021/acsnano.2c04729}, pages = {16143}, year = {2022}, language = {en} } @inproceedings{PerevoznikBoseBurgeretal.2021, author = {Perevoznik, Dmitrii and Bose, Surajit and Burger, Sven and Demircan, Ayhan and Morgner, Uwe}, title = {Photonic components in polymers made by femtosecond pulses}, 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}, year = {2021}, language = {en} } @inproceedings{AhibozAndresenManleyetal.2021, 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}, booktitle = {IEEE 48th Photovoltaic Specialists Conference (PVSC)}, doi = {10.1109/PVSC43889.2021.9518495}, pages = {2008 -- 2010}, year = {2021}, language = {en} } @article{BittracherMollenhauerKoltaietal.2023, 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}, volume = {21}, journal = {Multiscale Modelling \& Simulation}, number = {2}, arxiv = {http://arxiv.org/abs/2107.10158}, doi = {10.1137/21M1448367}, pages = {449 -- 488}, year = {2023}, 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{MollenhauerKlusSchuetteetal.2022, 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}, volume = {23}, journal = {Journal of Machine Learning Research}, number = {327}, arxiv = {http://arxiv.org/abs/2004.00891}, pages = {1 -- 34}, year = {2022}, 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} } @inproceedings{RickertGaoUrbanetal.2021, 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}, booktitle = {Quantum Information and Measurement VI}, doi = {10.1364/QIM.2021.M2C.1}, pages = {M2C.1}, year = {2021}, language = {en} } @article{HeidaSikorskiWeber2022, 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}, journal = {SIAM Journal on Numerical Analysis}, doi = {10.20347/WIAS.PREPRINT.2913}, year = {2022}, 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} } @inproceedings{SchneiderGarciaSantiagoWiegandetal.2021, 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}, booktitle = {OSA Advanced Photonics Congress}, doi = {10.1364/IPRSN.2021.JTh1E.2}, pages = {JTh1E.2}, year = {2021}, language = {en} } @article{ColomBinkowskiBetzetal.2022, author = {Colom, Remi and Binkowski, Felix and Betz, Fridtjof and Kivshar, Yuri and Burger, Sven}, title = {Enhanced Purcell factor for nanoantennas supporting interfering resonances}, volume = {4}, journal = {Phys. Rev. Research}, arxiv = {http://arxiv.org/abs/2111.03339}, doi = {10.1103/PhysRevResearch.4.023189}, pages = {023189}, year = {2022}, language = {en} } @article{LueckeNueske2022, author = {L{\"u}cke, Marvin and N{\"u}ske, Feliks}, title = {tgEDMD: Approximation of the Kolmogorov Operator in Tensor Train Format}, volume = {32}, journal = {Journal of Nonlinear Science}, doi = {10.1007/s00332-022-09801-0}, year = {2022}, 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} } @inproceedings{MusialZolnaczSrockaetal.2020, 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}, booktitle = {10th International Conference on Spontaneous Coherence in Excitonic Systems ICSCE10}, pages = {39}, year = {2020}, language = {en} } @article{FackeldeyGorgullaWeber2021, author = {Fackeldey, Konstantin and Gorgulla, Christoph and Weber, Marcus}, title = {Neue Medikamente dank Supercomputern}, journal = {Spektrum der Wissenschaft}, number = {11}, pages = {40 -- 46}, year = {2021}, 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{StoutColomBonodetal.2021, 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}, volume = {23}, journal = {New J. Phys.}, doi = {10.1088/1367-2630/ac10a6}, pages = {083004}, year = {2021}, language = {en} } @article{HungenbergSchwedeWulkowetal.2021, 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}, journal = {Canadian Journal of Chemical Engineering}, doi = {https://doi.org/10.1002/cjce.24330}, pages = {1 -- 10}, year = {2021}, 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} } @article{DriesenElKhatibWulkowetal.2021, 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}, volume = {18}, journal = {International Journal of Environmental Research and Public Health}, number = {9765}, doi = {https://doi.org/10.3390/ijerph18189765}, pages = {1 -- 29}, year = {2021}, 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{BirkRaharinirinaFackeldeyetal.2021, 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}, year = {2021}, 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} }