@phdthesis{Venkatareddy2020, author = {Venkatareddy, Narendra Lagumaddepalli}, title = {Revealing secrets of mussel-glue mimetic peptides - From advanced NMR to computational process modelling}, year = {2020}, language = {en} } @phdthesis{Eshtewy2020, author = {Eshtewy, Neveen Ali Salem}, title = {Mathematical Modeling of Metabolic-Genetic Networks}, year = {2020}, language = {en} } @article{OettingerMontefuscoPeletier2021, 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}, volume = {46}, journal = {Journal of Non-Equilibrium Thermodynamics}, number = {1}, publisher = {De Gruyter}, doi = {10.1515/jnet-2020-0068}, pages = {1 -- 13}, year = {2021}, 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{MontefuscoPeletierOettinger2021, author = {Montefusco, Alberto and Peletier, Mark A. and {\"O}ttinger, Hans Christian}, title = {A Framework of Nonequilibrium Statistical Mechanics. II. Coarse-Graining}, volume = {46}, journal = {Journal of Non-Equilibrium Thermodynamics}, number = {1}, publisher = {De Gruyter}, doi = {10.1515/jnet-2020-0069}, pages = {15 -- 33}, year = {2021}, 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{SunkaraHeinzHeinrichetal.2020, 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}, journal = {bioarxiv (Accepted in Osteoarthr. Cartil.)}, doi = {10.1101/2020.06.13.148056}, year = {2020}, language = {en} } @article{LangHelfmeierStefanowskietal.2020, 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}, journal = {bioarxiv}, doi = {10.1101/2020.07.02.182832}, year = {2020}, language = {en} } @article{LaydonSunkaraBoelenetal.2020, 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}, journal = {PLOS Computational Biology}, doi = {10.1371/journal.pcbi.1007470}, year = {2020}, language = {en} } @article{SchielaStoeckleinWeiser2021, author = {Schiela, Anton and St{\"o}cklein, Matthias and Weiser, Martin}, title = {A primal dual projection algorithm for efficient constraint preconditioning}, volume = {43}, journal = {SIAM Journal on Scientific Computing}, number = {6}, doi = {10.1137/20M1380739}, pages = {A4095 -- A4120}, year = {2021}, 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} } @article{MielkeMontefuscoPeletier2021, author = {Mielke, Alexander and Montefusco, Alberto and Peletier, Mark A.}, title = {Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence}, volume = {33}, journal = {Continuum Mechanics and Thermodynamics}, publisher = {Springer}, doi = {10.1007/s00161-020-00932-x}, pages = {611 -- 637}, year = {2021}, 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} } @phdthesis{Santiago2021, 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}, year = {2021}, language = {en} } @article{RaharinirinaAcevedoTrejosMerico2022, author = {Raharinirina, N. Alexia and Acevedo-Trejos, Esteban and Merico, Agostino}, title = {Modelling the acclimation capacity of coral reefs to a warming ocean}, journal = {PLOS COMPUTATIONAL BIOLOGY}, doi = {10.1371/journal.pcbi.1010099}, year = {2022}, 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} } @misc{SchuetteKlusHartmann2022, 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}, year = {2022}, 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{RamosLeiteZschiedrichKizilkayaetal.2022, 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}, volume = {22}, journal = {Nano Lett.}, doi = {10.1021/acs.nanolett.2c01724}, pages = {7343}, year = {2022}, language = {en} } @article{RejSantiagoBaturinaetal.2022, 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}, volume = {104}, journal = {Nano Energy}, arxiv = {http://arxiv.org/abs/2209.04678}, doi = {10.1016/j.nanoen.2022.107989}, pages = {107989}, year = {2022}, language = {en} } @inproceedings{BernerRichterUllrich2024, author = {Berner, Julius and Richter, Lorenz and Ullrich, Karen}, title = {An optimal control perspective on diffusion-based generative modeling}, booktitle = {Transactions on Machine Learning Research}, year = {2024}, 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} } @article{NueskenRichter2023, author = {N{\"u}sken, Nikolas and Richter, Lorenz}, title = {Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems}, volume = {2}, journal = {Journal of Machine Learning}, number = {1}, arxiv = {http://arxiv.org/abs/2112.03749}, doi = {0.4208/jml.220416}, pages = {31 -- 64}, year = {2023}, 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} } @article{HartmannRichter2024, author = {Hartmann, Carsten and Richter, Lorenz}, title = {Nonasymptotic bounds for suboptimal importance sampling}, volume = {12}, journal = {SIAM/ASA Journal on Uncertainty Quantification}, number = {2}, arxiv = {http://arxiv.org/abs/2102.09606}, doi = {10.1137/21M1427760}, pages = {309 -- 346}, year = {2024}, 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} } @article{RickertBetzPlocketal.2023, 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}, volume = {31}, journal = {Opt. Express}, arxiv = {http://arxiv.org/abs/2212.04883}, doi = {10.1364/OE.486060}, pages = {14750}, year = {2023}, language = {en} } @misc{RickertBetzPlocketal.2022, 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"}, journal = {Zenodo}, doi = {10.5281/zenodo.7360516}, pages = {7360516}, year = {2022}, language = {en} } @article{GorgullaJayarajFackeldeyetal.2022, 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}, volume = {69}, journal = {Current Opinion in Chemical Biology}, doi = {10.1016/j.cbpa.2022.102156}, pages = {102156 -- 102156-12}, year = {2022}, 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} } @misc{StraubeWinkelmannHoefling2022, 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}, year = {2022}, 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{DonatiWeber2022, author = {Donati, Luca and Weber, Marcus}, title = {Assessing transition rates as functions of environmental variables}, volume = {157}, journal = {The Journal of Chemical Physics}, number = {22}, publisher = {AIP Publishing}, doi = {10.1063/5.0109555}, pages = {224103-1 -- 224103-14}, year = {2022}, 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{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}, 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{DjurdjevacConradKoepplDjurdjevac2022, 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}, volume = {24(10)}, journal = {Entropy}, arxiv = {http://arxiv.org/abs/2209.07151}, doi = {10.3390/e24101352}, year = {2022}, 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{DonatiWeberKeller2022, 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}, volume = {63}, journal = {Journal of Mathematical Physics}, number = {12}, publisher = {AIP Publishing}, doi = {10.1063/5.0127227}, pages = {123306-1 -- 123306-21}, year = {2022}, 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{QuerRiberaBorrell2024, author = {Quer, Jannes and Ribera Borrell, Enric}, title = {Connecting Stochastic Optimal Control and Reinforcement Learning}, volume = {65}, journal = {Journal of Mathematical Physics}, number = {8}, doi = {10.1063/5.0140665}, year = {2024}, abstract = {In this paper the connection between stochastic optimal control and reinforcement learning is investigated. Our main motivation is to apply importance sampling to sampling rare events which can be reformulated as an optimal control problem. By using a parameterised approach the optimal control problem becomes a stochastic optimization problem which still raises some open questions regarding how to tackle the scalability to high-dimensional problems and how to deal with the intrinsic metastability of the system. To explore new methods we link the optimal control problem to reinforcement learning since both share the same underlying framework, namely a Markov Decision Process (MDP). For the optimal control problem we show how the MDP can be formulated. In addition we discuss how the stochastic optimal control problem can be interpreted in the framework of reinforcement learning. At the end of the article we present the application of two different reinforcement learning algorithms to the optimal control problem and a comparison of the advantages and disadvantages of the two algorithms.}, language = {en} } @article{RayFackeldeySteinetal.2023, 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}, volume = {3}, journal = {Biophysica}, number = {2}, doi = {10.3390/biophysica3020017}, pages = {263 -- 275}, year = {2023}, 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} } @inproceedings{RichterBerner2022, author = {Richter, Lorenz and Berner, Julius}, title = {Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning}, volume = {162}, booktitle = {Proceedings of the 39th International Conference on Machine Learning, PMLR}, pages = {18649 -- 18666}, year = {2022}, 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} } @article{delRazoWinkelmannKleinetal.2023, 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}, volume = {64}, journal = {Journal of Mathematical Physics}, number = {1}, arxiv = {http://arxiv.org/abs/2210.02268}, doi = {10.1063/5.0129620}, year = {2023}, 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{LueckeHeitzigKoltaietal.2023, 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}, volume = {166}, journal = {Stochastic Processes and their Applications}, arxiv = {http://arxiv.org/abs/2210.02934}, doi = {10.1016/j.spa.2023.09.007}, year = {2023}, 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{SchneiderZschiedrichHammerschmidtetal.2022, author = {Schneider, Philipp-Immanuel and Zschiedrich, Lin and Hammerschmidt, Martin and Kuen, Lilli and Sekulic, Ivan and Kluge, Julien and Leykauf, Bastian and Krutzik, Markus and Burger, Sven}, title = {Boosting quantum optics experiments with Bayesian optimization}, volume = {12227}, booktitle = {Proc. SPIE}, doi = {10.1117/12.2632419}, pages = {122270F}, year = {2022}, language = {en} } @inproceedings{KruegerManleyZschiedrichetal.2022, 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}, booktitle = {Proc. DGaO}, url = {http://nbn-resolving.de/urn:nbn:de:0287-2022-P005-6}, pages = {P5}, year = {2022}, language = {en} } @article{BoppPlockTuranetal.2024, 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}, volume = {12}, journal = {Adv. Opt. Mater.}, arxiv = {http://arxiv.org/abs/2210.04702}, doi = {10.1002/adom.202301286}, pages = {2301286}, year = {2024}, language = {en} } @inproceedings{ManleyKruegerZschiedrichetal.2022, 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}, volume = {266}, booktitle = {EPJ Web Conf.}, doi = {10.1051/epjconf/202226610010}, pages = {10010}, year = {2022}, language = {en} } @article{RaharinirinaFackeldeyWeber2022, author = {Raharinirina, N. Alexia and Fackeldey, Konstantin and Weber, Marcus}, title = {Qualitative Euclidean embedding of Disjoint Sets of Points}, year = {2022}, 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{BoegeFritzeGoergenetal.2023, 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}, volume = {130}, journal = {Eur. Math. Soc. Mag.}, doi = {10.4171/mag/152}, pages = {40 -- 47}, year = {2023}, 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} } @article{ReidelbachBaiZoellneretal.2022, 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}, journal = {Journal of Physical Chemistry}, year = {2022}, language = {en} } @misc{ReidelbachWeber2022, author = {Reidelbach, Marco and Weber, Marcus}, title = {MaRDI - The mathematical Research Data Initiative}, journal = {Aktionstag Forschungsdaten}, doi = {10.5281/zenodo.7397588}, year = {2022}, language = {en} } @article{BetzHammerschmidtZschiedrichetal.2024, 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}, volume = {18}, journal = {Laser Photonics Rev.}, arxiv = {http://arxiv.org/abs/2403.19404}, doi = {10.1002/lpor.202400584}, pages = {2400584}, year = {2024}, language = {en} } @misc{BetzHammerschmidtZschiedrichetal.2024, 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}, journal = {Zenodo}, doi = {10.5281/zenodo.10853692}, pages = {doi: 10.5281/zenodo.10853692}, year = {2024}, language = {en} } @article{SikorskiNiknejadWeberetal.2024, 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}, volume = {160}, journal = {Journal of Chemical Physics}, arxiv = {http://arxiv.org/abs/2311.09779}, doi = {10.1063/5.0187792}, pages = {104112}, year = {2024}, 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} } @inproceedings{SikorskiRabbenChewleetal.2025, author = {Sikorski, Alexander and Rabben, Robert Julian and Chewle, Surahit and Weber, Marcus}, title = {Capturing the Macroscopic Behaviour of Molecular Dynamics with Membership Functions}, booktitle = {Mathematical Optimization for Machine Learning: Proceedings of the MATH+ Thematic Einstein Semester 2023}, editor = {Fackeldey, K.}, publisher = {De Gruyter}, arxiv = {http://arxiv.org/abs/2404.10523}, doi = {10.1515/9783111376776-004}, pages = {41 -- 58}, year = {2025}, 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{MukherjeeKerteszZolnaietal.2025, 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}, volume = {425}, journal = {Sens. Actuators B Chem.}, doi = {10.1016/j.snb.2024.136875}, pages = {136875}, year = {2025}, language = {en} } @article{BetzBinkowskiKuenetal.2024, author = {Betz, Fridtjof and Binkowski, Felix and Kuen, Lilli and Burger, Sven}, title = {Version 2 — RPExpand: Software for Riesz projection expansion of resonance phenomena}, volume = {26}, journal = {SoftwareX}, doi = {10.1016/j.softx.2024.101694}, pages = {101694}, year = {2024}, language = {en} } @inproceedings{SteyerCheginiPotseetal.2023, 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}, volume = {50}, booktitle = {2023 Computing in Cardiology Conference (CinC)}, publisher = {Computing in Cardiology}, issn = {2325-887X}, doi = {10.22489/CinC.2023.385}, year = {2023}, 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{PlockBinkowskiZschiedrichetal.2024, 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}, volume = {41}, journal = {J. Opt. Soc. Am. B}, arxiv = {http://arxiv.org/abs/2402.09420}, doi = {10.1364/JOSAB.505767}, pages = {850}, year = {2024}, language = {en} } @misc{PlockBinkowskiZschiedrichetal.2024, 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"}, journal = {Zenodo}, doi = {10.5281/zenodo.8131611}, pages = {doi: 10.5281/zenodo.8131611}, year = {2024}, language = {en} } @misc{MusialSekSchneideretal.2024, author = {Musial, Anna and Sek, Grzegorz and Schneider, Philipp-Immanuel and Reitzenstein, Stephan}, title = {Fiber-coupled solid-state-based single-photon sources}, journal = {Specialty Optical Fibers}, publisher = {Woodhead Publishing}, doi = {10.1016/B978-0-443-18495-6.00004-4}, pages = {345 -- 384}, year = {2024}, language = {de} } @article{KuenLoefflerTsarapkinetal.2024, 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}, volume = {124}, journal = {Appl. Phys. Lett.}, arxiv = {http://arxiv.org/abs/2402.00664}, doi = {10.1063/5.0201748}, pages = {231102}, year = {2024}, language = {en} } @article{GaskinConradPavliotisetal.2024, 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}, volume = {19}, journal = {PLOS ONE}, number = {10}, arxiv = {http://arxiv.org/abs/2312.03147}, doi = {10.1371/journal.pone.0306704}, year = {2024}, 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} } @misc{BetzBinkowskiBurgeretal.2023, author = {Betz, Fridtjof and Binkowski, Felix and Burger, Sven and Kuen, Lilli}, title = {RPExpand (Version 2.0)}, journal = {Zenodo}, doi = {10.5281/zenodo.10371002}, pages = {doi: 10.5281/zenodo.10371002}, year = {2023}, language = {en} } @inproceedings{CheginiFroehlyHuynhetal.2023, 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}, booktitle = {10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023}, doi = {10.23967/c.coupled.2023.004}, year = {2023}, 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} } @inproceedings{SteyerCheginiStaryetal.2024, 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}, booktitle = {Workshop Biosignals 2024}, doi = {10.47952/gro-publ-194}, year = {2024}, 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{SteudleWinkelmannFuerstetal.2024, 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}, volume = {27}, journal = {Advances in Complex Systems}, doi = {10.1142/S0219525924400034}, year = {2024}, 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} } @phdthesis{Chewle2023, author = {Chewle, Surahit}, title = {Probing effects of organic solvents on paracetamol crystallization using in silico and orthogonal in situ methods}, year = {2023}, 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{TrepteSeckerKostovaetal.2023, 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}, journal = {bioRxiv}, doi = {10.1101/2023.06.14.544560}, year = {2023}, language = {en} } @article{BinkowskiKulligBetzetal.2024, 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}, volume = {6}, journal = {Phys. Rev. Research}, arxiv = {http://arxiv.org/abs/2402.17648}, doi = {10.1103/PhysRevResearch.6.023148}, pages = {023148}, year = {2024}, language = {en} } @misc{BinkowskiKulligBetzetal.2024, 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}, journal = {Zenodo}, doi = {10.5281/zenodo.10715639}, pages = {doi: 10.5281/zenodo.10715639}, year = {2024}, language = {en} } @inproceedings{WeiserChegini2022, author = {Weiser, Martin and Chegini, Fatemeh}, title = {Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods}, booktitle = {CMBE22 - 7th International Conference on Computational \& Mathematical Biomedical Engineering}, pages = {528 -- 531}, year = {2022}, 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} } @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}, 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{Schweigart2021, author = {Schweigart, Fleur}, title = {KARTHAGO, TUNESIEN Datengesteuerte Modellierung des Romanisierungsprozesses in Nordafrika}, 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}, year = {2021}, language = {de} } @inproceedings{KostreSunkaraDjurdjevacConrad2021, author = {Kostre, Margarita and Sunkara, Vikram and Djurdjevac Conrad, Natasa}, title = {Inference of historical influence networks}, booktitle = {International Conference on Complex Networks \& Their Applications Proceedings}, edition = {International Conference on Complex Networks \& Their Applications}, doi = {10.12752/8558}, pages = {110 -- 113}, year = {2021}, 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} } @masterthesis{Chemnitz2021, type = {Bachelor Thesis}, author = {Chemnitz, Robin}, title = {Spectral Coarse-Graining of SIS Dynamics on Networks}, year = {2021}, language = {en} } @phdthesis{Helfmann2022, 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}, year = {2022}, 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} } @inproceedings{RickertGaoUrbanetal.2022, 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}, booktitle = {Quantum 2.0}, doi = {10.1364/QUANTUM.2022.QTu4C.6}, pages = {QTu4C.6}, year = {2022}, language = {en} } @article{ErlekamZumbansenWeber2022, author = {Erlekam, Franziska and Zumbansen, Maximilian and Weber, Marcus}, title = {Parameter estimation on multivalent ITC data sets}, volume = {12}, journal = {Scientific Reports}, doi = {10.1038/s41598-022-17188-x}, pages = {13402}, year = {2022}, 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} } @misc{PlockAndrleBurgeretal.2022, 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"}, journal = {Zenodo}, doi = {10.5281/zenodo.6359594}, year = {2022}, language = {en} } @misc{BinkowskiBetzHammerschmidtetal.2022, 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}, journal = {Zenodo}, doi = {10.5281/zenodo.6614951}, year = {2022}, language = {en} } @article{FrankSikorskiRoeblitz2024, author = {Frank, Anna-Simone and Sikorski, Alexander and R{\"o}blitz, Susanna}, title = {Spectral clustering of Markov chain transition matrices with complex eigenvalues}, volume = {444}, journal = {Journal of Computational and Applied Mathematics}, arxiv = {http://arxiv.org/abs/2206.14537}, doi = {10.1016/j.cam.2024.115791}, pages = {115791}, year = {2024}, 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} } @misc{KostreSunkaraSchuetteetal.2022, 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}, 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{BoltzSirbuStelzeretal.2022, 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}, volume = {11}, journal = {Cells}, number = {10}, doi = {10.3390/cells11101660}, pages = {1660}, year = {2022}, 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{SchneiderManleyKruegeretal.2022, 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}, volume = {12137}, journal = {Proc. SPIE}, doi = {10.1117/12.2620762}, pages = {121370I}, year = {2022}, language = {en} } @inproceedings{JaegerSutterTockhornetal.2022, 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}, volume = {PC12150}, booktitle = {Proc. SPIE}, doi = {10.1117/12.2621255}, pages = {PC1215001}, year = {2022}, language = {en} } @article{AvalosOvandoSantiagoMovsesyanetal.2022, 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}, volume = {9}, journal = {ACS Photon.}, doi = {10.1021/acsphotonics.2c00445}, pages = {2219}, year = {2022}, language = {en} } @article{BremerJimenezThieleetal.2022, 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}, volume = {30}, journal = {Opt. Express}, arxiv = {http://arxiv.org/abs/2202.09562}, doi = {10.1364/OE.456777}, pages = {15913}, year = {2022}, language = {en} } @article{DassKuenPosnjaketal.2022, 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}, volume = {3}, journal = {Mater. Adv.}, doi = {10.1039/D1MA01211H}, pages = {3438}, year = {2022}, language = {en} } @article{PlockAndrleBurgeretal.2022, author = {Plock, Matthias and Andrle, Kas and Burger, Sven and Schneider, Philipp-Immanuel}, title = {Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction}, volume = {5}, journal = {Adv. Theory Simul.}, arxiv = {http://arxiv.org/abs/2202.11559}, doi = {10.1002/adts.202200112}, pages = {2200112}, year = {2022}, language = {en} } @article{VolkovaHeupelTrofimovetal.2022, 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}, volume = {12}, journal = {Nanomaterials}, doi = {10.3390/nano12091516}, pages = {1516}, year = {2022}, language = {en} } @article{WangVannucciBurgeretal.2022, 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}, volume = {2}, journal = {Mater. Quantum Technol.}, arxiv = {http://arxiv.org/abs/2207.02665}, doi = {10.1088/2633-4356/aca8e8}, pages = {045004}, year = {2022}, language = {en} } @article{LopezFraguasBinkowskiBurgeretal.2022, 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}, volume = {12}, journal = {Sci. Rep.}, doi = {10.1038/s41598-022-15499-7}, pages = {11480}, year = {2022}, language = {en} } @misc{BetzColomBurgeretal.2022, 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}, journal = {Zenodo}, doi = {10.5281/zenodo.6558815}, year = {2022}, language = {en} } @phdthesis{Niemann2022, 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}, year = {2022}, 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{BeronVeraOlascoagaHelfmannetal.2023, 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}, volume = {53}, journal = {Journal of Physical Oceanography}, number = {4}, arxiv = {http://arxiv.org/abs/2208.09499}, doi = {10.1175/JPO-D-22-0172.1}, pages = {1151 -- 1160}, year = {2023}, 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} } @article{BartelsFisikopoulosWeiser2023, author = {Bartels, Tinko and Fisikopoulos, Vissarion and Weiser, Martin}, title = {Fast Floating-Point Filters for Robust Predicates}, volume = {63}, journal = {BIT Numerical Mathematics}, arxiv = {http://arxiv.org/abs/2208.00497}, doi = {10.1007/s10543-023-00975-x}, year = {2023}, 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} } @inproceedings{DhanakotiMaddocksWeiser2022, author = {Dhanakoti, Siva Prasad Chakri and Maddocks, John and Weiser, Martin}, title = {Navigation of Concentric Tube Continuum Robots using Optimal Control}, booktitle = {Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics}, doi = {10.5220/0011271000003271}, pages = {146 -- 154}, year = {2022}, 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{BinkowskiBetzHammerschmidtetal.2022, 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}, volume = {5}, journal = {Commun. Phys.}, arxiv = {http://arxiv.org/abs/2203.11101}, doi = {10.1038/s42005-022-00977-1}, pages = {202}, year = {2022}, language = {en} } @article{TockhornSutterCruzetal.2022, 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}, volume = {17}, journal = {Nat. Nanotechnol.}, doi = {10.1038/s41565-022-01228-8}, pages = {1214}, year = {2022}, language = {en} } @article{MovsesyanSantiagoBurgeretal.2022, 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}, volume = {10}, journal = {Adv. Opt. Mater.}, arxiv = {http://arxiv.org/abs/2203.00930}, doi = {10.1002/adom.202102663}, pages = {2102663}, year = {2022}, language = {en} } @misc{ColomBinkowskiBetzetal.2022, 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}, journal = {Zenodo}, doi = {10.5281/zenodo.6565850}, year = {2022}, language = {en} } @article{KlusDjurdjevacConrad2022, author = {Klus, Stefan and Djurdjevac Conrad, Natasa}, title = {Koopman-based spectral clustering of directed and time-evolving graphs}, volume = {33}, journal = {Journal of Nonlinear Science}, arxiv = {http://arxiv.org/abs/2204.02951}, doi = {10.1007/s00332-022-09863-0}, pages = {8}, year = {2022}, 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} } @article{BennerBurgerGoeddekeetal.2022, 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)}, journal = {GAMM Rundbrief}, number = {1}, pages = {40 -- 43}, year = {2022}, language = {de} } @article{TillmannJaegerKarsentietal.2022, 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}, volume = {6}, journal = {Sol. RRL}, doi = {10.1002/solr.202200079}, pages = {2200079}, year = {2022}, language = {en} } @article{EngelOliconMendezWehlitzetal.2024, 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}, journal = {Journal of Dynamics and Differential Equations}, arxiv = {http://arxiv.org/abs/2207.00602}, doi = {10.1007/s10884-023-10345-4}, year = {2024}, 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} } @misc{BorndoerferDaneckerWeiser2023, 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}, year = {2023}, 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} } @phdthesis{Danecker2023, author = {Danecker, Fabian}, title = {A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization}, year = {2023}, 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{BorndoerferDaneckerWeiser2021, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {A Discrete-Continuous Algorithm for Free Flight Planning}, volume = {14}, journal = {Algorithms}, number = {1}, publisher = {MDPI}, issn = {1438-0064}, doi = {10.3390/a14010004}, pages = {4}, year = {2021}, 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{BorndoerferDaneckerWeiser2023, 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}, year = {2023}, 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} } @inproceedings{BorndoerferDaneckerWeiser2023, 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}, 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}, year = {2023}, 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{BorndoerferDaneckerWeiser2023, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Newton's Method for Global Free Flight Trajectory Optimization}, volume = {4}, journal = {Operations Research Forum}, doi = {10.1007/s43069-023-00238-z}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-91846}, year = {2023}, 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{BorndoerferDaneckerWeiser2023, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Error Bounds for Discrete-Continuous Free Flight Trajectory Optimization}, volume = {198}, journal = {Journal of Optimization Theory and Applications}, doi = {10.1007/s10957-023-02264-7}, pages = {830 -- 856}, year = {2023}, 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} }