TY - THES A1 - Eshtewy, Neveen Ali Salem T1 - Mathematical Modeling of Metabolic-Genetic Networks Y1 - 2020 ER - TY - JOUR A1 - Öttinger, Hans Christian A1 - Montefusco, Alberto A1 - Peletier, Mark A. T1 - A Framework of Nonequilibrium Statistical Mechanics. I. Role and Types of Fluctuations JF - Journal of Non-Equilibrium Thermodynamics N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1515/jnet-2020-0068 VL - 46 IS - 1 SP - 1 EP - 13 PB - De Gruyter ER - TY - JOUR A1 - Montefusco, Alberto A1 - Peletier, Mark A. A1 - Öttinger, Hans Christian T1 - A Framework of Nonequilibrium Statistical Mechanics. II. Coarse-Graining JF - Journal of Non-Equilibrium Thermodynamics N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1515/jnet-2020-0069 VL - 46 IS - 1 SP - 15 EP - 33 PB - De Gruyter ER - TY - JOUR A1 - Sunkara, Vikram A1 - Heinz, Gitta A. A1 - Heinrich, Frederik F. A1 - Durek, Pawel A1 - Mobasheri, Ali A1 - Mashreghi, Mir-Farzin A1 - Lang, Annemarie T1 - Combining segmental bulk- and single-cell RNA-sequencing to define the chondrocyte gene expression signature in the murine knee joint JF - bioarxiv (Accepted in Osteoarthr. Cartil.) Y1 - 2020 U6 - https://doi.org/10.1101/2020.06.13.148056 ER - TY - JOUR A1 - Lang, Annemarie A1 - Helfmeier, Sarah A1 - Stefanowski, Jonathan A1 - Kuppe, Aditi A1 - Sunkara, Vikram A1 - Pfeiffenberger, Moritz A1 - Wolter, Angelique A1 - Damerau, Alexandra A1 - Hemmati-Sadeghi, Shabnam A1 - Ringe, Jochen A1 - Haag, Rainer A1 - Hauser, Anja E. A1 - Löhning, Max A1 - Perka, Carsten A1 - Duda, Georg A1 - Hoff, Paula A1 - Schmidt-Bleek, Katharina A1 - Gaber, Timo A1 - Buttgereit, Frank T1 - HIF-stabilization prevents delayed fracture healing JF - bioarxiv Y1 - 2020 U6 - https://doi.org/10.1101/2020.07.02.182832 ER - TY - JOUR A1 - Laydon, Daniel J. A1 - Sunkara, Vikram A1 - Boelen, Lies A1 - Bangham, Charles R. M. A1 - Asquith, Becca T1 - The relative contributions of infectious and mitotic spread to HTLV-1 persistence JF - PLOS Computational Biology Y1 - 2020 U6 - https://doi.org/10.1371/journal.pcbi.1007470 ER - TY - JOUR A1 - Schiela, Anton A1 - Stöcklein, Matthias A1 - Weiser, Martin T1 - A primal dual projection algorithm for efficient constraint preconditioning JF - SIAM Journal on Scientific Computing N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1137/20M1380739 VL - 43 IS - 6 SP - A4095 EP - A4120 ER - TY - JOUR A1 - Mielke, Alexander A1 - Montefusco, Alberto A1 - Peletier, Mark A. T1 - Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence JF - Continuum Mechanics and Thermodynamics N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1007/s00161-020-00932-x VL - 33 SP - 611 EP - 637 PB - Springer ER - TY - THES A1 - Santiago, Xavier Garcia T1 - Numerical methods for shape optimization of photonic nanostructures Y1 - 2021 U6 - https://doi.org/10.5445/IR/1000131006 ER - TY - JOUR A1 - Raharinirina, N. Alexia A1 - Acevedo-Trejos, Esteban A1 - Merico, Agostino T1 - Modelling the acclimation capacity of coral reefs to a warming ocean JF - PLOS COMPUTATIONAL BIOLOGY N2 - 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. Y1 - 2022 U6 - https://doi.org/10.1371/journal.pcbi.1010099 ER - TY - GEN A1 - Schütte, Christof A1 - Klus, Stefan A1 - Hartmann, Carsten T1 - Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning N2 - 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. T3 - ZIB-Report - 22-25 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88637 SN - 1438-0064 ER - TY - JOUR A1 - Ramos Leite, Tiago A1 - Zschiedrich, Lin A1 - Kizilkaya, Orhan A1 - McPeak, Kevin M. T1 - Resonant Plasmonic–Biomolecular Chiral Interactions in the Far-Ultraviolet: Enantiomeric Discrimination of sub-10 nm Amino Acid Films JF - Nano Lett. Y1 - 2022 UR - https://digitalcommons.lsu.edu/chem_engineering_pubs/34/ U6 - https://doi.org/10.1021/acs.nanolett.2c01724 VL - 22 SP - 7343 ER - TY - JOUR A1 - Rej, Sourav A1 - Santiago, Eva Yazmin A1 - Baturina, Olga A1 - Zhang, Yu A1 - Burger, Sven A1 - Kment, Stepan A1 - Govorov, Alexander O. A1 - Naldoni, Alberto T1 - Colloidal Titanium Nitride Nanobars for Broadband Inexpensive Plasmonics and Photochemistry from Visible to Mid-IR Wavelengths JF - Nano Energy Y1 - 2022 U6 - https://doi.org/10.1016/j.nanoen.2022.107989 VL - 104 SP - 107989 ER - TY - CHAP A1 - Berner, Julius A1 - Richter, Lorenz A1 - Ullrich, Karen T1 - An optimal control perspective on diffusion-based generative modeling T2 - Transactions on Machine Learning Research N2 - 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. Y1 - 2024 UR - https://openreview.net/forum?id=oYIjw37pTP ER - TY - JOUR A1 - Nüsken, Nikolas A1 - Richter, Lorenz T1 - Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems JF - Journal of Machine Learning N2 - 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. Y1 - 2023 U6 - https://doi.org/0.4208/jml.220416 VL - 2 IS - 1 SP - 31 EP - 64 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Richter, Lorenz T1 - Nonasymptotic bounds for suboptimal importance sampling JF - SIAM/ASA Journal on Uncertainty Quantification N2 - 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. Y1 - 2024 U6 - https://doi.org/10.1137/21M1427760 VL - 12 IS - 2 SP - 309 EP - 346 ER - TY - JOUR A1 - Rickert, Lucas A1 - Betz, Fridtjof A1 - Plock, Matthias A1 - Burger, Sven A1 - Heindel, Tobias T1 - High-performance designs for fiber-pigtailed quantum-light sources based on quantum dots in electrically-controlled circular Bragg gratings JF - Opt. Express Y1 - 2023 U6 - https://doi.org/10.1364/OE.486060 VL - 31 SP - 14750 ER - TY - GEN A1 - Rickert, Lucas A1 - Betz, Fridtjof A1 - Plock, Matthias A1 - Burger, Sven A1 - Heindel, Tobias T1 - Data publication for "High-performance designs for fiber-pigtailed quantum-light sources based on quantum dots in electrically-controlled circular Bragg gratings" T2 - Zenodo Y1 - 2022 U6 - https://doi.org/10.5281/zenodo.7360516 SP - 7360516 ER - TY - JOUR A1 - Gorgulla, Christoph A1 - Jayaraj, Abhilash A1 - Fackeldey, Konstantin A1 - Arthanari, Haribabu T1 - Emerging frontiers in virtual drug discovery: From quantum mechanical methods to deep learning approaches JF - Current Opinion in Chemical Biology N2 - 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. Y1 - 2022 U6 - https://doi.org/10.1016/j.cbpa.2022.102156 VL - 69 SP - 102156 EP - 102156-12 ER - TY - GEN A1 - Straube, Arthur A1 - Winkelmann, Stefanie A1 - Höfling, Felix T1 - Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles N2 - 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. T3 - ZIB-Report - 22-21 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88179 SN - 1438-0064 ER - TY - JOUR A1 - Donati, Luca A1 - Weber, Marcus T1 - Assessing transition rates as functions of environmental variables JF - The Journal of Chemical Physics N2 - 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. Y1 - 2022 U6 - https://doi.org/10.1063/5.0109555 VL - 157 IS - 22 SP - 224103-1 EP - 224103-14 PB - AIP Publishing ER - TY - JOUR A1 - Sechi, Renata A1 - Fackeldey, Konstantin A1 - Chewle, Surahit A1 - Weber, Marcus T1 - SepFree NMF: A Toolbox for Analyzing the Kinetics of Sequential Spectroscopic Data JF - Algorithms N2 - 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. Y1 - 2022 U6 - https://doi.org/10.3390/a15090297 VL - 15 IS - 9 SP - 297 ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Köppl, Jonas A1 - Djurdjevac, Ana T1 - Feedback Loops in Opinion Dynamics of Agent-Based Models with Multiplicative Noise JF - Entropy N2 - 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. Y1 - 2022 U6 - https://doi.org/10.3390/e24101352 VL - 24(10) ER - TY - JOUR A1 - Donati, Luca A1 - Weber, Marcus A1 - Keller, Bettina G. T1 - A review of Girsanov Reweighting and of Square Root Approximation for building molecular Markov State Models JF - Journal of Mathematical Physics N2 - 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. Y1 - 2022 U6 - https://doi.org/10.1063/5.0127227 VL - 63 IS - 12 SP - 123306-1 EP - 123306-21 PB - AIP Publishing ER - TY - JOUR A1 - Quer, Jannes A1 - Ribera Borrell, Enric T1 - Connecting Stochastic Optimal Control and Reinforcement Learning JF - Journal of Mathematical Physics N2 - 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. Y1 - 2024 U6 - https://doi.org/10.1063/5.0140665 VL - 65 IS - 8 ER - TY - JOUR A1 - Ray, Sourav A1 - Fackeldey, Konstantin A1 - Stein, Christoph A1 - Weber, Marcus T1 - Coarse Grained MD Simulations of Opioid interactions with the µ-opioid receptor and the surrounding lipid membrane JF - Biophysica N2 - 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. Y1 - 2023 U6 - https://doi.org/10.3390/biophysica3020017 VL - 3 IS - 2 SP - 263 EP - 275 ER - TY - CHAP A1 - Richter, Lorenz A1 - Berner, Julius T1 - Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning T2 - Proceedings of the 39th International Conference on Machine Learning, PMLR N2 - 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. Y1 - 2022 VL - 162 SP - 18649 EP - 18666 ER - TY - JOUR A1 - del Razo, Mauricio A1 - Winkelmann, Stefanie A1 - Klein, Rupert A1 - Höfling, Felix T1 - Chemical diffusion master equation: formulations of reaction-diffusion processes on the molecular level JF - Journal of Mathematical Physics N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1063/5.0129620 VL - 64 IS - 1 ER - TY - JOUR A1 - Lücke, Marvin A1 - Heitzig, Jobst A1 - Koltai, Péter A1 - Molkethin, Nora A1 - Winkelmann, Stefanie T1 - Large population limits of Markov processes on random networks JF - Stochastic Processes and their Applications N2 - 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-Rényi 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. Y1 - 2023 U6 - https://doi.org/10.1016/j.spa.2023.09.007 VL - 166 ER - TY - CHAP A1 - Schneider, Philipp-Immanuel A1 - Zschiedrich, Lin A1 - Hammerschmidt, Martin A1 - Kuen, Lilli A1 - Sekulic, Ivan A1 - Kluge, Julien A1 - Leykauf, Bastian A1 - Krutzik, Markus A1 - Burger, Sven T1 - Boosting quantum optics experiments with Bayesian optimization T2 - Proc. SPIE Y1 - 2022 U6 - https://doi.org/10.1117/12.2632419 VL - 12227 SP - 122270F ER - TY - CHAP A1 - Krüger, Jan A1 - Manley, Phillip A1 - Zschiedrich, Lin A1 - Hammerschmidt, Martin A1 - Schneider, Philipp-Immanuel A1 - Köning, Rainer A1 - Bodermann, Bernd T1 - Untersuchung des Schwingungseinflusses auf gemessene Punktspreizfunktionen in der optischen Mikroskopie T2 - Proc. DGaO Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0287-2022-P005-6 SP - P5 ER - TY - JOUR A1 - Bopp, Julian M. A1 - Plock, Matthias A1 - Turan, Tim A1 - Pieplow, Gregor A1 - Burger, Sven A1 - Schröder, Tim T1 - Sawfish Photonic Crystal Cavity for Near-Unity Emitter-to-Fiber Interfacing in Quantum Network Applications JF - Adv. Opt. Mater. Y1 - 2024 U6 - https://doi.org/10.1002/adom.202301286 VL - 12 SP - 2301286 ER - TY - CHAP A1 - Manley, Phillip A1 - Krüger, Jan A1 - Zschiedrich, Lin A1 - Hammerschmidt, Martin A1 - Bodermann, Bernd A1 - Köning, Rainer A1 - Schneider, Philipp-Immanuel T1 - Elementary, my dear Zernike: model order reduction for accelerating optical dimensional microscopy T2 - EPJ Web Conf. Y1 - 2022 U6 - https://doi.org/10.1051/epjconf/202226610010 VL - 266 SP - 10010 ER - TY - JOUR A1 - Raharinirina, N. Alexia A1 - Fackeldey, Konstantin A1 - Weber, Marcus T1 - Qualitative Euclidean embedding of Disjoint Sets of Points N2 - 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). Y1 - 2022 UR - https://arxiv.org/abs/2212.00058 ER - TY - JOUR A1 - Boege, Tobias A1 - Fritze, René A1 - Görgen, Christiane A1 - Hanselmann, Jeroen A1 - Iglezakis, Dorothea A1 - Kastner, Lars A1 - Koprucki, Thomas A1 - Krause, Tabea A1 - Lehrenfeld, Christoph A1 - Polla, Silvia A1 - Reidelbach, Marco A1 - Riedel, Christian A1 - Saak, Jens A1 - Schembera, Björn A1 - Tabelow, Karsten A1 - Weber, Marcus T1 - Research-Data Management Planning in the German Mathematical Community JF - Eur. Math. Soc. Mag. N2 - 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. Y1 - 2023 U6 - https://doi.org/10.4171/mag/152 VL - 130 SP - 40 EP - 47 ER - TY - JOUR A1 - Reidelbach, Marco A1 - Bai, Mei A1 - Zöllner, Martin Sebastian A1 - Schneeberger, Michaela A1 - Kubicek, Katharina A1 - Kirchberg, Henning A1 - Bressler, Christian A1 - Thorwart, Michael A1 - Herrmann, Carmen T1 - Solvent dynamics of aqueous halides before and after photoionization JF - Journal of Physical Chemistry Y1 - 2022 ER - TY - GEN A1 - Reidelbach, Marco A1 - Weber, Marcus T1 - MaRDI - The mathematical Research Data Initiative T2 - Aktionstag Forschungsdaten Y1 - 2022 U6 - https://doi.org/10.5281/zenodo.7397588 ER - TY - JOUR A1 - Betz, Fridtjof A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Binkowski, Felix T1 - Efficient rational approximation of optical response functions with the AAA algorithm JF - Laser Photonics Rev. Y1 - 2024 U6 - https://doi.org/10.1002/lpor.202400584 VL - 18 SP - 2400584 ER - TY - GEN A1 - Betz, Fridtjof A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Binkowski, Felix T1 - Source code and simulation results: Efficient rational approximation of optical response functions with the AAA algorithm T2 - Zenodo Y1 - 2024 U6 - https://doi.org/10.5281/zenodo.10853692 SP - doi: 10.5281/zenodo.10853692 ER - TY - JOUR A1 - Sikorski, Alexander A1 - Niknejad, Amir A1 - Weber, Marcus A1 - Donati, Luca T1 - Tensor-SqRA: Modeling the transition rates of interacting molecular systems in terms of potential energies JF - Journal of Chemical Physics N2 - 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. Y1 - 2024 U6 - https://doi.org/10.1063/5.0187792 VL - 160 SP - 104112 ER - TY - CHAP A1 - Sikorski, Alexander A1 - Rabben, Robert Julian A1 - Chewle, Surahit A1 - Weber, Marcus ED - Fackeldey, K. T1 - Capturing the Macroscopic Behaviour of Molecular Dynamics with Membership Functions T2 - Mathematical Optimization for Machine Learning: Proceedings of the MATH+ Thematic Einstein Semester 2023 N2 - 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. Y1 - 2024 U6 - https://doi.org/10.1515/9783111376776-004 SP - 41 EP - 58 PB - De Gruyter ER - TY - JOUR A1 - Mukherjee, Deshabrato A1 - Kertész, Krisztián A1 - Zolnai, Zsolt A1 - Kovács, Zoltán A1 - Deák, András A1 - Pálinkás, András A1 - Osváth, Zoltán A1 - Olasz, Dániel A1 - Romanenko, Alekszej A1 - Fried, Miklós A1 - Burger, Sven A1 - Sáfrán, György A1 - Petrik, Peter T1 - Optimized Sensing on Gold Nanoparticles Created by Graded-Layer Magnetron Sputtering and Annealing JF - Sens. Actuators B Chem. Y1 - 2025 U6 - https://doi.org/10.1016/j.snb.2024.136875 VL - 425 SP - 136875 ER - TY - JOUR A1 - Betz, Fridtjof A1 - Binkowski, Felix A1 - Kuen, Lilli A1 - Burger, Sven T1 - Version 2 — RPExpand: Software for Riesz projection expansion of resonance phenomena JF - SoftwareX Y1 - 2024 U6 - https://doi.org/10.1016/j.softx.2024.101694 VL - 26 SP - 101694 ER - TY - CHAP A1 - Steyer, Joshua A1 - Chegini, Fatemeh A1 - Potse, Mark A1 - Loewe, Axel A1 - Weiser, Martin T1 - Continuity of Microscopic Cardiac Conduction in a Computational Cell-by-Cell Model T2 - 2023 Computing in Cardiology Conference (CinC) N2 - 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. Y1 - 2023 U6 - https://doi.org/10.22489/CinC.2023.385 SN - 2325-887X VL - 50 PB - Computing in Cardiology ER - TY - JOUR A1 - Plock, Matthias A1 - Binkowski, Felix A1 - Zschiedrich, Lin A1 - Schneider, Phillip-Immanuel A1 - Burger, Sven T1 - Fabrication uncertainty guided design optimization of a photonic crystal cavity by using Gaussian processes JF - J. Opt. Soc. Am. B Y1 - 2024 U6 - https://doi.org/10.1364/JOSAB.505767 VL - 41 SP - 850 ER - TY - GEN A1 - Plock, Matthias A1 - Binkowski, Felix A1 - Zschiedrich, Lin A1 - Schneider, Phillip-Immanuel A1 - Burger, Sven T1 - Research data for "Fabrication uncertainty guided design optimization of a photonic crystal cavity by using Gaussian processes" T2 - Zenodo Y1 - 2024 U6 - https://doi.org/10.5281/zenodo.8131611 SP - doi: 10.5281/zenodo.8131611 ER - TY - GEN A1 - Musial, Anna A1 - Sek, Grzegorz A1 - Schneider, Philipp-Immanuel A1 - Reitzenstein, Stephan T1 - Fiber-coupled solid-state-based single-photon sources T2 - Specialty Optical Fibers Y1 - 2024 U6 - https://doi.org/10.1016/B978-0-443-18495-6.00004-4 SP - 345 EP - 384 PB - Woodhead Publishing ER - TY - JOUR A1 - Kuen, Lilli A1 - Löffler, Lorenz A1 - Tsarapkin, Aleksei A1 - Zschiedrich, Lin A1 - Feichtner, Thorsten A1 - Burger, Sven A1 - Höflich, Katja T1 - Chiral and directional optical emission from a dipole source coupled to a helical plasmonic antenna JF - Appl. Phys. Lett. Y1 - 2024 U6 - https://doi.org/10.1063/5.0201748 VL - 124 SP - 231102 ER - TY - JOUR A1 - Gaskin, Thomas A1 - Conrad, Tim A1 - Pavliotis, Grigorios A. A1 - Schütte, Christof T1 - Neural parameter calibration and uncertainty quantification for epidemic forecasting JF - PLOS ONE N2 - 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. Y1 - 2024 U6 - https://doi.org/10.1371/journal.pone.0306704 VL - 19 IS - 10 ER - TY - GEN A1 - Betz, Fridtjof A1 - Binkowski, Felix A1 - Burger, Sven A1 - Kuen, Lilli T1 - RPExpand (Version 2.0) T2 - Zenodo Y1 - 2023 U6 - https://doi.org/10.5281/zenodo.10371002 SP - doi: 10.5281/zenodo.10371002 ER - TY - CHAP A1 - Chegini, Fatemeh A1 - Froehly, Algiane A1 - Huynh, Ngoc Mai Monica A1 - Pavarino, Luca A1 - Potse, Mark A1 - Scacchi, Simone A1 - Weiser, Martin T1 - Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution T2 - 10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023 N2 - 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. Y1 - 2023 UR - https://www.scipedia.com/public/2023f U6 - https://doi.org/10.23967/c.coupled.2023.004 ER - TY - CHAP A1 - Steyer, Joshua A1 - Chegini, Fatemeh A1 - Starý, Tomas A1 - Potse, Mark A1 - Weiser, Martin A1 - Loewe, Axel T1 - Electrograms in a Cardiac Cell-by-Cell Model T2 - Workshop Biosignals 2024 N2 - 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. Y1 - 2024 U6 - https://doi.org/10.47952/gro-publ-194 ER - TY - JOUR A1 - Steudle, Gesine A1 - Winkelmann, Stefanie A1 - Fürst, Steffen A1 - Wolf, Sarah T1 - Understanding Memory Mechanisms in Socio-Technical Systems: the Case of an Agent-based Mobility Model JF - Advances in Complex Systems N2 - 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. Y1 - 2024 U6 - https://doi.org/10.1142/S0219525924400034 VL - 27 ER - TY - THES A1 - Chewle, Surahit T1 - Probing effects of organic solvents on paracetamol crystallization using in silico and orthogonal in situ methods N2 - 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. Y1 - 2023 UR - https://edoc.hu-berlin.de/handle/18452/27957 ER - TY - JOUR A1 - Trepte, Philipp A1 - Secker, Christopher A1 - Kostova, Simona A1 - Maseko, Sibusiso B. A1 - Gang Choi, Soon A1 - Blavier, Jeremy A1 - Minia, Igor A1 - Silva Ramos, Eduardo A1 - Cassonnet, Patricia A1 - Golusik, Sabrina A1 - Zenkner, Martina A1 - Beetz, Stephanie A1 - Liebich, Mara J. A1 - Scharek, Nadine A1 - Schütz, Anja A1 - Sperling, Marcel A1 - Lisurek, Michael A1 - Wang, Yang A1 - Spirohn, Kerstin A1 - Hao, Tong A1 - Calderwood, Michael A. A1 - Hill, David E. A1 - Landthaler, Markus A1 - Olivet, Julien A1 - Twizere, Jean-Claude A1 - Vidal, Marc A1 - Wanker, Erich E. T1 - AI-guided pipeline for protein-protein interaction drug discovery identifies a SARS-CoV-2 inhibitor JF - bioRxiv Y1 - 2023 U6 - https://doi.org/10.1101/2023.06.14.544560 ER - TY - JOUR A1 - Binkowski, Felix A1 - Kullig, Julius A1 - Betz, Fridtjof A1 - Zschiedrich, Lin A1 - Walther, Andrea A1 - Wiersig, Jan A1 - Burger, Sven T1 - Computing eigenfrequency sensitivities near exceptional points JF - Phys. Rev. Research Y1 - 2024 U6 - https://doi.org/10.1103/PhysRevResearch.6.023148 VL - 6 SP - 023148 ER - TY - GEN A1 - Binkowski, Felix A1 - Kullig, Julius A1 - Betz, Fridtjof A1 - Zschiedrich, Lin A1 - Walther, Andrea A1 - Wiersig, Jan A1 - Burger, Sven T1 - Source code and simulation results: Computing eigenfrequency sensitivities near exceptional points T2 - Zenodo Y1 - 2024 U6 - https://doi.org/10.5281/zenodo.10715639 SP - doi: 10.5281/zenodo.10715639 ER - TY - CHAP A1 - Weiser, Martin A1 - Chegini, Fatemeh T1 - Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods T2 - CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering N2 - 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. Y1 - 2022 SP - 528 EP - 531 ER - TY - JOUR A1 - Kostré, Margarita A1 - Sunkara, Vikram A1 - Schütte, Christof A1 - Djurdjevac Conrad, Natasa T1 - Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia JF - Applied Network Science N2 - 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. KW - mesoscale spreading process KW - network inference KW - time-evolving network KW - romanization spreading KW - scarce data Y1 - 2022 U6 - https://doi.org/10.1007/s41109-022-00492-w VL - 7 PB - Springer Nature ER - TY - JOUR A1 - Schweigart, Fleur T1 - KARTHAGO, TUNESIEN Datengesteuerte Modellierung des Romanisierungsprozesses in Nordafrika JF - e-Forschungsberichte des Deutschen Archäologischen Instituts. Berlin: Deutsches Archäologisches Institut, Zentrale. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.34780/d469-84h2 VL - Fasc. 1 ER - TY - CHAP A1 - Kostre, Margarita A1 - Sunkara, Vikram A1 - Djurdjevac Conrad, Natasa T1 - Inference of historical influence networks T2 - International Conference on Complex Networks & Their Applications Proceedings N2 - 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. Y1 - 2021 U6 - https://doi.org/10.12752/8558 SP - 110 EP - 113 ET - International Conference on Complex Networks & Their Applications ER - TY - THES A1 - Chemnitz, Robin T1 - Spectral Coarse-Graining of SIS Dynamics on Networks Y1 - 2021 ER - TY - THES A1 - Helfmann, Luzie T1 - Non-stationary Transition Path Theory with applications to tipping and agent-based models N2 - 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. Y1 - 2022 UR - https://refubium.fu-berlin.de/handle/fub188/35660 U6 - https://doi.org/http://dx.doi.org/10.17169/refubium-35374 ER - TY - CHAP A1 - Rickert, Lucas A1 - Gao, Timm A1 - Urban, Felix A1 - Große, Jan A1 - Srocka, Nicole A1 - Rodt, Sven A1 - Musial, Anna A1 - Zolnacz, Kinga A1 - Mergo, Pawel A1 - Dybka, Kamil A1 - Urbanczyk, Waclaw A1 - Sek, Grzegorz A1 - Burger, Sven A1 - Reitzenstein, Stephan A1 - Heindel, Tobias T1 - A Plug&Play Telecom-Wavelength Single-Photon Source for Quantum Key Distribution T2 - Quantum 2.0 Y1 - 2022 U6 - https://doi.org/10.1364/QUANTUM.2022.QTu4C.6 SP - QTu4C.6 ER - TY - JOUR A1 - Erlekam, Franziska A1 - Zumbansen, Maximilian A1 - Weber, Marcus T1 - Parameter estimation on multivalent ITC data sets JF - Scientific Reports N2 - 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. Y1 - 2022 U6 - https://doi.org/10.1038/s41598-022-17188-x VL - 12 SP - 13402 ER - TY - GEN A1 - Plock, Matthias A1 - Andrle, Kas A1 - Burger, Sven A1 - Schneider, Philipp-Immanuel T1 - Research data and example scripts for the paper "Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction" T2 - Zenodo Y1 - 2022 U6 - https://doi.org/10.5281/zenodo.6359594 ER - TY - GEN A1 - Binkowski, Felix A1 - Betz, Fridtjof A1 - Hammerschmidt, Martin A1 - Schneider, Philipp-Immanuel A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Source code and simulation data for Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators T2 - Zenodo Y1 - 2022 U6 - https://doi.org/10.5281/zenodo.6614951 ER - TY - JOUR A1 - Frank, Anna-Simone A1 - Sikorski, Alexander A1 - Röblitz, Susanna T1 - Spectral clustering of Markov chain transition matrices with complex eigenvalues JF - Journal of Computational and Applied Mathematics N2 - 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. Y1 - 2024 U6 - https://doi.org/10.1016/j.cam.2024.115791 VL - 444 SP - 115791 ER - TY - GEN A1 - Kostré, Margarita A1 - Sunkara, Vikram A1 - Schütte, Christof A1 - Djurdjevac Conrad, Nataša T1 - Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia N2 - 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. T3 - ZIB-Report - 22-10 KW - mesoscale spreading process, network inference, time-evolving network, romanization spreading, scarce data Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86764 SN - 1438-0064 ER - TY - JOUR A1 - Boltz, Horst-Holger A1 - Sirbu, Alexei A1 - Stelzer, Nina A1 - de Lanerolle, Primal A1 - Winkelmann, Stefanie A1 - Annibale, Paolo T1 - The Impact of Membrane Protein Diffusion on GPCR Signaling JF - Cells N2 - 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 Y1 - 2022 U6 - https://doi.org/10.3390/cells11101660 VL - 11 IS - 10 SP - 1660 ER - TY - JOUR A1 - Schneider, Philipp-Immanuel A1 - Manley, Phillip A1 - Krüger, Jan A1 - Zschiedrich, Lin A1 - Köning, Rainer A1 - Bodermann, Bernd A1 - Burger, Sven T1 - Reconstructing phase aberrations for high-precision dimensional microscopy JF - Proc. SPIE Y1 - 2022 U6 - https://doi.org/10.1117/12.2620762 VL - 12137 SP - 121370I ER - TY - CHAP A1 - Jäger, Klaus A1 - Sutter, Johannes A1 - Tockhorn, Philipp A1 - Hammerschmidt, Martin A1 - Schneider, Philipp-Immanuel A1 - Albrecht, Steve A1 - Becker, Christiane T1 - Improving perovskite/silicon tandem solar cells with optical simulations T2 - Proc. SPIE Y1 - 2022 U6 - https://doi.org/10.1117/12.2621255 VL - PC12150 SP - PC1215001 ER - TY - JOUR A1 - Avalos-Ovando, Oscar A1 - Santiago, Eva Yazmin A1 - Movsesyan, Artur A1 - Kong, Xiang-Tian A1 - Yu, Peng A1 - Besteiro, Lucas V. A1 - Khosravi Khorashad, Larousse A1 - Okamoto, Hiromi A1 - Slocik, Joseph M. A1 - Correa-Duarte, Miguel A1 - Comesana-Hermo, Miguel A1 - Liedl, Tim A1 - Markovich, Gil A1 - Burger, Sven A1 - Govorov, Alexander O. T1 - Chiral Bioinspired Plasmonics: A Paradigm Shift for Optical Activity and Photochemistry JF - ACS Photon. Y1 - 2022 U6 - https://doi.org/10.1021/acsphotonics.2c00445 VL - 9 SP - 2219 ER - TY - JOUR A1 - Bremer, Lucas A1 - Jimenez, Carlos A1 - Thiele, Simon A1 - Weber, Ksenia A1 - Huber, Tobias A1 - Rodt, Sven A1 - Herkommer, Alois A1 - Burger, Sven A1 - Höfling, Sven A1 - Giessen, Harald A1 - Reitzenstein, Stephan T1 - Numerical optimization of single-mode fiber- coupled single-photon sources based on semiconductor quantum dots JF - Opt. Express Y1 - 2022 U6 - https://doi.org/10.1364/OE.456777 VL - 30 SP - 15913 ER - TY - JOUR A1 - Dass, Mihir A1 - Kuen, Lilli A1 - Posnjak, Gregor A1 - Burger, Sven A1 - Liedl, Tim T1 - Visible wavelength spectral tuning of absorption and circular dichroism of DNA-assembled Au/Ag core-shell nanorod assemblies JF - Mater. Adv. Y1 - 2022 U6 - https://doi.org/10.1039/D1MA01211H VL - 3 SP - 3438 ER - TY - JOUR A1 - Plock, Matthias A1 - Andrle, Kas A1 - Burger, Sven A1 - Schneider, Philipp-Immanuel T1 - Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction JF - Adv. Theory Simul. Y1 - 2022 U6 - https://doi.org/10.1002/adts.202200112 VL - 5 SP - 2200112 ER - TY - JOUR A1 - Volkova, Kseniia A1 - Heupel, Julia A1 - Trofimov, Sergei A1 - Betz, Fridtjof A1 - Colom, Rémi A1 - MacQueen, Rowan W. A1 - Akhundzada, Sapida A1 - Reginka, Meike A1 - Ehresmann, Arno A1 - Reithmeier, Johann Peter A1 - Burger, Sven A1 - Popov, Cyril A1 - Naydenov, Boris T1 - Optical and Spin Properties of NV Center Ensembles in Diamond Nano-Pillars JF - Nanomaterials Y1 - 2022 U6 - https://doi.org/10.3390/nano12091516 VL - 12 SP - 1516 ER - TY - JOUR A1 - Wang, Yujing A1 - Vannucci, Luca A1 - Burger, Sven A1 - Gregersen, Niels T1 - Near-unity efficiency in ridge waveguide-based, on-chip single-photon sources JF - Mater. Quantum Technol. Y1 - 2022 U6 - https://doi.org/10.1088/2633-4356/aca8e8 VL - 2 SP - 045004 ER - TY - JOUR A1 - Lopez-Fraguas, Eduardo A1 - Binkowski, Felix A1 - Burger, Sven A1 - Hagedorn, Sylvia A1 - Garcia-Camara, Braulio A1 - Vergaz, Ricardo A1 - Becker, Christiane A1 - Manley, Phillip T1 - Tripling the light extraction efficiency of a deep ultraviolet LED using a nanostructured p-contact JF - Sci. Rep. Y1 - 2022 U6 - https://doi.org/10.1038/s41598-022-15499-7 VL - 12 SP - 11480 ER - TY - GEN A1 - Betz, Fridtjof A1 - Colom, Remi A1 - Burger, Sven A1 - Naydenov, Boris T1 - Scripts for quantifying the effect of diamond nano-pillars on the fluorescence of NV centers T2 - Zenodo Y1 - 2022 U6 - https://doi.org/10.5281/zenodo.6558815 ER - TY - THES A1 - Niemann, Jan-Hendrik T1 - Learning Reduced Models for Large-Scale Agent-Based Systems N2 - 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. Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:188-refubium-35530-6 UR - https://refubium.fu-berlin.de/handle/fub188/35530 ER - TY - JOUR A1 - Beron-Vera, Francisco Javier A1 - Olascoaga, Maria Josefina A1 - Helfmann, Luzie A1 - Miron, Philippe T1 - Sampling-Dependent Transition Paths of Iceland-Scotland Overflow Water JF - Journal of Physical Oceanography N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1175/JPO-D-22-0172.1 VL - 53 IS - 4 SP - 1151 EP - 1160 ER - TY - JOUR A1 - Bartels, Tinko A1 - Fisikopoulos, Vissarion A1 - Weiser, Martin T1 - Fast Floating-Point Filters for Robust Predicates JF - BIT Numerical Mathematics N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1007/s10543-023-00975-x VL - 63 ER - TY - CHAP A1 - Dhanakoti, Siva Prasad Chakri A1 - Maddocks, John A1 - Weiser, Martin T1 - Navigation of Concentric Tube Continuum Robots using Optimal Control T2 - Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics N2 - 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. Y1 - 2022 U6 - https://doi.org/10.5220/0011271000003271 SP - 146 EP - 154 ER - TY - JOUR A1 - Binkowski, Felix A1 - Betz, Fridtjof A1 - Hammerschmidt, Martin A1 - Schneider, Philipp-Immanuel A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators JF - Commun. Phys. Y1 - 2022 U6 - https://doi.org/10.1038/s42005-022-00977-1 VL - 5 SP - 202 ER - TY - JOUR A1 - Tockhorn, Philipp A1 - Sutter, Johannes A1 - Cruz, Alexandros A1 - Wagner, Philipp A1 - Jäger, Klaus A1 - Yoo, Danbi A1 - Lang, Felix A1 - Grischek, Max A1 - Li, Bor A1 - Li, Jinzhao A1 - Shargaieva, Oleksandra A1 - Unger, Eva A1 - Al-Ashouri, Amran A1 - Köhnen, Eike A1 - Stolterfoth, Martin A1 - Neher, Dieter A1 - Schlatmann, Rutger A1 - Rech, Bernd A1 - Stannowski, Bernd A1 - Albrecht, Steve A1 - Becker, Christiane T1 - Nano-optical designs for high-efficiency monolithic perovskite–silicon tandem solar cells JF - Nat. Nanotechnol. Y1 - 2022 U6 - https://doi.org/10.1038/s41565-022-01228-8 VL - 17 SP - 1214 ER - TY - JOUR A1 - Movsesyan, Artur A1 - Santiago, Eva Yazmin A1 - Burger, Sven A1 - Correa-Duarte, Miguel A1 - Besteiro, Lucas V. A1 - Wang, Zhiming A1 - Govorov, Alexander O. T1 - Plasmonic nanocrystals with complex shapes for photocatalysis and growth: Contrasting anisotropic hot-electron generation with the photothermal effect JF - Adv. Opt. Mater. Y1 - 2022 U6 - https://doi.org/10.1002/adom.202102663 VL - 10 SP - 2102663 ER - TY - GEN A1 - Colom, Remi A1 - Binkowski, Felix A1 - Betz, Fridtjof A1 - Kivshar, Yuri A1 - Burger, Sven T1 - Source code and simulation results for nanoantennas supporting an enhanced Purcell factor due to interfering resonances T2 - Zenodo Y1 - 2022 U6 - https://doi.org/10.5281/zenodo.6565850 ER - TY - JOUR A1 - Klus, Stefan A1 - Djurdjevac Conrad, Natasa T1 - Koopman-based spectral clustering of directed and time-evolving graphs JF - Journal of Nonlinear Science N2 - 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. Y1 - 2022 U6 - https://doi.org/10.1007/s00332-022-09863-0 VL - 33 ER - TY - JOUR A1 - Benner, Peter A1 - Burger, Michael A1 - Göddeke, Dominik A1 - Görgen, Christiane A1 - Himpe, Christian A1 - Heiland, Jan A1 - Koprucki, Thomas A1 - Ohlberger, Mario A1 - Rave, Stephan A1 - Reidelbach, Marco A1 - Saak, Jens A1 - Schöbel, Anita A1 - Tabelow, Karsten A1 - Weber, Marcus T1 - Die mathematische Forschungsdateninitiative in der NFDI: MaRDI (Mathematical Research Data Initiative) JF - GAMM Rundbrief Y1 - 2022 IS - 1 SP - 40 EP - 43 ER - TY - JOUR A1 - Tillmann, Peter A1 - Jäger, Klaus A1 - Karsenti, Asher A1 - Kreinin, Lev A1 - Becker, Christiane T1 - Model-Chain Validation for Estimating the Energy Yield of Bifacial Perovskite/Silicon Tandem Solar Cells JF - Sol. RRL Y1 - 2022 U6 - https://doi.org/10.1002/solr.202200079 VL - 6 SP - 2200079 ER - TY - JOUR A1 - Engel, Maximilian A1 - Olicón-Méndez, Guillermo A1 - Wehlitz, Nathalie A1 - Winkelmann, Stefanie T1 - Synchronization and random attractors in reaction jump processes JF - Journal of Dynamics and Differential Equations N2 - 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. Y1 - 2024 U6 - https://doi.org/10.1007/s10884-023-10345-4 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization N2 - 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. T3 - ZIB-Report - 23-19 KW - shortest path KW - flight planning KW - free flight KW - optimal control KW - global optimization KW - Newton's method Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91309 SN - 1438-0064 ER - TY - THES A1 - Danecker, Fabian T1 - A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization N2 - 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. Y1 - 2023 UR - http://dx.doi.org/10.17169/refubium-43526 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - A Discrete-Continuous Algorithm for Free Flight Planning JF - Algorithms N2 - 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. KW - shortest path KW - flight planning KW - free flight KW - discrete-continuous algorithm KW - optimal control KW - discrete optimization Y1 - 2020 U6 - https://doi.org/10.3390/a14010004 SN - 1438-0064 VL - 14 IS - 1 SP - 4 PB - MDPI ER - TY - GEN A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Newton's Method for Global Free Flight Trajectory Optimization N2 - 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. T3 - ZIB-Report - 23-08 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89876 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Convergence Properties of Newton’s Method for Globally Optimal Free Flight Trajectory Optimization T2 - 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023) N2 - 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. Y1 - 2023 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2023.3 VL - 115 SP - 3:1 EP - 3:6 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Newton's Method for Global Free Flight Trajectory Optimization JF - Operations Research Forum N2 - 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. Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91846 VL - 4 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Error Bounds for Discrete-Continuous Free Flight Trajectory Optimization JF - Journal of Optimization Theory and Applications N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1007/s10957-023-02264-7 VL - 198 SP - 830 EP - 856 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization T2 - 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022) N2 - We present an efficient algorithm that finds a globally optimal solution to the 2D Free Flight Trajectory Optimization Problem (aka Zermelo Navigation Problem) up to arbitrary precision in finite time. The algorithm combines a discrete and a continuous optimization phase. In the discrete phase, a set of candidate paths that densely covers the trajectory space is created on a directed auxiliary graph. Then Yen’s algorithm provides a promising set of discrete candidate paths which subsequently undergo a locally convergent refinement stage. Provided that the auxiliary graph is sufficiently dense, the method finds a path that lies within the convex domain around the global minimizer. From this starting point, the second stage will converge rapidly to the optimum. The density of the auxiliary graph depends solely on the wind field, and not on the accuracy of the solution, such that the method inherits the superior asymptotic convergence properties of the optimal control stage. Y1 - 2022 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2022.2 VL - 106 SP - 1 EP - 13 ER -