TY - JOUR A1 - Götschel, Sebastian A1 - Weiser, Martin T1 - Compression Challenges in Large Scale Partial Differential Equation Solvers JF - Algorithms N2 - Solvers for partial differential equations (PDEs) are one of the cornerstones of computational science. For large problems, they involve huge amounts of data that need to be stored and transmitted on all levels of the memory hierarchy. Often, bandwidth is the limiting factor due to the relatively small arithmetic intensity, and increasingly due to the growing disparity between computing power and bandwidth. Consequently, data compression techniques have been investigated and tailored towards the specific requirements of PDE solvers over the recent decades. This paper surveys data compression challenges and discusses examples of corresponding solution approaches for PDE problems, covering all levels of the memory hierarchy from mass storage up to the main memory. We illustrate concepts for particular methods, with examples, and give references to alternatives. Y1 - 2019 U6 - https://doi.org/10.3390/a12090197 VL - 12 IS - 9 SP - 197 ER - TY - JOUR A1 - Santiago, Xavier Garcia A1 - Hammerschmidt, Martin A1 - Burger, Sven A1 - Rockstuhl, Carsten A1 - Fernandez-Corbaton, Ivan A1 - Zschiedrich, Lin T1 - Decomposition of scattered electromagnetic fields into vector spherical wave functions on surfaces with general shapes JF - Phys. Rev. B Y1 - 2019 U6 - https://doi.org/10.1103/PhysRevB.99.045406 VL - 99 SP - 045406 ER - TY - CHAP A1 - Schnauber, Peter A1 - Schall, Johannes A1 - Bounouar, Samir A1 - Höhne, Theresa A1 - Park, Suk-In A1 - Ryu, Geun-Hwan A1 - Heindel, Tobias A1 - Burger, Sven A1 - Song, Jin-Dong A1 - Rodt, Sven A1 - Reitzenstein, Stephan T1 - Deterministic integration of quantum dots into on-chip multi-mode interference couplers via in-situ electron beam lithography T2 - Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference (CLEO/EQEC) Y1 - 2019 U6 - https://doi.org/10.1109/CLEOE-EQEC.2019.8872583 SP - EB2.2 ER - TY - JOUR A1 - Götschel, Sebastian A1 - Minion, Michael L. T1 - An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs JF - SIAM J. Sci. Comput. N2 - To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method. In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE-constrained optimization. In order to develop an efficient fully time-parallel algorithm, we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and the adjoint equations simultaneously. We also explore the additional gains in efficiency from reusing information from previous optimization iterations when solving each equation. Numerical results for both a linear and a nonlinear reaction-diffusion optimal control problem demonstrate the parallel speedup and efficiency of different approaches. Y1 - 2019 U6 - https://doi.org/10.1137/19M1239313 VL - 41 IS - 6 SP - C603 EP - C626 ER - TY - JOUR A1 - Girolami, Mark A. A1 - Ipsen, Ilse C. F. A1 - Oates, Chris A1 - Owen, Art B. A1 - Sullivan, T. J. T1 - Editorial: Special edition on probabilistic numerics JF - Statistics and Computing Y1 - 2019 U6 - https://doi.org/doi:10.1007/s11222-019-09892-y VL - 29 IS - 6 SP - 1181 EP - 1183 ER - TY - GEN A1 - Omari, Mohamed A1 - Plöntzke, Julia A1 - Röblitz, Susanna T1 - A pharmacokinetic-pharmacodynamic model for single dose administration of Dexamethasone in dairy cows N2 - We present a mechanistic pharmacokinetic-pharmacodynamic model to simulate the effect of dexamethasone on the glucose metabolism in dairy cows. The coupling of the pharmacokinetic model to the pharmacodynamic model is based on mechanisms underlying homeostasis regulation by dexamethasone. In particular, the coupling takes into account the predominant role of dexamethasone in stimulating glucagon secretion, glycogenolysis and lipolysis and in impairing the sensitivity of cells to insulin. Simulating the effect of a single dose of dexamethasone on the physiological behaviour of the system shows that the adopted mechanisms are able to induce a temporary hyperglycemia and hyperinsulinemia, which captures the observed data in non-lactating cows. In lactating cows, the model simulations show that a single dose of dexamethasone reduces the lipolytic effect, owing to the reduction of glucose uptake by the mammary gland. T3 - ZIB-Report - 19-53 KW - systems biology; modelling; differential equations; metabolism; nutrition; bovine; fertility; reproduction; hormones; follicles; Dexamethasone; PK-PD Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-75043 SN - 1438-0064 ER - TY - JOUR A1 - Erlekam, Franziska A1 - Igde, Sinaida A1 - Röblitz, Susanna A1 - Hartmann, Laura A1 - Weber, Marcus T1 - Modeling of Multivalent Ligand-Receptor Binding Measured by kinITC JF - Computation N2 - In addition to the conventional Isothermal Titration Calorimetry (ITC), kinetic ITC (kinITC) not only gains thermodynamic information, but also kinetic data from a biochemical binding process. Moreover, kinITC gives insights into reactions consisting of two separate kinetic steps, such as protein folding or sequential binding processes. The ITC method alone cannot deliver kinetic parameters, especially not for multivalent bindings. This paper describes how to solve the problem using kinITC and an invariant subspace projection. The algorithm is tested for multivalent systems with different valencies. Y1 - 2019 U6 - https://doi.org/10.3390/computation7030046 VL - 7 IS - 3 SP - 46 ER - TY - JOUR A1 - Weber, Marcus T1 - Transformationsprodukte im Klärwerk: Mathematische Ansätze der Bewertung JF - KA Korrespondenz Abwasser, Abfall Y1 - 2019 VL - 7 SP - 551 EP - 557 ER - TY - JOUR A1 - Venkatareddy, Narendra Lagumaddepalli A1 - Wilke, Patrick A1 - Ernst, Natalia A1 - Horch, Justus A1 - Weber, Marcus A1 - Dallmann, Andre A1 - Börner, Hans G. T1 - Mussel-glue inspired adhesives: A study on the relevance of L-Dopa and the function of the sequence at nanomaterial-peptide interfaces JF - Advanced Materials Interfaces N2 - Mussel glue‐proteins undergo structural transitions at material interfaces to optimize adhesive surface contacts. Those intriguing structure responses are mimicked by a mussel‐glue mimetic peptide (HSY*SGWSPY*RSG (Y* = l‐Dopa)) that was previously selected by phage‐display to adhere to Al2O3 after enzymatic activation. Molecular level insights into the full‐length adhesion domain at Al2O3 surfaces are provided by a divergent‐convergent analysis, combining nuclear Overhauser enhancement based 2D NOESY and saturation transfer difference NMR analysis of submotifs along with molecular dynamics simulations of the full‐length peptide. The peptide is divided into two submotifs, each containing one Dopa “anchor” (Motif‐1 and 2). The analysis proves Motif‐1 to constitute a dynamic Al2O3 binder and adopting an “M”‐structure with multiple surface contacts. Motif‐2 binds stronger by two surface contacts, forming a compact “C”‐structure. Taking these datasets as constraints enables to predict the structure and propose a binding process model of the full‐length peptide adhering to Al2O3. Y1 - 2019 U6 - https://doi.org/10.1002/admi.201900501 VL - 6 IS - 13 SP - 1900501 ER - TY - JOUR A1 - Del Vecchio, Giovanna A1 - Labuz, Dominika A1 - Temp, Julia A1 - Seitz, Viola A1 - Kloner, Michael A1 - Negrete, Roger A1 - Rodriguez-Gaztelumendi, Antonio A1 - Weber, Marcus A1 - Machelska, Halina A1 - Stein, Christoph T1 - pKa of opioid ligands as a discriminating factor for side effects JF - Scientific Reports N2 - The non-selective activation of central and peripheral opioid receptors is a major shortcoming of currently available opioids. Targeting peripheral opioid receptors is a promising strategy to preclude side effects. Recently, we showed that fentanyl-derived μ-opioid receptor (MOR) agonists with reduced acid dissociation constants (pKa) due to introducing single fluorine atoms produced injury-restricted antinociception in rat models of inflammatory, postoperative and neuropathic pain. Here, we report that a new double-fluorinated compound (FF6) and fentanyl show similar pKa, MOR affinity and [35S]-GTPγS binding at low and physiological pH values. In vivo, FF6 produced antinociception in injured and non-injured tissue, and induced sedation and constipation. The comparison of several fentanyl derivatives revealed a correlation between pKa values and pH-dependent MOR activation, antinociception and side effects. An opioid ligand's pKa value may be used as discriminating factor to design safer analgesics. Y1 - 2019 U6 - https://doi.org/10.1038/s41598-019-55886-1 VL - 9 SP - 19344 ER - TY - JOUR A1 - Schulz, Robert A1 - Yamamoto, Kenji A1 - Klossek, André A1 - Rancan, Fiorenza A1 - Vogt, Annika A1 - Schütte, Christof A1 - Rühl, Eckart A1 - Netz, Roland R. T1 - Modeling of Drug Diffusion Based on Concentration Profiles in Healthy and Damaged Human Skin JF - Biophysical Journal N2 - Based on experimental drug concentration profiles in healthy as well as tape-stripped ex vivo human skin, we model the penetration of the antiinflammatory drug dexamethasone into the skin layers by the one-dimensional generalized diffusion equation. We estimate the position-dependent free-energy and diffusivity profiles by solving the conjugated minimization problem, in which the only inputs are concentration profiles of dexamethasone in skin at three consecutive penetration times. The resulting free-energy profiles for damaged and healthy skin show only minor differences. In contrast, the drug diffusivity in the first 10 μm of the upper skin layer of damaged skin is 200-fold increased compared to healthy skin, which reflects the corrupted barrier function of tape-stripped skin. For the case of healthy skin, we examine the robustness of our method by analyzing the behavior of the extracted skin parameters when the number of input and output parameters are reduced. We also discuss techniques for the regularization of our parameter extraction method. Y1 - 2019 U6 - https://doi.org/10.1016/j.bpj.2019.07.027 VL - 117 IS - 5 SP - 998 EP - 1008 ER - TY - THES A1 - Bender, Wilhelm T1 - On a Novel Approach for Global Optimization of Non-Convex Problems N2 - In this work new approaches for global optimization are developed. We move from theoretical connections in complexity theory to very practical results in protein-ligand docking. In regard to the efficiency of the suggested optimizer, continuity methods are motivated, that yield an improved optimization method. Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-77074 ER - TY - THES A1 - Gaedke-Merzhäuser, Lisa T1 - Adaptive Multigrid Solvers for Space-Time Discretisations Y1 - 2019 ER - TY - THES A1 - Ribera Borrell, Enric T1 - From ergodic infinite-time to finite-time transition path theory Y1 - 2019 ER - TY - THES A1 - Meitzner, Felix T1 - Influence of Ordinary Differential Equations on Neural Networks N2 - In this thesis, I want to analyze how neural networks trained to resemble a given function based on particular values react to additional knowledge about the function in terms of a differential equation that the function satisfies. In the first chapter, I will recall the definition of initial value problems and discuss the existence and uniqueness of their solutions, as well as touch on a method to numerically approximate them. Furthermore, I will give a mathematical introduction to neural networks. Then, I will consider a system of two first-order differential equations and test how their solution will be approximated by a neural net. In the next step, I want to see how added noise to the training data and the influence of the differential equation on the loss functional of the neural net will affect the error of the predicted solution against the exact data. Furthermore, I will test if this influence can help reduce the amount of necessary data points in order to reach similar degrees of accuracy. Y1 - 2019 ER - TY - JOUR A1 - Koltai, Péter A1 - Lie, Han Cheng A1 - Plonka, Martin T1 - Fréchet differentiable drift dependence of Perron–Frobenius and Koopman operators for non-deterministic dynamics JF - Nonlinearity N2 - We prove the Fréchet differentiability with respect to the drift of Perron–Frobenius and Koopman operators associated to time-inhomogeneous ordinary stochastic differential equations. This result relies on a similar differentiability result for pathwise expectations of path functionals of the solution of the stochastic differential equation, which we establish using Girsanov's formula. We demonstrate the significance of our result in the context of dynamical systems and operator theory, by proving continuously differentiable drift dependence of the simple eigen- and singular values and the corresponding eigen- and singular functions of the stochastic Perron–Frobenius and Koopman operators. Y1 - 2019 U6 - https://doi.org/10.1088/1361-6544/ab1f2a VL - 32 IS - 11 SP - 4232 EP - 4257 ER - TY - JOUR A1 - Klus, Stefan A1 - Husic, Brooke E. A1 - Mollenhauer, Mattes A1 - Noe, Frank T1 - Kernel methods for detecting coherent structures in dynamical data JF - Chaos: An Interdisciplinary Journal of Nonlinear Science Y1 - 2019 U6 - https://doi.org/10.1063/1.5100267 VL - 29 IS - 12 ER - TY - CHAP A1 - Höhne, Theresa A1 - Schnauber, Peter A1 - Rodt, Sven A1 - Reitzenstein, Stephan A1 - Burger, Sven ED - Novotny, Lukas ED - Quidant, Romain T1 - Numerical Investigation of Integrated Single-Photon Emitters in Low-Index-Contrast Waveguides T2 - Nanophotonics: Foundations & Applications, CSF Conference Book of Abstracts Y1 - 2019 SP - B11 ER - TY - CHAP A1 - Zschiedrich, Lin A1 - Binkowski, Felix A1 - Burger, Sven ED - Kaltenbacher, Manfred T1 - Spectral resonance expansion by Riesz projections T2 - 14 th International Conference on Mathematical and Numerical Aspects of Wave Propagation Book of Abstracts Y1 - 2019 U6 - https://doi.org/10.34726/waves2019 SP - 234 ER - TY - JOUR A1 - Haase, Tobias A1 - Sunkara, Vikram A1 - Kohl, Benjamin A1 - Meier, Carola A1 - Bußmann, Patricia A1 - Becker, Jessica A1 - Jagielski, Michal A1 - von Kleist, Max A1 - Ertel, Wolfgang T1 - Discerning the spatio-temporal disease patterns of surgically induced OA mouse models JF - PLOS One N2 - Osteoarthritis (OA) is the most common cause of disability in ageing societies, with no effective therapies available to date. Two preclinical models are widely used to validate novel OA interventions (MCL-MM and DMM). Our aim is to discern disease dynamics in these models to provide a clear timeline in which various pathological changes occur. OA was surgically induced in mice by destabilisation of the medial meniscus. Analysis of OA progression revealed that the intensity and duration of chondrocyte loss and cartilage lesion formation were significantly different in MCL-MM vs DMM. Firstly, apoptosis was seen prior to week two and was narrowly restricted to the weight bearing area. Four weeks post injury the magnitude of apoptosis led to a 40–60% reduction of chondrocytes in the non-calcified zone. Secondly, the progression of cell loss preceded the structural changes of the cartilage spatio-temporally. Lastly, while proteoglycan loss was similar in both models, collagen type II degradation only occurred more prominently in MCL-MM. Dynamics of chondrocyte loss and lesion formation in preclinical models has important implications for validating new therapeutic strategies. Our work could be helpful in assessing the feasibility and expected response of the DMM- and the MCL-MM models to chondrocyte mediated therapies. Y1 - 2019 U6 - https://doi.org/10.1371/journal.pone.0213734 VL - 14 IS - 4 PB - PLOS One ER - TY - JOUR A1 - Sunkara, Vikram T1 - On the Properties of the Reaction Counts Chemical Master Equation JF - Entropy N2 - The reaction counts chemical master equation (CME) is a high-dimensional variant of the classical population counts CME. In the reaction counts CME setting, we count the reactions which have fired over time rather than monitoring the population state over time. Since a reaction either fires or not, the reaction counts CME transitions are only forward stepping. Typically there are more reactions in a system than species, this results in the reaction counts CME being higher in dimension, but simpler in dynamics. In this work, we revisit the reaction counts CME framework and its key theoretical results. Then we will extend the theory by exploiting the reactions counts’ forward stepping feature, by decomposing the state space into independent continuous-time Markov chains (CTMC). We extend the reaction counts CME theory to derive analytical forms and estimates for the CTMC decomposition of the CME. This new theory gives new insights into solving hitting times-, rare events-, and a priori domain construction problems. Y1 - 2019 U6 - https://doi.org/10.3390/e21060607 VL - 21 IS - 6 SP - 607 ER - TY - THES A1 - Rabben, Robert Julian T1 - Bestimmung invarianter Unterräume des Koopman-Operators einer Overdamped Langevin-Dynamik mithilfe eines Muli-Layer Neural Networks Y1 - 2019 ER - TY - THES A1 - Wachsmann, Ole T1 - Computational Models for the prediction of drug-induced Nephrotoxicity Y1 - 2019 ER - TY - CHAP A1 - Burger, Sven A1 - Schneider, Philipp-Immanuel A1 - Höhne, Theresa A1 - Zschiedrich, Lin ED - Reitzenstein, Stephan ED - Heindel, Tobias T1 - Numerical methods for simulation and optimization of the extraction efficiency from quantum-dot based single-photon emitters T2 - 7th International Workshop on Engineering of Quantum Emitter Properties (EQEP) Y1 - 2019 SP - 20 ER - TY - THES A1 - Boz, Seyma T1 - Classification of the toxicity profile of the withdrawn drugs using computational prediction platform ProTox-II Y1 - 2019 ER - TY - THES A1 - Basaleh, Rascha T1 - Prediction and Analysis of Drugs Inducing Liver Injury (DILI) using ProTox-II Computational-Tool Y1 - 2019 ER - TY - CHAP A1 - Höhne, Theresa A1 - Schnauber, Peter A1 - Rodt, Sven A1 - Reitzenstein, Stephan A1 - Burger, Sven ED - Reitzenstein, Stephan ED - Heindel, Tobias T1 - Numerical Studies of Integrated Single-Photon Emitters in Low-Index-Contrast Waveguides T2 - 7th International Workshop on Engineering of Quantum Emitter Properties (EQEP) Y1 - 2019 SP - 49 ER - TY - THES A1 - Kostré, Margarita T1 - Hybrid Models and Simulations of Reaction-Diffusion Processes N2 - In this thesis,we are interested in multiscale models for particle-based reaction diffusion (PBRD) simulations,where we focus on coupling particle-based simulations to macroscopic chemical reservoirs. These reservoirs are given by a mean concentration of chemical species that can vary in time and space. We model these reservoirs as reaction-diffusion partial differential equations (PDEs). The goal of this work is to achieve a mathematically consistent coupling between the PBRD simulations and the reaction-diffusion PDEs. Y1 - 2019 ER - TY - CHAP A1 - Kewes, Günter A1 - Binkowski, Felix A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Stete, Felix A1 - Koopman, Wouter A1 - Bargheer, Matias A1 - Benson, Oliver ED - Asquini, Rita T1 - Line Broadening Mechanisms in Hybrid Plasmonic Systems for Strong Coupling T2 - Photonics & Electromagnetics Research Symposium Abstracts (PIERS Rome) Y1 - 2019 SP - 704 ER - TY - CHAP A1 - Zschiedrich, Lin A1 - Binkowski, Felix A1 - Burger, Sven ED - Asquini, Rita T1 - Light-matter Interaction in Optical Resonators: Spectral Expansion by Riesz Projection T2 - Photonics & Electromagnetics Research Symposium Abstracts (PIERS Rome) Y1 - 2019 SP - 1067 ER - TY - THES A1 - Omari, Mohamed T1 - A Mathematical Model of Bovine Metabolism and Reproduction: Application to Feeding Strategies, Drug Administration and Experimental Design Y1 - 2019 ER - TY - CHAP A1 - Binkowski, Felix A1 - Zschiedrich, Lin A1 - Schneider, Philipp-Immanuel A1 - Hammerschmidt, Martin A1 - Santiago, Xavier Garcia A1 - Betz, Fridtjof A1 - Burger, Sven ED - Saastamoinen, Kimmo T1 - Spectral Expansion of the Scattering Response of Resonant Nanostructures T2 - EOS Topical Meeting on Diffractive Optics Y1 - 2019 SN - 978-952-68553-8-7 SP - 1 ER - TY - THES A1 - Reidelbach, Marco T1 - Optimal Network Generation for the Simulation of Proton Transfer Processes Y1 - 2019 ER - TY - THES A1 - Donati, Luca T1 - Reweighting methods for Molecular Dynamics N2 - The dynamical response of molecular systems, when the potential energy function is perturbed at a microscopic level, is difficult to predict without a numerical or laboratory experiment. This is due to the non-linearity and high-dimensionality of molecular systems. An efficient investigation of such a behaviour is necessary to better understand the nature of molecules and to improve the predictability of Molecular Dynamics simulations. In this thesis we propose a reweighting scheme for Markov State Models (MSMs), based on the Girsanov theorem, that permits to reduce the computational cost of the analysis when the potential energy function of a molecule is perturbed. The method has been successfully extended and implemented with metadynamics, in order to build the MSM of a molecular system in a significantly shorter computational time compared to a standard unbiased MD simulation. We also propose a new method to discretize the infinitesimal generator into a rate matrix, that could be used to efficiently study Hamiltonian perturbations as well. Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:188-refubium-24541-6 PB - Freie Universität Berlin ER - TY - CHAP A1 - Binkowski, Felix A1 - Schneider, Philipp-Immanuel A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven ED - Matijević, Milica ED - Krstić, Marko ED - Beličev, Petra T1 - Numerical optimization of resonant nanophotonic devices T2 - The Seventh International School and Conference on Photonics (PHOTONICA Belgrade) Y1 - 2019 SN - 978-86-7306-153-5 SP - 10 ER - TY - THES A1 - Zumbansen, Max T1 - Parameter estimation of multivalent processes on ITC datasets Y1 - 2019 ER - TY - THES A1 - Hoffmann, Lara T1 - Automating PCCA+ applied to Eye-Tracking Data Y1 - 2019 ER - TY - GEN ED - Ernst, Oliver ED - Nobile, Fabio ED - Schillings, Claudia ED - Sullivan, T. J. T1 - Uncertainty Quantification, 11-15 March 2019 T2 - Oberwolfach Reports Y1 - 2019 U6 - https://doi.org/10.4171/OWR/2019/12 VL - 16 IS - 1 SP - 695 EP - 772 ER - TY - CHAP A1 - Burger, Sven A1 - Binkowski, Felix A1 - Zschiedrich, Lin ED - Zhoudi, Said ED - Topa, Antonio T1 - Computing resonances in nano-photonic devices using Riesz-projection-based methods T2 - The 10th International Conference on Metamaterials, Photonic Crystals and Plasmonics (META 2019) Y1 - 2019 SN - 2429-1390 SP - 92 ER - TY - CHAP A1 - Manley, Phillip A1 - Hammerschmidt, Martin A1 - Burger, Sven A1 - Becker, Christiane ED - Zhoudi, Said ED - Topa, Antonio T1 - Nanophotonic Enhancement of Light Out-Coupling for Deep-UV LEDs T2 - The 10th International Conference on Metamaterials, Photonic Crystals and Plasmonics (META 2019) Y1 - 2019 SN - 2429-1390 SP - 745 ER - TY - CHAP A1 - Becker, Christiane A1 - Manley, Phillip A1 - Jäger, Klaus A1 - Eisenhauer, David A1 - Sutter, Johannes A1 - Albrecht, Steve A1 - Zheng, Kaibo A1 - Pullerits, Tonu A1 - Burger, Sven ED - Zhoudi, Said ED - Topa, Antonio T1 - Nanophotonic enhanced perovskite-silicon solar cell devices T2 - The 10th International Conference on Metamaterials, Photonic Crystals and Plasmonics (META 2019) Y1 - 2019 SN - 2429-1390 SP - 858 ER - TY - CHAP A1 - Binkowski, Felix A1 - Zschiedrich, Lin A1 - Burger, Sven ED - Asquini, Rita T1 - Computing Optical Resonances in Plasmonic Systems Using a Contour Integral Method T2 - Photonics & Electromagnetics Research Symposium Abstracts (PIERS Rome) Y1 - 2019 SP - 1068 ER - TY - CHAP A1 - Burger, Sven A1 - Binkowski, Felix A1 - Zschiedrich, Lin ED - Asquini, Rita T1 - Finite Element Simulations of Optical Resonances in Dispersive Nanoresonators T2 - Photonics & Electromagnetics Research Symposium Abstracts (PIERS Rome) Y1 - 2019 SP - 699 ER - TY - JOUR A1 - Lie, Han Cheng A1 - Sullivan, T. J. A1 - Stuart, Andrew T1 - Strong convergence rates of probabilistic integrators for ordinary differential equations JF - Statistics and Computing N2 - Probabilistic integration of a continuous dynamical system is a way of systematically introducing model error, at scales no larger than errors inroduced by standard numerical discretisation, in order to enable thorough exploration of possible responses of the system to inputs. It is thus a potentially useful approach in a number of applications such as forward uncertainty quantification, inverse problems, and data assimilation. We extend the convergence analysis of probabilistic integrators for deterministic ordinary differential equations, as proposed by Conrad et al.\ (\textit{Stat.\ Comput.}, 2016), to establish mean-square convergence in the uniform norm on discrete- or continuous-time solutions under relaxed regularity assumptions on the driving vector fields and their induced flows. Specifically, we show that randomised high-order integrators for globally Lipschitz flows and randomised Euler integrators for dissipative vector fields with polynomially-bounded local Lipschitz constants all have the same mean-square convergence rate as their deterministic counterparts, provided that the variance of the integration noise is not of higher order than the corresponding deterministic integrator. Y1 - 2019 U6 - https://doi.org/10.1007/s11222-019-09898-6 VL - 29 IS - 6 SP - 1265 EP - 1283 ER - TY - GEN A1 - Helfmann, Luzie A1 - Djurdjevac Conrad, Natasa A1 - Djurdjevac, Ana A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - From interacting agents to density-based modeling with stochastic PDEs N2 - Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models. T3 - ZIB-Report - 19-21 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73456 SN - 1438-0064 ER - TY - GEN A1 - Omari, Mohamed A1 - Lange, Alexander A1 - Plöntzke, Julia A1 - Röblitz, Susanna T1 - A Mathematical Model for the Influence of Glucose-Insulin Dynamics on the Estrous Cycle in Dairy Cows N2 - Nutrition plays a crucial role in regulating reproductive hormones and follicular development in cattle. This is visible particularly during the time of negative energy balance at the onset of milk production after calving. Here, elongated periods of anovulation have been observed, resulting from alterations in luteiniz- ing hormone concentrations, likely caused by lower glucose and insulin concen- trations in the blood. The mechanisms that result in a reduced fertility are not completely understood, although a close relationship to the glucose-insulin metabolism is widely supported. Following this idea, a mathematical model of the hormonal network combining reproductive hormones and hormones that are coupled to the glucose compartments within the body of the cow was developed. The model is built on ordinary differential equations and relies on previously introduced models on the bovine estrous cycle and the glucose-insulin dynam- ics. Necessary modifications and coupling mechanisms are thoroughly discussed. Depending on the composition and the amount of food, in particular the glu- cose content in the dry matter, the model quantifies reproductive hormones and follicular development over time. Simulation results for different nutritional regimes in lactating and non-lactating dairy cows are examined and compared with experimental studies. Regarding its applicability, this work is an early attempt towards developing in silico feeding strategies and may eventually help refining and reducing animal experiments. T3 - ZIB-Report - 19-22 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73475 SN - 1438-0064 ER - TY - JOUR A1 - Mrowinski, Paweł A1 - Schnauber, Peter A1 - Gutsche, Philipp A1 - Kaganskiy, Arsenty A1 - Schall, Johannes A1 - Burger, Sven A1 - Rodt, Sven A1 - Reitzenstein, Stephan T1 - Directional emission of a deterministically fabricated quantum dot – Bragg reflection multi-mode waveguide system JF - ACS Photonics Y1 - 2019 U6 - https://doi.org/10.1021/acsphotonics.9b00369 VL - 6 SP - 2231 ER - TY - JOUR A1 - Werdehausen, Daniel A1 - Burger, Sven A1 - Staude, Isabelle A1 - Pertsch, Thomas A1 - Decker, Manuel T1 - Dispersion-engineered nanocomposites enable achromatic diffractive optical elements JF - Optica Y1 - 2019 U6 - https://doi.org/10.1364/OPTICA.6.001031 VL - 6 SP - 1031 ER - TY - JOUR A1 - Weber, Marie-Christin A1 - Fischer, Lisa A1 - Damerau, Alexandra A1 - Ponomarev, Igor A1 - Pfeiffenberger, Moritz A1 - Gaber, Timo A1 - Götschel, Sebastian A1 - Lang, Jens A1 - Röblitz, Susanna A1 - Buttgereit, Frank A1 - Ehrig, Rainald A1 - Lang, Annemarie T1 - In vitro and in silico modeling of cellular and matrix-related changes during the early phase of osteoarthritis JF - BioRxiv N2 - Understanding the pathophysiological processes of osteoarthritis (OA) require adequate model systems. Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific parts of the disease. This study aimed to combine in vitro and in silico modeling to describe cellular and matrix-related changes during the early phase of OA. We developed an in vitro OA model based on scaffold-free cartilage-like constructs (SFCCs), which was mathematically modeled using a partial differential equation (PDE) system to resemble the processes during the onset of OA. SFCCs were produced from mesenchymal stromal cells and analyzed weekly by histology and qPCR to characterize the cellular and matrix-related composition. To simulate the early phase of OA, SFCCs were treated with interleukin-1β (IL-1β), tumor necrosis factor α (TNFα) and examined after 3 weeks or cultivated another 3 weeks without inflammatory cytokines to validate the regeneration potential. Mathematical modeling was performed in parallel to the in vitro experiments. SFCCs expressed cartilage-specific markers, and after stimulation an increased expression of inflammatory markers, matrix degrading enzymes, a loss of collagen II (Col-2) and a reduced cell density was observed which could be partially reversed by retraction of stimulation. Based on the PDEs, the distribution processes within the SFCCs, including those of IL-1β, Col-2 degradation and cell number reduction was simulated. By combining in vitro and in silico methods, we aimed to develop a valid, efficient alternative approach to examine and predict disease progression and new therapeutic strategies. Y1 - 2019 U6 - https://doi.org/10.1101/725317 ER - TY - GEN A1 - Özel, M. Neset A1 - Kulkarni, Abhishek A1 - Hasan, Amr A1 - Brummer, Josephine A1 - Moldenhauer, Marian A1 - Daumann, Ilsa-Maria A1 - Wolfenberg, Heike A1 - Dercksen, Vincent J. A1 - Kiral, F. Ridvan A1 - Weiser, Martin A1 - Prohaska, Steffen A1 - von Kleist, Max A1 - Hiesinger, Peter Robin T1 - Serial synapse formation through filopodial competition for synaptic seeding factors N2 - Following axon pathfinding, growth cones transition from stochastic filopodial exploration to the formation of a limited number of synapses. How the interplay of filopodia and synapse assembly ensures robust connectivity in the brain has remained a challenging problem. Here, we developed a new 4D analysis method for filopodial dynamics and a data-driven computational model of synapse formation for R7 photoreceptor axons in developing Drosophila brains. Our live data support a 'serial synapse formation' model, where at any time point only a single 'synaptogenic' filopodium suppresses the synaptic competence of other filopodia through competition for synaptic seeding factors. Loss of the synaptic seeding factors Syd-1 and Liprin-α leads to a loss of this suppression, filopodial destabilization and reduced synapse formation, which is sufficient to cause the destabilization of entire axon terminals. Our model provides a filopodial 'winner-takes-all' mechanism that ensures the formation of an appropriate number of synapses. T3 - ZIB-Report - 19-45 KW - filopodia KW - growth cone dynamics KW - brain wiring KW - 2-photon microscopy KW - model Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-74397 SN - 1438-0064 ER -