@article{PomplunBurgerZschiedrichetal.2016, author = {Pomplun, Jan and Burger, Sven and Zschiedrich, Lin and Gutsche, Philipp and Schmidt, Frank}, title = {Method for fast computation of angular light scattering spectra from 2D periodic arrays}, volume = {9778}, journal = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1603.04169}, doi = {10.1117/12.2219666}, pages = {977839}, year = {2016}, language = {en} } @misc{KoltaiCiccottiSchuette2016, author = {Koltai, Peter and Ciccotti, Giovanni and Sch{\"u}tte, Christof}, title = {On metastability and Markov state models for non-stationary molecular dynamics}, volume = {174103}, journal = {The Journal of Chemical Physics}, edition = {145}, issn = {1438-0064}, doi = {10.1063/1.4966157}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57869}, year = {2016}, abstract = {We utilize the theory of coherent sets to build Markov state models for non- equilibrium molecular dynamical systems. Unlike for systems in equilibrium, "meta- stable" sets in the non-equilibrium case may move as time evolves. We formalize this concept by relying on the theory of coherent sets, based on this we derive finite-time non-stationary Markov state models, and illustrate the concept and its main differences to equilibrium Markov state modeling on simple, one-dimensional examples.}, language = {en} } @article{GutschePoulikakosHammerschmidtetal.2016, author = {Gutsche, Philipp and Poulikakos, Lisa and Hammerschmidt, Martin and Burger, Sven and Schmidt, Frank}, title = {Time-harmonic optical chirality in inhomogeneous space}, volume = {9756}, journal = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1603.05011}, doi = {10.1117/12.2209551}, pages = {97560X}, year = {2016}, language = {en} } @article{DjurdjevacConradWeberSchuette2016, author = {Djurdjevac Conrad, Natasa and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Finding dominant structures of nonreversible Markov processes}, volume = {14}, journal = {Multiscale Modeling and Simulation}, number = {4}, doi = {10.1137/15M1032272}, pages = {1319 -- 1340}, year = {2016}, language = {en} } @article{HammerschmidtBarthPomplunetal.2016, author = {Hammerschmidt, Martin and Barth, Carlo and Pomplun, Jan and Burger, Sven and Becker, Christiane and Schmidt, Frank}, title = {Reconstruction of photonic crystal geometries using a reduced basis method for nonlinear outputs}, volume = {9756}, journal = {Proc. SPIE}, doi = {10.1117/12.2212482}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-58187}, pages = {97561R}, year = {2016}, abstract = {Maxwell solvers based on the hp-adaptive finite element method allow for accurate geometrical modeling and high numerical accuracy. These features are indispensable for the optimization of optical properties or reconstruction of parameters through inverse processes. High computational complexity prohibits the evaluation of the solution for many parameters. We present a reduced basis method (RBM) for the time-harmonic electromagnetic scattering problem allowing to compute solutions for a parameter configuration orders of magnitude faster. The RBM allows to evaluate linear and nonlinear outputs of interest like Fourier transform or the enhancement of the electromagnetic field in milliseconds. We apply the RBM to compute light-scattering off two dimensional photonic crystal structures made of silicon and reconstruct geometrical parameters.}, language = {en} } @article{HammerschmidtHerrmannPomplunetal.2016, author = {Hammerschmidt, Martin and Herrmann, Sven and Pomplun, Jan and Burger, Sven and Schmidt, Frank}, title = {Model order reduction for the time-harmonic Maxwell equation applied to complex nanostructures}, volume = {9742}, journal = {Proc. SPIE}, doi = {10.1117/12.2212367}, pages = {97420M}, year = {2016}, abstract = {Fields such as optical metrology and computational lithography require fast and efficient methods for solving the time-harmonic Maxwell's equation. Highly accurate geometrical modelling and numerical accuracy at low computational costs are a prerequisite for any simulation study of complex nano-structured photonic devices. We present a reduced basis method (RBM) for the time-harmonic electromagnetic scattering problem based on the hp-adaptive finite element solver JCMsuite capable of handling geometric and non-geometric parameter dependencies allowing for online evaluations in milliseconds. We apply the RBM to compute light-scattering at optical wavelengths of periodic arrays of fin field-effect transistors (FinFETs) where geometrical properties such as the width and height of the fin and gate can vary in a large range.}, language = {en} } @misc{GutscheLaeuterSchmidt2016, author = {Gutsche, Philipp and L{\"a}uter, Matthias and Schmidt, Frank}, title = {Parameter-dependent Parallel Block Sparse Arnoldi and D{\"o}hler Algorithms on Distributed Systems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-58202}, year = {2016}, abstract = {We summarize the basics and first results of the analyses within our ZIB Bridge Project and give an outlook on further studies broadening the usage of hardware acceleration within the Finite Element Method (FEM) based solution of Maxwell's equations.}, language = {en} } @article{HammerschmidtHerrmannPomplunetal.2016, author = {Hammerschmidt, Martin and Herrmann, Sven and Pomplun, Jan and Burger, Sven and Schmidt, Frank}, title = {Reduced basis method for electromagnetic scattering problem: a case study for FinFETs}, volume = {48}, journal = {Optical and Quantum Electronics}, doi = {10.1007/s11082-016-0530-1}, pages = {250}, year = {2016}, abstract = {Optical 3D simulations in many-query and real-time contexts require new solution strategies. We study an adaptive, error controlled reduced basis method for solving parametrized time-harmonic optical scattering problems. Application fields are, among others, design and optimization problems of nano-optical devices as well as inverse problems for parameter reconstructions occurring e. g. in optical metrology. The reduced basis method pre- sented here relies on a finite element modeling of the scattering problem with parametrization of materials, geometries and sources.}, language = {en} } @phdthesis{Nielsen2016, author = {Nielsen, Adam}, title = {Computation Schemes for Transfer Operators}, year = {2016}, language = {en} } @masterthesis{Sikorski2015, type = {Bachelor Thesis}, author = {Sikorski, Alexander}, title = {PCCA+ and Its Application to Spatial Time Series Clustering}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-58769}, year = {2015}, language = {en} } @misc{BojarovskiHegeLieetal.2015, author = {Bojarovski, Stefan and Hege, Hans-Christian and Lie, Han Cheng and Weber, Marcus}, title = {Topological analysis and visualization of scalar functions characterizing conformational transitions of molecules on multiple time-scales}, journal = {Shape Up 2015 - Exercises in Materials Geometry and Topology, 14-18 Sept. 2015, Berlin, Germany}, year = {2015}, abstract = {Molecular processes such as protein folding or ligand-receptor-binding can be understood by analyzing the free energy landscape. Those processes are often metastable, i.e. the molecular systems remain in basins around local minima of the free energy landscape, and in rare cases undergo gauche transitions between metastable states by passing saddle-points of this landscape. By discretizing the configuration space, this can be modeled as a discrete Markov process. One way to compute the transition rates between conformations of a molecular system is by utilizing Transition Path Theory and the concept of committor functions. A fundamental problem from the computational point of view is that many time-scales are involved, ranging from 10^(-14) sec for the fastest motion to 10^(-6) sec or more for conformation changes that cause biological effects. The goal of our work is to provide a better understanding of such transitions in configuration space on various time-scales by analyzing characteristic scalar functions topologically and geometrically. We are developing suitable visualization and interaction techniques to support our analysis. For example, we are analyzing a transition rate indicator function by computing and visualizing its Reeb graph together with the sets of molecular states corresponding to maxima of the transition rate indicator function. A particular challenge is the high dimensionality of the domain which does not allow for a straightforward visualization of the function. The computational topology approach to the analysis of the transition rate indicator functions for a molecular system allows to explore different time scales of the system by utilizing coarser or finer topological partitioning of the function. A specific goal is the development of tools for analyzing the hierarchy of these partitionings. This approach tackles the analysis of a complex and sparse dataset from a different angle than the well-known spectral analysis of Markov State Models.}, language = {en} } @book{Weiser2016, author = {Weiser, Martin}, title = {Inside Finite Elements}, publisher = {De Gruyter}, year = {2016}, abstract = {All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms.Throughout the exercises a complete FE-solver for scalar 2D problems will be implemented in Matlab/Octave.}, language = {en} } @article{KrebekvonAchaziSollederetal.2016, author = {Krebek, von, Larissa K. S. and Achazi, Andreas J. and Solleder, Marthe and Weber, Marcus and Paulus, Beate and Schalley, Christoph A.}, title = {Allosteric and Chelate Cooperativity in Divalent Crown Ether-Ammonium Complexes with Strong Binding Enhancements}, volume = {22}, journal = {Chem. Eur. J.}, number = {43}, doi = {10.1002/chem.201603098}, pages = {15475 -- 15484}, year = {2016}, language = {en} } @phdthesis{Fackeldey2015, author = {Fackeldey, Konstantin}, title = {Crossing the Scales in Structural Mechanics and Molecular Research}, year = {2015}, language = {en} } @article{OwhadiScovelSullivan2015, author = {Owhadi, Houman and Scovel, Clint and Sullivan, T. J.}, title = {On the Brittleness of Bayesian Inference}, volume = {57}, journal = {SIAM Review}, number = {4}, doi = {10.1137/130938633}, pages = {566 -- 582}, year = {2015}, abstract = {With the advent of high-performance computing, Bayesian methods are becoming increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods can impact the making of sometimes critical decisions in increasingly complicated contexts, the sensitivity of their posterior conclusions with respect to the underlying models and prior beliefs is a pressing question to which there currently exist positive and negative answers. We report new results suggesting that, although Bayesian methods are robust when the number of possible outcomes is finite or when only a finite number of marginals of the data-generating distribution are unknown, they could be generically brittle when applied to continuous systems (and their discretizations) with finite information on the data-generating distribution. If closeness is defined in terms of the total variation (TV) metric or the matching of a finite system of generalized moments, then (1) two practitioners who use arbitrarily close models and observe the same (possibly arbitrarily large amount of) data may reach opposite conclusions; and (2) any given prior and model can be slightly perturbed to achieve any desired posterior conclusion. The mechanism causing brittleness/robustness suggests that learning and robustness are antagonistic requirements, which raises the possibility of a missing stability condition when using Bayesian inference in a continuous world under finite information.}, language = {en} } @book{Sullivan2015, author = {Sullivan, T. J.}, title = {Introduction to Uncertainty Quantification}, volume = {63}, publisher = {Springer}, isbn = {978-3-319-23394-9}, doi = {10.1007/978-3-319-23395-6}, year = {2015}, language = {en} } @inproceedings{BienefeldSpoetterReinschetal.2015, author = {Bienefeld, Kaspar and Sp{\"o}tter, Andreas and Reinsch, Norbert and Mayer, Manfred and Gupta, Pooja}, title = {A new approach for honeybee breeding - genomic selection}, booktitle = {44th Apimondia International Apicultural congress, 2015. Daejeon, South Korea}, year = {2015}, language = {en} } @phdthesis{Gupta2013, author = {Gupta, Pooja}, title = {Integrating high-density marker information into the genetic evaluation of the honey bee}, year = {2013}, language = {en} } @misc{GuptaRoeblitzKrauseetal.2013, author = {Gupta, Pooja and R{\"o}blitz, Susanna and Krause, Carola and Knaus, Petra and Sch{\"u}tte, Christof}, title = {Mathematical modeling of the Smad and Non-Smad BMP signaling pathways in context of cell density}, journal = {Computational Models in biology and medicine, 2013, Dresden, Germany}, year = {2013}, language = {en} } @inproceedings{GuptaKrauseRikeitetal.2014, author = {Gupta, Pooja and Krause, Carola and Rikeit, Paul and R{\"o}blitz, Susanna and Knaus, Petra and Sch{\"u}tte, Christof}, title = {Modeling of the BMP mediated co-regulation of the Smad and Non-Smad pathways in the context of cell density}, booktitle = {10th International BMP conference, 2014, Berlin, Germany}, year = {2014}, language = {en} } @misc{Brust2017, type = {Master Thesis}, author = {Brust, Lisa}, title = {Molek{\"u}ldynamik-Simulation via eines Faltungsansatzes im Potential}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65198}, year = {2017}, language = {de} } @misc{Roehl2017, type = {Master Thesis}, author = {R{\"o}hl, Susanne}, title = {Computing the minimal rebinding effect for nonreversible processes}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65203}, year = {2017}, language = {en} } @misc{Roehm2017, type = {Master Thesis}, author = {R{\"o}hm, Jonas}, title = {Non-Negative Matrix Factorization for Raman Data Spectral Analysis}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65217}, year = {2017}, language = {en} } @misc{Grever2016, type = {Master Thesis}, author = {Grever, Andreas}, title = {Estimating Missing Entries of a Partial Mean First Passage Time Matrix}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65228}, year = {2016}, language = {en} } @misc{Solleder2016, type = {Master Thesis}, author = {Solleder, Marthe}, title = {Molecular Dynamics Simulations : What is the Effect of a Spin Probe on the Drug Loading of a Nanocarrier}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65239}, year = {2016}, language = {en} } @misc{Schoepke2015, type = {Master Thesis}, author = {Sch{\"o}pke, Jessica}, title = {Korrelation f{\"u}r lineare und nichtlineare Zusammenh{\"a}nge}, year = {2015}, language = {de} } @misc{Tumescheit2014, type = {Master Thesis}, author = {Tumescheit, Charlotte}, title = {Using Birkhoff-von Neumann und Sinkhorn Algorithm to Find Dominating Cycles}, year = {2014}, language = {en} } @misc{Frech2014, type = {Master Thesis}, author = {Frech, Ralf}, title = {Das Konzept der Flussdichte und sein Bezug zur Bohmschen Mechanik}, year = {2014}, language = {de} } @misc{Makarenko2017, type = {Master Thesis}, author = {Makarenko, Oleksandra}, title = {Square Root Approximation und statistische Umgewichtungstechnik f{\"u}r das Faltungsverhalten von Polymerb{\"u}rsten}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65283}, year = {2017}, language = {de} } @article{BergPloentzkeLeonhardMareketal.2017, author = {Berg, Mascha and Pl{\"o}ntzke, Julia and Leonhard-Marek, Sabine and M{\"u}ller, Kerstin-Elisabeth and R{\"o}blitz, Susanna}, title = {A dynamic model to simulate potassium balance in dairy cows}, volume = {100}, journal = {Journal of Dairy Science}, number = {12}, doi = {10.3168/jds.2016-12443}, pages = {9799 -- 9814}, year = {2017}, abstract = {High-performing dairy cows require a particular composition of nutritional ingredients, adapted to their individual requirements and depending on their production status. The optimal dimensioning of minerals in the diet, one being potassium, is indispensable for the prevention of imbalances. Potassium balance in cows is the result of potassium intake, distribution in the organism, and excretion, and it is closely related to glucose and electrolyte metabolism. In this paper, we present a dynamical model for potassium balance in lactating and nonlactating dairy cows based on ordinary differential equations. Parameter values were obtained from clinical trial data and from the literature. To verify the consistency of the model, we present simulation outcomes for 3 different scenarios: potassium balance in (1) nonlactating cows with varying feed intake, (2) nonlactating cows with varying potassium fraction in the diet, and (3) lactating cows with varying milk production levels. The results give insights into the short- and long-term potassium metabolism, providing an important step toward the understanding of the potassium network, the design of prophylactic feed additives, and possible treatment strategies.}, language = {en} } @article{GulSchuetteBernhard2016, author = {Gul, Raheem and Sch{\"u}tte, Christof and Bernhard, Stefan}, title = {Mathematical modeling and sensitivity analysis of arterial anastomosis in arm arteries}, journal = {Applied Mathematical Modelling}, doi = {10.1016/j.apm.2016.03.041}, year = {2016}, language = {en} } @incollection{Schmidt2017, author = {Schmidt, Frank}, title = {Photonics}, booktitle = {Handbook of Optoelectronic Device Modeling and Simulation}, editor = {Piprek, Joachim}, publisher = {CRC Press}, isbn = {9781498749381}, year = {2017}, language = {en} } @inproceedings{GregersendeLassonFrandsenetal.2017, author = {Gregersen, Niels and de Lasson, Jakob Rosenkrantz and Frandsen, Lars Hagedorn and Kim, Oleksiy S. and Breinbjerg, Olav and Wang, Fengwen and Sigmund, Ole and Ivinskaya, Aliaksandra and Lavrinenko, Andrei and Gutsche, Philipp and Burger, Sven and H{\"a}yrynen, Teppo and Merk, Jesper}, title = {Comparison of five numerical methods for computing quality factors and resonance wavelengths in photonic crystal membrane cavities}, booktitle = {CLEO/Europe-EQEC}, doi = {10.1109/CLEOE-EQEC.2017.8087750}, year = {2017}, language = {en} } @article{EhrigHeller2019, author = {Ehrig, Rainald and Heller, Markus O.}, title = {On intrinsic equivalences of the finite helical axis, the instantaneous helical axis, and the SARA approach. A mathematical perspective.}, volume = {84}, journal = {Journal of Biomechanics}, doi = {10.1016/j.jbiomech.2018.12.034}, pages = {4 -- 10}, year = {2019}, language = {en} } @misc{FackeldeyKoltaiNeviretal.2017, author = {Fackeldey, Konstantin and Koltai, P{\´e}ter and N{\´e}vir, Peter and Rust, Henning and Schild, Axel and Weber, Marcus}, title = {From Metastable to Coherent Sets - time-discretization schemes}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66074}, year = {2017}, abstract = {Given a time-dependent stochastic process with trajectories x(t) in a space \$\Omega\$, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable sets M are defined in space \$M\subset\Omega\$, coherent sets \$M(t)\subset\Omega\$ are defined in space and time. Hence, if we extend the space by the time-variable t, coherent sets are metastable sets in \$\Omega\times[0,\infty]\$. This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article we show that these well-established spectral algorithms (like PCCA+) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-timediscretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.}, language = {en} } @article{SchnauberSchallBounouaretal.2018, author = {Schnauber, Peter and Schall, Johannes and Bounouar, Samir and H{\"o}hne, Theresa and Park, Suk-In and Ryu, Geun-Hwan and Heindel, Tobias and Burger, Sven and Song, Jin-Dong and Rodt, Sven and Reitzenstein, Stephan}, title = {Deterministic integration of quantum dots into on-chip multi-mode interference beamsplitters using in-situ electron beam lithography}, volume = {18}, journal = {Nano Lett.}, arxiv = {http://arxiv.org/abs/1712.03837}, doi = {10.1021/acs.nanolett.7b05218}, pages = {2336}, year = {2018}, language = {en} } @article{JaegerKoeppelHammerschmidtetal.2018, author = {J{\"a}ger, Klaus and K{\"o}ppel, Grit and Hammerschmidt, Martin and Burger, Sven and Becker, Christiane}, title = {On accurate simulations of thin-film solar cells with a thick glass superstrate}, volume = {26}, journal = {Opt. Express}, doi = {10.1364/OE.26.000A99}, pages = {A99}, year = {2018}, language = {en} } @article{CockayneOatesSullivanetal.2019, author = {Cockayne, Jon and Oates, Chris and Sullivan, T. J. and Girolami, Mark}, title = {Bayesian Probabilistic Numerical Methods}, volume = {61}, journal = {SIAM Review}, number = {4}, arxiv = {http://arxiv.org/abs/1702.03673}, doi = {10.1137/17M1139357}, pages = {756 -- 789}, year = {2019}, abstract = {Over forty years ago average-case error was proposed in the applied mathematics literature as an alternative criterion with which to assess numerical methods. In contrast to worst-case error, this criterion relies on the construction of a probability measure over candidate numerical tasks, and numerical methods are assessed based on their average performance over those tasks with respect to the measure. This paper goes further and establishes Bayesian probabilistic numerical methods as solutions to certain inverse problems based upon the numerical task within the Bayesian framework. This allows us to establish general conditions under which Bayesian probabilistic numerical methods are well defined, encompassing both the non-linear and non-Gaussian context. For general computation, a numerical approximation scheme is proposed and its asymptotic convergence established. The theoretical development is extended to pipelines of computation, wherein probabilistic numerical methods are composed to solve more challenging numerical tasks. The contribution highlights an important research frontier at the interface of numerical analysis and uncertainty quantification, and a challenging industrial application is presented.}, language = {en} } @misc{BittracherBanischSchuette2017, author = {Bittracher, Andreas and Banisch, Ralf and Sch{\"u}tte, Christof}, title = {Data-driven Computation of Molecular Reaction Coordinates}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66179}, year = {2017}, abstract = {The identification of meaningful reaction coordinates plays a key role in the study of complex molecular systems whose essential dynamics is characterized by rare or slow transition events. In a recent publication, the authors identified a condition under which such reaction coordinates exist - the existence of a so-called transition manifold - and proposed a numerical method for their point-wise computation that relies on short bursts of MD simulations. This article represents an extension of the method towards practical applicability in computational chemistry. It describes an alternative computational scheme that instead relies on more commonly available types of simulation data, such as single long molecular trajectories, or the push-forward of arbitrary canonically-distributed point clouds. It is based on a Galerkin approximation of the transition manifold reaction coordinates, that can be tuned to individual requirements by the choice of the Galerkin ansatz functions. Moreover, we propose a ready-to-implement variant of the new scheme, that computes data-fitted, mesh-free ansatz functions directly from the available simulation data. The efficacy of the new method is demonstrated on a realistic peptide system.}, language = {en} } @misc{LieSullivanTeckentrup2018, author = {Lie, Han Cheng and Sullivan, T. J. and Teckentrup, Aretha}, title = {Random forward models and log-likelihoods in Bayesian inverse problems}, volume = {6}, journal = {SIAM/ASA Journal on Uncertainty Quantification}, number = {4}, issn = {1438-0064}, arxiv = {http://arxiv.org/abs/1712.05717}, doi = {10.1137/18M1166523}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66324}, pages = {1600 -- 1629}, year = {2018}, abstract = {We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive model is approximated using a cheaper stochastic surrogate, as in Gaussian process emulation (kriging), or in the field of probabilistic numerical methods. We show that the Hellinger distance between the exact and approximate Bayesian posteriors is bounded by moments of the difference between the true and approximate log-likelihoods. Example applications of these stability results are given for randomised misfit models in large data applications and the probabilistic solution of ordinary differential equations.}, language = {en} } @inproceedings{AbebeGomardZschiedrichetal.2017, author = {Abebe, Muluneh G. and Gomard, Guillaume and Zschiedrich, Lin and Rockstuhl, Carsten and Paetzold, Ulrich W. and Abass, Aimi}, title = {Thermodynamics of Photon Recycling in Four Terminal Perovskite/si Tandem Solar Cells}, booktitle = {Optical Nanostructures and Advanced Materials for Photovoltaics}, doi = {10.1364/PV.2017.PM4A.2}, pages = {PM4A.2}, year = {2017}, language = {en} } @phdthesis{DjurdjevacConrad2012, author = {Djurdjevac Conrad, Natasa}, title = {Methods for analyzing complex networks using random walker}, year = {2012}, language = {en} } @article{BanischDjurdjevacConrad2014, author = {Banisch, Ralf and Djurdjevac Conrad, Natasa}, title = {Cycle-flow-based module detection in directed recurrence networks}, volume = {108}, journal = {EPL (Europhysics Letters)}, number = {6}, doi = {10.1209/0295-5075/108/68008}, year = {2014}, language = {en} } @article{LorenzWolfBraunetal.2017, author = {Lorenz, Philipp and Wolf, Frederik and Braun, Jonas and Djurdjevac Conrad, Natasa and H{\"o}vel, Philipp}, title = {Capturing the Dynamics of Hashtag-Communities}, journal = {International Workshop on Complex Networks and their Applications}, doi = {10.1007/978-3-319-72150-7_33}, pages = {401 -- 413}, year = {2017}, language = {en} } @article{VillatoroZuehlkeRiebeetal.2016, author = {Villatoro, Jose and Z{\"u}hlke, Martin and Riebe, Daniel and Riedel, Jens and Beitz, Toralf and L{\"o}hmannsr{\"o}ben, Hans-Gerd}, title = {IR-MALDI ion mobility spectrometry}, volume = {408}, journal = {Analytical and Bioanalytical Chemistry}, number = {23}, doi = {10.1007/s00216-016-9739-x}, pages = {6259 -- 6268}, year = {2016}, language = {en} } @article{IgdeRoeblitzMuelleretal.2017, author = {Igde, Sinaida and R{\"o}blitz, Susanna and M{\"u}ller, Anne and Kolbe, Katharina and Boden, Sophia and Fessele, Claudia and Lindhorst, Thisbe and Weber, Marcus and Hartmann, Laura}, title = {Linear Precision Glycomacromolecules with Varying Interligand Spacing and Linker Functionalities Binding to Concanavalin A and the Bacterial Lectin FimH}, volume = {17}, journal = {Marcomolecular Bioscience}, number = {12}, doi = {10.1002/mabi.201700198}, pages = {1700198}, year = {2017}, language = {en} } @misc{VolkweinWeiser2000, author = {Volkwein, Stefan and Weiser, Martin}, title = {Affine Invariant Convergence Analysis for Inexact Augmented Lagrangian-SQP Methods}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6243}, number = {00-56}, year = {2000}, abstract = {An affine invariant convergence analysis for inexact augmented Lagrangian-SQP methods is presented. The theory is used for the construction of an accuracy matching between iteration errors and truncation errors, which arise from the inexact linear system solves. The theoretical investigations are illustrated numerically by an optimal control problem for the Burgers equation.}, language = {en} } @misc{ErdmannKoberLangetal.2001, author = {Erdmann, Bodo and Kober, Cornelia and Lang, Jens and Sader, Robert and Zeilhofer, Hans-Florian and Deuflhard, Peter}, title = {Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6403}, number = {01-14}, year = {2001}, abstract = {By computed tomography data (CT), the individual geometry of the mandible is quite well reproduced, also the separation between cortical and trabecular bone. Using anatomical knowledge about the architecture and the functional potential of the masticatory muscles, realistic situations were approximated. The solution of the underlying partial differential equations describing linear elastic material behaviour is provided by an adaptive finite element method. Estimations of the discretization error, local grid refinement, and multilevel techniques guarantee the reliability and efficiency of the method.}, language = {en} } @misc{Weiser2002, author = {Weiser, Martin}, title = {Linear convergence of an interior point method for linear control constrained optimal control problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6809}, number = {02-13}, year = {2002}, abstract = {The paper provides a detailed analysis of a short step interior point algorithm applied to linear control constrained optimal control problems. Using an affine invariant local norm and an inexact Newton corrector, the well-known convergence results from finite dimensional linear programming can be extended to the infinite dimensional setting of optimal control. The present work complements a recent paper of Weiser and Deuflhard, where convergence rates have not been derived. The choice of free parameters, i.e. the corrector accuracy and the number of corrector steps, is discussed.}, language = {en} } @misc{HinzeSchiela2007, author = {Hinze, Michael and Schiela, Anton}, title = {Discretization of Interior Point Methods for State Constrained Elliptic Optimal Control Problems: Optimal Error Estimates and Parameter Adjustment}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10414}, number = {07-40}, year = {2007}, abstract = {An adjustment scheme for the relaxation parameter of interior point approaches to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced. The method is based on error estimates of an associated finite element discretization of the relaxed problems and optimally selects the relaxation parameter in dependence on the mesh size of discretization. The finite element analysis for the relaxed problems is carried out and a numerical example is presented which confirms our analytical findings.}, language = {en} } @misc{Schiela2007, author = {Schiela, Anton}, title = {An Interior Point Method in Function Space for the Efficient Solution of State Constrained Optimal Control Problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10471}, number = {07-44}, year = {2007}, abstract = {We propose and analyse an interior point path-following method in function space for state constrained optimal control. Our emphasis is on proving convergence in function space and on constructing a practical path-following algorithm. In particular, the introduction of a pointwise damping step leads to a very efficient method, as verified by numerical experiments.}, language = {en} } @misc{Weiser2007, author = {Weiser, Martin}, title = {Pointwise Nonlinear Scaling for Reaction-Diffusion-Equations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10493}, number = {07-45}, year = {2007}, abstract = {Parabolic reaction-diffusion systems may develop sharp moving reaction fronts which pose a challenge even for adaptive finite element methods. We propose a method to transform the equation into an equivalent form that usually exhibits solutions which are easier to discretize, giving higher accuracy for a given number of degrees of freedom. The transformation is realized as an efficiently computable pointwise nonlinear scaling that is optimized for prototypical planar travelling wave solutions of the underlying reaction-diffusion equation. The gain in either performance or accuracy is demonstrated on different numerical examples.}, language = {en} }