@misc{SchielaWeiser2009, author = {Schiela, Anton and Weiser, Martin}, title = {Barrier methods for a control problem from hyperthermia treatment planning}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11567}, number = {09-36}, year = {2009}, abstract = {We consider an optimal control problem from hyperthermia treatment planning and its barrier regularization. We derive basic results, which lay the groundwork for the computation of optimal solutions via an interior point path-following method. Further, we report on a numerical implementation of such a method and its performance at an example problem.}, language = {en} } @phdthesis{Zschiedrich2009, author = {Zschiedrich, Lin}, title = {Transparent boundary conditions for Maxwell's equations: Numerical concepts beyond the PML method}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000013994-8}, year = {2009}, abstract = {Optical technologies are ubiquitously used in hi-tech devices. As a common feature of such devices one finds structures with dimensions in the order of the wavelength of the used light. To design and produce such devices, the wave nature of light must be taken into account. Accordingly, robust simulation tools are required which are based on rigorously solving Maxwell's equations, the governing equations of light propagation within macroscopic media. This thesis contributes to the modeling and the numerical computation of light scattering problems: Light scattering problems are typically posed on the entire space. The Perfectly-Matched -Layer method (PML) is widely used to restrict the simulation problem onto a bounded computational domain. We propose an adaptive PML method which exhibits a good convergence even for critical problems where standard PML implementations fail. Besides the computation of the near field, that is the electromagnetic field within the computational domain, it is of major interest to evaluate the electromagnetic field in the exterior domain and to compute the far field. So far, this was numerically only possible for simple geometries such as homogeneous exterior domains or layered media. To deal with more complicated devices, for example with waveguide inhomogeneities, we develop an evaluation formula based on the PML solution which allows for an exterior domain field evaluation in a half space above the device. Finally, we generalize the PML method to problems with multiply structured exterior domains. The term "multiply structured exterior domain" is defined in this thesis and means that the exterior domain exhibits several half-infinite structures. Mathematically, this gives rise to various complications. For example, no analytical solutions to Maxwell's equations for standard light sources are available in the exterior domain, which are needed to describe the incoming field in a light scattering problem. To tackle this we propose a new light scattering problem formulation which fits well into the PML method framework and which may be regarded as an extension of classical contributions by Sommerfeld, Wiener and Hopf. An exterior domain evaluation formula for multiply structured exterior domains with an extended illumination is derived as well.}, language = {en} } @phdthesis{Roeblitz2009, author = {R{\"o}blitz, Susanna}, title = {Statistical Error Estimation and Grid-free Hierarchical Refinement in Conformation Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000008079-9}, year = {2009}, abstract = {The understanding of geometric structures and dynamical properties of molecular conformations gives insight into molecular long-term behavior. The identification of metastable conformations together with their life times and transition patterns is the intention of conformation dynamics. Conformation dynamics is a multi-scale approach that leads to a reduced description of the dynamical system in terms of a stochastic transition probability matrix. The present thesis deals with the error analysis of computed matrices and the resulting matrix functions. Since conformational membership vectors, as they are computed by the Robust Perron Cluster Analysis (PCCA+), form an invariant subspace of the transition matrix, subspace-based error estimators are of particular interest. The decomposition of the state space into basis functions and the approximation of integrals by Monte-Carlo quadrature give rise to row-wise correlated random matrices, for which stochastic norms are computed. Together with an appropriate statistical model for the distribution of matrix rows, this allows for the calculation of error bounds and error distributions of the invariant subspace and other variables of interest. Equilibration of errors among the basis functions can be achieved by enhanced sampling in regions where the trajectories are mixing slowly. Hierarchical refinement of such basis functions systematically improves the clustering into metastable conformations by reducing the error in the corresponding invariant subspace. These techniques allow for an evaluation of simulation results and pave the way for the analysis of larger molecules. Moreover, the extension of PCCA+ to non-reversible Markov chains, verified by the corresponding perturbation theory, and the modification of the objective function for the case of soft membership vectors represent a further generalization of the clustering method, thus continuing the development from PCCA over PCCA+ to PCCA++. The methods developed in this thesis are useful for but not limited to conformation dynamics. In fact, they are applicable to a broader class of problems which combine domain decomposition with Monte-Carlo quadrature. Possible application areas may include the chemical master equation or quantum dynamical systems.}, language = {en} } @misc{KilianMuench2009, author = {Kilian, Susanne and M{\"u}nch, Matthias}, title = {A new generalized domain decomposition strategy for the efficient parallel solution of the FDS-pressure equation. Part I: Theory, Concept and Implementation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11332}, number = {09-19}, year = {2009}, abstract = {A world-wide used program for the simulation of fire-induced flows is the Fire Dynamics Simulator (FDS) which originally was developed for a purely serial execution on single-processor computing systems. Due to steadily increasing problem sizes and accuracy requirements as well as restrictions in storage capacity and computing power on single-processor systems, the efficient simulation of the considered fire scenarios can only be achieved on modern high-performance systems based on multi-processor architectures. The transition to those systems requires the elaborate parallelization of the underlying numerical methods which must guarantee the same result for a given problem as the corresponding serial execution. Unfortunately, one fundamental serial serial solver of FDS, the pressure solver, only possesses a low degree of inherent parallelizm. Its current parallelization may cause additional numerical errors, casually leading to significant losses of accuracy or even numerical instabilities. In order to ensure that the parallelization errors are limited by the leading error of the numerical scheme such that second order convergence for the whole method can be acchieved, optimized parallelization concepts must be designed. With respect to these considerations this articles gives an overview of the current parallel pressure solver as well as the problems related to it and presents an alternative method, SCARC, to overcome the existing complicacies. Part I explains the theory, concept and implementation of this new strategy, whereas Part II describes a series of validation and verification tests to proof its correctness.}, language = {en} } @misc{MuenchKilian2009, author = {M{\"u}nch, Matthias and Kilian, Susanne}, title = {A new generalized domain decomposition strategy for the efficient parallel solution of the FDS-pressure equation. Part II: Verification and Validation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11340}, number = {09-20}, year = {2009}, abstract = {Because CFD programs, like FDS, generally consist of a large number of different components representing the variety of participating numerical algorithms and chemical / physical processes, it is nearly impossible to verify such codes in their entirety, for example with comparisons of fire tests. Instead, a careful verification and validation with respect to the underlying mathematical conditions and applied numerical schemes is indispensable. In particular, error cancelations between single program components can only be detected by such detailed component-level tests. In part I of this article series a conceptual deficiency of the FDS program package with regard to multi-mesh computations was illustrated and an alternative domain decomposition strategy FDS-ScaRC was introduced. In this second part we will present the structure of a comprehensive test concept and the needs for a more mathematically and numerically orientated test procedure that is much more suited for a reliable evaluation than only a simple visual comparison of the numerical results with experimental fire tests. After a general introduction of our test concept we will demonstrate the high potential of the new FDS-\scarc{} technique compared to the FDS-FFT technique which is used in the FDS program package as yet. Based on this concept, we will present a comprehensive set of analytical and numerical test results.}, language = {en} } @misc{RuprechtKleinMajda2009, author = {Ruprecht, Daniel and Klein, Rupert and Majda, Andrew J.}, title = {Moisture-Gravity Wave Interactions in a Multiscale Environment}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11358}, number = {09-21}, year = {2009}, abstract = {Starting from the conservation laws for mass, momentum and energy together with a three species, bulk microphysic model, a model for the interaction of internal gravity waves and deep convective hot towers is derived by using multiscale asymptotic techniques. From the resulting leading order equations, a closed model is obtained by applying weighted averages to the smallscale hot towers without requiring further closure approximations. The resulting model is an extension of the linear, anelastic equations, into which moisture enters as the area fraction of saturated regions on the microscale with two way coupling between the large and small scale. Moisture reduces the effective stability in the model and defines a potential temperature sourceterm related to the net effect of latent heat release or consumption by microscale up- and downdrafts. The dispersion relation and group velocity of the system is analyzed and moisture is found to have several effects: It reduces energy transport by waves, increases the vertical wavenumber but decreases the slope at which wave packets travel and it introduces a lower horizontal cutoff wavenumber, below which modes turn into evanescent. Further, moisture can cause critical layers. Numerical examples for steadystate and timedependent mountain waves are shown and the effects of moisture on these waves are investigated.}, language = {en} } @misc{Massing2009, type = {Master Thesis}, author = {Massing, Andr{\´e}}, title = {1D-Reduktion thermal signifikanter Aderstr{\"a}nge in der Hyperthermie-Modellierung}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11407}, school = {Zuse Institute Berlin (ZIB)}, year = {2009}, abstract = {In dieser Arbeit wird ein neuer Ansatz zur Modellierung von thermal signifikanten Gef{\"a}ßstr{\"a}ngen im Hyperthermie-Kontext betrachtet. Ausgehend von einer Konvektions-Diffusions-Gleichung wird durch Reskalierung des Massenflussterms eine Reduktion des Adergebietes auf eine 1D-Struktur erreicht. Nach numerischen Vorbetrachtungen wird die Grenzgleichung innerhalb einer verallgemeinerten Sobolev-Algebra formuliert. Die Untersuchung der L{\"o}sungsfamilie in klassischen Funktionenr{\"a}umen zeigt, dass deren schwacher Grenzwert die L{\"o}sung der korrespondierenden Diffusions-Gleichung ist. Die Diskretisierung einer formalen Grenzgleichung mit Linienstromanteil stellt jedoch eine gute Approximation an die Diskretisierung des urspr{\"u}nglichen Problems dar, wenn man die lokale Maschenweite an die Gef{\"a}ßradien koppelt und bei erh{\"o}htem Genauigkeitsbedarf auf ein vollst{\"a}ndiges 3D-Modell umschaltet.}, language = {de} } @misc{SchmidtOevermannBastiaansetal.2009, author = {Schmidt, Heiko and Oevermann, Michael and Bastiaans, Rob J.M. and Kerstein, Alan R.}, title = {A Priori Tabulation of Turbulent Flame Speeds via a Combination of a Stochastic Mixing Model and Flamelet Generated Manifolds, Extended to Incorporate Strain Effects}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11214}, number = {09-09}, year = {2009}, abstract = {In this paper we revisit the a priori turbulent flame speed tabulation (TFST) technique for a given parameter space within the region of flamelet combustion-regimes. It can be used as a subgrid-scale (SGS) model in Large Eddy Simulation (LES). In a first step, stationary laminar flamelets are computed and stored over the progress variable following the ideas of flamelet generated manifolds (FGM). In a second step, the incompressible one-dimensional Navier-Stokes equations supplemented by the equation for the progress variable are solved on a grid that resolves all turbulent scales. Additionally, turbulent transport is implemented via the linear eddy model (LEM). The turbulent flame structures are solved until a statistically stationary mean value of the turbulent flame speed has been reached. The results are stored in a table that could be used by large scale premixed combustion models, e.g. front tracking schemes. First results are compared quantitatively with direct numerical simulations (DNS) taken from literature. Then it is illustrated in one example how the new method could help to fix constants in algebraic models for turbulent flame speeds. Further it is shown how the technique can be extended to incorporate turbulent strain effects. Finally we investigate the effect of the use of detailed and tabulated chemistry under unsteady conditions.}, language = {en} } @misc{Weber2009, author = {Weber, Marcus}, title = {A Subspace Approach to Molecular Markov State Models via an Infinitesimal Generator}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11432}, number = {09-27}, year = {2009}, abstract = {Supercomputers can simulate complex molecular systems. However, there is a very large gap between the fastest oscillations of covalent bonds of a molecule and the time-scale of the dominant processes. In order to extract the dominant time-scales and to identify the dominant processes, a clustering of information is needed. This thesis shows that only the subspace-based Robust Perron Cluster Analysis (PCCA+) can solve this problem correctly by the construction of a Markov State Model. PCCA+ allows for time-extrapolation in molecular kinetics. This thesis shows the difference between molecular dynamics and molecular kinetics. Only in the molecular kinetics framework a definition of transition rates is possible. In this context, the existence of an infinitesimal generator of the dynamical processes is discussed. If the existence is assumed, the Theorem of Gauß can be applied in order to compute transition rates efficiently. Molecular dynamics, however, is not able to provide a suitable statistical basis for the determination of the transition pattern.}, language = {en} } @misc{LasserRoeblitz2009, author = {Lasser, Caroline and R{\"o}blitz, Susanna}, title = {Computing expectation values for molecular quantum dynamics}, issn = {1438-0064}, doi = {/10.1137/090770461}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11461}, number = {09-30}, year = {2009}, abstract = {We compute expectation values for the solution of the nuclear Schr{\"o}dinger equation. The proposed particle method consists of three steps: sampling of the initial Wigner function, classical transport of the sampling points, weighted phase space summation for the final computation of the expectation values. The Egorov theorem guarantees that the algorithm is second order accurate with respect to the semiclassical parameter. We present numerical experiments for a two-dimensional torsional potential with three different sets of initial data and for a six-dimensional Henon-Heiles potential. By construction, the computing times scale linearly with the number of initial sampling points and range between three seconds and one hour.}, language = {en} } @misc{SchmidtJimenez2009, author = {Schmidt, Heiko and Jimen{\´e}z, Carmen}, title = {Numerical study of the direct pressure effect of acoustic waves in planar premixed flames}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11476}, number = {09-31}, year = {2009}, abstract = {Recently the unsteady response of 1-D premixed flames to acoustic pressure waves for the range of frequencies below and above the inverse of the flame transit time was investigated experimentally by Wangher et al. using OH chemiluminescence. They compared the frequency dependence of the measured response to the prediction of an analytical model proposed by Clavin et al., derived from the standard flame model (one-step Arrhenius kinetics). Discrepancies between the experimental results and the model led to the conclusion that the standard model does not provide an adequate description of the unsteady response of real flames and that it is necessary to investigate more realistic chemical models. Here we follow exactly this suggestion and perform numerical studies of the reponse of lean methane flames using different reaction mechanisms. We find that the global flame response obtained with both detailed chemistry (GRI3.0) and a reduced multi-step model by Peters lies slightly above the predictions of the analytical model, but is close to experimental results. We additionally used an irreversible one-step reaction model which yields good results at least for frequencies close to the inverse flame transit time.}, language = {en} } @misc{Weiser2008, author = {Weiser, Martin}, title = {Optimization and Identification in Regional Hyperthermia}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10916}, number = {08-40}, year = {2008}, abstract = {Regional hyperthermia is a cancer therapy aiming at heating tumors using phased array applicators. This article provides an overview over current mathematical challenges of delivering individually optimal treatments. The focus is on therapy planning and identification of technical as well as physiological quantities from MR thermometry measurements.}, language = {en} } @misc{WeiserErdmannDeuflhard2008, author = {Weiser, Martin and Erdmann, Bodo and Deuflhard, Peter}, title = {On Efficiency and Accuracy in Cardioelectric Simulation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10934}, number = {08-41}, year = {2008}, abstract = {Reasons for the failure of adaptive methods to deliver improved efficiency when integrating monodomain models for myocardiac excitation are discussed. Two closely related techniques for reducing the computational complexity of linearly implicit integrators, deliberate sparsing and splitting, are investigated with respect to their impact on computing time and accuracy.}, language = {en} } @misc{Haack2008, author = {Haack, Fiete}, title = {Properties of Reduced Reversible Markov Chains}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10941}, number = {08-42}, year = {2008}, abstract = {The enormous time lag between fast atomic motion and complex pro- tein folding events makes it almost impossible to compute molecular dy- namics on a high resolution. A common way to tackle this problem is to model the system dynamics as a Markov process. Yet for large molec- ular systems the resulting Markov chains can hardly be handled due to the curse of dimensionality. Coarse graining methods can be used to re- duce the dimension of a Markov chain, but it is still unclear how far the coarse grained Markov chain resembles the original system. In order to answer this question, two different coarse-graining methods were analysed and compared: a classical set-based reduction method and an alternative subspace-based approach, which is based on membership vectors instead of sets. On the basis of a small toy system, it could be shown, that in con- trast to the subset-based approach, the subspace-based reduction method preserves the Markov property as well as the essential dynamics of the original system.}, language = {en} } @misc{CarqueSchmidtStevensetal.2008, author = {Carqu{\´e}, Gunter and Schmidt, Heiko and Stevens, Bjorn and Klein, Rupert}, title = {Plausibility Check of an Asymptotic Column Model for Deep Convective Clouds}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10967}, number = {08-44}, year = {2008}, abstract = {By use of asymptotic analysis Carqu{\´e} et al. [ZIB-Report 08-03] derived an asymptotic column model for deep convective clouds based on the three dimensional compressible flow equations and a bulk microphysics parameterization. In the present study we check the plausibility of the reduced model equations by comparing implications of the model for the scaling of various terms in the governing equations with those extracted from large eddy simulation data based on the computational model UCLA-LES1.1. This code solves an anelastic system of equations with complete droplet based microphysics and LES closures. We observe that the simulation data corroborate the basic assumptions of the asymptotic analysis and the main conclusions implied by the asymptotically reduced model. The code output reflects the scales of space and time: The deep convective clouds show an anisotropic structure where the horizontal scale is considerably narrower than the vertical scale; with a period of about 20 min, from emergence to breakup, the life cycle of one particular deep convective cloud corresponds exactly to the reference time of the reduced model. The characteristic properties of dynamics as predicted by the reduced model are also reflected in the simulation data: The horizontal flow is controlled by the pressure field; the vertical velocity develops freely independent of pressure over the depth of the convective column; the vertical velocity is directly determined by the buoyancy induced by the potential temperature deviation relative to the background stratification. With respect to grid resolution we observe that refining the spatial step size of the equidistant computational grid from 125 m to 62.5 m does not influence the results: Even with the coarser grid the relevant physical phenomena are sufficiently resolved. Somewhat surprisingly, the Coriolis term involving vertical velocity and acting on the horizontal (east-west) velocity component appears at leading order in the asymptotics. Accordingly, we expected to find a nontrivial impact of this Coriolis effect on the horizontal flow velocity components within columns of updrafts. However, switching the term on and off in subsequent simulations did not sizeably affect the results.}, language = {en} } @misc{WeiserRoelligArndtetal.2008, author = {Weiser, Martin and R{\"o}llig, Mathias and Arndt, Ralf and Erdmann, Bodo}, title = {Development and test of a numerical model for pulse thermography in civil engineering}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10980}, number = {08-45}, year = {2008}, abstract = {Pulse thermography of concrete structures is used in civil engineering for detecting voids, honeycombing and delamination. The physical situation is readily modeled by Fourier's law. Despite the simplicity of the PDE structure, quantitatively realistic numerical 3D simulation faces two major obstacles. First, the short heating pulse induces a thin boundary layer at the heated surface which encapsulates all information and therefore has to be resolved faithfully. Even with adaptive mesh refinement techniques, obtaining useful accuracies requires an unsatisfactorily fine discretization. Second, bulk material parameters and boundary conditions are barely known exactly. We address both issues by a semi-analytic reformulation of the heat transport problem and by parameter identification. Numerical results are compared with measurements of test specimens.}, language = {en} } @misc{SchielaGuenther2008, author = {Schiela, Anton and G{\"u}nther, Andreas}, title = {Interior Point Methods in Function Space for State Constraints - Inexact Newton and Adaptivity}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11007}, number = {09-01}, year = {2008}, abstract = {We consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is controlled by adaptive grid refinement in the innermost loop. This allows to perform most of the required Newton steps on coarse grids, such that the overall computational time is dominated by the last few steps. For this purpose we propose an a-posteriori error estimator for a problem suited norm.}, language = {en} } @misc{PruefertSchiela2008, author = {Pr{\"u}fert, Uwe and Schiela, Anton}, title = {The minimization of an L^{\infty}-functional subject to an elliptic PDE and state constraints}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10714}, number = {08-17}, year = {2008}, abstract = {We study the optimal control of a maximum-norm objective functional subject to an elliptic-type PDE and pointwise state constraints. The problem is transformed into a problem where the non-differentiable L^{\infty}-norm in the functional will be replaced by a scalar variable and additional state constraints. This problem is solved by barrier methods. We will show the existence and convergence of the central path for a class of barrier functions. Numerical experiments complete the presentation.}, language = {en} } @misc{DeuflhardDoesselLouisetal.2008, author = {Deuflhard, Peter and D{\"o}ssel, Olaf and Louis, Alfred and Zachow, Stefan}, title = {Mehr Mathematik wagen in der Medizin}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10776}, number = {08-25}, year = {2008}, abstract = {Der Artikel gibt einen Einblick in das reiche Feld der Zusammenarbeit zwischen Mathematik und Medizin. Beispielhaft werden drei Erfolgsmodelle dargestellt: Medizinische Bildgebung, mathematische Modellierung und Biosignalverarbeitung im Bereich der Dynamik des Herzens sowie mathematische Modellierung und Simulation in der Krebstherapie Hyperthermie und der Mund-Kiefer-Gesichts-Chirurgie. In allen F{\"a}llen existiert ein Gleichklang der Interessen von Medizin und Mathematik: Beide Disziplinen wollen die Resultate schnell und zuverl{\"a}ssig. F{\"u}r die Klinik heißt das, dass notwendige Rechnungen in m{\"o}glichst kurzer Zeit, und zwar auf dem PC, ablaufen m{\"u}ssen und dass die Resultate so genau und belastbar sein m{\"u}ssen, dass medizinische Entscheidungen darauf aufbauen k{\"o}nnen. F{\"u}r die Mathematik folgt daraus, dass h{\"o}chste Anforderungen an die Effizienz der verwendeten Algorithmen und die darauf aufbauende Software in Numerik und Visualisierung zu stellen sind. Jedes Kapitel endet mit einer Darstellung der Perspektive des jeweiligen Gebietes. Abschließend werden m{\"o}gliche Handlungsoptionen f{\"u}r Politik und Wirtschaft diskutiert.}, language = {de} } @misc{KlapprothDeuflhardSchiela2008, author = {Klapproth, Corinna and Deuflhard, Peter and Schiela, Anton}, title = {A Perturbation Result for Dynamical Contact Problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10793}, number = {08-27}, year = {2008}, abstract = {This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover, it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method. We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions. For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law, we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space. This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries. Furthermore, we present perturbation results for two well-established approximations of the classical Signorini condition: The Signorini condition formulated in velocities and the model of normal compliance, both satisfying even a sharper version of our stability condition.}, language = {en} } @misc{Weber2008, author = {Weber, Marcus}, title = {An efficient analysis of rare events in canonical ensemble dynamics}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10871}, number = {08-36}, year = {2008}, abstract = {For an analysis of a molecular system from a computational statistical thermodynamics point of view, extensive molecular dynamics simulations are very inefficient. During this procedure, at lot of redundant data is generated. Whereas the algorithms spend most of the computing time for a sampling of configurations within the basins of the potential energy landscape of the molecular system, the important information about the long-time behaviour of the molecules is given by transition regions and barriers between the basins, which are sampled rarely only. Thinking of molecular dynamics trajectories, researchers try to figure out which kind of dynamical model is suitable for an efficient simulation. This article suggests to change the point of view from extensive simulation of molecular dynamics trajectories to more efficient sampling strategies of the conformation dynamics approach.}, language = {en} } @misc{SchielaWollner2008, author = {Schiela, Anton and Wollner, Winnifried}, title = {Barrier Methods for Optimal Control Problems with Convex Nonlinear Gradient Constraints}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11014}, number = {08-47}, year = {2008}, abstract = {In this paper we are concerned with the application of interior point methods in function space to gradient constrained optimal control problems, governed by partial differential equations. We will derive existence of solutions together with first order optimality conditions. Afterwards we show continuity of the central path, together with convergence rates depending on the interior point parameter.}, language = {en} } @misc{MelladoStevensSchmidtetal.2008, author = {Mellado, Juan Pedro and Stevens, Bjorn and Schmidt, Heiko and Peters, Norbert}, title = {Buoyancy-reversal in cloud-top mixing layers}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11046}, number = {08-50}, year = {2008}, abstract = {A theoretical and numerical small-scale study of the evaporative cooling phenomenon that might appear in the stratocumulus-topped boundary layers is presented. An ideal configuration of a cloud-top mixing layer is considered as defined by two nonturbulent horizontal layers, stably stratified and with buoyancy reversal within a certain range of mixture fractions due to the evaporative cooling. Linear stability analysis of the shear-free configuration is employed to provide a new interpretation of the buoyancy reversal parameter, namely, in terms of a time-scale ratio between the unstable and the stable modes of the system. An incompressible high-order numerical algorithm to perform direct numerical simulation of the configuration is described and two-dimensional simulations of single-mode perturbations are discussed. These simulations confirm the role of the different parameters identified in the linear stability analysis and show that convoluted flow patterns can be generated by the evaporative cooling even for the low levels of buoyancy reversal found in stratocumulus clouds. They also show that there is no enhancement of entrainment of upper layer fluid in the shear-free configuration, and mixing enhancement by the evaporative cooling is restricted to the lower layer.}, language = {en} } @phdthesis{Ruprecht2010, author = {Ruprecht, Daniel}, title = {Analysis of a multi-scale asymptotic model for internal gravity waves in a moist atmosphere}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000018355-1}, year = {2010}, abstract = {The thesis presents the analysis of a reduced model for modulation of internal gravity waves by deep convective clouds. The starting point for the derivation are conservation laws for mass, momentum and energy coupled with a bulk micro-physics model describing the evolution of mixing ratios of water vapor, cloud water and rain water. A reduced model for the identified scales of the regime is derived, using multi-scale asymptotics. The closure of the model employs conditional averaging over the horizontal scale of the convective clouds. The resulting reduced model is an extension of the anelastic equations, linearized around a constant background state, which are well-known from meteorology. The closure of the model is achieved purely by analytical means and involves no additional physically motivated assumptions. The essential new parameter arising from the coupling to a micro-physics model is the area fraction of saturated regions on the horizontal scale of the convective clouds. It turns out that this parameter is constant on the employed short timescale. Hence the clouds constitute a constant background, modulating the characteristics of propagation of internal waves. The model is then investigated by analytical as well as numerical means. Important results are, among others, that in the model moisture (i) inhibits propagation of internal waves by reducing the modulus of the group velocity, (ii) reduces the angle between the propagation direction of a wave-packet and the horizontal, (iii) causes critical layers and (iv) introduces a maximum horizontal wavelength beyond which waves are no longer propagating but become evanescent. The investigated examples of orographically generated gravity waves also feature a significant reduction of vertical momentum flux by moisture. The model is extended by assuming systematically small under-saturation, that is saturation at leading order. The closure is similar to the original case but requires additional assumptions. The saturated area fraction in the obtained model is no longer constant but now depends nonlinearly on vertical displacement and thus on vertical velocity.}, language = {en} } @misc{GoetschelWeiserSchiela2010, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Schiela, Anton}, title = {Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11909}, number = {10-25}, year = {2010}, abstract = {This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a flexible C++ code for solving elliptic and parabolic PDE systems. Issues such as problem formulation, assembly and adaptivity are discussed at the example of optimal control problems. Trajectory compression for parabolic optimization problems is considered as a case study.}, language = {en} } @misc{SchielaWachsmuth2011, author = {Schiela, Anton and Wachsmuth, Daniel}, title = {Convergence Analysis of Smoothing Methods for Optimal Control of Stationary Variational Inequalities}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13125}, number = {11-23}, year = {2011}, abstract = {In the article an optimal control problem subject to a stationary variational inequality is investigated. The optimal control problem is complemented with pointwise control constraints. The convergence of a smoothing scheme is analyzed. There, the variational inequality is replaced by a semilinear elliptic equation. It is shown that solutions of the regularized optimal control problem converge to solutions of the original one. Passing to the limit in the optimality system of the regularized problem allows to prove C-stationarity of local solutions of the original problem. Moreover, convergence rates with respect to the regularization parameter for the error in the control are obtained. These rates coincide with rates obtained by numerical experiments, which are included in the paper.}, language = {en} } @misc{FackeldeyRoeblitzScharkoietal.2011, author = {Fackeldey, Konstantin and R{\"o}blitz, Susanna and Scharkoi, Olga and Weber, Marcus}, title = {Soft Versus Hard Metastable Conformations in Molecular Simulations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13189}, number = {11-27}, year = {2011}, abstract = {Particle methods have become indispensible in conformation dynamics to compute transition rates in protein folding, binding processes and molecular design, to mention a few. Conformation dynamics requires at a decomposition of a molecule's position space into metastable conformations. In this paper, we show how this decomposition can be obtained via the design of either ``soft'' or ``hard'' molecular conformations. We show, that the soft approach results in a larger metastabilitiy of the decomposition and is thus more advantegous. This is illustrated by a simulation of Alanine Dipeptide.}, language = {en} } @phdthesis{Weber2011, author = {Weber, Marcus}, title = {A Subspace Approach to Molecular Markov State Models via a New Infinitesimal Generator}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14025}, school = {Zuse Institute Berlin (ZIB)}, year = {2011}, abstract = {Supercomputers can simulate complex molecular systems. However, there is a very large gap between the fastest oscillations of covalent bonds of a molecule and the time-scale of the dominant processes. In order to extract the dominant time-scales and to identify the dominant processes, a clustering of information is needed. This thesis shows that only the subspace-based Robust Perron Cluster Analysis (PCCA+) can solve this problem correctly by the construction of a Markov State Model. PCCA+ allows for time-extrapolation in molecular kinetics. This thesis shows the difference between molecular dynamics and molecular kinetics. Only in the molecular kinetics framework a definition of transition rates is possible. In this context, the existence of an infinitesimal generator of the dynamical processes is discussed. If the existence is assumed, the Theorem of Gauß can be applied in order to compute transition rates efficiently. Molecular dynamics, however, is not able to provide a suitable statistical basis for the determination of the transition pattern.}, language = {en} } @misc{SchielaHintermueller2011, author = {Schiela, Anton and Hinterm{\"u}ller, Michael}, title = {On the Length of the Primal-Dual Path in Moreau-Yosida-based Path-following for State Constrained Optimal Control: Analysis and Numerics}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14071}, number = {11-37}, year = {2011}, abstract = {We derive a-priori estimates on the length of the primal-dual path that results from a Moreau-Yosida approximation of the feasible set for state constrained optimal control problems. These bounds depend on the regularity of the state and the dimension of the problem. Comparison with numerical results indicates that these bounds are sharp and are attained for the case of a single active point.}, language = {en} } @misc{WeiserGoetschel2010, author = {Weiser, Martin and G{\"o}tschel, Sebastian}, title = {State Trajectory Compression for Optimal Control with Parabolic PDEs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11676}, number = {10-05}, year = {2010}, abstract = {In optimal control problems with nonlinear time-dependent 3D PDEs, full 4D discretizations are usually prohibitive due to the storage requirement. For this reason gradient and quasi-Newton methods working on the reduced functional are often employed. The computation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. The state enters into the adjoint equation, again requiring the storage of a full 4D data set. We propose a lossy compression algorithm using an inexact but cheap predictor for the state data, with additional entropy coding of prediction errors. As the data is used inside a discretized, iterative algorithm, lossy coding maintaining an error bound is sufficient.}, language = {en} } @misc{BoerStoetzelRoeblitzetal.2010, author = {Boer, H. Marike T. and St{\"o}tzel, Claudia and R{\"o}blitz, Susanna and Deuflhard, Peter and Veerkamp, Roel F. and Woelders, Henri}, title = {A simple mathematical model of the bovine estrous cycle: follicle development and endocrine interactions}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11682}, number = {10-06}, year = {2010}, abstract = {Bovine fertility is the subject of extensive research in animal sciences, especially because fertility of dairy cows has declined during the last decades. The regulation of estrus is controlled by the complex interplay of various organs and hormones. Mathematical modeling of the bovine estrous cycle could help in understanding the dynamics of this complex biological system. In this paper we present a mathematical model of the bovine estrous cycle that includes the processes of follicle and corpus luteum development and the key hormones that interact to control these processes. Focus in this paper is on development of the model, but also some simulation results are presented, showing that a set of equations and parameters is obtained that describes the system consistent with empirical knowledge. Even though the majority of the mechanisms that are included are only known qualitatively as stimulatory or inhibitory effects, the model surprisingly well features quantitative observations made in reality. This model of the bovine estrous cycle could be used as a basis for more elaborate models with the ability to study effects of external manipulations and genetic differences.}, language = {en} } @misc{DierkesWadeNowaketal.2011, author = {Dierkes, Thomas and Wade, Moritz and Nowak, Ulrich and R{\"o}blitz, Susanna}, title = {BioPARKIN - Biology-related Parameter Identification in Large Kinetic Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12706}, number = {11-15}, year = {2011}, abstract = {Modelling, parameter identification, and simulation play an important r{\^o}le in Systems Biology. In recent years, various software packages have been established for scientific use in both licencing types, open source as well as commercial. Many of these codes are based on inefficient and mathematically outdated algorithms. By introducing the package BioPARKIN recently developed at ZIB, we want to improve this situation significantly. The development of the software BioPARKIN involves long standing mathematical ideas that, however, have not yet entered the field of Systems Biology, as well as new ideas and tools that are particularly important for the analysis of the dynamics of biological networks. BioPARKIN originates from the package PARKIN, written by P.Deuflhard and U.Nowak, that has been applied successfully for parameter identification in physical chemistry for many years.}, language = {en} } @misc{RoeblitzStoetzelDeuflhardetal.2011, author = {R{\"o}blitz, Susanna and St{\"o}tzel, Claudia and Deuflhard, Peter and Jones, Hannah M. and Azulay, David-Olivier and van der Graaf, Piet and Martin, Steven}, title = {A mathematical model of the human menstrual cycle for the administration of GnRH analogues}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12732}, number = {11-16}, year = {2011}, abstract = {This study presents a differential equation model for the feedback mechanisms between Gonadotropin-releasing Hormone (GnRH), Follicle-Stimulating Hormone (FSH), Luteinizing Hormone (LH), development of follicles and corpus luteum, and the production of estradiol (E2), progesterone (P4), inhibin A (IhA), and inhibin B (IhB) during the female menstrual cycle. In contrast to other models, this model does not involve delay differential equations and is based on deterministic modelling of the GnRH pulse pattern, which allows for faster simulation times and efficient parameter identification. These steps were essential to tackle the task of developing a mathematical model for the administration of GnRH analogues. The focus of this paper is on model development for GnRH receptor binding and the integration of a pharmacokinetic/pharmacodynamic model for the GnRH agonist Nafarelin and the GnRH antagonist Cetrorelix into the menstrual cycle model. The final mathematical model describes the hormone profiles (LH, FSH, P4, E2) throughout the menstrual cycle in 12 healthy women. Moreover, it correctly predicts the changes in the cycle following single and multiple dose administration of Nafarelin or Cetrorelix at different stages in the cycle.}, language = {en} } @misc{StoetzelPloentzkeRoeblitz2011, author = {St{\"o}tzel, Claudia and Pl{\"o}ntzke, Julia and R{\"o}blitz, Susanna}, title = {Advances in modelling of the bovine estrous cycle: Administration of PGF2alpha}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12740}, number = {11-17}, year = {2011}, abstract = {Our model of the bovine estrous cycle is a set of ordinary differential equations which generates hormone profiles of successive estrous cycles with several follicular waves per cycle. It describes the growth and decay of the follicles and the corpus luteum, as well as the change of the key substances over time. In this work we describe recent improvements of this model, including the introduction of new components, and elimination of time delays. We validate our model by showing that the simulations agree with observations from synchronization studies and with measured progesterone data after a single dose administration of synthetic prostaglandin F2alpha.}, language = {en} } @misc{GuentherLameckerWeiser2011, author = {G{\"u}nther, Andreas and Lamecker, Hans and Weiser, Martin}, title = {Direct LDDMM of Discrete Currents with Adaptive Finite Elements}, doi = {10.1007/s11263-012-0599-3}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13090}, number = {11-22}, year = {2011}, abstract = {We consider Large Deformation Diffeomorphic Metric Mapping of general \$m\$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete \$m\$-current attributes.}, language = {en} } @misc{MeyerPanizziSchiela2010, author = {Meyer, Christian and Panizzi, Lucia and Schiela, Anton}, title = {Uniqueness criteria for solutions of the adjoint equation in state-constrained optimal control}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11933}, number = {10-28}, year = {2010}, abstract = {The paper considers linear elliptic equations with regular Borel measures as inhomogeneity. Such equations frequently appear in state-constrained optimal control problems. By a counter-example of Serrin, it is known that, in the presence of non-smooth data, a standard weak formulation does not ensure uniqueness for such equations. Therefore several notions of solution have been developed that guarantee uniqueness. In this note, we compare different definitions of solutions, namely the ones of Stampacchia and the two notions of solutions of Casas and Alibert-Raymond, and show that they are the same. As side results, we reformulate the solution in the sense of Stampacchia, and prove the existence and uniqueness of solutions in in case of mixed boundary conditions.}, language = {en} } @misc{BergRitterRoeblitz2011, author = {Berg, Mascha and Ritter, Julia and R{\"o}blitz, Susanna}, title = {A mathematical model for the Zinc response of young pigs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12191}, number = {11-05}, year = {2011}, abstract = {In a number of studies the feeding of pharmacological levels of Zinc to weanling pigs was examined. The publications agree in the fact that the achieved performance increase of the pigs depends on the amount of Zinc as well as on the type of mineral complex used as feed additive. The results are based on measurements of the animals' body weight and the Zinc concentration in the blood within the first two weeks of the experiments. From the measurement values, conclusions are drawn about adequate Zinc doses, but a deeper understanding of the physiological processes that influence the Zinc distribution in the organism is still missing. In this report, we want to close this gap by using a systems biology approach. We present a small mathematical model that describes the organic feedback mechanisms with the help of differential equations. The simulation results not only match with measurement values, but also give insight into non-measurable processes, which will hopefully contribute to animal experiments being organized in a more selective and reduced way.}, language = {en} } @misc{DeuflhardSchielaWeiser2011, author = {Deuflhard, Peter and Schiela, Anton and Weiser, Martin}, title = {Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14204}, number = {11-39}, year = {2011}, abstract = {This paper surveys the required mathematics for a typical challenging problem from computational medicine, the cancer therapy planning in deep regional hyperthermia. In the course of many years of close cooperation with clinics, the medical problem gave rise to quite a number of subtle mathematical problems, part of which had been unsolved when the common project started. Efficiency of numerical algorithms, i.e. computational speed and monitored reliability, play a decisive role for the medical treatment. Off-the-shelf software had turned out to be not sufficient to meet the requirements of medicine. Rather, new mathematical theory as well as new numerical algorithms had to be developed. In order to make our algorithms useful in the clinical environment, new visualization software, a virtual lab, including 3D geometry processing of individual virtual patients had to be designed and implemented. Moreover, before the problems could be attacked by numerical algorithms, careful mathematical modelling had to be done. Finally, parameter identification and constrained optimization for the PDEs had to be newly analyzed and realized over the individual patient's geometry. Our new techniques had an impact on the specificity of the individual patients' treatment and on the construction of an improved hyperthermia applicator.}, language = {en} } @misc{SanderKlapprothYouettetal.2012, author = {Sander, Oliver and Klapproth, Corinna and Youett, Jonathan and Kornhuber, Ralf and Deuflhard, Peter}, title = {Towards an Efficient Numerical Simulation of Complex 3D Knee Joint Motion}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14512}, number = {12-06}, year = {2012}, abstract = {We present a time-dependent finite element model of the human knee joint of full 3D geometric complexity. Its efficient numerical simulation requires advanced numerical algorithms that have been developed just recently. Up to now, the model comprises bones, cartilage, and the major ligaments (patella and menisci are still missing). Bones (femur, tibia, and fibula) are modelled by linear elastic materials, cartilage by viscoelastic materials, ligaments by one-dimensional so-called Cosserat rods. In order to capture the dynamical contact problems correctly, we solve the full PDEs of elasticity in the presence of strict contact inequalities. For the total spatio-temporal discretization we apply a method of layers approach (first time, then space discretization). For the time discretization of the elastic and viscoelastic parts, we apply a new contact-stabilized Newmark method, while for the Cosserat rods we choose an energy-momentum method. For the space discretization, we use linear finite elements for the elastic and viscoelastic parts and novel geodesic finite elements for the Cosserat rods. The coupled system is solved by a Dirichlet-Neumann method, and the arising large algebraic systems are solved by a recent fast multigrid solver, the truncated non-smooth Newton multigrid method.}, language = {en} } @misc{LubkollSchielaWeiser2012, author = {Lubkoll, Lars and Schiela, Anton and Weiser, Martin}, title = {An optimal control problem in polyconvex hyperelasticity}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14745}, number = {12-08}, year = {2012}, abstract = {We consider a shape implant design problem that arises in the context of facial surgery. We introduce a reformulation as an optimal control problem, where the control acts as a boundary force. The state is modelled as a minimizer of a polyconvex hyperelastic energy functional. We show existence of optimal solutions and derive - on a formal level - first order optimality conditions. Finally, preliminary numerical results are presented.}, language = {en} } @misc{Weber2012, author = {Weber, Marcus}, title = {The funnel trap paradox}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14765}, number = {12-12}, year = {2012}, abstract = {In this article, an illustrative example is given for the coarse-graining of a Markov process which leads to a shift in the statistical weights of a two-states-system. The example is based on a 2D-funnel trap. The funnel trap is constructed in such a way, that the area inside and outside of the trap is identical. However, observing the flight of the insect as a Markov process, the probability for being "in the trap" is higher. This example can be transferred to several kinds of processes (like receptor-ligandbinding processes in chemistry) and describes the influence of "re-entering events".}, language = {en} } @misc{KlapprothSchielaDeuflhard2010, author = {Klapproth, Corinna and Schiela, Anton and Deuflhard, Peter}, title = {Adaptive Timestep Control for the Contact-Stabilized Newmark Method}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11714}, number = {10-09}, year = {2010}, abstract = {The aim of this paper is to devise an adaptive timestep control in the contact--stabilized Newmark method (CONTACX) for dynamical contact problems between two viscoelastic bodies in the framework of Signorini's condition. In order to construct a comparative scheme of higher order accuracy, we extend extrapolation techniques. This approach demands a subtle theoretical investigation of an asymptotic error expansion of the contact--stabilized Newmark scheme. On the basis of theoretical insight and numerical observations, we suggest an error estimator and a timestep selection which also cover the presence of contact. Finally, we give a numerical example.}, language = {en} } @misc{Fackeldey2010, author = {Fackeldey, Konstantin}, title = {Coupling Meshbased and Meshfree Methods by a Transfer Operator Approach}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11755}, number = {10-12}, year = {2010}, abstract = {In contrast to the well known meshbased methods like the finite element method, meshfree methods do not rely on a mesh. However besides their great applicability, meshfree methods are rather time consuming. Thus, it seems favorable to combine both methods, by using meshfree methods only in a small part of the domain, where a mesh is disadvantageous, and a meshbased method for the rest of the domain. We motivate, that this coupling between the two simulation techniques can be considered as saddle point problem and show the stability of this coupling. Thereby a novel transfer operator is introduced, which interacts in the transition zone, where both methods coexist.}, language = {en} } @misc{SchaedleZschiedrich2005, author = {Sch{\"a}dle, Achim and Zschiedrich, Lin}, title = {Additive Schwarz method for scattering problems using the PML method at interfaces}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8613}, number = {05-27}, year = {2005}, abstract = {Scattering problems in integrated optics can be modeled in simple cases by the Helmholtz equation. The computational domain is truncated by a non-reflecting boundary condition. We investigate Schwarz algorithms with a sort of DtN operator, realized by the PML-method, at the interfaces of the sub-domains as an iterative solver.}, language = {en} } @misc{FranzoneDeuflhardErdmannetal.2005, author = {Franzone, Piero Colli and Deuflhard, Peter and Erdmann, Bodo and Lang, Jens and Pavarino, Luca Franco}, title = {Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8649}, number = {05-30}, year = {2005}, abstract = {Adaptive numerical methods in space and time are introduced and studied for multiscale cardiac reaction-diffusion models in three dimensions. The evolution of a complete heartbeat, from the excitation to the recovery phase, is simulated with both the anisotropic Bidomain and Monodomain models, coupled with either a variant of the simple FitzHugh-Nagumo model or the more complex phase-I Luo-Rudy ionic model. The simulations are performed with the {\sc kardos} library, that employs adaptive finite elements in space and adaptive linearly implicit methods in time. The numerical results show that this adaptive method successfully solves these complex cardiac reaction-diffusion models on three-dimensional domains of moderate sizes. By automatically adapting the spatial meshes and time steps to the proper scales in each phase of the heartbeat, the method accurately resolves the evolution of the intra- and extra-cellular potentials, gating variables and ion concentrations during the excitation, plateau and recovery phases.}, language = {en} } @phdthesis{Friese1998, author = {Friese, Tilmann}, title = {Eine Mehrgitter-Methode zur L{\"o}sung des Eigenwertproblems der komplexen Helmholtzgleichung}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-1999000133}, year = {1998}, language = {en} } @misc{PruefertTroeltzschWeiser2004, author = {Pr{\"u}fert, Uwe and Tr{\"o}ltzsch, Fredi and Weiser, Martin}, title = {The convergence of an interior point method for an elliptic control problem with mixed control-state constraints}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8223}, number = {04-47}, year = {2004}, abstract = {The paper addresses primal interior point method for state constrained PDE optimal control problems. By a Lavrentiev regularization, the state constraint is transformed to a mixed control-state constraint with bounded Lagrange multiplier. Existence and convergence of the central path are established, and linear convergence of a short-step pathfollowing method is shown. The behaviour of the regularizations are demonstrated by numerical examples.}, language = {en} } @misc{LopezFernandezLubichSchaedle2006, author = {Lopez-Fernandez, Maria and Lubich, Christian and Sch{\"a}dle, Achim}, title = {Adaptive, Fast and Oblivious Convolution in Evolution Equations with Memory}, doi = {10.1137/060674168}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9399}, number = {06-45}, year = {2006}, abstract = {To approximate convolutions which occur in evolution equations with memory terms, a variable-stepsize algorithm is presented for which advancing \$N\$ steps requires only \$O(N\log N)\$ operations and \$O(\log N)\$ active memory, in place of \$O(N^2)\$ operations and \$O(N)\$ memory for a direct implementation. A basic feature of the fast algorithm is the reduction, via contour integral representations, to differential equations which are solved numerically with adaptive step sizes. Rather than the kernel itself, its Laplace transform is used in the algorithm. The algorithm is illustrated on three examples: a blow-up example originating from a Schr{\"o}dinger equation with concentrated nonlinearity, chemical reactions with inhibited diffusion, and viscoelasticity with a fractional order constitutive law.}, language = {en} } @misc{WeiserDeuflhardErdmann2004, author = {Weiser, Martin and Deuflhard, Peter and Erdmann, Bodo}, title = {Affine conjugate adaptive Newton methods for nonlinear elastomechanics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7768}, number = {04-01}, year = {2004}, abstract = {The paper extends affine conjugate Newton methods from convex to nonconvex minimization, with particular emphasis on PDE problems originating from compressible hyperelasticity. Based on well-known schemes from finite dimensional nonlinear optimization, three different algorithmic variants are worked out in a function space setting, which permits an adaptive multilevel finite element implementation. These algorithms are tested on two well-known 3D test problems and a real-life example from surgical operation planning.}, language = {en} } @misc{WeiserGaenzlerSchiela2004, author = {Weiser, Martin and G{\"a}nzler, Tobias and Schiela, Anton}, title = {A Control Reduced Primal Interior Point Method for PDE Constrained Optimization}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8138}, number = {04-38}, year = {2004}, abstract = {A primal interior point method for control constrained optimal control problems with PDE constraints is considered. Pointwise elimination of the control leads to a homotopy in the remaining state and dual variables, which is addressed by a short step pathfollowing method. The algorithm is applied to the continuous, infinite dimensional problem, where discretization is performed only in the innermost loop when solving linear equations. The a priori elimination of the least regular control permits to obtain the required accuracy with comparable coarse meshes. Convergence of the method and discretization errors are studied, and the method is illustrated at two numerical examples.}, language = {en} } @misc{DeuflhardHuisingaJahnkeetal.2007, author = {Deuflhard, Peter and Huisinga, Wilhelm and Jahnke, Tobias and Wulkow, Michael}, title = {Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9471}, number = {07-04}, year = {2007}, abstract = {\begin{abstract} In systems biology, the stochastic description of biochemical reaction kinetics is increasingly being employed to model gene regulatory networks and signalling pathways. Mathematically speaking, such models require the numerical solution of the underlying evolution equat ion, also known as the chemical master equation (CME). Up to now, the CME has almost exclusively been treated by Monte-Carlo techniques, the most prominent of which is the simulation algorithm suggest ed by Gillespie in 1976. Since this algorithm requires an update for each single reaction event, realizations can be computationally very costly. As an alternative, we here propose a novel approach, which focuses on the discrete partial differential equation (PDE) structure of the CME and thus allows to adopt ideas from adaptive discrete Galerkin methods (as designed by two of the present authors in 1989), which have proven to be highly efficient in the mathematical modelling of polyreaction kinetics. Among the two different options of discretizing the CME as a discrete PDE, the method of lines approach (first space, then time) and the Rothe method (first time, then space), we select the latter one for clear theoretical and algorithmic reasons. First numeric al experiments at a challenging model problem illustrate the promising features of the proposed method and, at the same time, indicate lines of necessary further research. \end{abstract}}, language = {en} } @misc{SchaedleZschiedrichBurgeretal.2006, author = {Sch{\"a}dle, Achim and Zschiedrich, Lin and Burger, Sven and Klose, Roland and Schmidt, Frank}, title = {Domain Decomposition Method for Maxwell's Equations: Scattering off Periodic Structures}, doi = {/10.1016/j.jcp.2007.04.017}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8984}, number = {06-04}, year = {2006}, abstract = {We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer method (PML). To cope with Wood anomalies appearing in periodic structures an adaptive strategy to determine optimal PML parameters is developed. We focus on the application to typical EUV lithography line masks. Light propagation within the multi-layer stack of the EUV mask is treated analytically. This results in a drastic reduction of the computational costs and allows for the simulation of next generation lithography masks on a standard personal computer.}, language = {en} } @misc{LopezFernandezPalenciaSchaedle2005, author = {Lopez-Fernandez, Maria and Palencia, Cesar and Sch{\"a}dle, Achim}, title = {A spectral order method for inverting sectorial Laplace transforms}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8607}, number = {05-26}, year = {2005}, abstract = {Laplace transforms which admit a holomorphic extension to some sector strictly containing the right half plane and exhibiting a potential behavior are considered. A spectral order, parallelizable method for their numerical inversion is proposed. The method takes into account the available information about the errors arising in the evaluations. Several numerical illustrations are provided.}, language = {en} } @phdthesis{Weber2006, author = {Weber, Marcus}, title = {Meshless Methods in Confirmation Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10232}, year = {2006}, language = {en} } @phdthesis{Galliat2002, author = {Galliat, Tobias}, title = {Adaptive Multilevel Cluster Analysis by Self-Organizing Box Maps}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-2002001258}, year = {2002}, abstract = {Als Cluster Analyse bezeichnet man den Prozess der Suche und Beschreibung von Gruppen (Clustern) von Objekten, so daß die Objekte innerhalb eines Clusters bez{\"u}glich eines gegebenen Maßes maximal homogen sind. Die Homogenit{\"a}t der Objekte h{\"a}ngt dabei direkt oder indirekt von den Auspr{\"a}gungen ab, die sie f{\"u}r eine Anzahl festgelegter Attribute besitzen. Die Suche nach Clustern l{\"a}ßt sich somit als Optimierungsproblem auffassen, wobei die Anzahl der Cluster vorher bekannt sein muß. Wenn die Anzahl der Objekte und der Attribute groß ist, spricht man von komplexen, hoch-dimensionalen Cluster Problemen. In diesem Fall ist eine direkte Optimierung zu aufwendig, und man ben{\"o}tigt entweder heuristische Optimierungsverfahren oder Methoden zur Reduktion der Komplexit{\"a}t. In der Vergangenheit wurden in der Forschung fast ausschließlich Verfahren f{\"u}r geometrisch basierte Clusterprobleme entwickelt. Bei diesen Problemen lassen sich die Objekte als Punkte in einem von den Attributen aufgespannten metrischen Raum modellieren; das verwendete Homogenit{\"a}tsmaß basiert auf der geometrischen Distanz der den Objekten zugeordneten Punkte. Insbesondere zur Bestimmung sogenannter metastabiler Cluster sind solche Verfahren aber offensichtlich nicht geeignet, da metastabile Cluster, die z.B. in der Konformationsanalyse von Biomolek{\"u}len von zentraler Bedeutung sind, nicht auf einer geometrischen, sondern einer dynamischen {\"A}hnlichkeit beruhen. In der vorliegenden Arbeit wird ein allgemeines Clustermodell vorgeschlagen, das zur Modellierung geometrischer, wie auch dynamischer Clusterprobleme geeignet ist. Es wird eine Methode zur Komplexit{\"a}tsreduktion von Clusterproblemen vorgestellt, die auf einer zuvor generierten Komprimierung der Objekte innerhalb des Datenraumes basiert. Dabei wird bewiesen, daß eine solche Reduktion die Clusterstruktur nicht zerst{\"o}rt, wenn die Komprimierung fein genug ist. Mittels selbstorganisierter neuronaler Netze lassen sich geeignete Komprimierungen berechnen. Um eine signifikante Komplexit{\"a}tsreduktion ohne Zerst{\"o}rung der Clusterstruktur zu erzielen, werden die genannten Methoden in ein mehrstufiges Verfahren eingebettet. Da neben der Identifizierung der Cluster auch deren effiziente Beschreibung notwendig ist, wird ferner eine spezielle Art der Komprimierung vorgestellt, der eine Boxdiskretisierung des Datenraumes zugrunde liegt. Diese erm{\"o}glicht die einfache Generierung von regelbasierten Clusterbeschreibungen. F{\"u}r einen speziellen Typ von Homogenit{\"a}tsfunktionen, die eine stochastische Eigenschaft besitzen, wird das mehrstufige Clusterverfahren um eine Perroncluster Analyse erweitert. Dadurch wird die Anzahl der Cluster, im Gegensatz zu herk{\"o}mmlichen Verfahren, nicht mehr als Eingabeparameter ben{\"o}tigt. Mit dem entwickelten Clusterverfahren kann erstmalig eine computergest{\"u}tzte Konformationsanalyse großer, f{\"u}r die Praxis relevanter Biomolek{\"u}le durchgef{\"u}hrt werden. Am Beispiel des HIV Protease Inhibitors VX-478 wird dies detailliert beschrieben.}, language = {en} } @misc{WeberBeckerKoeppenetal.2007, author = {Weber, Marcus and Becker, Roland and K{\"o}ppen, Robert and Durmaz, Vedat}, title = {Classical hybrid Monte-Carlo simulations of the interconversion of hexabromocyclododecane}, organization = {Zuse-Institut Berlin}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10308}, number = {07-31}, year = {2007}, abstract = {In this paper, we investigate the interconversion processes of the major flame retardant -- 1,2,5,6,9,10-hexabromocyclododecane (HBCD) -- by the means of statistical thermodynamics based on classical force-fields. Three ideas will be presented. First, the application of classical hybrid Monte-Carlo simulations for quantum mechanical processes will be justified. Second, the problem of insufficient convergence properties of hybrid Monte-Carlo methods for the generation of low temperature canonical ensembles will be solved by an interpolation approach. Furthermore, it will be shown how free energy differences can be used for a rate matrix computation. The results of our numerical simulations will be compared to experimental results.}, language = {en} } @misc{GoetschelNagaiahKunischetal.2013, author = {G{\"o}tschel, Sebastian and Nagaiah, Chamakuri and Kunisch, Karl and Weiser, Martin}, title = {Lossy Compression in Optimal Control of Cardiac Defibrillation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18566}, year = {2013}, abstract = {This paper presents efficient computational techniques for solving an optimization problem in cardiac defibrillation governed by the monodomain equations. Time-dependent electrical currents injected at different spatial positions act as the control. Inexact Newton-CG methods are used, with reduced gradient computation by adjoint solves. In order to reduce the computational complexity, adaptive mesh refinement for state and adjoint equations is performed. To reduce the high storage and bandwidth demand imposed by adjoint gradient and Hessian-vector evaluations, a lossy compression technique for storing trajectory data is applied. An adaptive choice of quantization tolerance based on error estimates is developed in order to ensure convergence. The efficiency of the proposed approach is demonstrated on numerical examples.}, language = {en} } @misc{GoetschelWeiser2013, author = {G{\"o}tschel, Sebastian and Weiser, Martin}, title = {Lossy Compression for PDE-constrained Optimization: Adaptive Error Control}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18575}, year = {2013}, abstract = {For the solution of optimal control problems governed by nonlinear parabolic PDEs, methods working on the reduced objective functional are often employed to avoid a full spatio-temporal discretization of the problem. The evaluation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the ad-joint equation. The state enters into the adjoint equation, requiring the storage of a full 4D data set. If Newton-CG methods are used, two additional trajectories have to be stored. To get numerical results which are accurate enough, in many case very fine discretizations in time and space are necessary, which leads to a significant amount of data to be stored and transmitted to mass storage. Lossy compression methods were developed to overcome the storage problem by reducing the accuracy of the stored trajectories. The inexact data induces errors in the reduced gradient and reduced Hessian. In this paper, we analyze the influence of such a lossy trajectory compression method on Newton-CG methods for optimal control of parabolic PDEs and design an adaptive strategy for choosing appropriate quantization tolerances.}, language = {en} } @misc{Weiser2013, author = {Weiser, Martin}, title = {Faster SDC convergence on non-equidistant grids by DIRK sweeps}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18662}, year = {2013}, abstract = {Spectral deferred correction methods for solving stiff ODEs are known to converge rapidly towards the collocation limit solution on equidistant grids, but show a much less favourable contraction on non-equidistant grids such as Radau-IIa points. We interprete SDC methods as fixed point iterations for the collocation system and propose new DIRK-type sweeps for stiff problems based on purely linear algebraic considerations. Good convergence is recovered also on non-equidistant grids. The properties of different variants are explored on a couple of numerical examples.}, language = {en} } @misc{BondouyRoeblitz2012, author = {Bondouy, Manon and R{\"o}blitz, Susanna}, title = {Mathematical modeling of follicular development in bovine estrous cycles}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15585}, year = {2012}, abstract = {Normal follicular growth is a prerequisite for successful fertilization of dairy cows. However, submission rates have been decreasing during the last decades because animals are not ovulating at the planned time of mating or insemination. In this study we use a mathematical model to investigate mechanisms that lead to anestrus. This model is derived by coupling two previously published models: a small model for the development of multiple follicles (Smith et al., 2004), and a large estrous cycle model (St\"otzel et al., 2012). We first investigate the influence of synchronization protocols on the time-shift of ovulation. In a second scenario we simulate an extended period of anestrus as it typically occurs after calving.}, language = {en} } @misc{TungaWeber2012, author = {Tunga, Burcu and Weber, Marcus}, title = {Free Energy Calculation Using Mayer Cluster Expansion and Fluctuation Free Integration}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-16031}, year = {2012}, abstract = {This work aims to develop a new algorithm to calculate the free energy of water molecules by using a deterministic way. For this purpose, we assume a closed system confined to a physical volume, having water molecules in gas phase. To calculate the free energy of this sytem we utilized Mayer cluster expansion and the fluctuation free integration method.}, language = {en} } @misc{PloentzkeBergOlanyetal.2013, author = {Pl{\"o}ntzke, Julia and Berg, Mascha and Olany, Amiya and Leonhard-Marek, Sabine and M{\"u}ller, Kerstin-Elisabeth and R{\"o}blitz, Susanna}, title = {Modeling potassium balance in dairy cows}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17749}, year = {2013}, abstract = {Potassium is fundamental for cell functioning including signal transduction, acid-base- and water-metabolism. Since diet of dairy cows is generally rich in potassium, hypokalemia was not in the focus of research for long time. Furthermore, hypokalemia was not frequently diagnosed because blood potassium content is difficult to measure. In recent years, measurement methods have been improved. Nowadays hypokalemia is increasingly diagnosed in cows with disorders such as abomasal displacement, ketosis or down cow syndrome, calling for intensified research on this topic. In this report we describe the development of a basic mechanistic, dynamic model of potassium balance based on ordinary differential and algebraic equations. Parameter values are obtained from data of a clinical trial in which potassium balance and the influence of therapeutic intervention in glucose and electrolyte metabolism on potassium balance in non-lactating dairy cows were studied. The model is formulated at a high abstraction level and includes information and hypotheses from literature. This work represents a first step towards the understanding and design of effective prophylactic feed additives and treatment strategies.}, language = {en} } @misc{WeberFackeldey2013, author = {Weber, Marcus and Fackeldey, Konstantin}, title = {Computing the Minimal Rebinding Effect Included in a Given Kinetics}, issn = {1438-0064}, doi = {10.1137/13091124X}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17796}, year = {2013}, abstract = {The rebinding effect is a phenomenon which occurs when observing a ligand-receptor binding process. On the macro scale this process comprises the Markov property. This Makovian view is spoiled when switching to the atomistic scale of a binding process. We therefore suggest a model which accurately describes the rebinding effect on the atomistic scale by allowing ''intermediate'' bound states. This allows us to define an indicator for the magnitude of rebinding and to formulate an optimization problem. The results form our examples show good agreement with data form laboratory.}, language = {en} } @misc{WinkelmannSchuettevonKleist2013, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof and von Kleist, Max}, title = {Markov Control Processes with Rare State Observation: Theory and Application to Treatment Scheduling in HIV-1}, issn = {1438-0064}, doi = {10.4310/CMS.2014.v12.n5.a4}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-41955}, year = {2013}, abstract = {Markov Decision Processes (MDP) or Partially Observable MDPs (POMDP) are used for modelling situations in which the evolution of a process is partly random and partly controllable. These MDP theories allow for computing the optimal control policy for processes that can continuously or frequently be observed, even if only partially. However, they cannot be applied if state observation is very costly and therefore rare (in time). We present a novel MDP theory for rare, costly observations and derive the corresponding Bellman equation. In the new theory, state information can be derived for a particular cost after certain, rather long time intervals. The resulting information costs enter into the total cost and thus into the optimization criterion. This approach applies to many real world problems, particularly in the medical context, where the medical condition is examined rather rarely because examination costs are high. At the same time, the approach allows for efficient numerical realization. We demonstrate the usefulness of the novel theory by determining, from the national economic perspective, optimal therapeutic policies for the treatment of the human immunodefficiency virus (HIV) in resource-rich and resource-poor settings. Based on the developed theory and models, we discover that available drugs may not be utilized efficiently in resource-poor settings due to exorbitant diagnostic costs.}, language = {en} } @inproceedings{SkibinaIliewBethgeetal.2009, author = {Skibina, Julia and Iliew, Rumen and Bethge, Jens and Bock, Martin and Fischer, Dorit and Beloglazov, Valentin and Wedell, Reiner and Burger, Sven and Steinmeyer, G{\"u}nter}, title = {A chirped photonic crystal fiber for high-fidelity guiding of sub-100 fs pluses}, booktitle = {CLEO/QELS}, doi = {10.1364/CLEO.2009.CMHH1}, pages = {CMHH1}, year = {2009}, language = {en} } @misc{LieFackeldeyWeber2013, author = {Lie, Han Cheng and Fackeldey, Konstantin and Weber, Marcus}, title = {A square root approximation of transition rates for a Markov State Model}, issn = {1438-0064}, doi = {10.1137/120899959}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42195}, year = {2013}, abstract = {Trajectory- or mesh-based methods for analyzing the dynamical behavior of large molecules tend to be impractical due to the curse of dimensionality - their computational cost increases exponentially with the size of the molecule. We propose a method to break the curse by a novel square root approximation of transition rates, Monte Carlo quadrature and a discretization approach based on solving linear programs. With randomly sampled points on the molecular energy landscape and randomly generated discretizations of the molecular configuration space as our initial data, we construct a matrix describing the transition rates between adjacent discretization regions. This transition rate matrix yields a Markov State Model of the molecular dynamics. We use Perron cluster analysis and coarse-graining techniques in order to identify metastable sets in configuration space and approximate the transition rates between the metastable sets. Application of our method to a simple energy landscape on a two-dimensional configuration space provides proof of concept and an example for which we compare the performance of different discretizations. We show that the computational cost of our method grows only polynomially with the size of the molecule. However, finding discretizations of higher-dimensional configuration spaces in which metastable sets can be identified remains a challenge.}, language = {en} } @inproceedings{BurgerZschiedrichPomplunetal.2013, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank}, title = {Finite-element based electromagnetic field simulations: Benchmark results for isolated structures}, volume = {8880}, booktitle = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1310.2732}, doi = {10.1117/12.2026213}, pages = {88801Z}, year = {2013}, language = {en} } @phdthesis{MoualeuNgangue2013, author = {Moualeu-Ngangue, Dany Pascal}, title = {A Mathematical Tuberculosis Model in Cameroon}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000095327-7}, school = {Freie Universit{\"a}t Berlin}, pages = {154}, year = {2013}, abstract = {This thesis firstly presents a nonlinear extended deterministic model for the transmission dynamics of tuberculosis, based on realistic assumptions and data collected from the WHO. This model enables a comprehensive qualitative analysis of various aspects in the outbreak and control of tuberculosis in Sub-Saharan Africa countries and successfully reproduces the epidemiology of tuberculosis in Cameroon for the past (from 1994-2010). Some particular properties of the model and its solution have been presented using the comparison theorem applied to the theory of differential equations. The existence and the stability of a disease free equilibrium has been discussed using the Perron-Frobenius theorem and Metzler stable matrices. Furthermore, we computed the basic reproduction number, i.e. the number of cases that one case generates on average over the course of its infectious period. Rigorous qualitative analysis of the model reveals that, in contrast to the model without reinfections, the full model with reinfection exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium coexists with a stable endemic equilibrium when a certain threshold quantity, known as the basic reproduction ratio (R0), is less than unity. The global stability of the disease-free equilibrium has been discussed using the concepts of Lyapunov stability and bifurcation theory. With the help of a sensitivity analysis using data of Cameroon, we identified the relevant parameters which play a key role for the transmission and the control of the disease. This was possible applying sophisticated numerical methods (POEM) developed at ZIB. Using advanced approaches for optimal control considering the costs for chemoprophylaxis, treatment and educational campaigns should provide a framework for designing realistic cost effective strategies with different intervention methods. The forward-backward sweep method has been used to solve the numerical optimal control problem. The numerical result of the optimal control problem reveals that combined effort in education and chemoprophylaxis may lead to a reduction of 80\\% in the number of infected people in 10 years. The mathematical and numerical approaches developed in this thesis could be similarly applied in many other Sub-Saharan countries where TB is a public health problem.}, language = {en} } @misc{MoualeuNgangueRoeblitzEhrigetal.2013, author = {Moualeu-Ngangue, Dany Pascal and R{\"o}blitz, Susanna and Ehrig, Rainald and Deuflhard, Peter}, title = {Parameter Identification for a Tuberculosis Model in Cameroon}, issn = {1438-0064}, doi = {10.1371/journal.pone.0120607}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-43087}, year = {2013}, abstract = {A deterministic model of tuberculosis in sub-Saharan Africa in general and Cameroon in particular including lack of access to the treatment and weak diagnose capacity is designed and analyzed with respect to its transmission dynamics. The model includes both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and most sensitive parameters of the model are identified using a state-of-the-art Gauss-Newton Method. In particular, parameters representing the proportion of individuals having access to medical facilities have a large impact on the dynamics of the disease. It has been shown that an increase of these parameter values over the time can significantly reduce the disease burden in the population within the next 15 years.}, language = {en} } @misc{MoualeuNgangueWeiserEhrigetal.2013, author = {Moualeu-Ngangue, Dany Pascal and Weiser, Martin and Ehrig, Rainald and Deuflhard, Peter}, title = {Optimal control for a tuberculosis model with undetected cases in Cameroon}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-43142}, year = {2013}, abstract = {This paper considers the optimal control of tuberculosis through education, diagnosis campaign and chemoprophylaxis of latently infected. A mathematical model which includes important components such as undiagnosed infectious, diagnosed infectious, latently infected and lost-sight infectious is formulated. The model combines a frequency dependent and a density dependent force of infection for TB transmission. Through optimal control theory and numerical simulations, a cost-effective balance of two different intervention methods is obtained. Seeking to minimize the amount of money the government spends when tuberculosis remain endemic in the Cameroonian population, Pontryagin's maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods. It comes out that combining chemoprophylaxis and education, the burden of TB can be reduced by 80 \% in 10 years}, language = {en} } @misc{NielsenFackeldeyWeber2013, author = {Nielsen, Adam and Fackeldey, Konstantin and Weber, Marcus}, title = {On a Generalized Transfer Operator}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-43162}, year = {2013}, abstract = {We introduce a generalized operator for arbitrary stochastic processes by using a pre-kernel, which is a generalization of the Markov kernel. For deterministic processes, such an operator is already known as the Frobenius-Perron operator, which is defined for a large class of measures. For Markov processes, there exists transfer operators being only well defined for stationary measures in \$L^2\$. Our novel generalized transfer operator is well defined for arbitrary stochastic processes, in particular also for deterministic ones. We can show that this operator is acting on \$L^1\$. For stationary measures, this operator is also an endomorphism of \$L^2\$ and, therefore, allows for a mathematical analysis in Hilbert spaces.}, language = {en} } @misc{Lehmann2013, author = {Lehmann, Felix}, title = {Inexaktheit in Newton-Lagrange-Verfahren f{\"u}r Optimierungsprobleme mit Elliptischen PDGL-Nebenbedingungen}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-41972}, year = {2013}, abstract = {Bei der numerischen L{\"o}sung von Optimalsteuerungsproblemen mit elliptischen partiellen Differentialgleichungen als Nebenbedingung treten unvermeidlich Diskretisierungs- und Iterationsfehler auf. Man ist aus Aufwandsgr{\"u}nden daran interessiert die dabei entstehenden Fehler nicht sehr klein w{\"a}hlen zu m{\"u}ssen. In der Folge werden die linearisierten Nebenbedingungen in einem Composite-Step-Verfahren nicht exakt erf{\"u}llt. In dieser Arbeit wird der Einfluss dieser Ungenauigkeit auf das Konvergenzverhalten von Newton-Lagrange-Verfahren untersucht. Dabei sollen mehrere einschl{\"a}gige lokale Konvergenzresultate diskutiert werden. Anschließend wird ein konkretes Composite-Step-Verfahren formuliert, in dem die Genauigkeit der inneren Iterationsverfahren adaptiv gesteuert werden kann. Am Ende der Arbeit wird an zwei Musterproblemen die hohe {\"U}bereinstimmung der analytischen Voraussagen und der tats{\"a}chlichen Performanz der dargestellten Methoden demonstriert.}, language = {de} } @misc{MeiselRoeblitz2013, author = {Meisel, Kristin and R{\"o}blitz, Susanna}, title = {Mathematische Modellierung der Knochenremodellierung}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42010}, year = {2013}, abstract = {Knochenremodellierung beinhaltet den Auf- und Abbau der Knochenmasse durch die verschiedenen Knochenzellen und findet fast {\"u}berall, auch am Skelett Erwachsener, statt. F{\"u}r die Erneuerung der Knochensubstanz sind die Osteoblasten zust{\"a}ndig. Sie ersetzen exakt die Menge der Knochenmasse, welche zuvor durch Osteoklasten abgebaut wurde. St{\"o}rungen dieses, durch viele Faktoren beeinflussten Prozesses f{\"u}hren zu pathologischen Ver{\"a}nderungen, beispielsweise zu Osteoporose oder Arthritis. Auf der Grundlage analysierter publizierter Modelle wurde ein Modell entwickelt, welches den Einfluss einiger dieser Faktoren realistisch abbildet. Auf diese Weise kann die Wirkung von basalem PTH, des RANKL-OPG-Systems ( RANKL: Receptor activator of nuclear factor kappa-B ligand, OPG: Osteoprotegerin) und des Estradiols auf den Knochenstoffwechsel am vorgestellten System untersucht werden. Außerdem wurde durch Estradiolmangel hervorgerufene Osteoporose und der kurative Effekt von synthetischen Medikamenten wie Estradiol oder intermittierend verabreichtem PTH modelliert. Mit der Parametersch{\"a}tzung anhand des Gauß-Newton-Verfahrens wird des Weiteren eine Methode vorgestellt, die es erm{\"o}glicht, mathematische Modelle bestm{\"o}glich durch Variation der Parameterwerte an experimentelle Daten anzupassen. Das am Zuse-Institut Berlin entwickelte Softwarepaket POEM wendet diesen Algorithmus an und wird ebenfalls erl{\"a}utert.}, language = {de} } @inproceedings{PomplunBurgerRozovaetal.2011, author = {Pomplun, Jan and Burger, Sven and Rozova, Maria and Zschiedrich, Lin and Schmidt, Frank}, title = {Finite element simulation of optical modes in VCSELs}, booktitle = {Numerical Simulation of Optoelectronic Devices (NUSOD), 11th International Conference on}, doi = {10.1109/NUSOD.2011.6041170}, pages = {119 -- 120}, year = {2011}, language = {en} } @article{FackeldeyKoltaiNeviretal.2019, author = {Fackeldey, Konstantin and Koltai, Peter and Nevir, Peter and Rust, Henning and Schild, Axel and Weber, Marcus}, title = {From metastable to coherent sets - Time-discretization schemes}, volume = {29}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, doi = {10.1063/1.5058128}, pages = {012101 -- 012101}, year = {2019}, abstract = {In this article, we show that these well-established spectral algorithms (like PCCA+, Perron Cluster Cluster Analysis) 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-time-discretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.}, language = {en} } @inproceedings{MalureanudeLassonFrandsenetal.2018, author = {Malureanu, Radu and de Lasson, Jakob Rosenkrantz and Frandsen, Lars Hagedorn and Gutsche, Philipp and Burger, Sven and Kim, Oleksiy S. and Breinbjerg, Olav and Ivinskaya, Aliaksandra and Wang, Fengwen and Sigmund, Ole and H{\"a}yrynen, Teppo and Lavrinenko, Andrei and M{\o}rk, Jesper and Gregersen, Niels}, title = {Which Computational Methods Are Good for Analyzing Large Photonic Crystal Membrane Cavities?}, booktitle = {20th International Conference on Transparent Optical Networks (ICTON)}, doi = {10.1109/ICTON.2018.8473951}, year = {2018}, language = {en} } @article{AbbasSchneiderBollmannetal.2019, author = {Abbas, Aennes and Schneider, Ilona and Bollmann, Anna and Funke, Jan and Oehlmann, J{\"o}rg and Prasse, Carsten and Schulte-Oehlmann, Ulrike and Seitz, Wolfram and Ternes, Thomas and Weber, Marcus and Wesely, Henning and Wagner, Martin}, title = {What you extract is what you see: Optimising the preparation of water and wastewater samples for in vitro bioassays}, volume = {152}, journal = {Water Research}, doi = {10.1016/j.watres.2018.12.049}, pages = {47 -- 60}, year = {2019}, abstract = {The assessment of water quality is crucial for safeguarding drinking water resources and ecosystem integrity. To this end, sample preparation and extraction is critically important, especially when investigating emerging contaminants and the toxicity of water samples. As extraction methods are rarely optimised for bioassays but rather adopted from chemical analysis, this may result in a misrepresentation of the actual toxicity. In this study, surface water, groundwater, hospital and municipal wastewater were used to characterise the impacts of common sample preparation techniques (acidification, filtration and solid phase extraction (SPE)) on the outcomes of eleven in vitro bioassays. The latter covered endocrine activity (reporter gene assays for estrogen, androgen, aryl-hydrocarbon, retinoic acid, retinoid X, vitamin D, thyroid receptor), mutagenicity (Ames fluctuation test), genotoxicity (umu test) and cytotoxicity. Water samples extracted using different SPE sorbents (Oasis HLB, Supelco ENVI-Carb+, Telos C18/ENV) at acidic and neutral pH were compared for their performance in recovering biological effects. Acidification, commonly used for stabilisation, significantly altered the endocrine activity and toxicity of most (waste)water samples. Sample filtration did not affect the majority of endpoints but in certain cases affected the (anti-)estrogenic and dioxin-like activities. SPE extracts (10.4 × final concentration), including WWTP effluents, induced significant endocrine effects that were not detected in aqueous samples (0.63 × final concentration), such as estrogenic, (anti-)androgenic and dioxin-like activities. When ranking the SPE methods using multivariate Pareto optimisation an extraction with Telos C18/ENV at pH 7 was most effective in recovering toxicity. At the same time, these extracts were highly cytotoxic masking the endpoint under investigation. Compared to that, extraction at pH 2.5 enriched less cytotoxicity. In summary, our study demonstrates that sample preparation and extraction critically affect the outcome of bioassays when assessing the toxicity of water samples. Depending on the water matrix and the bioassay, these methods need to be optimised to accurately assess water quality.}, language = {en} } @misc{Helfmann2018, type = {Master Thesis}, author = {Helfmann, Luzie}, title = {Stochastic Modeling of Interacting Agent Systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71887}, pages = {68}, year = {2018}, language = {en} } @article{RettigHaasePletnyovetal.2019, author = {Rettig, Anika and Haase, Tobias and Pletnyov, Alexandr and Kohl, Benjamin and Ertel, Wolfgang and von Kleist, Max and Sunkara, Vikram}, title = {SLCV - A Supervised Learning - Computer Vision combined strategy for automated muscle fibre detection in cross sectional images}, journal = {PeerJ}, publisher = {PeerJ}, address = {PeerJ}, doi = {10.7717/peerj.7053}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72639}, year = {2019}, abstract = {Muscle fibre cross sectional area (CSA) is an important biomedical measure used to determine the structural composition of skeletal muscle, and it is relevant for tackling research questions in many different fields of research. To date, time consuming and tedious manual delineation of muscle fibres is often used to determine the CSA. Few methods are able to automatically detect muscle fibres in muscle fibre cross sections to quantify CSA due to challenges posed by variation of bright- ness and noise in the staining images. In this paper, we introduce SLCV, a robust semi-automatic pipeline for muscle fibre detection, which combines supervised learning (SL) with computer vision (CV). SLCV is adaptable to different staining methods and is quickly and intuitively tunable by the user. We are the first to perform an error analysis with respect to cell count and area, based on which we compare SLCV to the best purely CV-based pipeline in order to identify the contribution of SL and CV steps to muscle fibre detection. Our results obtained on 27 fluorescence-stained cross sectional images of varying staining quality suggest that combining SL and CV performs signifi- cantly better than both SL based and CV based methods with regards to both the cell separation- and the area reconstruction error. Furthermore, applying SLCV to our test set images yielded fibre detection results of very high quality, with average sensitivity values of 0.93 or higher on different cluster sizes and an average Dice Similarity Coefficient (DSC) of 0.9778.}, language = {en} } @article{ReuterFackeldeyWeber2019, author = {Reuter, Bernhard and Fackeldey, Konstantin and Weber, Marcus}, title = {Generalized Markov modeling of nonreversible molecular kinetics}, volume = {17}, journal = {The Journal of Chemical Physics}, number = {150}, doi = {10.1063/1.5064530}, pages = {174103}, year = {2019}, abstract = {Markov state models are to date the gold standard for modeling molecular kinetics since they enable the identification and analysis of metastable states and related kinetics in a very instructive manner. The state-of-the-art Markov state modeling methods and tools are very well developed for the modeling of reversible processes in closed equilibrium systems. On the contrary, they are largely not well suited to deal with nonreversible or even nonautonomous processes of nonequilibrium systems. Thus, we generalized the common Robust Perron Cluster Cluster Analysis (PCCA+) method to enable straightforward modeling of nonequilibrium systems as well. The resulting Generalized PCCA (G-PCCA) method readily handles equilibrium as well as nonequilibrium data by utilizing real Schur vectors instead of eigenvectors. This is implemented in the G-PCCA algorithm that enables the semiautomatic coarse graining of molecular kinetics. G-PCCA is not limited to the detection of metastable states but also enables the identification and modeling of cyclic processes. This is demonstrated by three typical examples of nonreversible systems.}, language = {en} } @article{ErnstFackeldeyVolkameretal.2019, author = {Ernst, Natalia and Fackeldey, Konstantin and Volkamer, Andrea and Opatz, Oliver and Weber, Marcus}, title = {Computation of temperature-dependent dissociation rates of metastable protein-ligand complexes}, volume = {45}, journal = {Molecular Simulation}, number = {11}, doi = {10.1080/08927022.2019.1610949}, pages = {904 -- 911}, year = {2019}, abstract = {Molecular simulations are often used to analyse the stability of protein-ligand complexes. The stability can be characterised by exit rates or using the exit time approach, i.e. by computing the expected holding time of the complex before its dissociation. However determining exit rates by straightforward molecular dynamics methods can be challenging for stochastic processes in which the exit event occurs very rarely. Finding a low variance procedure for collecting rare event statistics is still an open problem. In this work we discuss a novel method for computing exit rates which uses results of Robust Perron Cluster Analysis (PCCA+). This clustering method gives the possibility to define a fuzzy set by a membership function, which provides additional information of the kind 'the process is being about to leave the set'. Thus, the derived approach is not based on the exit event occurrence and, therefore, is also applicable in case of rare events. The novel method can be used to analyse the temperature effect of protein-ligand systems through the differences in exit rates, and, thus, open up new drug design strategies and therapeutic applications.}, language = {en} } @article{GelssKlusEisertetal.2019, author = {Gelß, Patrick and Klus, Stefan and Eisert, Jens and Sch{\"u}tte, Christof}, title = {Multidimensional Approximation of Nonlinear Dynamical Systems}, volume = {14}, journal = {Journal of Computational and Nonlinear Dynamics}, number = {6}, doi = {10.1115/1.4043148}, year = {2019}, abstract = {A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system identification, ranging from industrial engineering and acoustic signal processing to stock market models. In order to find appropriate representations of underlying dynamical systems, various data-driven methods have been proposed by different communities. However, if the given data sets are high-dimensional, then these methods typically suffer from the curse of dimensionality. To significantly reduce the computational costs and storage consumption, we propose the method multidimensional approximation of nonlinear dynamical systems (MANDy) which combines data-driven methods with tensor network decompositions. The efficiency of the introduced approach will be illustrated with the aid of several high-dimensional nonlinear dynamical systems.}, language = {en} } @article{BeckerBurgerJaeger2019, author = {Becker, Christiane and Burger, Sven and J{\"a}ger, Klaus}, title = {Nanooptische Simulationen f{\"u}r optoelektronische Anwendungen}, volume = {2019}, journal = {Photonik: Fachzeitschrift f{\"u}r die optischen Technologien}, number = {2}, issn = {1432-9778}, pages = {42 -- 45}, year = {2019}, language = {de} } @inproceedings{LassilaShpakVaiguetal.2016, author = {Lassila, Antti and Shpak, Maksim and Vaigu, A. and Smid, M. and Velasco, A. and Pokatilov, A. and Fatadin, I. and Ferguson, R. and Robinson, D. and Walbaum, T. and Burger, Sven and Haapalainen, Mertsi and Vahimaa, P. and Lukner, H. and Pernice, W. and Pitwon, R. and Deninger, A. and Morel, Jacques and Castagna, Natascia and Peters, O. and Husu, H.}, title = {Joint research for photonics fibres, waveguides and interconnects}, booktitle = {Proc. Europ. Opt. Soc. Ann. Meet. 2016 (EOSAM)}, isbn = {978-1-5108-4796-5}, pages = {25}, year = {2016}, language = {en} } @inproceedings{ZschiedrichSchmidtPomplunetal.2016, author = {Zschiedrich, Lin and Schmidt, Frank and Pomplun, Jan and Burger, Sven}, title = {Finite elements for nano-optics applications}, booktitle = {Proc. Europ. Opt. Soc. Ann. Meet. 2016 (EOSAM)}, isbn = {978-1-5108-4796-5}, pages = {178}, year = {2016}, language = {en} } @inproceedings{BarthRoderBrodoceanuetal.2016, author = {Barth, Carlo and Roder, Sebastian and Brodoceanu, Daniel and Kraus, Tobias and Burger, Sven and Hammerschmidt, Martin and Schmidt, Frank and Becker, Christiane}, title = {Increased fluorescence of PbS quantum dots on photonic crystal slab structures}, booktitle = {Proc. Europ. Opt. Soc. Ann. Meet. 2016 (EOSAM)}, isbn = {978-1-5108-4796-5}, pages = {181}, year = {2016}, language = {en} } @inproceedings{HammerschmidtBarthBurgeretal.2016, author = {Hammerschmidt, Martin and Barth, Carlo and Burger, Sven and Becker, Christiane and Schmidt, Frank}, title = {Determining 2D photonic crystal geometries from reflectance spectra with a reduced basis method}, booktitle = {Proc. Europ. Opt. Soc. Ann. Meet. 2016 (EOSAM)}, isbn = {978-1-5108-4796-5}, pages = {281}, year = {2016}, language = {en} } @article{SchneiderHammerschmidtZschiedrichetal.2019, author = {Schneider, Philipp-Immanuel and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven}, title = {Using Gaussian process regression for efficient parameter reconstruction}, volume = {10959}, journal = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1903.12128}, doi = {10.1117/12.2513268}, pages = {1095911}, year = {2019}, language = {en} } @misc{Niemann2019, type = {Master Thesis}, author = {Niemann, Jan-Hendrik}, title = {A Dynamic Memory Approach for Consensus Problems with Packet Loss}, pages = {64}, year = {2019}, language = {en} } @article{BinkowskiZschiedrichBurger2019, author = {Binkowski, Felix and Zschiedrich, Lin and Burger, Sven}, title = {An auxiliary field approach for computing optical resonances in dispersive media}, volume = {15}, journal = {J. Eur. Opt. Soc.-Rapid}, doi = {10.1186/s41476-019-0098-z}, pages = {3}, year = {2019}, language = {en} } @article{GrafFeisSantiagoetal.2019, author = {Graf, Florian and Feis, Joshua and Santiago, Xavier Garcia and Wegener, Martin and Rockstuhl, Carsten and Fernandez-Corbaton, Ivan}, title = {Achiral, Helicity Preserving, and Resonant Structures for Enhanced Sensing of Chiral Molecules}, volume = {6}, journal = {ACS Photonics}, doi = {10.1021/acsphotonics.8b01454}, pages = {482}, year = {2019}, language = {en} } @article{VillatoroWeberZuehlkeetal.2019, author = {Villatoro, Jos{\´e} and Weber, Marcus and Z{\"u}hlke, Martin and Lehmann, Andreas and Zechiowski, Karl and Riebe, Daniel and Beitz, Toralf and L{\"o}hmannsr{\"o}ben, Hans-Gerd and Kreuzer, Oliver}, title = {Structural characterization of synthetic peptides using electronspray ion mobility spectrometry and molecular dynamics simulations}, volume = {436}, journal = {International Journal of Mass Spectrometry}, doi = {10.1016/j.ijms.2018.10.036}, pages = {108 -- 117}, year = {2019}, abstract = {Electrospray ionization-ion mobility spectrometry was employed for the determination of collision cross sections (CCS) of 25 synthetically produced peptides in the mass range between 540-3310 Da. The experimental measurement of the CCS is complemented by their calculation applying two different methods. One prediction method is the intrinsic size parameter (ISP) method developed by the Clemmer group. The second new method is based on the evaluation of molecular dynamics (MD) simulation trajectories as a whole, resulting in a single, averaged collision cross-section value for a given peptide in the gas phase. A high temperature MD simulation is run in order to scan through the whole conformational space. The lower temperature conformational distribution is obtained through thermodynamic reweighting. In the first part, various correlations, e.g. CCS vs. mass and inverse mobility vs. m/z correlations, are presented. Differences in CCS between peptides are also discussed in terms of their respective mass and m/z differences, as well as their respective structures. In the second part, measured and calculated CCS are compared. The agreement between the prediction results and the experimental values is in the same range for both calculation methods. While the calculation effort of the ISP method is much lower, the MD method comprises several tools providing deeper insights into the conformations of peptides. Advantages and limitations of both methods are discussed. Based on the separation of two pairs of linear and cyclic peptides of virtually the same mass, the influence of the structure on the cross sections is discussed. The shift in cross section differences and peak shape after transition from the linear to the cyclic peptide can be well understood by applying different MD tools, e.g. the root-mean-square deviation (RMSD) and the root mean square fluctuation (RMSF).}, language = {en} } @phdthesis{Reuter2018, author = {Reuter, Bernhard}, title = {Generalisierte Markov-Modellierung von Nichtgleichgewichtssystemen - Simulation und Modellierung der Amyloid-beta(1-40)-Konformationsdynamik unter Mikrowelleneinfluss}, year = {2018}, language = {de} } @phdthesis{Quer2018, author = {Quer, Jannes}, title = {Importance Sampling for metastable dynamical systems in molecular dynamics}, year = {2018}, language = {en} } @phdthesis{Klimm2018, author = {Klimm, Martina}, title = {New Strategies in Conformation Dynamics}, year = {2018}, language = {en} } @phdthesis{Villatoro2018, author = {Villatoro, Jos{\´e}}, title = {A combined approach for the analysis of biomolecules using IR-MALDI ion mobility spectrometry and molecular dynamics simulations of peptide ions in the gas phase}, year = {2018}, language = {en} } @article{LorenzSpreenWolfBraunetal.2018, author = {Lorenz-Spreen, Philipp and Wolf, Frederik and Braun, Jonas and Ghoshal, Gourab and Djurdjevac Conrad, Natasa and H{\"o}vel, Philipp}, title = {Tracking online topics over time: understanding dynamic hashtag communities}, volume = {5}, journal = {Computational Social Networks}, number = {9}, doi = {10.1186/s40649-018-0058-6}, year = {2018}, abstract = {Background: Hashtags are widely used for communication in online media. As a condensed version of information, they characterize topics and discussions. For their analysis, we apply methods from network science and propose novel tools for tracing their dynamics in time-dependent data. The observations are characterized by bursty behaviors in the increases and decreases of hashtag usage. These features can be reproduced with a novel model of dynamic rankings. Hashtag communities in time: We build temporal and weighted co-occurrence networks from hashtags. On static snapshots, we infer the community structure using customized methods. On temporal networks, we solve the bipartite matching problem of detected communities at subsequent timesteps by taking into account higher-order memory. This results in a matching protocol that is robust toward temporal fluctuations and instabilities of the static community detection. The proposed methodology is broadly applicable and its outcomes reveal the temporal behavior of online topics. Modeling topic-dynamics: We consider the size of the communities in time as a proxy for online popularity dynamics. We find that the distributions of gains and losses, as well as the interevent times are fat-tailed indicating occasional, but large and sudden changes in the usage of hashtags. Inspired by typical website designs, we propose a stochastic model that incorporates a ranking with respect to a time-dependent prestige score. This causes occasional cascades of rank shift events and reproduces the observations with good agreement. This offers an explanation for the observed dynamics, based on characteristic elements of online media.}, language = {en} } @article{Deuflhard2018, author = {Deuflhard, Peter}, title = {The Grand Four. Affine Invariant Globalizations of Newton's Method}, volume = {46}, journal = {Vietnam Journal of Mathematics}, number = {4}, doi = {10.1007/s10013-018-0301-3}, pages = {761 -- 777}, year = {2018}, language = {en} } @misc{PloentzkeBergRoeblitz2018, author = {Pl{\"o}ntzke, Julia and Berg, Mascha and R{\"o}blitz, Susanna}, title = {A mathematical modelling approach to the insight of dynamic networks: Potassium homeostasis and glucose-insulin in dairy cows}, volume = {101 Suppl. 2}, journal = {ADSA 2018 Annual Meeting}, edition = {Journal of Dairy Science}, publisher = {American Dairy Science Association}, pages = {226 -- 227}, year = {2018}, abstract = {Lactating dairy cows require a particular composition of nutritional ingredients depending on their production status. The optimal supply of energy and minerals in diet, one of them potassium, is indispensable for the prevention of disbalances like hypokalemia or hypoglycaemia. Potassium balance in cows is the result of potassium intake, distribution in the organism, and excretion, and closely interacts with glucose and electrolyte metabolism, in which postpartum veterinary treatments frequently intervene. We present a mechanistic, dynamic model for potassium balance together with a glucose insulin model in non-lactating and lactating dairy cows based on ordinary differential equations. Parameter values were obtained from data of a clinical trial as well as from literature. To verify the mechanistic functioning of the model, we validate the model by comparing simulation outcomes with clinical study findings. Furthermore we perform numerical experiments and compare them with expected behaviour according to mechanistic knowledge. The results give insight into the dynamic behaviour of the network and open the way for further open questions and hypothesis to be tested.}, language = {en} } @article{HoehneSchnauberRodtetal.2019, author = {H{\"o}hne, Theresa and Schnauber, Peter and Rodt, Sven and Reitzenstein, Stephan and Burger, Sven}, title = {Numerical Investigation of Light Emission from Quantum Dots Embedded into On-Chip, Low Index Contrast Optical Waveguides}, volume = {256}, journal = {Phys. Status Solidi B}, arxiv = {http://arxiv.org/abs/2006.10466}, doi = {10.1002/pssb.201800437}, pages = {1800437}, year = {2019}, language = {en} }