TY  - JOUR
A1  - Reich, Sebastian
T1  - A dynamical systems framework for intermittent data assimilation
JF  - BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians
N2  - We consider the problem of discrete time filtering (intermittent data assimilation) for differential equation models and discuss methods for its numerical approximation. The focus is on methods based on ensemble/particle techniques and on the ensemble Kalman filter technique in particular. We summarize as well as extend recent work on continuous ensemble Kalman filter formulations, which provide a concise dynamical systems formulation of the combined dynamics-assimilation problem. Possible extensions to fully nonlinear ensemble/particle based filters are also outlined using the framework of optimal transportation theory.
KW  - Data assimilation
KW  - Ensemble Kalman filter
KW  - Dynamical systems
KW  - Nonlinear filters
KW  - Optimal transportation
Y1  - 2011
U6  - https://doi.org/10.1007/s10543-010-0302-4
SN  - 0006-3835
VL  - 51
IS  - 1
SP  - 235
EP  - 249
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - INPR
A1  - Méléard, Sylvie
A1  - Roelly, Sylvie
T1  - A host-parasite multilevel interacting process and continuous approximations
N2  - We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in these individuals. The ecological parameters of the individual dynamics depend on the number of cells of each type contained by the individual and the cell dynamics depends on the trait of the invaded individual. Our models are rooted in the microscopic description of a random (discrete) population of individuals characterized by one or several adaptive traits and cells characterized by their type. The population is modeled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation and death for individuals and birth and death for cells. The interaction between individuals (resp. between cells) is described by a competition between individual traits (resp. between cell types). We look for tractable large population approximations. By combining various scalings on population size, birth and death rates and mutation step, the single microscopic model is shown to lead to contrasting nonlinear macroscopic limits of different nature: deterministic approximations, in the form of ordinary, integro- or partial differential equations, or probabilistic ones, like stochastic partial differential equations or superprocesses. The study of the long time behavior of these processes seems very hard and we only develop some simple cases enlightening the difficulties involved.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2011, 01 
KW  - two-level interacting processes
KW  - birth-death-mutation-competition point process
KW  - host-parasite stochastic particle system
Y1  - 2011
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51694
ER  - 
TY  - JOUR
A1  - Shin, Seoleun
A1  - Zöller, Gert
A1  - Holschneider, Matthias
A1  - Reich, Sebastian
T1  - A multigrid solver for modeling complex interseismic stress fields
JF  - Computers & geosciences : an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets ; an official journal of the International Association for Mathematical Geology
N2  - We develop a multigrid, multiple time stepping scheme to reduce computational efforts for calculating complex stress interactions in a strike-slip 2D planar fault for the simulation of seismicity. The key elements of the multilevel solver are separation of length scale, grid-coarsening, and hierarchy. In this study the complex stress interactions are split into two parts: the first with a small contribution is computed on a coarse level, and the rest for strong interactions is on a fine level. This partition leads to a significant reduction of the number of computations. The reduction of complexity is even enhanced by combining the multigrid with multiple time stepping. Computational efficiency is enhanced by a factor of 10 while retaining a reasonable accuracy, compared to the original full matrix-vortex multiplication. The accuracy of solution and computational efficiency depend on a given cut-off radius that splits multiplications into the two parts. The multigrid scheme is constructed in such a way that it conserves stress in the entire half-space.
KW  - Multigrid
KW  - Multiple time stepping
KW  - Strike-slip fault model
Y1  - 2011
U6  - https://doi.org/10.1016/j.cageo.2010.11.011
SN  - 0098-3004
VL  - 37
IS  - 8
SP  - 1075
EP  - 1082
PB  - Elsevier
CY  - Oxford
ER  - 
TY  - THES
A1  - Sarasit, Napaporn
T1  - Algebraic properties of sets of terms
Y1  - 2011
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Klein, Markus
A1  - Rosenberger, Elke
T1  - Asymptotic eigenfunctions for a class of difference operators
JF  - Asymptotic analysis
N2  - We analyze a general class of difference operators H(epsilon) = T(epsilon) + V(epsilon) on l(2)((epsilon Z)(d)), where V(epsilon) is a one-well potential and epsilon is a small parameter. We construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low lying eigenvalues of H(epsilon). These are obtained from eigenfunctions or quasimodes for the operator H(epsilon), acting on L(2)(R(d)), via restriction to the lattice (epsilon Z)(d).
KW  - difference operator
KW  - tunneling
KW  - WKB-expansion
KW  - quasimodes
Y1  - 2011
U6  - https://doi.org/10.3233/ASY-2010-1025
SN  - 0921-7134
VL  - 73
IS  - 1-2
SP  - 1
EP  - 36
PB  - IOS Press
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Debussche, Arnaud
A1  - Högele, Michael
A1  - Imkeller, Peter
T1  - Asymptotic first exit times of the chafee-infante equation with small heavy-tailed levy noise
JF  - Electronic communications in probability
N2  - This article studies the behavior of stochastic reaction-diffusion equations driven by additive regularly varying pure jump Levy noise in the limit of small noise intensity. It is shown that the law of the suitably renormalized first exit times from the domain of attraction of a stable state converges to an exponential law of parameter 1 in a strong sense of Laplace transforms, including exponential moments. As a consequence, the expected exit times increase polynomially in the inverse intensity, in contrast to Gaussian perturbations, where this growth is known to be of exponential rate.
KW  - stochastic reaction diffusion equation with heavy-tailed Levy noise
KW  - first exit times
KW  - regularly varying Levy process
KW  - small noise asymptotics
Y1  - 2011
SN  - 1083-589X
VL  - 16
IS  - 3-4
SP  - 213
EP  - 225
PB  - Univ. of Washington, Mathematics Dep.
CY  - Seattle
ER  - 
TY  - JOUR
A1  - Böckmann, Christine
A1  - Kammanee, Athassawat
T1  - Broyden method for inverse non-symmetric Sturm-Liouville problems
JF  - BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians
N2  - In this paper, we propose a derivative-free method for recovering symmetric and non-symmetric potential functions of inverse Sturm-Liouville problems from the knowledge of eigenvalues. A class of boundary value methods obtained as an extension of Numerov's method is the major tool for approximating the eigenvalues in each Broyden iteration step. Numerical examples demonstrate that the method is able to reduce the number of iteration steps, in particular for non-symmetric potentials, without accuracy loss.
KW  - Inverse Sturm-Liouville problem
KW  - Non-symmetric potential
KW  - Broyden's method
KW  - Boundary value method
Y1  - 2011
U6  - https://doi.org/10.1007/s10543-011-0317-5
SN  - 0006-3835
VL  - 51
IS  - 3
SP  - 513
EP  - 528
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - BOOK
A1  - Murr, Rüdiger
T1  - Characterization of Lévy Processes by a duality formula and related results
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Mathematische Statistik un
Y1  - 2011
SN  - 1613-3307
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Murr, Rüdiger
T1  - Characterization of Lévy Processes by a duality formula and related results
N2  - Processes with independent increments are characterized via a duality formula, including Malliavin derivative and difference operators. This result is based on a characterization of infinitely divisible random vectors by a functional equation. A construction of the difference operator by a variational method is introduced and compared to approaches used by other authors for L´evy processes involving the chaos decomposition. Finally we extend our method to characterize infinitely divisible random measures.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2011, 02 
Y1  - 2011
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-43538
ER  - 
TY  - JOUR
A1  - Gottwald, Georg A.
A1  - Mitchell, Lewis
A1  - Reich, Sebastian
T1  - Controlling overestimation of error covariance in ensemble kalman filters with sparse observations a variance-limiting kalman filter
JF  - Monthly weather review
N2  - The problem of an ensemble Kalman filter when only partial observations are available is considered. In particular, the situation is investigated where the observational space consists of variables that are directly observable with known observational error, and of variables of which only their climatic variance and mean are given. To limit the variance of the latter poorly resolved variables a variance-limiting Kalman filter (VLKF) is derived in a variational setting. The VLKF for a simple linear toy model is analyzed and its range of optimal performance is determined. The VLKF is explored in an ensemble transform setting for the Lorenz-96 system, and it is shown that incorporating the information of the variance of some unobservable variables can improve the skill and also increase the stability of the data assimilation procedure.
Y1  - 2011
U6  - https://doi.org/10.1175/2011MWR3557.1
SN  - 0027-0644
VL  - 139
IS  - 8
SP  - 2650
EP  - 2667
PB  - American Meteorological Soc.
CY  - Boston
ER  - 
TY  - JOUR
A1  - Skeel, R. D.
A1  - Reich, Sebastian
T1  - Corrected potential energy functions for constrained molecular dynamics
JF  - European physical journal special topics
N2  - Atomic oscillations present in classical molecular dynamics restrict the step size that can be used. Multiple time stepping schemes offer only modest improvements, and implicit integrators are costly and inaccurate. The best approach may be to actually remove the highest frequency oscillations by constraining bond lengths and bond angles, thus permitting perhaps a 4-fold increase in the step size. However, omitting degrees of freedom produces errors in statistical averages, and rigid angles do not bend for strong excluded volume forces. These difficulties can be addressed by an enhanced treatment of holonomic constrained dynamics using ideas from papers of Fixman (1974) and Reich (1995, 1999). In particular, the 1995 paper proposes the use of "flexible" constraints, and the 1999 paper uses a modified potential energy function with rigid constraints to emulate flexible constraints. Presented here is a more direct and rigorous derivation of the latter approach, together with justification for the use of constraints in molecular modeling. With rigor comes limitations, so practical compromises are proposed: simplifications of the equations and their judicious application when assumptions are violated. Included are suggestions for new approaches.
Y1  - 2011
U6  - https://doi.org/10.1140/epjst/e2011-01518-8
SN  - 1951-6355
VL  - 200
IS  - 1
SP  - 55
EP  - 72
PB  - Springer
CY  - Heidelberg
ER  - 
TY  - THES
A1  - Schachtschneider, Reyko
T1  - Error distribution in regional inversions of potential fields from satellite data
Y1  - 2011
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Weiss, Andrea Y.
A1  - Huisinga, Wilhelm
T1  - Error-controlled global sensitivity analysis of ordinary differential equations
JF  - Journal of computational physics
N2  - We propose a novel strategy for global sensitivity analysis of ordinary differential equations. It is based on an error-controlled solution of the partial differential equation (PDE) that describes the evolution of the probability density function associated with the input uncertainty/variability. The density yields a more accurate estimate of the output uncertainty/variability, where not only some observables (such as mean and variance) but also structural properties (e.g., skewness, heavy tails, bi-modality) can be resolved up to a selected accuracy. For the adaptive solution of the PDE Cauchy problem we use the Rothe method with multiplicative error correction, which was originally developed for the solution of parabolic PDEs. We show that, unlike in parabolic problems, conservation properties necessitate a coupling of temporal and spatial accuracy to avoid accumulation of spatial approximation errors over time. We provide convergence conditions for the numerical scheme and suggest an implementation using approximate approximations for spatial discretization to efficiently resolve the coupling of temporal and spatial accuracy. The performance of the method is studied by means of low-dimensional case studies. The favorable properties of the spatial discretization technique suggest that this may be the starting point for an error-controlled sensitivity analysis in higher dimensions.
KW  - ODE with random initial conditions
KW  - Global sensitivity analysis
KW  - Cauchy problem
KW  - Error control/adaptivity
KW  - Rothe method
KW  - Approximate approximations
Y1  - 2011
U6  - https://doi.org/10.1016/j.jcp.2011.05.011
SN  - 0021-9991
VL  - 230
IS  - 17
SP  - 6824
EP  - 6842
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - JOUR
A1  - Holschneider, Matthias
A1  - Zöller, Gert
A1  - Hainzl, Sebastian
T1  - Estimation of the maximum possible magnitude in the framework of a doubly truncated Gutenberg-Richter Model
JF  - Bulletin of the Seismological Society of America
N2  - We discuss to what extent a given earthquake catalog and the assumption of a doubly truncated Gutenberg-Richter distribution for the earthquake magnitudes allow for the calculation of confidence intervals for the maximum possible magnitude M. We show that, without further assumptions such as the existence of an upper bound of M, only very limited information may be obtained. In a frequentist formulation, for each confidence level alpha the confidence interval diverges with finite probability. In a Bayesian formulation, the posterior distribution of the upper magnitude is not normalizable. We conclude that the common approach to derive confidence intervals from the variance of a point estimator fails. Technically, this problem can be overcome by introducing an upper bound (M) over tilde for the maximum magnitude. Then the Bayesian posterior distribution can be normalized, and its variance decreases with the number of observed events. However, because the posterior depends significantly on the choice of the unknown value of (M) over tilde, the resulting confidence intervals are essentially meaningless. The use of an informative prior distribution accounting for pre-knowledge of M is also of little use, because the prior is only modified in the case of the occurrence of an extreme event. Our results suggest that the maximum possible magnitude M should be better replaced by M(T), the maximum expected magnitude in a given time interval T, for which the calculation of exact confidence intervals becomes straightforward. From a physical point of view, numerical models of the earthquake process adjusted to specific fault regions may be a powerful alternative to overcome the shortcomings of purely statistical inference.
Y1  - 2011
U6  - https://doi.org/10.1785/0120100289
SN  - 0037-1106
VL  - 101
IS  - 4
SP  - 1649
EP  - 1659
PB  - Seismological Society of America
CY  - El Cerrito
ER  - 
TY  - JOUR
A1  - Flad, Heinz-Jürgen
A1  - Harutyunyan, Gohar
A1  - Schneider, Reinhold
A1  - Schulze, Bert-Wolfgang
T1  - Explicit Green operators for quantum mechanical Hamiltonians
BT  - I. The hydrogen atom
JF  - Manuscripta mathematica
N2  - We study a new approach to determine the asymptotic behaviour of quantum many-particle systems near coalescence points of particles which interact via singular Coulomb potentials. This problem is of fundamental interest in electronic structure theory in order to establish accurate and efficient models for numerical simulations. Within our approach, coalescence points of particles are treated as embedded geometric singularities in the configuration space of electrons. Based on a general singular pseudo-differential calculus, we provide a recursive scheme for the calculation of the parametrix and corresponding Green operator of a nonrelativistic Hamiltonian. In our singular calculus, the Green operator encodes all the asymptotic information of the eigenfunctions. Explicit calculations and an asymptotic representation for the Green operator of the hydrogen atom and isoelectronic ions are presented.
Y1  - 2011
U6  - https://doi.org/10.1007/s00229-011-0429-x
SN  - 0025-2611
VL  - 135
IS  - 3-4
SP  - 497
EP  - 519
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Lamm, Tobias
A1  - Metzger, Jan
A1  - Schulze, Felix
T1  - Foliations of asymptotically flat manifolds by surfaces of Willmore type
JF  - Mathematische Annalen
N2  - The goal of this paper is to establish the existence of a foliation of the asymptotic region of an asymptotically flat manifold with positive mass by surfaces which are critical points of the Willmore functional subject to an area constraint. Equivalently these surfaces are critical points of the Geroch-Hawking mass. Thus our result has applications in the theory of general relativity.
Y1  - 2011
U6  - https://doi.org/10.1007/s00208-010-0550-2
SN  - 0025-5831
VL  - 350
IS  - 1
SP  - 1
EP  - 78
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Glebov, Sergei
A1  - Kiselev, Oleg
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Forced nonlinear resonance in a system of coupled oscillators
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time t similar to s(-2) one component of the system is described for the most part by the inhomogeneous Mathieu equation while the other component represents pulsation of large amplitude. A Hamiltonian system is obtained which describes for the most part the behavior of the envelope in a special case. The analytic results agree with numerical simulations.
Y1  - 2011
U6  - https://doi.org/10.1063/1.3578047
SN  - 1054-1500
VL  - 21
IS  - 2
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Schmidt, Hans-Jürgen
T1  - Gauss-Bonnet Lagrangian G ln G and cosmological exact solutions
N2  - For the Lagrangian L = G ln G where G is the Gauss-Bonnet curvature scalar we deduce the field equation and solve it in closed form for 3-flat Friedman models using a statefinder parametrization. Further we show, that among all lagrangians F(G) this L is the only one not having the form G^r with a real constant r but possessing a scale-invariant field equation. This turns out to be one of its analogies to f(R)-theories in 2-dimensional space-time. In the appendix, we systematically list several formulas for the decomposition of the Riemann tensor in arbitrary dimensions n, which are applied in the main deduction for n=4.
Y1  - 2011
UR  - http://arxiv.org/pdf/1102.0241v2
SN  - 1550-7998
ER  - 
TY  - JOUR
A1  - Pilari, Sabine
A1  - Preusse, Cornelia
A1  - Huisinga, Wilhelm
T1  - Gestational influences on the pharmacokinetics of gestagenic drugs a combined in silico, in vitro and in vivo analysis
JF  - European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences, EUFEPS
N2  - During preclinical development of a gestagenic drug, a significant increase of the total plasma concentration was observed after multiple dosing in pregnant rabbits, but not in (non-pregnant) rats or monkeys. We used a PBPK modeling approach in combination with in vitro and in vivo data to address the question to what extent the pharmacologically active free drug concentration is affected by pregnancy induced processes. In human, a significant increase in sex hormone binding globulin (SHBG), and an induction of hepatic CYP3A4 as well as plasma esterases is observed during pregnancy. We find that the observed increase in total plasma trough levels in rabbits can be explained as a combined result of (i) drug accumulation due to multiple dosing, (ii) increase of the binding protein SHBG, and (iii) clearance induction. For human, we predict that free drug concentrations in plasma would not increase during pregnancy above the steady state trough level for non-pregnant women.
KW  - PBPK
KW  - Pregnancy
KW  - Gestagenic drug
KW  - Protein binding
KW  - SHBG
KW  - Clearance induction
Y1  - 2011
U6  - https://doi.org/10.1016/j.ejps.2010.12.003
SN  - 0928-0987
VL  - 42
IS  - 4
SP  - 318
EP  - 331
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Förster, M.
A1  - Namgaladze, Alexander A.
A1  - Doronina, E. N.
A1  - Prokhorov, Boris E.
T1  - High-latitude thermospheric winds: Satellite data and model calculations
JF  - Russian journal of physical chemistry : B, Focus on physics
N2  - The thermospheric crosswind velocities at an altitude of 400 km measured by an accelerometer on board of the CHAMP satellite are compared with the results of model calculations performed using the Upper Atmosphere Model (UAM). The results of measurements averaged over the year in 2003 reveal a two-vortex structure of high-latitude winds corresponding to magnetospheric-ionospheric convection of ions in the F2 ionosphere region. A similar picture with similar speed values was obtained in model calculations. A comparison of the crosswind speed obtained in individual measurements on October 28, 2003 with the corresponding model values revealed close agreement between them in some flights and differences in others. Taking into account the dependence of convection electric field on the B (y) component of interplanetary magnetic field sometimes improved agreement between thermospheric crosswind speeds obtained in model calculations and measured using the satellite.
KW  - CHAMP satellite
KW  - upper atmosphere model
KW  - thermospheric wind
KW  - ionospheric convection
Y1  - 2011
U6  - https://doi.org/10.1134/S1990793111030043
SN  - 1990-7931
VL  - 5
IS  - 3
SP  - 439
EP  - 446
PB  - Pleiades Publ.
CY  - New York
ER  - 
TY  - JOUR
A1  - von Kleist, Max
A1  - Menz, Stephan
A1  - Stocker, Hartmut
A1  - Arasteh, Keikawus
A1  - Schuette, Christof
A1  - Huisinga, Wilhelm
T1  - HIV quasispecies dynamics during pro-active treatment switching impact on multi-drug resistance and resistance archiving in latent reservoirs
JF  - PLoS one
N2  - The human immunodeficiency virus (HIV) can be suppressed by highly active anti-retroviral therapy (HAART) in the majority of infected patients. Nevertheless, treatment interruptions inevitably result in viral rebounds from persistent, latently infected cells, necessitating lifelong treatment. Virological failure due to resistance development is a frequent event and the major threat to treatment success. Currently, it is recommended to change treatment after the confirmation of virological failure. However, at the moment virological failure is detected, drug resistant mutants already replicate in great numbers. They infect numerous cells, many of which will turn into latently infected cells. This pool of cells represents an archive of resistance, which has the potential of limiting future treatment options. The objective of this study was to design a treatment strategy for treatment-naive patients that decreases the likelihood of early treatment failure and preserves future treatment options. We propose to apply a single, pro-active treatment switch, following a period of treatment with an induction regimen. The main goal of the induction regimen is to decrease the abundance of randomly generated mutants that confer resistance to the maintenance regimen, thereby increasing subsequent treatment success. Treatment is switched before the overgrowth and archiving of mutant strains that carry resistance against the induction regimen and would limit its future re-use. In silico modelling shows that an optimal trade-off is achieved by switching treatment at & 80 days after the initiation of antiviral therapy. Evaluation of the proposed treatment strategy demonstrated significant improvements in terms of resistance archiving and virological response, as compared to conventional HAART. While continuous pro-active treatment alternation improved the clinical outcome in a randomized trial, our results indicate that a similar improvement might also be reached after a single pro-active treatment switch. The clinical validity of this finding, however, remains to be shown by a corresponding trial.
Y1  - 2011
U6  - https://doi.org/10.1371/journal.pone.0018204
SN  - 1932-6203
VL  - 6
IS  - 3
PB  - PLoS
CY  - San Fransisco
ER  - 
TY  - BOOK
A1  - Blanchard, Gilles
T1  - Komplexitätsanalyse in Statistik und Lerntheorie : Antrittsvorlesung 2011-05-04
N2  - Gilles Blanchards Vortrag gewährt Einblicke in seine Arbeiten zur Entwicklung und Analyse statistischer Eigenschaften von Lernalgorithmen. In vielen modernen Anwendungen, beispielsweise bei der Schrifterkennung oder dem Spam- Filtering, kann ein Computerprogramm auf der Basis vorgegebener Beispiele automatisch lernen, relevante Vorhersagen für weitere Fälle zu treffen. Mit der mathematischen Analyse der Eigenschaften solcher Methoden beschäftigt sich die Lerntheorie, die mit der Statistik eng zusammenhängt. Dabei spielt der Begriff der Komplexität der erlernten Vorhersageregel eine wichtige Rolle. Ist die Regel zu einfach, wird sie wichtige Einzelheiten ignorieren. Ist sie zu komplex, wird sie die vorgegebenen Beispiele "auswendig" lernen und keine Verallgemeinerungskraft haben. Blanchard wird erläutern, wie Mathematische Werkzeuge dabei helfen, den richtigen Kompromiss zwischen diesen beiden Extremen zu finden.
Y1  - 2011
UR  - http://info.ub.uni-potsdam.de/multimedia/show_multimediafile.php?mediafile_id=551
PB  - Univ.-Bibl.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Böckmann, Christine
A1  - Kammanee, Athassawat
A1  - Braunss, Andreas
T1  - Logarithmic convergence rate of Levenberg-Marquardt method with application to an inverse potential problem
JF  - Journal of inverse and ill-posed problems
N2  - We prove logarithmic convergence rate of the Levenberg-Marquardt method in a Hilbert space if a logarithmic source condition is satisfied. This method is applied to an inverse potential problem. Numerical implementations demonstrate the convergence rate.
KW  - Levenberg-Marquardt method
KW  - inverse potential problems
KW  - logarithmic convergence rate
KW  - discrepancy principle
KW  - logarithmic source condition
Y1  - 2011
U6  - https://doi.org/10.1515/JIIP.2011.034
SN  - 0928-0219
VL  - 19
IS  - 3
SP  - 345
EP  - 367
PB  - De Gruyter
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Roul, Pradip
T1  - Numerical solutions of time fractional degenerate parabolic equations by variational iteration method with Jumarie-modified Riemann-Liouville derivative
JF  - Mathematical methods in the applied sciences
N2  - In this article, the fractional variational iteration method is employed for computing the approximate analytical solutions of degenerate parabolic equations with fractional time derivative. The time-fractional derivatives are described by the use of a new approach, the so-called Jumarie modified Riemann-Liouville derivative, instead in the sense of Caputo. The approximate solutions of our model problem are calculated in the form of convergent series with easily computable components. Moreover, the numerical solution is compared with the exact solution and the quantitative estimate of accuracy is obtained. The results of the study reveal that the proposed method with modified fractional Riemann-Liouville derivatives is efficient, accurate, and convenient for solving the fractional partial differential equations in multi-dimensional spaces without using any linearization, perturbation or restrictive assumptions.
KW  - variational iteration method
KW  - biological population equations
KW  - fractional calculus
KW  - exact solution
KW  - Mittag-Leffler function
Y1  - 2011
U6  - https://doi.org/10.1002/mma.1418
SN  - 0170-4214
VL  - 34
IS  - 9
SP  - 1025
EP  - 1035
PB  - Wiley-Blackwell
CY  - Malden
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On the maximal regular subsemigroups of ideals of order-preserving or order-reversing transformations
JF  - Semigroup forum
N2  - We characterize the maximal regular subsemigroups of the ideals of the semigroup of all order-preserving transformations as well as of the semigroup of all order-preserving or order-reversing transformations on a finite ordered set.
KW  - Transformation semigroups
KW  - Regular semigroups
KW  - Order-preserving transformations
KW  - Order-reversing transformations
KW  - Maximal subsemigroups
Y1  - 2011
U6  - https://doi.org/10.1007/s00233-010-9272-8
SN  - 0037-1912
VL  - 82
IS  - 1
SP  - 172
EP  - 180
PB  - Springer
CY  - New York
ER  - 
TY  - BOOK
A1  - Keller, Peter
A1  - Roelly, Sylvie
A1  - Valleriana, Angelo
T1  - On Time Duality for Markov Chains with Asborbing Boundardies
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Mathematische Statistik un
Y1  - 2011
SN  - 1613-3307
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Enders, Jörg
A1  - Müller, Reto
A1  - Topping, Peter M.
T1  - On Type-I singularities in Ricci flow
JF  - Communications in analysis and geometry
N2  - We define several notions of singular set for Type-I Ricci flows and show that they all coincide. In order to do this, we prove that blow-ups around singular points converge to nontrivial gradient shrinking solitons, thus extending work of Naber [15]. As a by-product we conclude that the volume of a finite-volume singular set vanishes at the singular time.
 We also define a notion of density for Type-I Ricci flows and use it to prove a regularity theorem reminiscent of White's partial regularity result for mean curvature flow [22].
Y1  - 2011
SN  - 1019-8385
VL  - 19
IS  - 5
SP  - 905
EP  - 922
PB  - International Press of Boston
CY  - Somerville
ER  - 
TY  - JOUR
A1  - Schmidt, Hans-Jürgen
T1  - Perihelion advance for orbits with large eccentricities in the Schwarzschild black hole
N2  - We deduce a new formula for the perihelion advance $Theta$ of a test particle in the Schwarzschild black hole by applying a newly developed non-linear transformation within the Schwarzschild space-time. By this transformation we are able to apply the well-known formula valid in the weak-field approximation near infinity also to trajectories in the strong-field regime near the horizon of the black hole. The resulting formula has the structure $Theta = c_1 - c_2 ln(c^2_3 - e^2) $ with positive constants $c_{1,2,3}$ depending on the angular momentum of the test particle. It is especially useful for orbits with large eccentricities $e < c_3 < 1$ showing that $Theta 	o infty$ as $e 	o c_3$.
Y1  - 2011
UR  - http://link.aps.org/doi/10.1103/PhysRevD.83.124010
SN  - 1550-7998
ER  - 
TY  - JOUR
A1  - Ramadan, Ayad M.
T1  - Range of lower bounds
JF  - Applied mathematics and computation
N2  - Each of n jobs is to be processed without interruption on a single machine. Each job becomes available for processing at time zero. The objective is to find a processing order of the jobs which minimizes the sum of weighted completion times added with maximum weighted tardiness. In this paper we give a general case of the theorem that given in [6]. This theorem shows a relation between the number of efficient solutions, lower bound LB and optimal solution. It restricts the range of the lower bound, which is the main factor to find the optimal solution. Also, the theorem opens algebraic operations and concepts to find new lower bounds.
KW  - Lower bound
KW  - Multi objective function
KW  - Efficient solutions
Y1  - 2011
U6  - https://doi.org/10.1016/j.amc.2011.03.066
SN  - 0096-3003
VL  - 218
IS  - 3
SP  - 1008
EP  - 1011
PB  - Elsevier
CY  - New York
ER  - 
TY  - JOUR
A1  - Gaci, Said
A1  - Zaourar, Naima
A1  - Briqueu, Louis
A1  - Holschneider, Matthias
T1  - Regularity analysis applied to sonic logs data a case study from KTB borehole site
JF  - Arabian journal of geosciences
N2  - Borehole logs provide in situ information about the fluctuations of petrophysical properties with depth and thus allow the characterization of the crustal heterogeneities. A detailed investigation of these measurements may lead to extract features of the geological media. In this study, we suggest a regularity analysis based on the continuous wavelet transform to examine sonic logs data. The description of the local behavior of the logs at each depth is carried out using the local Hurst exponent estimated by two (02) approaches: the local wavelet approach and the average-local wavelet approach. Firstly, a synthetic log, generated using the random midpoints displacement algorithm, is processed by the regularity analysis. The obtained Hurst curves allowed the discernment of the different layers composing the simulated geological model. Next, this analysis is extended to real sonic logs data recorded at the Kontinentales Tiefbohrprogramm (KTB) pilot borehole (Continental Deep Drilling Program, Germany). The results show a significant correlation between the estimated Hurst exponents and the lithological discontinuities crossed by the well. Hence, the Hurst exponent can be used as a tool to characterize underground heterogeneities.
KW  - Regularity analysis
KW  - Wavelet transform
KW  - Well log
KW  - Fractal
KW  - Lithology
Y1  - 2011
U6  - https://doi.org/10.1007/s12517-010-0129-y
SN  - 1866-7511
VL  - 4
IS  - 1-2
SP  - 221
EP  - 227
PB  - Springer
CY  - Heidelberg
ER  - 
TY  - JOUR
A1  - Elin, Mark
A1  - Shoikhet, David
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Separation of boundary singularities for holomorphic generators
JF  - Annali di matematica pura ed applicata
N2  - We prove a theorem on separation of boundary null points for generators of continuous semigroups of holomorphic self-mappings of the unit disk in the complex plane. Our construction demonstrates rather strikingly the particular role of the binary operation au broken vertical bar given by 1/ f au broken vertical bar g = 1/f + 1/g on generators.
KW  - Semigroup
KW  - Holomorphic map
KW  - Unit disk
KW  - Angular derivatives
Y1  - 2011
U6  - https://doi.org/10.1007/s10231-010-0165-y
SN  - 0373-3114
VL  - 190
IS  - 4
SP  - 595
EP  - 618
PB  - Springer
CY  - Heidelberg
ER  - 
TY  - JOUR
A1  - Roul, Pradip
A1  - Schinner, Alexander
A1  - Kassner, Klaus
T1  - Simulation of the strain distribution under a two-dimensional sand pile
JF  - Powder technology : an international journal on the science and technology of wet and dry particulate systems
N2  - We study the averaged macroscopic strain tensor for a sand pile consisting of soft convex polygonal particles numerically, using the discrete-element method (DEM). First, we construct two types of "sand piles" by two different pouring protocols. Afterwards, we deform the sand piles, relaxing them under a 10% reduction of gravity. Four different types of methods, three best-fit strains and a derivative strain, are adopted for determining the strain distribution under a sand pile. The results of four different versions of strains obtained from DEM simulation are compared with each other. Moreover, we compare the vertical normal strain tensor between two types of sand piles qualitatively and show how the construction history of the piles affects their strain distribution.
KW  - Numerical simulation
KW  - Sand pile
KW  - Stress
KW  - Strain
KW  - Granular matter
KW  - Discrete-element method
Y1  - 2011
U6  - https://doi.org/10.1016/j.powtec.2011.08.039
SN  - 0032-5910
VL  - 214
IS  - 3
SP  - 406
EP  - 414
PB  - Elsevier
CY  - Lausanne
ER  - 
TY  - BOOK
ED  - Blath, Jochen
ED  - Imkeller, Peter
ED  - Roelly, Sylvie
T1  - Surveys in stochastic processes
Y1  - 2011
SN  - 978-3-03719-072-2
PB  - European Mathematical Society
CY  - Zürich
ER  - 
TY  - JOUR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - The dirichlet to Neumann operator for elliptic complexes
JF  - Transactions of the American Mathematical Society
N2  - We define the Dirichlet to Neumann operator for an elliptic complex of first order differential operators on a compact Riemannian manifold with boundary. Under reasonable conditions the Betti numbers of the complex prove to be completely determined by the Dirichlet to Neumann operator on the boundary.
KW  - Elliptic complexes
KW  - Dirichlet to Neumann operator
KW  - inverse problems
Y1  - 2011
SN  - 0002-9947
VL  - 363
IS  - 12
SP  - 6421
EP  - 6437
PB  - American Mathematical Soc.
CY  - Providence
ER  - 
TY  - JOUR
A1  - Pfäffle, Frank
A1  - Stephan, Christoph A.
T1  - The holst action by the spectral action principle
JF  - Communications in mathematical physics
N2  - We investigate the Holst action for closed Riemannian 4-manifolds with orthogonal connections. For connections whose torsion has zero Cartan type component we show that the Holst action can be recovered from the heat asymptotics for the natural Dirac operator acting on left-handed spinor fields.
Y1  - 2011
U6  - https://doi.org/10.1007/s00220-011-1303-0
SN  - 0010-3616
VL  - 307
IS  - 1
SP  - 261
EP  - 273
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Nehring, Benjamin
A1  - Zessin, Hans
T1  - The Papangelou process a concept for gibbs, fermi and bose processes
JF  - Journal of contemporary mathematical analysis
N2  - This note is a revised and enlarged version of the german article [16] in a slightly different framework. We here correct a serious mistake in the first version and generalize the class of Polya sum processes considered there. (A corrected version of the same results can be found already in the thesis of Mathias Rafler [12].) Moreover, the class of Polya difference processes is constructed here for the first time. In analogy to classical statistical mechanics we propose a theory of interacting Bosons and Fermions. We consider Papangelou processes. These are point processes specified by some kernel which represents the conditional intensity of the process. The main result is a general construction of a large class of such processes which contains Cox, Gibbs processes of classical statistical mechanics, but also interacting Bose and Fermi processes.
KW  - Papangelou process
KW  - Polya sum
KW  - Polya difference process
Y1  - 2011
U6  - https://doi.org/10.3103/S1068362311060069
SN  - 1068-3623
VL  - 46
IS  - 6
SP  - 326
EP  - 337
PB  - Allerton
CY  - New York
ER  - 
TY  - THES
A1  - Hanisch, Florian
T1  - Variational problems on supermanifolds
T1  - Variationsprobleme auf Supermannigfaltigkeiten
N2  - In this thesis, we discuss the formulation of variational problems on supermanifolds. Supermanifolds incorporate bosonic as well as fermionic degrees of freedom. Fermionic fields take values in the odd part of an appropriate Grassmann algebra and are thus showing an anticommutative behaviour. However, a systematic treatment of these Grassmann parameters requires a description of spaces as functors, e.g. from the category of Grassmann algberas into the category of sets (or topological spaces, manifolds). After an introduction to the general ideas of this approach, we use it to give a description of the resulting supermanifolds of fields/maps. We show that each map is uniquely characterized by a family of differential operators of appropriate order. Moreover, we demonstrate that each of this maps is uniquely characterized by its component fields, i.e. by the coefficients in a Taylor expansion w.r.t. the odd coordinates. In general, the component fields are only locally defined. We present a way how to circumvent this limitation. In fact, by enlarging the supermanifold in question, we show that it is possible to work with globally defined components. We eventually use this formalism to study variational problems. More precisely, we study a super version of the geodesic and a generalization of harmonic maps to supermanifolds. Equations of motion are derived from an energy functional and we show how to decompose them into components. Finally, in special cases, we can prove the existence of critical points by reducing the problem to equations from ordinary geometric analysis. After solving these component equations, it is possible to show that their solutions give rise to critical points in the functor spaces of fields.
N2  - In dieser Dissertation wird die Formulierung von Variationsproblemen auf Supermannigfaltigkeiten diskutiert. Supermannigfaltigkeiten enthalten sowohl bosonische als auch fermionische Freiheitsgrade. Fermionische Felder nehmen Werte im ungeraden Teil einer Grassmannalgebra an, sie antikommutieren deshalb untereinander. Eine systematische Behandlung dieser Grassmann-Parameter erfordert jedoch die Beschreibung von Räumen durch Funktoren, z.B. von der Kategorie der Grassmannalgebren in diejenige der Mengen (der topologischen Räume, Mannigfaltigkeiten, ...). Nach einer Einführung in das allgemeine Konzept dieses Zugangs verwenden wir es um eine Beschreibung der resultierenden Supermannigfaltigkeit der Felder bzw. Abbildungen anzugeben. Wir zeigen, dass jede Abbildung eindeutig durch eine Familie von Differentialoperatoren geeigneter Ordnung charakterisiert wird. Darüber hinaus beweisen wir, dass jede solche Abbildung eineindeutig durch ihre Komponentenfelder, d.h. durch die Koeffizienten einer Taylorentwickelung bzgl. von ungeraden Koordinaten bestimmt ist. Im Allgemeinen sind Komponentenfelder nur lokal definiert. Wir stellen einen Weg vor, der diese Einschränkung umgeht: Durch das Vergrößern der betreffenden Supermannigfaltigkeit ist es immer möglich, mit globalen Koordinaten zu arbeiten. Schließlich wenden wir diesen Formalismus an, um Variationsprobleme zu untersuchen, genauer betrachten wir eine super-Version der Geodäte und eine Verallgemeinerung von harmonischen Abbildungen auf Supermannigfaltigkeiten. Bewegungsgleichungen werden von Energiefunktionalen abgeleitet und wir zeigen, wie sie sich in Komponenten zerlegen lassen. Schließlich kann in Spezialfällen die Existenz von kritischen Punkten gezeigt werden, indem das Problem auf Gleichungen der gewöhnlichen geometrischen Analysis reduziert wird. Es kann dann gezeigt werden, dass die Lösungen dieser Gleichungen sich zu kritischen Punkten im betreffenden Funktor-Raum der Felder zusammensetzt.
KW  - Supergeometrie
KW  - Variationsrechnung
KW  - Differentialoperatoren
KW  - Funktorgeometrie
KW  - supergeometry
KW  - variational calculus
KW  - differential operators
KW  - functor geometry
Y1  - 2011
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59757
ER  - 
TY  - JOUR
A1  - Zolotov, O. V.
A1  - Prokhorov, Boris E.
A1  - Namgaladze, Alexander A.
A1  - Martynenko, O. V.
T1  - Variations in the total electron content of the ionosphere during preparation of earthquakes
JF  - Russian journal of physical chemistry : B, Focus on physics
N2  - The morphological features in the deviations of the total electron content (TEC) of the ionosphere from the background undisturbed state as possible precursors of the earthquake of January 12, 2010 (21:53 UT (16:53 LT), 18.46A degrees N, 72.5A degrees W, 7.0 M) in Haiti are analyzed. To identify these features, global and regional differential TEC maps based on global 2-h TEC maps provided by NASA in the IONEX format were plotted. For the considered earthquake, long-lived disturbances, presumably of seismic origin, were localized in the near-epicenter area and were accompanied by similar effects in the magnetoconjugate region. Both decreases and increases in the local TEC over the period from 22 UT of January 10 to 08 UT of January 12, 2010 were observed. The horizontal dimensions of the anomalies were similar to 40A degrees in longitude and similar to 20A degrees in latitude, with the magnitude of TEC disturbances reaching similar to 40% relative to the background near the epicenter and more than 50% in the magnetoconjugate area. No significant geomagnetic disturbances within January 1-12, 2010 were observed, i.e., the detected TEC anomalies were manifestations of interplay between processes in the lithosphere-atmosphere-ionosphere system.
KW  - TEC
KW  - ionospheric precursors of earthquakes
KW  - GPS
Y1  - 2011
U6  - https://doi.org/10.1134/S1990793111030146
SN  - 1990-7931
VL  - 5
IS  - 3
SP  - 435
EP  - 438
PB  - Pleiades Publ.
CY  - New York
ER  -