@article{DimitrovaKoppitz2011, author = {Dimitrova, Ilinka and Koppitz, J{\"o}rg}, title = {On the maximal regular subsemigroups of ideals of order-preserving or order-reversing transformations}, series = {Semigroup forum}, volume = {82}, journal = {Semigroup forum}, number = {1}, publisher = {Springer}, address = {New York}, issn = {0037-1912}, doi = {10.1007/s00233-010-9272-8}, pages = {172 -- 180}, year = {2011}, abstract = {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.}, language = {en} } @article{KleinRosenberger2011, author = {Klein, Markus and Rosenberger, Elke}, title = {Asymptotic eigenfunctions for a class of difference operators}, series = {Asymptotic analysis}, volume = {73}, journal = {Asymptotic analysis}, number = {1-2}, publisher = {IOS Press}, address = {Amsterdam}, issn = {0921-7134}, doi = {10.3233/ASY-2010-1025}, pages = {1 -- 36}, year = {2011}, abstract = {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).}, language = {en} } @article{GaciZaourarBriqueuetal.2011, author = {Gaci, Said and Zaourar, Naima and Briqueu, Louis and Holschneider, Matthias}, title = {Regularity analysis applied to sonic logs data a case study from KTB borehole site}, series = {Arabian journal of geosciences}, volume = {4}, journal = {Arabian journal of geosciences}, number = {1-2}, publisher = {Springer}, address = {Heidelberg}, issn = {1866-7511}, doi = {10.1007/s12517-010-0129-y}, pages = {221 -- 227}, year = {2011}, abstract = {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.}, language = {en} } @article{Reich2011, author = {Reich, Sebastian}, title = {A dynamical systems framework for intermittent data assimilation}, series = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians}, volume = {51}, journal = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians}, number = {1}, publisher = {Springer}, address = {Dordrecht}, issn = {0006-3835}, doi = {10.1007/s10543-010-0302-4}, pages = {235 -- 249}, year = {2011}, abstract = {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.}, language = {en} } @article{PilariPreusseHuisinga2011, author = {Pilari, Sabine and Preusse, Cornelia and Huisinga, Wilhelm}, title = {Gestational influences on the pharmacokinetics of gestagenic drugs a combined in silico, in vitro and in vivo analysis}, series = {European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences, EUFEPS}, volume = {42}, journal = {European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences, EUFEPS}, number = {4}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0928-0987}, doi = {10.1016/j.ejps.2010.12.003}, pages = {318 -- 331}, year = {2011}, abstract = {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.}, language = {en} } @article{vonKleistMenzStockeretal.2011, author = {von Kleist, Max and Menz, Stephan and Stocker, Hartmut and Arasteh, Keikawus and Schuette, Christof and Huisinga, Wilhelm}, title = {HIV quasispecies dynamics during pro-active treatment switching impact on multi-drug resistance and resistance archiving in latent reservoirs}, series = {PLoS one}, volume = {6}, journal = {PLoS one}, number = {3}, publisher = {PLoS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0018204}, pages = {12}, year = {2011}, abstract = {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.}, language = {en} } @article{DebusscheHoegeleImkeller2011, author = {Debussche, Arnaud and H{\"o}gele, Michael and Imkeller, Peter}, title = {Asymptotic first exit times of the chafee-infante equation with small heavy-tailed levy noise}, series = {Electronic communications in probability}, volume = {16}, journal = {Electronic communications in probability}, number = {3-4}, publisher = {Univ. of Washington, Mathematics Dep.}, address = {Seattle}, issn = {1083-589X}, pages = {213 -- 225}, year = {2011}, abstract = {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.}, language = {en} } @article{LammMetzgerSchulze2011, author = {Lamm, Tobias and Metzger, Jan and Schulze, Felix}, title = {Foliations of asymptotically flat manifolds by surfaces of Willmore type}, series = {Mathematische Annalen}, volume = {350}, journal = {Mathematische Annalen}, number = {1}, publisher = {Springer}, address = {New York}, issn = {0025-5831}, doi = {10.1007/s00208-010-0550-2}, pages = {1 -- 78}, year = {2011}, abstract = {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.}, language = {en} } @article{Roul2011, author = {Roul, Pradip}, title = {Numerical solutions of time fractional degenerate parabolic equations by variational iteration method with Jumarie-modified Riemann-Liouville derivative}, series = {Mathematical methods in the applied sciences}, volume = {34}, journal = {Mathematical methods in the applied sciences}, number = {9}, publisher = {Wiley-Blackwell}, address = {Malden}, issn = {0170-4214}, doi = {10.1002/mma.1418}, pages = {1025 -- 1035}, year = {2011}, abstract = {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.}, language = {en} } @article{GlebovKiselevTarkhanov2011, author = {Glebov, Sergei and Kiselev, Oleg and Tarkhanov, Nikolai Nikolaevich}, title = {Forced nonlinear resonance in a system of coupled oscillators}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {21}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {2}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.3578047}, pages = {7}, year = {2011}, abstract = {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.}, language = {en} } @article{FoersterNamgaladzeDoroninaetal.2011, author = {F{\"o}rster, M. and Namgaladze, Alexander A. and Doronina, E. N. and Prokhorov, Boris E.}, title = {High-latitude thermospheric winds: Satellite data and model calculations}, series = {Russian journal of physical chemistry : B, Focus on physics}, volume = {5}, journal = {Russian journal of physical chemistry : B, Focus on physics}, number = {3}, publisher = {Pleiades Publ.}, address = {New York}, issn = {1990-7931}, doi = {10.1134/S1990793111030043}, pages = {439 -- 446}, year = {2011}, abstract = {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.}, language = {en} } @article{ZolotovProkhorovNamgaladzeetal.2011, author = {Zolotov, O. V. and Prokhorov, Boris E. and Namgaladze, Alexander A. and Martynenko, O. V.}, title = {Variations in the total electron content of the ionosphere during preparation of earthquakes}, series = {Russian journal of physical chemistry : B, Focus on physics}, volume = {5}, journal = {Russian journal of physical chemistry : B, Focus on physics}, number = {3}, publisher = {Pleiades Publ.}, address = {New York}, issn = {1990-7931}, doi = {10.1134/S1990793111030146}, pages = {435 -- 438}, year = {2011}, abstract = {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.}, language = {en} } @article{FladHarutyunyanSchneideretal.2011, author = {Flad, Heinz-J{\"u}rgen and Harutyunyan, Gohar and Schneider, Reinhold and Schulze, Bert-Wolfgang}, title = {Explicit Green operators for quantum mechanical Hamiltonians}, series = {Manuscripta mathematica}, volume = {135}, journal = {Manuscripta mathematica}, number = {3-4}, publisher = {Springer}, address = {New York}, issn = {0025-2611}, doi = {10.1007/s00229-011-0429-x}, pages = {497 -- 519}, year = {2011}, abstract = {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.}, language = {en} } @article{WeissHuisinga2011, author = {Weiss, Andrea Y. and Huisinga, Wilhelm}, title = {Error-controlled global sensitivity analysis of ordinary differential equations}, series = {Journal of computational physics}, volume = {230}, journal = {Journal of computational physics}, number = {17}, publisher = {Elsevier}, address = {San Diego}, issn = {0021-9991}, doi = {10.1016/j.jcp.2011.05.011}, pages = {6824 -- 6842}, year = {2011}, abstract = {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.}, language = {en} } @article{BoeckmannKammaneeBraunss2011, author = {B{\"o}ckmann, Christine and Kammanee, Athassawat and Braunss, Andreas}, title = {Logarithmic convergence rate of Levenberg-Marquardt method with application to an inverse potential problem}, series = {Journal of inverse and ill-posed problems}, volume = {19}, journal = {Journal of inverse and ill-posed problems}, number = {3}, publisher = {De Gruyter}, address = {Berlin}, issn = {0928-0219}, doi = {10.1515/JIIP.2011.034}, pages = {345 -- 367}, year = {2011}, abstract = {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.}, language = {en} } @article{HolschneiderZoellerHainzl2011, author = {Holschneider, Matthias and Z{\"o}ller, Gert and Hainzl, Sebastian}, title = {Estimation of the maximum possible magnitude in the framework of a doubly truncated Gutenberg-Richter Model}, series = {Bulletin of the Seismological Society of America}, volume = {101}, journal = {Bulletin of the Seismological Society of America}, number = {4}, publisher = {Seismological Society of America}, address = {El Cerrito}, issn = {0037-1106}, doi = {10.1785/0120100289}, pages = {1649 -- 1659}, year = {2011}, abstract = {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.}, language = {en} } @article{GottwaldMitchellReich2011, author = {Gottwald, Georg A. and Mitchell, Lewis and Reich, Sebastian}, title = {Controlling overestimation of error covariance in ensemble kalman filters with sparse observations a variance-limiting kalman filter}, series = {Monthly weather review}, volume = {139}, journal = {Monthly weather review}, number = {8}, publisher = {American Meteorological Soc.}, address = {Boston}, issn = {0027-0644}, doi = {10.1175/2011MWR3557.1}, pages = {2650 -- 2667}, year = {2011}, abstract = {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.}, language = {en} } @article{ShinZoellerHolschneideretal.2011, author = {Shin, Seoleun and Z{\"o}ller, Gert and Holschneider, Matthias and Reich, Sebastian}, title = {A multigrid solver for modeling complex interseismic stress fields}, series = {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}, volume = {37}, journal = {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}, number = {8}, publisher = {Elsevier}, address = {Oxford}, issn = {0098-3004}, doi = {10.1016/j.cageo.2010.11.011}, pages = {1075 -- 1082}, year = {2011}, abstract = {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.}, language = {en} } @article{BoeckmannKammanee2011, author = {B{\"o}ckmann, Christine and Kammanee, Athassawat}, title = {Broyden method for inverse non-symmetric Sturm-Liouville problems}, series = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians}, volume = {51}, journal = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians}, number = {3}, publisher = {Springer}, address = {Dordrecht}, issn = {0006-3835}, doi = {10.1007/s10543-011-0317-5}, pages = {513 -- 528}, year = {2011}, abstract = {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.}, language = {en} } @article{PfaeffleStephan2011, author = {Pf{\"a}ffle, Frank and Stephan, Christoph A.}, title = {The holst action by the spectral action principle}, series = {Communications in mathematical physics}, volume = {307}, journal = {Communications in mathematical physics}, number = {1}, publisher = {Springer}, address = {New York}, issn = {0010-3616}, doi = {10.1007/s00220-011-1303-0}, pages = {261 -- 273}, year = {2011}, abstract = {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.}, language = {en} } @article{Ramadan2011, author = {Ramadan, Ayad M.}, title = {Range of lower bounds}, series = {Applied mathematics and computation}, volume = {218}, journal = {Applied mathematics and computation}, number = {3}, publisher = {Elsevier}, address = {New York}, issn = {0096-3003}, doi = {10.1016/j.amc.2011.03.066}, pages = {1008 -- 1011}, year = {2011}, abstract = {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.}, language = {en} } @article{SkeelReich2011, author = {Skeel, R. D. and Reich, Sebastian}, title = {Corrected potential energy functions for constrained molecular dynamics}, series = {European physical journal special topics}, volume = {200}, journal = {European physical journal special topics}, number = {1}, publisher = {Springer}, address = {Heidelberg}, issn = {1951-6355}, doi = {10.1140/epjst/e2011-01518-8}, pages = {55 -- 72}, year = {2011}, abstract = {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.}, language = {en} } @article{Tarkhanov2011, author = {Tarkhanov, Nikolai Nikolaevich}, title = {The dirichlet to Neumann operator for elliptic complexes}, series = {Transactions of the American Mathematical Society}, volume = {363}, journal = {Transactions of the American Mathematical Society}, number = {12}, publisher = {American Mathematical Soc.}, address = {Providence}, issn = {0002-9947}, pages = {6421 -- 6437}, year = {2011}, abstract = {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.}, language = {en} } @article{ElinShoikhetTarkhanov2011, author = {Elin, Mark and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich}, title = {Separation of boundary singularities for holomorphic generators}, series = {Annali di matematica pura ed applicata}, volume = {190}, journal = {Annali di matematica pura ed applicata}, number = {4}, publisher = {Springer}, address = {Heidelberg}, issn = {0373-3114}, doi = {10.1007/s10231-010-0165-y}, pages = {595 -- 618}, year = {2011}, abstract = {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.}, language = {en} } @article{NehringZessin2011, author = {Nehring, Benjamin and Zessin, Hans}, title = {The Papangelou process a concept for gibbs, fermi and bose processes}, series = {Journal of contemporary mathematical analysis}, volume = {46}, journal = {Journal of contemporary mathematical analysis}, number = {6}, publisher = {Allerton}, address = {New York}, issn = {1068-3623}, doi = {10.3103/S1068362311060069}, pages = {326 -- 337}, year = {2011}, abstract = {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.}, language = {en} } @article{EndersMuellerTopping2011, author = {Enders, J{\"o}rg and M{\"u}ller, Reto and Topping, Peter M.}, title = {On Type-I singularities in Ricci flow}, series = {Communications in analysis and geometry}, volume = {19}, journal = {Communications in analysis and geometry}, number = {5}, publisher = {International Press of Boston}, address = {Somerville}, issn = {1019-8385}, pages = {905 -- 922}, year = {2011}, abstract = {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].}, language = {en} } @article{RoulSchinnerKassner2011, author = {Roul, Pradip and Schinner, Alexander and Kassner, Klaus}, title = {Simulation of the strain distribution under a two-dimensional sand pile}, series = {Powder technology : an international journal on the science and technology of wet and dry particulate systems}, volume = {214}, journal = {Powder technology : an international journal on the science and technology of wet and dry particulate systems}, number = {3}, publisher = {Elsevier}, address = {Lausanne}, issn = {0032-5910}, doi = {10.1016/j.powtec.2011.08.039}, pages = {406 -- 414}, year = {2011}, abstract = {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.}, language = {en} } @book{Blanchard2011, author = {Blanchard, Gilles}, title = {Komplexit{\"a}tsanalyse in Statistik und Lerntheorie : Antrittsvorlesung 2011-05-04}, publisher = {Univ.-Bibl.}, address = {Potsdam}, year = {2011}, abstract = {Gilles Blanchards Vortrag gew{\"a}hrt 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 f{\"u}r weitere F{\"a}lle zu treffen. Mit der mathematischen Analyse der Eigenschaften solcher Methoden besch{\"a}ftigt sich die Lerntheorie, die mit der Statistik eng zusammenh{\"a}ngt. Dabei spielt der Begriff der Komplexit{\"a}t 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 erl{\"a}utern, wie Mathematische Werkzeuge dabei helfen, den richtigen Kompromiss zwischen diesen beiden Extremen zu finden.}, language = {de} } @book{OPUS4-33496, title = {Surveys in stochastic processes}, editor = {Blath, Jochen and Imkeller, Peter and Roelly, Sylvie}, publisher = {European Mathematical Society}, address = {Z{\"u}rich}, isbn = {978-3-03719-072-2}, pages = {XIII, 248 S.}, year = {2011}, language = {en} } @phdthesis{Schachtschneider2011, author = {Schachtschneider, Reyko}, title = {Error distribution in regional inversions of potential fields from satellite data}, address = {Potsdam}, pages = {118 S.}, year = {2011}, language = {en} } @phdthesis{Sarasit2011, author = {Sarasit, Napaporn}, title = {Algebraic properties of sets of terms}, address = {Potsdam}, pages = {91 S.}, year = {2011}, language = {en} } @article{Schmidt2011, author = {Schmidt, Hans-J{\"u}rgen}, title = {Perihelion advance for orbits with large eccentricities in the Schwarzschild black hole}, issn = {1550-7998}, year = {2011}, abstract = {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\$.}, language = {en} } @article{Schmidt2011, author = {Schmidt, Hans-J{\"u}rgen}, title = {Gauss-Bonnet Lagrangian G ln G and cosmological exact solutions}, issn = {1550-7998}, year = {2011}, abstract = {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.}, language = {en} } @book{KellerRoellyValleriana2011, author = {Keller, Peter and Roelly, Sylvie and Valleriana, Angelo}, title = {On Time Duality for Markov Chains with Asborbing Boundardies}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Mathematische Statistik un}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Mathematische Statistik un}, publisher = {Univ.}, address = {Potsdam}, issn = {1613-3307}, pages = {18 S.}, year = {2011}, language = {en} } @book{Murr2011, author = {Murr, R{\"u}diger}, title = {Characterization of L{\´e}vy Processes by a duality formula and related results}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Mathematische Statistik un}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Mathematische Statistik un}, publisher = {Univ.}, address = {Potsdam}, issn = {1613-3307}, pages = {19 S.}, year = {2011}, language = {en} } @phdthesis{Hanisch2011, author = {Hanisch, Florian}, title = {Variational problems on supermanifolds}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59757}, school = {Universit{\"a}t Potsdam}, year = {2011}, abstract = {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.}, language = {en} } @unpublished{Murr2011, author = {Murr, R{\"u}diger}, title = {Characterization of L{\´e}vy Processes by a duality formula and related results}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-43538}, year = {2011}, abstract = {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.}, language = {en} } @unpublished{MeleardRoelly2011, author = {M{\´e}l{\´e}ard, Sylvie and Roelly, Sylvie}, title = {A host-parasite multilevel interacting process and continuous approximations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51694}, year = {2011}, abstract = {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.}, language = {en} }