@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un}, publisher = {Univ.}, address = {Potsdam}, issn = {1613-3307}, pages = {19 S.}, year = {2011}, language = {en} } @unpublished{Murr2011, author = {Murr, R{\"u}diger}, title = {Characterization of L{\´e}vy Processes by a duality formula and related results}, url =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 Finally we extend our method to characterize infinitely divisible random measures.}, language = {en} } @unpublished{MeleardRoelly2011, author = {M{\´e}l{\´e}ard, Sylvie and Roelly, Sylvie}, title = {A host-parasite multilevel interacting process and continuous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} } @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{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{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{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} } @phdthesis{Sarasit2011, author = {Sarasit, Napaporn}, title = {Algebraic properties of sets of terms}, address = {Potsdam}, pages = {91 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} } @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} } @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} } @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{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{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{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{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{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{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{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} }