@unpublished{DereudreRoelly2014, author = {Dereudre, David and Roelly, Sylvie}, title = {Path-dependent infinite-dimensional SDE with non-regular drift : an existence result}, volume = {3}, number = {11}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72084}, pages = {27}, year = {2014}, abstract = {We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither small or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy. Our result strongly improves the previous ones obtained for free dynamics with a small perturbative drift. The originality of our method leads in the use of the specific entropy as a tightness tool and on a description of such stochastic differential equation as solution of a variational problem on the path space.}, language = {en} } @article{GreweBrinkopJoeckeletal.2014, author = {Grewe, Volker and Brinkop, Sabine and Joeckel, Patrick and Shin, Seoleun and Reich, Sebastian and Yserentant, Harry}, title = {On the theory of mass conserving transformations for Lagrangian methods in 3D atmosphere-chemistry models}, series = {Meteorologische Zeitschrift}, volume = {23}, journal = {Meteorologische Zeitschrift}, number = {4}, publisher = {Schweizerbart}, address = {Stuttgart}, issn = {0941-2948}, doi = {10.1127/0941-2948/2014/0552}, pages = {441 -- 447}, year = {2014}, language = {en} } @unpublished{GairingHoegeleKosenkovaetal.2014, author = {Gairing, Jan and H{\"o}gele, Michael and Kosenkova, Tetiana and Kulik, Alexei Michajlovič}, title = {On the calibration of L{\´e}vy driven time series with coupling distances : an application in paleoclimate}, volume = {3}, number = {2}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-69781}, pages = {18}, year = {2014}, abstract = {This article aims at the statistical assessment of time series with large fluctuations in short time, which are assumed to stem from a continuous process perturbed by a L{\´e}vy process exhibiting a heavy tail behavior. We propose an easily implementable procedure to estimate efficiently the statistical difference between the noisy behavior of the data and a given reference jump measure in terms of so-called coupling distances. After a short introduction to L{\´e}vy processes and coupling distances we recall basic statistical approximation results and derive rates of convergence. In the sequel the procedure is elaborated in detail in an abstract setting and eventually applied in a case study to simulated and paleoclimate data. It indicates the dominant presence of a non-stable heavy-tailed jump L{\´e}vy component for some tail index greater than 2.}, language = {en} } @article{BlanchardDickhausRoquainetal.2014, author = {Blanchard, Gilles and Dickhaus, Thorsten and Roquain, Etienne and Villers, Fanny}, title = {On least favorable configurations for step-up-down tests}, series = {Statistica Sinica}, volume = {24}, journal = {Statistica Sinica}, number = {1}, publisher = {Statistica Sinica, Institute of Statistical Science, Academia Sinica}, address = {Taipei}, issn = {1017-0405}, doi = {10.5705/ss.2011.205}, pages = {1 -- U31}, year = {2014}, language = {en} } @article{AlsaedyTarkhanov2014, author = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich}, title = {Normally solvable nonlinear boundary value problems}, series = {Nonlinear analysis : theory, methods \& applications ; an international multidisciplinary journal}, volume = {95}, journal = {Nonlinear analysis : theory, methods \& applications ; an international multidisciplinary journal}, publisher = {Elsevier}, address = {Oxford}, issn = {0362-546X}, doi = {10.1016/j.na.2013.09.024}, pages = {468 -- 482}, year = {2014}, abstract = {We investigate nonlinear problems which appear as Euler-Lagrange equations for a variational problem. They include in particular variational boundary value problems for nonlinear elliptic equations studied by F. Browder in the 1960s. We establish a solvability criterion of such problems and elaborate an efficient orthogonal projection method for constructing approximate solutions.}, language = {en} } @article{HaferKiyLucke2014, author = {Hafer, J{\"o}rg and Kiy, Alexander and Lucke, Ulrike}, title = {Moodle \& Co. auf dem Weg zur Personal Learning Environment}, series = {eleed}, volume = {2014}, journal = {eleed}, number = {10}, issn = {1860-7470}, year = {2014}, abstract = {Ausgehend von der typischen IT-Infrastruktur f{\"u}r E-Learning an Hochschulen auf der einen Seite sowie vom bisherigen Stand der Forschung zu Personal Learning Environments (PLEs) auf der anderen Seite zeigt dieser Beitrag auf, wie bestehende Werkzeuge bzw. Dienste zusammengef{\"u}hrt und f{\"u}r die Anforderungen der modernen, rechnergest{\"u}tzten Pr{\"a}senzlehre aufbereitet werden k{\"o}nnen. F{\"u}r diesen interdisziplin{\"a}ren Entwicklungsprozess bieten sowohl klassische Softwareentwicklungsverfahren als auch bestehende PLE-Modelle wenig Hilfestellung an. Der Beitrag beschreibt die in einem campusweiten Projekt an der Universit{\"a}t Potsdam verfolgten Ans{\"a}tze und die damit erzielten Ergebnisse. Daf{\"u}r werden zun{\"a}chst typische Lehr-/Lern-bzw. Kommunikations-Szenarien identifiziert, aus denen Anforderungen an eine unterst{\"u}tzende Plattform abgeleitet werden. Dies f{\"u}hrt zu einer umfassenden Sammlung zu ber{\"u}cksichtigender Dienste und deren Funktionen, die gem{\"a}ß den Spezifika ihrer Nutzung in ein Gesamtsystem zu integrieren sind. Auf dieser Basis werden grunds{\"a}tzliche Integrationsans{\"a}tze und technische Details dieses Mash-Ups in einer Gesamtschau aller relevanten Dienste betrachtet und in eine integrierende Systemarchitektur {\"u}berf{\"u}hrt. Deren konkrete Realisierung mit Hilfe der Portal-Technologie Liferay wird dargestellt, wobei die eingangs definierten Szenarien aufgegriffen und exemplarisch vorgestellt werden. Erg{\"a}nzende Anpassungen im Sinne einer personalisierbaren bzw. adaptiven Lern-(und Arbeits-)Umgebung werden ebenfalls unterst{\"u}tzt und kurz aufgezeigt.}, language = {en} } @unpublished{PornsawadBoeckmann2014, author = {Pornsawad, Pornsarp and B{\"o}ckmann, Christine}, title = {Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems}, volume = {3}, number = {7}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70834}, pages = {30}, year = {2014}, abstract = {This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under H{\"o}lder-type source-wise condition if the Fr{\´e}chet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods.}, language = {en} } @unpublished{HoegelePavlyukevich2014, author = {H{\"o}gele, Michael and Pavlyukevich, Ilya}, title = {Metastability of Morse-Smale dynamical systems perturbed by heavy-tailed L{\´e}vy type noise}, volume = {3}, number = {5}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70639}, pages = {27}, year = {2014}, abstract = {We consider a general class of finite dimensional deterministic dynamical systems with finitely many local attractors each of which supports a unique ergodic probability measure, which includes in particular the class of Morse-Smale systems in any finite dimension. The dynamical system is perturbed by a multiplicative non-Gaussian heavytailed L{\´e}vy type noise of small intensity ε > 0. Specifically we consider perturbations leading to a It{\^o}, Stratonovich and canonical (Marcus) stochastic differential equation. The respective asymptotic first exit time and location problem from each of the domains of attractions in case of inward pointing vector fields in the limit of ε-> 0 has been investigated by the authors. We extend these results to domains with characteristic boundaries and show that the perturbed system exhibits a metastable behavior in the sense that there exits a unique ε-dependent time scale on which the random system converges to a continuous time Markov chain switching between the invariant measures. As examples we consider α-stable perturbations of the Duffing equation and a chemical system exhibiting a birhythmic behavior.}, language = {en} } @article{KoppitzMusunthia2014, author = {Koppitz, J{\"o}rg and Musunthia, Tiwadee}, title = {Maximal subsemigroups containing a particular semigroup}, series = {Mathematica Slovaca}, volume = {64}, journal = {Mathematica Slovaca}, number = {6}, publisher = {De Gruyter}, address = {Warsaw}, issn = {0139-9918}, doi = {10.2478/s12175-014-0280-0}, pages = {1369 -- 1380}, year = {2014}, abstract = {We characterize maximal subsemigroups of the monoid T(X) of all transformations on the set X = a"center dot of natural numbers containing a given subsemigroup W of T(X) such that T(X) is finitely generated over W. This paper gives a contribution to the characterization of maximal subsemigroups on the monoid of all transformations on an infinite set.}, language = {en} } @article{ZoellerBenZion2014, author = {Z{\"o}ller, Gert and Ben-Zion, Yehuda}, title = {Large earthquake hazard of the San Jacinto fault zone, CA, from long record of simulated seismicity assimilating the available instrumental and paleoseismic data}, series = {Pure and applied geophysics}, volume = {171}, journal = {Pure and applied geophysics}, number = {11}, publisher = {Springer}, address = {Basel}, issn = {0033-4553}, doi = {10.1007/s00024-014-0783-1}, pages = {2955 -- 2965}, year = {2014}, abstract = {We investigate spatio-temporal properties of earthquake patterns in the San Jacinto fault zone (SJFZ), California, between Cajon Pass and the Superstition Hill Fault, using a long record of simulated seismicity constrained by available seismological and geological data. The model provides an effective realization of a large segmented strike-slip fault zone in a 3D elastic half-space, with heterogeneous distribution of static friction chosen to represent several clear step-overs at the surface. The simulated synthetic catalog reproduces well the basic statistical features of the instrumental seismicity recorded at the SJFZ area since 1981. The model also produces events larger than those included in the short instrumental record, consistent with paleo-earthquakes documented at sites along the SJFZ for the last 1,400 years. The general agreement between the synthetic and observed data allows us to address with the long-simulated seismicity questions related to large earthquakes and expected seismic hazard. The interaction between m a parts per thousand yen 7 events on different sections of the SJFZ is found to be close to random. The hazard associated with m a parts per thousand yen 7 events on the SJFZ increases significantly if the long record of simulated seismicity is taken into account. The model simulations indicate that the recent increased number of observed intermediate SJFZ earthquakes is a robust statistical feature heralding the occurrence of m a parts per thousand yen 7 earthquakes. The hypocenters of the m a parts per thousand yen 5 events in the simulation results move progressively towards the hypocenter of the upcoming m a parts per thousand yen 7 earthquake.}, language = {en} } @article{RungrottheeraSchulzeWong2014, author = {Rungrottheera, Wannarut and Schulze, Bert-Wolfgang and Wong, M. W.}, title = {Iterative properties of pseudo-differential operators on edge spaces}, series = {Journal of pseudo-differential operators and applications}, volume = {5}, journal = {Journal of pseudo-differential operators and applications}, number = {4}, publisher = {Springer}, address = {Basel}, issn = {1662-9981}, doi = {10.1007/s11868-014-0100-x}, pages = {455 -- 479}, year = {2014}, abstract = {Pseudo-differential operators with twisted symbolic estimates play a large role in the calculus on manifolds with edge singularities. We study here aspects of the underlying abstract concept and establish a new result on iteration of quantizations.}, language = {en} } @article{ZoellerHolschneider2014, author = {Z{\"o}ller, Gert and Holschneider, Matthias}, title = {Induced seismicity: What is the size of the largest expected earthquake?}, series = {The bulletin of the Seismological Society of America}, volume = {104}, journal = {The bulletin of the Seismological Society of America}, number = {6}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120140195}, pages = {3153 -- 3158}, year = {2014}, abstract = {The injection of fluids is a well-known origin for the triggering of earthquake sequences. The growing number of projects related to enhanced geothermal systems, fracking, and others has led to the question, which maximum earthquake magnitude can be expected as a consequence of fluid injection? This question is addressed from the perspective of statistical analysis. Using basic empirical laws of earthquake statistics, we estimate the magnitude M-T of the maximum expected earthquake in a predefined future time window T-f. A case study of the fluid injection site at Paradox Valley, Colorado, demonstrates that the magnitude m 4.3 of the largest observed earthquake on 27 May 2000 lies very well within the expectation from past seismicity without adjusting any parameters. Vice versa, for a given maximum tolerable earthquake at an injection site, we can constrain the corresponding amount of injected fluids that must not be exceeded within predefined confidence bounds.}, language = {en} } @phdthesis{Ziese2014, author = {Ziese, Ramona}, title = {Geometric electroelasticity}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72504}, school = {Universit{\"a}t Potsdam}, pages = {vi, 113}, year = {2014}, abstract = {In this work a diffential geometric formulation of the theory of electroelasticity is developed which also includes thermal and magnetic influences. We study the motion of bodies consisting of an elastic material that are deformed by the influence of mechanical forces, heat and an external electromagnetic field. To this end physical balance laws (conservation of mass, balance of momentum, angular momentum and energy) are established. These provide an equation that describes the motion of the body during the deformation. Here the body and the surrounding space are modeled as Riemannian manifolds, and we allow that the body has a lower dimension than the surrounding space. In this way one is not (as usual) restricted to the description of the deformation of three-dimensional bodies in a three-dimensional space, but one can also describe the deformation of membranes and the deformation in a curved space. Moreover, we formulate so-called constitutive relations that encode the properties of the used material. Balance of energy as a scalar law can easily be formulated on a Riemannian manifold. The remaining balance laws are then obtained by demanding that balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space. This generalizes a result by Marsden and Hughes that pertains to bodies that have the same dimension as the surrounding space and does not allow the presence of electromagnetic fields. Usually, in works on electroelasticity the entropy inequality is used to decide which otherwise allowed deformations are physically admissible and which are not. It is alsoemployed to derive restrictions to the possible forms of constitutive relations describing the material. Unfortunately, the opinions on the physically correct statement of the entropy inequality diverge when electromagnetic fields are present. Moreover, it is unclear how to formulate the entropy inequality in the case of a membrane that is subjected to an electromagnetic field. Thus, we show that one can replace the use of the entropy inequality by the demand that for a given process balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space and under linear rescalings of the temperature. On the one hand, this demand also yields the desired restrictions to the form of the constitutive relations. On the other hand, it needs much weaker assumptions than the arguments in physics literature that are employing the entropy inequality. Again, our result generalizes a theorem of Marsden and Hughes. This time, our result is, like theirs, only valid for bodies that have the same dimension as the surrounding space.}, language = {en} } @article{AmezcuaIdeKalnayetal.2014, author = {Amezcua, Javier and Ide, Kayo and Kalnay, Eugenia and Reich, Sebastian}, title = {Ensemble transform Kalman-Bucy filters}, series = {Quarterly journal of the Royal Meteorological Society}, volume = {140}, journal = {Quarterly journal of the Royal Meteorological Society}, number = {680}, publisher = {Wiley-Blackwell}, address = {Hoboken}, issn = {0035-9009}, doi = {10.1002/qj.2186}, pages = {995 -- 1004}, year = {2014}, abstract = {Two recent works have adapted the Kalman-Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyse the behaviour of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background error to observational error variance, and that using the integration scheme proposed in both formulations can lead to failure. A numerical integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman-Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.}, language = {en} } @phdthesis{Dyachenko2014, author = {Dyachenko, Evgeniya}, title = {Elliptic problems with small parameter}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72056}, school = {Universit{\"a}t Potsdam}, year = {2014}, abstract = {In this thesis we consider diverse aspects of existence and correctness of asymptotic solutions to elliptic differential and pseudodifferential equations. We begin our studies with the case of a general elliptic boundary value problem in partial derivatives. A small parameter enters the coefficients of the main equation as well as into the boundary conditions. Such equations have already been investigated satisfactory, but there still exist certain theoretical deficiencies. Our aim is to present the general theory of elliptic problems with a small parameter. For this purpose we examine in detail the case of a bounded domain with a smooth boundary. First of all, we construct formal solutions as power series in the small parameter. Then we examine their asymptotic properties. It suffices to carry out sharp two-sided \emph{a priori} estimates for the operators of boundary value problems which are uniform in the small parameter. Such estimates failed to hold in functional spaces used in classical elliptic theory. To circumvent this limitation we exploit norms depending on the small parameter for the functions defined on a bounded domain. Similar norms are widely used in literature, but their properties have not been investigated extensively. Our theoretical investigation shows that the usual elliptic technique can be correctly carried out in these norms. The obtained results also allow one to extend the norms to compact manifolds with boundaries. We complete our investigation by formulating algebraic conditions on the operators and showing their equivalence to the existence of a priori estimates. In the second step, we extend the concept of ellipticity with a small parameter to more general classes of operators. Firstly, we want to compare the difference in asymptotic patterns between the obtained series and expansions for similar differential problems. Therefore we investigate the heat equation in a bounded domain with a small parameter near the time derivative. In this case the characteristics touch the boundary at a finite number of points. It is known that the solutions are not regular in a neighbourhood of such points in advance. We suppose moreover that the boundary at such points can be non-smooth but have cuspidal singularities. We find a formal asymptotic expansion and show that when a set of parameters comes through a threshold value, the expansions fail to be asymptotic. The last part of the work is devoted to general concept of ellipticity with a small parameter. Several theoretical extensions to pseudodifferential operators have already been suggested in previous studies. As a new contribution we involve the analysis on manifolds with edge singularities which allows us to consider wider classes of perturbed elliptic operators. We examine that introduced classes possess a priori estimates of elliptic type. As a further application we demonstrate how developed tools can be used to reduce singularly perturbed problems to regular ones.}, language = {en} } @unpublished{SultanovKalyakinTarkhanov2014, author = {Sultanov, Oskar and Kalyakin, Leonid and Tarkhanov, Nikolai Nikolaevich}, title = {Elliptic perturbations of dynamical systems with a proper node}, volume = {3}, number = {4}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70460}, pages = {12}, year = {2014}, abstract = {The paper is devoted to asymptotic analysis of the Dirichlet problem for a second order partial differential equation containing a small parameter multiplying the highest order derivatives. It corresponds to a small perturbation of a dynamical system having a stationary solution in the domain. We focus on the case where the trajectories of the system go into the domain and the stationary solution is a proper node.}, language = {en} } @article{BagderinaTarkhanov2014, author = {Bagderina, Yulia Yu. and Tarkhanov, Nikolai Nikolaevich}, title = {Differential invariants of a class of Lagrangian systems with two degrees of freedom}, series = {Journal of mathematical analysis and applications}, volume = {410}, journal = {Journal of mathematical analysis and applications}, number = {2}, publisher = {Elsevier}, address = {San Diego}, issn = {0022-247X}, doi = {10.1016/j.jmaa.2013.08.015}, pages = {733 -- 749}, year = {2014}, language = {en} } @article{BaerBecker2014, author = {B{\"a}r, Christian and Becker, Christian}, title = {Differential characters and geometric chains}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2112}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-07034-6; 978-3-319-07033-9}, issn = {0075-8434}, doi = {10.1007/978-3-319-07034-6_1}, pages = {1 -- 90}, year = {2014}, abstract = {We study Cheeger-Simons differential characters and provide geometric descriptions of the ring structure and of the fiber integration map. The uniqueness of differential cohomology (up to unique natural transformation) is proved by deriving an explicit formula for any natural transformation between a differential cohomology theory and the model given by differential characters. Fiber integration for fibers with boundary is treated in the context of relative differential characters. As applications we treat higher-dimensional holonomy, parallel transport, and transgression.}, language = {en} } @article{Bubenzer2014, author = {Bubenzer, Johannes}, title = {Cycle-aware minimization of acyclic deterministic finite-state automata}, series = {Discrete applied mathematics}, volume = {163}, journal = {Discrete applied mathematics}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0166-218X}, doi = {10.1016/j.dam.2013.08.003}, pages = {238 -- +}, year = {2014}, abstract = {In this paper a linear-time algorithm for the minimization of acyclic deterministic finite-state automata is presented. The algorithm runs significantly faster than previous algorithms for the same task. This is shown by a comparison of the running times of both algorithms. Additionally, a variation of the new algorithm is presented which handles cyclic automata as input. The new cycle-aware algorithm minimizes acyclic automata in the desired way. In case of cyclic input, the algorithm minimizes all acyclic suffixes of the input automaton.}, language = {en} } @article{Kind2014, author = {Kind, Josephine}, title = {Creation of topographic maps}, series = {Process design for natural scientists: an agile model-driven approach}, journal = {Process design for natural scientists: an agile model-driven approach}, number = {500}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-662-45005-5}, pages = {229 -- 238}, year = {2014}, abstract = {Location analyses are among the most common tasks while working with spatial data and geographic information systems. Automating the most frequently used procedures is therefore an important aspect of improving their usability. In this context, this project aims to design and implement a workflow, providing some basic tools for a location analysis. For the implementation with jABC, the workflow was applied to the problem of finding a suitable location for placing an artificial reef. For this analysis three parameters (bathymetry, slope and grain size of the ground material) were taken into account, processed, and visualized with the The Generic Mapping Tools (GMT), which were integrated into the workflow as jETI-SIBs. The implemented workflow thereby showed that the approach to combine jABC with GMT resulted in an user-centric yet user-friendly tool with high-quality cartographic outputs.}, language = {en} }