@unpublished{AizenbergTarkhanov2014, author = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich}, title = {An integral formula for the number of lattice points in a domain}, volume = {3}, number = {3}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70453}, pages = {7}, year = {2014}, abstract = {Using the multidimensional logarithmic residue we show a simple formula for the difference between the number of integer points in a bounded domain of R^n and the volume of this domain. The difference proves to be the integral of an explicit differential form over the boundary of the domain.}, 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{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} } @inproceedings{AnderssonKeuneckeEseretal.2014, author = {Andersson, H. and Keunecke, A. and Eser, A. and Huisinga, Wilhelm and Reinisch, W. and Kloft, Charlotte}, title = {Pharmacokinetic considerations for optimising dosing regimens of a potsdam univ infliximab in patients with Crohn's disease}, series = {JOURNAL OF CROHNS \& COLITIS}, volume = {8}, booktitle = {JOURNAL OF CROHNS \& COLITIS}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {1873-9946}, doi = {10.1016/S1873-9946(14)60086-6}, pages = {S44 -- S44}, year = {2014}, language = {en} } @article{BaerenzungHolschneiderLesur2014, author = {Baerenzung, Julien and Holschneider, Matthias and Lesur, Vincent}, title = {Bayesian inversion for the filtered flow at the Earth's core-mantle boundary}, series = {Journal of geophysical research : Solid earth}, volume = {119}, journal = {Journal of geophysical research : Solid earth}, number = {4}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1002/2013JB010358}, pages = {2695 -- 2720}, year = {2014}, abstract = {The inverse problem of determining the flow at the Earth's core-mantle boundary according to an outer core magnetic field and secular variation model has been investigated through a Bayesian formalism. To circumvent the issue arising from the truncated nature of the available fields, we combined two modeling methods. In the first step, we applied a filter on the magnetic field to isolate its large scales by reducing the energy contained in its small scales, we then derived the dynamical equation, referred as filtered frozen flux equation, describing the spatiotemporal evolution of the filtered part of the field. In the second step, we proposed a statistical parametrization of the filtered magnetic field in order to account for both its remaining unresolved scales and its large-scale uncertainties. These two modeling techniques were then included in the Bayesian formulation of the inverse problem. To explore the complex posterior distribution of the velocity field resulting from this development, we numerically implemented an algorithm based on Markov chain Monte Carlo methods. After evaluating our approach on synthetic data and comparing it to previously introduced methods, we applied it to a magnetic field model derived from satellite data for the single epoch 2005.0. We could confirm the existence of specific features already observed in previous studies. In particular, we retrieved the planetary scale eccentric gyre characteristic of flow evaluated under the compressible quasi-geostrophy assumption although this hypothesis was not considered in our study. In addition, through the sampling of the velocity field posterior distribution, we could evaluate the reliability, at any spatial location and at any scale, of the flow we calculated. The flow uncertainties we determined are nevertheless conditioned by the choice of the prior constraints we applied to the velocity field.}, 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{Becker2014, author = {Becker, Christian}, title = {Relative differential cohomology}, 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_2}, pages = {91 -- 180}, year = {2014}, abstract = {We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone complex. We discuss the relation of the two notions of relative differential cohomology to each other. We discuss long exact sequences for both notions, thereby clarifying their relation to absolute differential cohomology. We construct the external and internal product of relative and absolute characters and show that relative differential cohomology is a right module over the absolute differential cohomology ring. Finally we construct fiber integration and transgression for relative differential characters.}, language = {en} } @article{BlanchardDelattreRoquain2014, author = {Blanchard, Gilles and Delattre, Sylvain and Roquain, Etienne}, title = {Testing over a continuum of null hypotheses with False Discovery Rate control}, series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, volume = {20}, journal = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, number = {1}, publisher = {International Statistical Institute}, address = {Voorburg}, issn = {1350-7265}, doi = {10.3150/12-BEJ488}, pages = {304 -- 333}, year = {2014}, abstract = {We consider statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses, under the assumption that a suitable single test (and corresponding p-value) is known for each individual hypothesis. We extend to this setting the notion of false discovery rate (FDR) as a measure of type I error. Our main result studies specific procedures based on the observation of the p-value process. Control of the FDR at a nominal level is ensured either under arbitrary dependence of p-values, or under the assumption that the finite dimensional distributions of the p-value process have positive correlations of a specific type (weak PRDS). Both cases generalize existing results established in the finite setting. Its interest is demonstrated in several non-parametric examples: testing the mean/signal in a Gaussian white noise model, testing the intensity of a Poisson process and testing the c.d.f. of i.i.d. random variables.}, 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{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{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{BoeckmannOsterloh2014, author = {B{\"o}ckmann, Christine and Osterloh, Lukas}, title = {Runge-Kutta type regularization method for inversion of spheroidal particle distribution from limited optical data}, series = {Inverse problems in science and engineering}, volume = {22}, journal = {Inverse problems in science and engineering}, number = {1}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {1741-5977}, doi = {10.1080/17415977.2013.830615}, pages = {150 -- 165}, year = {2014}, abstract = {The Runge-Kutta type regularization method was recently proposed as a potent tool for the iterative solution of nonlinear ill-posed problems. In this paper we analyze the applicability of this regularization method for solving inverse problems arising in atmospheric remote sensing, particularly for the retrieval of spheroidal particle distribution. Our numerical simulations reveal that the Runge-Kutta type regularization method is able to retrieve two-dimensional particle distributions using optical backscatter and extinction coefficient profiles, as well as depolarization information.}, language = {en} } @article{ChangHabalSchulze2014, author = {Chang, Der-Chen and Habal, Nadia and Schulze, Bert-Wolfgang}, title = {The edge algebra structure of the Zaremba problem}, series = {Journal of pseudo-differential operators and applications}, volume = {5}, journal = {Journal of pseudo-differential operators and applications}, number = {1}, publisher = {Springer}, address = {Basel}, issn = {1662-9981}, doi = {10.1007/s11868-013-0088-7}, pages = {69 -- 155}, year = {2014}, abstract = {We study mixed boundary value problems, here mainly of Zaremba type for the Laplacian within an edge algebra of boundary value problems. The edge here is the interface of the jump from the Dirichlet to the Neumann condition. In contrast to earlier descriptions of mixed problems within such an edge calculus, cf. (Harutjunjan and Schulze, Elliptic mixed, transmission and singular crack problems, 2008), we focus on new Mellin edge quantisations of the Dirichlet-to-Neumann operator on the Neumann side of the boundary and employ a pseudo-differential calculus of corresponding boundary value problems without the transmission property at the interface. This allows us to construct parametrices for the original mixed problem in a new and transparent way.}, language = {en} } @unpublished{ConfortiDaiPraRoelly2014, author = {Conforti, Giovanni and Dai Pra, Paolo and Roelly, Sylvie}, title = {Reciprocal class of jump processes}, volume = {3}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70776}, pages = {30}, year = {2014}, abstract = {Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of compound Poisson processes whose jumps belong to a finite set A in R^d. We propose a characterization of the reciprocal class as the unique set of probability measures on which a family of time and space transformations induces the same density, expressed in terms of the reciprocal invariants. The geometry of A plays a crucial role in the design of the transformations, and we use tools from discrete geometry to obtain an optimal characterization. We deduce explicit conditions for two Markov jump processes to belong to the same class. Finally, we provide a natural interpretation of the invariants as short-time asymptotics for the probability that the reference process makes a cycle around its current state.}, language = {en} } @unpublished{ConfortiLeonardMurretal.2014, author = {Conforti, Giovanni and L{\´e}onard, Christian and Murr, R{\"u}diger and Roelly, Sylvie}, title = {Bridges of Markov counting processes : reciprocal classes and duality formulas}, volume = {3}, number = {9}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-71855}, pages = {12}, year = {2014}, abstract = {Processes having the same bridges are said to belong to the same reciprocal class. In this article we analyze reciprocal classes of Markov counting processes by identifying their reciprocal invariants and we characterize them as the set of counting processes satisfying some duality formula.}, language = {en} } @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} } @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{DyachenkoTarkhanov2014, author = {Dyachenko, Evgueniya and Tarkhanov, Nikolai Nikolaevich}, title = {Singular perturbations of elliptic operators}, volume = {3}, number = {1}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-69502}, pages = {21}, year = {2014}, abstract = {We develop a new approach to the analysis of pseudodifferential operators with small parameter 'epsilon' in (0,1] on a compact smooth manifold X. The standard approach assumes action of operators in Sobolev spaces whose norms depend on 'epsilon'. Instead we consider the cylinder [0,1] x X over X and study pseudodifferential operators on the cylinder which act, by the very nature, on functions depending on 'epsilon' as well. The action in 'epsilon' reduces to multiplication by functions of this variable and does not include any differentiation. As but one result we mention asymptotic of solutions to singular perturbation problems for small values of 'epsilon'.}, language = {en} } @unpublished{FedchenkoTarkhanov2014, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {An index formula for Toeplitz operators}, volume = {3}, number = {12}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72499}, pages = {24}, year = {2014}, abstract = {We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first order partial differential equations in a bounded domain of Euclidean space with infinitely differentiable boundary.}, language = {en} } @unpublished{FlandoliHoegele2014, author = {Flandoli, Franco and H{\"o}gele, Michael}, title = {A solution selection problem with small stable perturbations}, volume = {3}, number = {8}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-71205}, pages = {43}, year = {2014}, abstract = {The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is a general alpha-stable process. It is proved that extremal solutions are selected and the probability of selection is computed. Detailed analysis of the characteristic function of an exit time form on the half-line is performed, with a suitable decomposition in small and large jumps adapted to the singular drift.}, language = {en} }