@misc{Scharrer2016,
  type      = {Master Thesis},
  author    = {Scharrer, Christian},
  title     = {Relating diameter and mean curvature for varifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-97013},
  school      = {Universit{\"a}t Potsdam},
  pages     = {42},
  year      = {2016},
  abstract  = {The main results of this thesis are formulated in a class of surfaces (varifolds) generalizing closed and connected smooth submanifolds of Euclidean space which allows singularities. Given an indecomposable varifold with dimension at least two in some Euclidean space such that the first variation is locally bounded, the total variation is absolutely continuous with respect to the weight measure, the density of the weight measure is at least one outside a set of weight measure zero and the generalized mean curvature is locally summable to a natural power (dimension of the varifold minus one) with respect to the weight measure. The thesis presents an improved estimate of the set where the lower density is small in terms of the one dimensional Hausdorff measure. Moreover, if the support of the weight measure is compact, then the intrinsic diameter with respect to the support of the weight measure is estimated in terms of the generalized mean curvature. This estimate is in analogy to the diameter control for closed connected manifolds smoothly immersed in some Euclidean space of Peter Topping. Previously, it was not known whether the hypothesis in this thesis implies that two points in the support of the weight measure have finite geodesic distance.},
  language  = {en}
}
@unpublished{ShlapunovTarkhanov2016,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {An open mapping theorem for the Navier-Stokes equations},
  volume    = {5},
  number    = {10},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-98687},
  pages     = {80},
  year      = {2016},
  abstract  = {We consider the Navier-Stokes equations in the layer R^n x [0,T] over R^n with finite T > 0. Using the standard fundamental solutions of the Laplace operator and the heat operator, we reduce the Navier-Stokes equations to a nonlinear Fredholm equation of the form (I+K) u = f, where K is a compact continuous operator in anisotropic normed H{\"o}lder spaces weighted at the point at infinity with respect to the space variables. Actually, the weight function is included to provide a finite energy estimate for solutions to the Navier-Stokes equations for all t in [0,T]. On using the particular properties of the de Rham complex we conclude that the Fr{\´e}chet derivative (I+K)' is continuously invertible at each point of the Banach space under consideration and the map I+K is open and injective in the space. In this way the Navier-Stokes equations prove to induce an open one-to-one mapping in the scale of H{\"o}lder spaces.},
  language  = {en}
}
@unpublished{BlanchardKraemer2016,
  author    = {Blanchard, Gilles and Kr{\"a}mer, Nicole},
  title     = {Convergence rates of kernel conjugate gradient for random design regression},
  volume    = {5},
  number    = {8},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-94195},
  pages     = {31},
  year      = {2016},
  abstract  = {We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensionality reduction with least squares projection. Following the setting introduced in earlier related literature, we study so-called "fast convergence rates" depending on the regularity of the target regression function (measured by a source condition in terms of the kernel integral operator) and on the effective dimensionality of the data mapped into the kernel space. We obtain upper bounds, essentially matching known minimax lower bounds, for the L^2 (prediction) norm as well as for the stronger Hilbert norm, if the true regression function belongs to the reproducing kernel Hilbert space. If the latter assumption is not fulfilled, we obtain similar convergence rates for appropriate norms, provided additional unlabeled data are available.},
  language  = {en}
}
@phdthesis{Chutsagulprom2016,
  author    = {Chutsagulprom, Nawinda},
  title     = {Ensemble-based filters dealing with non-Gaussianity and nonlinearity},
  school      = {Universit{\"a}t Potsdam},
  pages     = {95},
  year      = {2016},
  language  = {en}
}
@unpublished{RoellyVallois2016,
  author    = {Roelly, Sylvie and Vallois, Pierre},
  title     = {Convoluted Brownian motion},
  volume    = {5},
  number    = {9},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-96339},
  pages     = {37},
  year      = {2016},
  abstract  = {In this paper we analyse semimartingale properties of a class of Gaussian periodic processes, called convoluted Brownian motions, obtained by convolution between a deterministic function and a Brownian motion. A classical example in this class is the periodic Ornstein-Uhlenbeck process. We compute their characteristics and show that in general, they are neither Markovian nor satisfy a time-Markov field property. Nevertheless, by enlargement of filtration and/or addition of a one-dimensional component, one can in some case recover the Markovianity. We treat exhaustively the case of the bidimensional trigonometric convoluted Brownian motion and the higher-dimensional monomial convoluted Brownian motion.},
  language  = {en}
}
@unpublished{VasilievTarkhanov2016,
  author    = {Vasiliev, Serguei and Tarkhanov, Nikolai Nikolaevich},
  title     = {Construction of series of perfect lattices by layer superposition},
  volume    = {5},
  number    = {11},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-100591},
  pages     = {11},
  year      = {2016},
  abstract  = {We construct a new series of perfect lattices in n dimensions by the layer superposition method of Delaunay-Barnes.},
  language  = {en}
}
@article{AntoniniAzzaliSkandalis2016,
  author    = {Antonini, Paolo and Azzali, Sara and Skandalis, Georges},
  title     = {Bivariant K-theory with R/Z-coefficients and rho classes of unitary representations},
  series = {Journal of functional analysis},
  volume    = {270},
  journal   = {Journal of functional analysis},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0022-1236},
  doi       = {10.1016/j.jfa.2015.06.017},
  pages     = {447 -- 481},
  year      = {2016},
  abstract  = {We construct equivariant KK-theory with coefficients in and R/Z as suitable inductive limits over II1-factors. We show that the Kasparov product, together with its usual functorial properties, extends to KK-theory with real coefficients. Let Gamma be a group. We define a Gamma-algebra A to be K-theoretically free and proper (KFP) if the group trace tr of Gamma acts as the unit element in KKR Gamma (A, A). We show that free and proper Gamma-algebras (in the sense of Kasparov) have the (KFP) property. Moreover, if Gamma is torsion free and satisfies the KK Gamma-form of the Baum-Connes conjecture, then every Gamma-algebra satisfies (KFP). If alpha : Gamma -> U-n is a unitary representation and A satisfies property (KFP), we construct in a canonical way a rho class rho(A)(alpha) is an element of KKR/Z1,Gamma (A A) This construction generalizes the Atiyah-Patodi-Singer K-theory class with R/Z-coefficients associated to alpha. (C) 2015 Elsevier Inc. All rights reserved.},
  language  = {en}
}
@phdthesis{Berner2016,
  author    = {Berner, Nadine},
  title     = {Deciphering multiple changes in complex climate time series using Bayesian inference},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-100065},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xvi, 135},
  year      = {2016},
  abstract  = {Change points in time series are perceived as heterogeneities in the statistical or dynamical characteristics of the observations. Unraveling such transitions yields essential information for the understanding of the observed system's intrinsic evolution and potential external influences. A precise detection of multiple changes is therefore of great importance for various research disciplines, such as environmental sciences, bioinformatics and economics. The primary purpose of the detection approach introduced in this thesis is the investigation of transitions underlying direct or indirect climate observations. In order to develop a diagnostic approach capable to capture such a variety of natural processes, the generic statistical features in terms of central tendency and dispersion are employed in the light of Bayesian inversion. In contrast to established Bayesian approaches to multiple changes, the generic approach proposed in this thesis is not formulated in the framework of specialized partition models of high dimensionality requiring prior specification, but as a robust kernel-based approach of low dimensionality employing least informative prior distributions. First of all, a local Bayesian inversion approach is developed to robustly infer on the location and the generic patterns of a single transition. The analysis of synthetic time series comprising changes of different observational evidence, data loss and outliers validates the performance, consistency and sensitivity of the inference algorithm. To systematically investigate time series for multiple changes, the Bayesian inversion is extended to a kernel-based inference approach. By introducing basic kernel measures, the weighted kernel inference results are composed into a proxy probability to a posterior distribution of multiple transitions. The detection approach is applied to environmental time series from the Nile river in Aswan and the weather station Tuscaloosa, Alabama comprising documented changes. The method's performance confirms the approach as a powerful diagnostic tool to decipher multiple changes underlying direct climate observations. Finally, the kernel-based Bayesian inference approach is used to investigate a set of complex terrigenous dust records interpreted as climate indicators of the African region of the Plio-Pleistocene period. A detailed inference unravels multiple transitions underlying the indirect climate observations, that are interpreted as conjoint changes. The identified conjoint changes coincide with established global climate events. In particular, the two-step transition associated to the establishment of the modern Walker-Circulation contributes to the current discussion about the influence of paleoclimate changes on the environmental conditions in tropical and subtropical Africa at around two million years ago.},
  language  = {en}
}
@article{KellerMuenchPogorzelski2016,
  author    = {Keller, Matthias and M{\"u}nch, Florentin and Pogorzelski, Felix},
  title     = {Geometry and spectrum of rapidly branching graphs},
  series = {Mathematische Nachrichten},
  volume    = {289},
  journal   = {Mathematische Nachrichten},
  publisher = {Wiley-VCH},
  address   = {Weinheim},
  issn      = {0025-584X},
  doi       = {10.1002/mana.201400349},
  pages     = {1636 -- 1647},
  year      = {2016},
  abstract  = {We study graphs whose vertex degree tends to infinity and which are, therefore, called rapidly branching. We prove spectral estimates, discreteness of spectrum, first order eigenvalue and Weyl asymptotics solely in terms of the vertex degree growth. The underlying techniques are estimates on the isoperimetric constant. Furthermore, we give lower volume growth bounds and we provide a new criterion for stochastic incompleteness. (C) 2016 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim},
  language  = {en}
}
@article{HolschneiderLesurMauerbergeretal.2016,
  author    = {Holschneider, Matthias and Lesur, Vincent and Mauerberger, Stefan and Baerenzung, Julien},
  title     = {Correlation-based modeling and separation of geomagnetic field components},
  series = {Journal of geophysical research : Solid earth},
  volume    = {121},
  journal   = {Journal of geophysical research : Solid earth},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9313},
  doi       = {10.1002/2015JB012629},
  pages     = {3142 -- 3160},
  year      = {2016},
  abstract  = {We introduce a technique for the modeling and separation of geomagnetic field components that is based on an analysis of their correlation structures alone. The inversion is based on a Bayesian formulation, which allows the computation of uncertainties. The technique allows the incorporation of complex measurement geometries like observatory data in a simple way. We show how our technique is linked to other well-known inversion techniques. A case study based on observational data is given.},
  language  = {en}
}
@article{Benini2016,
  author    = {Benini, Marco},
  title     = {Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies},
  series = {Journal of mathematical physics},
  volume    = {57},
  journal   = {Journal of mathematical physics},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0022-2488},
  doi       = {10.1063/1.4947563},
  pages     = {1249 -- 1279},
  year      = {2016},
  abstract  = {Being motivated by open questions in gauge field theories, we consider non-standard de Rham cohomology groups for timelike compact and spacelike compact support systems. These cohomology groups are shown to be isomorphic respectively to the usual de Rham cohomology of a spacelike Cauchy surface and its counterpart with compact support. Furthermore, an analog of the usual Poincare duality for de Rham cohomology is shown to hold for the case with non-standard supports as well. We apply these results to find optimal spaces of linear observables for analogs of arbitrary degree k of both the vector potential and the Faraday tensor. The term optimal has to be intended in the following sense: The spaces of linear observables we consider distinguish between different configurations; in addition to that, there are no redundant observables. This last point in particular heavily relies on the analog of Poincare duality for the new cohomology groups. Published by AIP Publishing.},
  language  = {en}
}
@article{CattiauxFradonKuliketal.2016,
  author    = {Cattiaux, Patrick and Fradon, Myriam and Kulik, Alexei M. and Roelly, Sylvie},
  title     = {Long time behavior of stochastic hard ball systems},
  series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability},
  volume    = {22},
  journal   = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability},
  publisher = {International Statistical Institute},
  address   = {Voorburg},
  issn      = {1350-7265},
  doi       = {10.3150/14-BEJ672},
  pages     = {681 -- 710},
  year      = {2016},
  abstract  = {We study the long time behavior of a system of n = 2, 3 Brownian hard balls, living in R-d for d >= 2, submitted to a mutual attraction and to elastic collisions.},
  language  = {en}
}
@article{AcevedoReichCubasch2016,
  author    = {Acevedo, Walter and Reich, Sebastian and Cubasch, Ulrich},
  title     = {Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques},
  series = {Climate dynamics : observational, theoretical and computational research on the climate system},
  volume    = {46},
  journal   = {Climate dynamics : observational, theoretical and computational research on the climate system},
  publisher = {Springer},
  address   = {New York},
  issn      = {0930-7575},
  doi       = {10.1007/s00382-015-2683-1},
  pages     = {1909 -- 1920},
  year      = {2016},
  abstract  = {This paper investigates the applicability of the Vaganov-Shashkin-Lite (VSL) forward model for tree-ring-width chronologies as observation operator within a proxy data assimilation (DA) setting. Based on the principle of limiting factors, VSL combines temperature and moisture time series in a nonlinear fashion to obtain simulated TRW chronologies. When used as observation operator, this modelling approach implies three compounding, challenging features: (1) time averaging, (2) "switching recording" of 2 variables and (3) bounded response windows leading to "thresholded response". We generate pseudo-TRW observations from a chaotic 2-scale dynamical system, used as a cartoon of the atmosphere-land system, and attempt to assimilate them via ensemble Kalman filtering techniques. Results within our simplified setting reveal that VSL's nonlinearities may lead to considerable loss of assimilation skill, as compared to the utilization of a time-averaged (TA) linear observation operator. In order to understand this undesired effect, we embed VSL's formulation into the framework of fuzzy logic (FL) theory, which thereby exposes multiple representations of the principle of limiting factors. DA experiments employing three alternative growth rate functions disclose a strong link between the lack of smoothness of the growth rate function and the loss of optimality in the estimate of the TA state. Accordingly, VSL's performance as observation operator can be enhanced by resorting to smoother FL representations of the principle of limiting factors. This finding fosters new interpretations of tree-ring-growth limitation processes.},
  language  = {en}
}
@article{ShtrakovKoppitz2016,
  author    = {Shtrakov, Slavcho and Koppitz, J{\"o}rg},
  title     = {Stable varieties of semigroups and groupoids},
  series = {Algebra universalis},
  volume    = {75},
  journal   = {Algebra universalis},
  publisher = {Springer},
  address   = {Basel},
  issn      = {0002-5240},
  doi       = {10.1007/s00012-015-0359-7},
  pages     = {85 -- 106},
  year      = {2016},
  abstract  = {The paper deals with Sigma-composition and Sigma-essential composition of terms which lead to stable and s-stable varieties of algebras. A full description of all stable varieties of semigroups, commutative and idempotent groupoids is obtained. We use an abstract reduction system which simplifies the presentations of terms of type tau - (2) to study the variety of idempotent groupoids and s-stable varieties of groupoids. S-stable varieties are a variation of stable varieties, used to highlight replacement of subterms of a term in a deductive system instead of the usual replacement of variables by terms.},
  language  = {en}
}
@article{GregoryCotterReich2016,
  author    = {Gregory, A. and Cotter, C. J. and Reich, Sebastian},
  title     = {MULTILEVEL ENSEMBLE TRANSFORM PARTICLE FILTERING},
  series = {SIAM journal on scientific computing},
  volume    = {38},
  journal   = {SIAM journal on scientific computing},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {1064-8275},
  doi       = {10.1137/15M1038232},
  pages     = {A1317 -- A1338},
  year      = {2016},
  abstract  = {This paper extends the multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, multilevel Monte Carlo is applied to a certain variant of the particle filter, the ensemble transform particle filter (EPTF). A key aspect is the use of optimal transport methods to re-establish correlation between coarse and fine ensembles after resampling; this controls the variance of the estimator. Numerical examples present a proof of concept of the effectiveness of the proposed method, demonstrating significant computational cost reductions (relative to the single-level ETPF counterpart) in the propagation of ensembles.},
  language  = {en}
}
@article{Menne2016,
  author    = {Menne, Ulrich},
  title     = {Weakly Differentiable Functions on Varifolds},
  series = {Indiana University mathematics journal},
  volume    = {65},
  journal   = {Indiana University mathematics journal},
  publisher = {Indiana University, Department of Mathematics},
  address   = {Bloomington},
  issn      = {0022-2518},
  doi       = {10.1512/iumj.2016.65.5829},
  pages     = {977 -- 1088},
  year      = {2016},
  abstract  = {The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration-by-parts identities for certain compositions with smooth functions. In this class, the idea of zero boundary values is realised using the relative perimeter of superlevel sets. Results include a variety of Sobolev Poincare-type embeddings, embeddings into spaces of continuous and sometimes Holder-continuous functions, and point wise differentiability results both of approximate and integral type as well as coarea formulae. As a prerequisite for this study, decomposition properties of such varifolds and a relative isoperimetric inequality are established. Both involve a concept of distributional boundary of a set introduced for this purpose. As applications, the finiteness of the geodesic distance associated with varifolds with suitable summability of the mean curvature and a characterisation of curvature varifolds are obtained.},
  language  = {en}
}
@article{TinpunKoppitz2016,
  author    = {Tinpun, Kittisak and Koppitz, J{\"o}rg},
  title     = {Generating sets of infinite full transformation semigroups with restricted range},
  series = {Acta scientiarum mathematicarum},
  volume    = {82},
  journal   = {Acta scientiarum mathematicarum},
  publisher = {Institutum Bolyaianum Universitatis Szegediensis},
  address   = {Szeged},
  issn      = {0001-6969},
  doi       = {10.14232/actasm-015-502-4},
  pages     = {55 -- 63},
  year      = {2016},
  abstract  = {In the present paper, we consider minimal generating sets of infinite full transformation semigroups with restricted range modulo specific subsets. In particular, we determine relative ranks.},
  language  = {en}
}
@article{ZoellerHolschneider2016,
  author    = {Z{\"o}ller, Gert and Holschneider, Matthias},
  title     = {The Maximum Possible and the Maximum Expected Earthquake Magnitude for Production-Induced Earthquakes at the Gas Field in Groningen, The Netherlands},
  series = {Bulletin of the Seismological Society of America},
  volume    = {106},
  journal   = {Bulletin of the Seismological Society of America},
  publisher = {Seismological Society of America},
  address   = {Albany},
  issn      = {0037-1106},
  doi       = {10.1785/0120160220},
  pages     = {2917 -- 2921},
  year      = {2016},
  abstract  = {The Groningen gas field serves as a natural laboratory for production-induced earthquakes, because no earthquakes were observed before the beginning of gas production. Increasing gas production rates resulted in growing earthquake activity and eventually in the occurrence of the 2012M(w) 3.6 Huizinge earthquake. At least since this event, a detailed seismic hazard and risk assessment including estimation of the maximum earthquake magnitude is considered to be necessary to decide on the future gas production. In this short note, we first apply state-of-the-art methods of mathematical statistics to derive confidence intervals for the maximum possible earthquake magnitude m(max). Second, we calculate the maximum expected magnitude M-T in the time between 2016 and 2024 for three assumed gas-production scenarios. Using broadly accepted physical assumptions and 90\% confidence level, we suggest a value of m(max) 4.4, whereas M-T varies between 3.9 and 4.3, depending on the production scenario.},
  language  = {en}
}
@article{Menne2016,
  author    = {Menne, Ulrich},
  title     = {Sobolev functions on varifolds},
  series = {Proceedings of the London Mathematical Society},
  volume    = {113},
  journal   = {Proceedings of the London Mathematical Society},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0024-6115},
  doi       = {10.1112/plms/pdw023},
  pages     = {725 -- 774},
  year      = {2016},
  abstract  = {This paper introduces first-order Sobolev spaces on certain rectifiable varifolds. These complete locally convex spaces are contained in the generally non-linear class of generalised weakly differentiable functions and share key functional analytic properties with their Euclidean counterparts. Assuming the varifold to satisfy a uniform lower density bound and a dimensionally critical summability condition on its mean curvature, the following statements hold. Firstly, continuous and compact embeddings of Sobolev spaces into Lebesgue spaces and spaces of continuous functions are available. Secondly, the geodesic distance associated to the varifold is a continuous, not necessarily Holder continuous Sobolev function with bounded derivative. Thirdly, if the varifold additionally has bounded mean curvature and finite measure, then the present Sobolev spaces are isomorphic to those previously available for finite Radon measures yielding many new results for those classes as well. Suitable versions of the embedding results obtained for Sobolev functions hold in the larger class of generalised weakly differentiable functions.},
  language  = {en}
}
@article{KellerLenzMuenchetal.2016,
  author    = {Keller, Matthias and Lenz, Daniel and M{\"u}nch, Florentin and Schmidt, Marcel and Telcs, Andras},
  title     = {Note on short-time behavior of semigroups associated to self-adjoint operators},
  series = {Bulletin of the London Mathematical Society},
  volume    = {48},
  journal   = {Bulletin of the London Mathematical Society},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0024-6093},
  doi       = {10.1112/blms/bdw054},
  pages     = {935 -- 944},
  year      = {2016},
  abstract  = {We present a simple observation showing that the heat kernel on a locally finite graph behaves for short times t roughly like t(d), where d is the combinatorial distance. This is very different from the classical Varadhan-type behavior on manifolds. Moreover, this also gives that short-time behavior and global behavior of the heat kernel are governed by two different metrics whenever the degree of the graph is not uniformly bounded.},
  language  = {en}
}