@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 This finding fosters new interpretations of tree-ring-growth limitation processes.}, language = {en} } @unpublished{Alsaedy2016, author = {Alsaedy, Ammar}, title = {Variational primitive of a differential form}, volume = {5}, number = {4}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-89223}, pages = {8}, year = {2016}, abstract = {In this paper we specify the Dirichlet to Neumann operator related to the Cauchy problem for the gradient operator with data on a part of the boundary. To this end, we consider a nonlinear relaxation of this problem which is a mixed boundary problem of Zaremba type for the p-Laplace equation.}, language = {en} } @unpublished{AlsaedyTarkhanov2016, author = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich}, title = {A Hilbert boundary value problem for generalised Cauchy-Riemann equations}, volume = {5}, number = {1}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86109}, pages = {21}, year = {2016}, abstract = {We elaborate a boundary Fourier method for studying an analogue of the Hilbert problem for analytic functions within the framework of generalised Cauchy-Riemann equations. The boundary value problem need not satisfy the Shapiro-Lopatinskij condition and so it fails to be Fredholm in Sobolev spaces. We show a solvability condition of the Hilbert problem, which looks like those for ill-posed problems, and construct an explicit formula for approximate solutions.}, 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} } @article{Becker2016, author = {Becker, Christian}, title = {Cheeger-Chern-Simons Theory and Differential String Classes}, series = {Annales de l'Institut Henri Poincar{\~A}©}, volume = {17}, journal = {Annales de l'Institut Henri Poincar{\~A}©}, publisher = {Springer}, address = {Basel}, issn = {1424-0637}, doi = {10.1007/s00023-016-0485-6}, pages = {1529 -- 1594}, year = {2016}, abstract = {We construct new concrete examples of relative differential characters, which we call Cheeger-Chern-Simons characters. They combine the well-known Cheeger-Simons characters with Chern-Simons forms. In the same way as Cheeger-Simons characters generalize Chern-Simons invariants of oriented closed manifolds, Cheeger-Chern-Simons characters generalize Chern-Simons invariants of oriented manifolds with boundary. We study the differential cohomology of compact Lie groups G and their classifying spaces BG. We show that the even degree differential cohomology of BG canonically splits into Cheeger-Simons characters and topologically trivial characters. We discuss the transgression in principal G-bundles and in the universal bundle. We introduce two methods to lift the universal transgression to a differential cohomology valued map. They generalize the Dijkgraaf-Witten correspondence between 3-dimensional Chern-Simons theories and Wess-Zumino-Witten terms to fully extended higher-order Chern-Simons theories. Using these lifts, we also prove two versions of a differential Hopf theorem. Using Cheeger-Chern-Simons characters and transgression, we introduce the notion of differential trivializations of universal characteristic classes. It generalizes well-established notions of differential String classes to arbitrary degree. Specializing to the class , we recover isomorphism classes of geometric string structures on Spin (n) -bundles with connection and the corresponding spin structures on the free loop space. The Cheeger-Chern-Simons character associated with the class together with its transgressions to loop space and higher mapping spaces defines a Chern-Simons theory, extended down to points. Differential String classes provide trivializations of this extended Chern-Simons theory. This setting immediately generalizes to arbitrary degree: for any universal characteristic class of principal G-bundles, we have an associated Cheeger-Chern-Simons character and extended Chern-Simons theory. Differential trivialization classes yield trivializations of this extended Chern-Simons theory.}, language = {en} } @article{BeinruckerDoganBlanchard2016, author = {Beinrucker, Andre and Dogan, Urun and Blanchard, Gilles}, title = {Extensions of stability selection using subsamples of observations and covariates}, series = {Statistics and Computing}, volume = {26}, journal = {Statistics and Computing}, publisher = {Springer}, address = {Dordrecht}, issn = {0960-3174}, doi = {10.1007/s11222-015-9589-y}, pages = {1059 -- 1077}, year = {2016}, abstract = {We introduce extensions of stability selection, a method to stabilise variable selection methods introduced by Meinshausen and Buhlmann (J R Stat Soc 72:417-473, 2010). We propose to apply a base selection method repeatedly to random subsamples of observations and subsets of covariates under scrutiny, and to select covariates based on their selection frequency. We analyse the effects and benefits of these extensions. Our analysis generalizes the theoretical results of Meinshausen and Buhlmann (J R Stat Soc 72:417-473, 2010) from the case of half-samples to subsamples of arbitrary size. We study, in a theoretical manner, the effect of taking random covariate subsets using a simplified score model. Finally we validate these extensions on numerical experiments on both synthetic and real datasets, and compare the obtained results in detail to the original stability selection method.}, 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} } @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{BlanchardFlaskaHandyetal.2016, author = {Blanchard, Gilles and Flaska, Marek and Handy, Gregory and Pozzi, Sara and Scott, Clayton}, title = {Classification with asymmetric label noise: Consistency and maximal denoising}, series = {Electronic journal of statistics}, volume = {10}, journal = {Electronic journal of statistics}, publisher = {Institute of Mathematical Statistics}, address = {Cleveland}, issn = {1935-7524}, doi = {10.1214/16-EJS1193}, pages = {2780 -- 2824}, year = {2016}, abstract = {In many real-world classification problems, the labels of training examples are randomly corrupted. Most previous theoretical work on classification with label noise assumes that the two classes are separable, that the label noise is independent of the true class label, or that the noise proportions for each class are known. In this work, we give conditions that are necessary and sufficient for the true class-conditional distributions to be identifiable. These conditions are weaker than those analyzed previously, and allow for the classes to be nonseparable and the noise levels to be asymmetric and unknown. The conditions essentially state that a majority of the observed labels are correct and that the true class-conditional distributions are "mutually irreducible," a concept we introduce that limits the similarity of the two distributions. For any label noise problem, there is a unique pair of true class-conditional distributions satisfying the proposed conditions, and we argue that this pair corresponds in a certain sense to maximal denoising of the observed distributions. Our results are facilitated by a connection to "mixture proportion estimation," which is the problem of estimating the maximal proportion of one distribution that is present in another. We establish a novel rate of convergence result for mixture proportion estimation, and apply this to obtain consistency of a discrimination rule based on surrogate loss minimization. Experimental results on benchmark data and a nuclear particle classification problem demonstrate the efficacy of our approach.}, language = {en} } @article{BlanchardKraemer2016, author = {Blanchard, Gilles and Kraemer, Nicole}, title = {Convergence rates of Kernel Conjugate Gradient for random design regression}, series = {Analysis and applications}, volume = {14}, journal = {Analysis and applications}, publisher = {World Scientific}, address = {Singapore}, issn = {0219-5305}, doi = {10.1142/S0219530516400017}, pages = {763 -- 794}, year = {2016}, abstract = {We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient (CG) algorithm, where regularization against over-fitting 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} } @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} } @unpublished{BlanchardMuecke2016, author = {Blanchard, Gilles and M{\"u}cke, Nicole}, title = {Optimal rates for regularization of statistical inverse learning problems}, volume = {5}, number = {5}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-89782}, pages = {36}, year = {2016}, abstract = {We consider a statistical inverse learning problem, where we observe the image of a function f through a linear operator A at i.i.d. random design points X_i, superposed with an additional noise. The distribution of the design points is unknown and can be very general. We analyze simultaneously the direct (estimation of Af) and the inverse (estimation of f) learning problems. In this general framework, we obtain strong and weak minimax optimal rates of convergence (as the number of observations n grows large) for a large class of spectral regularization methods over regularity classes defined through appropriate source conditions. This improves on or completes previous results obtained in related settings. The optimality of the obtained rates is shown not only in the exponent in n but also in the explicit dependence of the constant factor in the variance of the noise and the radius of the source condition set.}, language = {en} } @article{BomansonJanhunenSchaubetal.2016, author = {Bomanson, Jori and Janhunen, Tomi and Schaub, Torsten and Gebser, Martin and Kaufmann, Benjamin}, title = {Answer Set Programming Modulo Acyclicity}, series = {Fundamenta informaticae}, volume = {147}, journal = {Fundamenta informaticae}, publisher = {IOS Press}, address = {Amsterdam}, issn = {0169-2968}, doi = {10.3233/FI-2016-1398}, pages = {63 -- 91}, year = {2016}, abstract = {Acyclicity constraints are prevalent in knowledge representation and applications where acyclic data structures such as DAGs and trees play a role. Recently, such constraints have been considered in the satisfiability modulo theories (SMT) framework, and in this paper we carry out an analogous extension to the answer set programming (ASP) paradigm. The resulting formalism, ASP modulo acyclicity, offers a rich set of primitives to express constraints related to recursive structures. In the technical results of the paper, we relate the new generalization with standard ASP by showing (i) how acyclicity extensions translate into normal rules, (ii) how weight constraint programs can be instrumented by acyclicity extensions to capture stability in analogy to unfounded set checking, and (iii) how the gap between supported and stable models is effectively closed in the presence of such an extension. Moreover, we present an efficient implementation of acyclicity constraints by incorporating a respective propagator into the state-of-the-art ASP solver CLASP. The implementation provides a unique combination of traditional unfounded set checking with acyclicity propagation. In the experimental part, we evaluate the interplay of these orthogonal checks by equipping logic programs with supplementary acyclicity constraints. The performance results show that native support for acyclicity constraints is a worthwhile addition, furnishing a complementary modeling construct in ASP itself as well as effective means for translation-based ASP solving.}, language = {en} } @article{BaerStrohmaier2016, author = {B{\"a}r, Christian and Strohmaier, Alexander}, title = {A Rigorous Geometric Derivation of the Chiral Anomaly in Curved Backgrounds}, series = {Communications in mathematical physics}, volume = {347}, journal = {Communications in mathematical physics}, publisher = {Springer}, address = {New York}, issn = {0010-3616}, doi = {10.1007/s00220-016-2664-1}, pages = {703 -- 721}, year = {2016}, abstract = {We discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived directly in Lorentzian signature and in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah-Singer index theorem and another term involving the.-invariant of the Cauchy hypersurfaces.}, language = {en} } @article{BaerenzungHolschneiderLesur2016, author = {B{\"a}renzung, Julien and Holschneider, Matthias and Lesur, Vincent}, title = {constraints}, 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 = {10.1002/2015JB012464}, pages = {1343 -- 1364}, year = {2016}, abstract = {Prior information in ill-posed inverse problem is of critical importance because it is conditioning the posterior solution and its associated variability. The problem of determining the flow evolving at the Earth's core-mantle boundary through magnetic field models derived from satellite or observatory data is no exception to the rule. This study aims to estimate what information can be extracted on the velocity field at the core-mantle boundary, when the frozen flux equation is inverted under very weakly informative, but realistic, prior constraints. Instead of imposing a converging spectrum to the flow, we simply assume that its poloidal and toroidal energy spectra are characterized by power laws. The parameters of the spectra, namely, their magnitudes, and slopes are unknown. The connection between the velocity field, its spectra parameters, and the magnetic field model is established through the Bayesian formulation of the problem. Working in two steps, we determined the time-averaged spectra of the flow within the 2001-2009.5 period, as well as the flow itself and its associated uncertainties in 2005.0. According to the spectra we obtained, we can conclude that the large-scale approximation of the velocity field is not an appropriate assumption within the time window we considered. For the flow itself, we show that although it is dominated by its equatorial symmetric component, it is very unlikely to be perfectly symmetric. We also demonstrate that its geostrophic state is questioned in different locations of the outer core.}, 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{ChangViahmoudiSchulze2016, author = {Chang, D. -C. and Viahmoudi, M. Hedayat and Schulze, Bert-Wolfgang}, title = {PSEUDO-DIFFERENTIAL ANALYSIS WITH TWISTED SYMBOLIC STRUCTURE}, series = {Journal of nonlinear and convex analysis : an international journal}, volume = {17}, journal = {Journal of nonlinear and convex analysis : an international journal}, publisher = {Yokohama Publishers}, address = {Yokohama}, issn = {1345-4773}, pages = {1889 -- 1937}, year = {2016}, abstract = {This paper is devoted to pseudo-differential operators and new applications. We establish necessary extensions of the standard calculus to specific classes of operator-valued symbols occurring in principal symbolic hierarchies of operators on manifolds with singularities or stratified spaces.}, language = {en} } @phdthesis{Cheng2016, author = {Cheng, Yuan}, title = {Recursive state estimation in dynamical systems}, school = {Universit{\"a}t Potsdam}, pages = {84}, year = {2016}, 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} } @article{Denecke2016, author = {Denecke, Klaus-Dieter}, title = {The partial clone of linear terms}, series = {Siberian Mathematical Journal}, volume = {57}, journal = {Siberian Mathematical Journal}, publisher = {Pleiades Publ.}, address = {New York}, issn = {0037-4466}, doi = {10.1134/S0037446616040030}, pages = {589 -- 598}, year = {2016}, abstract = {Generalizing a linear expression over a vector space, we call a term of an arbitrary type tau linear if its every variable occurs only once. Instead of the usual superposition of terms and of the total many-sorted clone of all terms in the case of linear terms, we define the partial many-sorted superposition operation and the partial many-sorted clone that satisfies the superassociative law as weak identity. The extensions of linear hypersubstitutions are weak endomorphisms of this partial clone. For a variety V of one-sorted total algebras of type tau, we define the partial many-sorted linear clone of V as the partial quotient algebra of the partial many-sorted clone of all linear terms by the set of all linear identities of V. We prove then that weak identities of this clone correspond to linear hyperidentities of V.}, language = {en} }