@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{BomansonJanhunenSchaubetal.2016, author = {Bomanson, Jori and Janhunen, Tomi and Schaub, Torsten H. 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{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} } @article{WichitsaNguanLaeuterLiero2016, author = {Wichitsa-Nguan, Korakot and L{\"a}uter, Henning and Liero, Hannelore}, title = {Estimability in Cox models}, series = {Statistical Papers}, volume = {57}, journal = {Statistical Papers}, publisher = {Springer}, address = {New York}, issn = {0932-5026}, doi = {10.1007/s00362-016-0755-x}, pages = {1121 -- 1140}, year = {2016}, abstract = {Our procedure of estimating is the maximum partial likelihood estimate (MPLE) which is the appropriate estimate in the Cox model with a general censoring distribution, covariates and an unknown baseline hazard rate . We find conditions for estimability and asymptotic estimability. The asymptotic variance matrix of the MPLE is represented and properties are discussed.}, language = {en} } @article{MuellerBoeckmannKolgotinetal.2016, author = {M{\"u}ller, Detlef and B{\"o}ckmann, Christine and Kolgotin, Alexei and Schneidenbach, Lars and Chemyakin, Eduard and Rosemann, Julia and Znak, Pavel and Romanov, Anton}, title = {Microphysical particle properties derived from inversion algorithms developed in the framework of EARLINET}, series = {Atmospheric measurement techniques : an interactive open access journal of the European Geosciences Union}, volume = {9}, journal = {Atmospheric measurement techniques : an interactive open access journal of the European Geosciences Union}, publisher = {Copernicus}, address = {G{\"o}ttingen}, issn = {1867-1381}, doi = {10.5194/amt-9-5007-2016}, pages = {5007 -- 5035}, year = {2016}, abstract = {We present a summary on the current status of two inversion algorithms that are used in EARLINET (European Aerosol Research Lidar Network) for the inversion of data collected with EARLINET multiwavelength Raman lidars. These instruments measure backscatter coefficients at 355, 532, and 1064 nm, and extinction coefficients at 355 and 532 nm. Development of these two algorithms started in 2000 when EARLINET was founded. The algorithms are based on a manually controlled inversion of optical data which allows for detailed sensitivity studies. The algorithms allow us to derive particle effective radius as well as volume and surface area concentration with comparably high confidence. The retrieval of the real and imaginary parts of the complex refractive index still is a challenge in view of the accuracy required for these parameters in climate change studies in which light absorption needs to be known with high accuracy. It is an extreme challenge to retrieve the real part with an accuracy better than 0.05 and the imaginary part with accuracy better than 0.005-0.1 or +/- 50 \%. Single-scattering albedo can be computed from the retrieved microphysical parameters and allows us to categorize aerosols into high-and low-absorbing aerosols. On the basis of a few exemplary simulations with synthetic optical data we discuss the current status of these manually operated algorithms, the potentially achievable accuracy of data products, and the goals for future work. One algorithm was used with the purpose of testing how well microphysical parameters can be derived if the real part of the complex refractive index is known to at least 0.05 or 0.1. The other algorithm was used to find out how well microphysical parameters can be derived if this constraint for the real part is not applied. The optical data used in our study cover a range of Angstrom exponents and extinction-to-backscatter (lidar) ratios that are found from lidar measurements of various aerosol types. We also tested aerosol scenarios that are considered highly unlikely, e.g. the lidar ratios fall outside the commonly accepted range of values measured with Raman lidar, even though the underlying microphysical particle properties are not uncommon. The goal of this part of the study is to test the robustness of the algorithms towards their ability to identify aerosol types that have not been measured so far, but cannot be ruled out based on our current knowledge of aerosol physics. We computed the optical data from monomodal logarithmic particle size distributions, i.e. we explicitly excluded the more complicated case of bimodal particle size distributions which is a topic of ongoing research work. Another constraint is that we only considered particles of spherical shape in our simulations. We considered particle radii as large as 7-10 mu m in our simulations where the Potsdam algorithm is limited to the lower value. We considered optical-data errors of 15\% in the simulation studies. We target 50\% uncertainty as a reasonable threshold for our data products, though we attempt to obtain data products with less uncertainty in future work.}, 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{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{Kroencke2016, author = {Kr{\"o}ncke, Klaus}, title = {Rigidity and Infinitesimal Deformability of Ricci Solitons}, series = {The journal of geometric analysis}, volume = {26}, journal = {The journal of geometric analysis}, publisher = {Springer}, address = {New York}, issn = {1050-6926}, doi = {10.1007/s12220-015-9608-4}, pages = {1795 -- 1807}, year = {2016}, abstract = {In this paper, an obstruction against the integrability of certain infinitesimal solitonic deformations is given. Using this obstruction, we show that the complex projective spaces of even complex dimension are rigid as Ricci solitons although they have infinitesimal solitonic deformations.}, language = {en} } @article{MiethKloftRodriguezetal.2016, author = {Mieth, Bettina and Kloft, Marius and Rodriguez, Juan Antonio and Sonnenburg, Soren and Vobruba, Robin and Morcillo-Suarez, Carlos and Farre, Xavier and Marigorta, Urko M. and Fehr, Ernst and Dickhaus, Thorsten and Blanchard, Gilles and Schunk, Daniel and Navarro, Arcadi and M{\"u}ller, Klaus-Robert}, title = {Combining Multiple Hypothesis Testing with Machine Learning Increases the Statistical Power of Genome-wide Association Studies}, series = {Scientific reports}, volume = {6}, journal = {Scientific reports}, publisher = {Nature Publ. Group}, address = {London}, issn = {2045-2322}, doi = {10.1038/srep36671}, pages = {14}, year = {2016}, abstract = {The standard approach to the analysis of genome-wide association studies (GWAS) is based on testing each position in the genome individually for statistical significance of its association with the phenotype under investigation. To improve the analysis of GWAS, we propose a combination of machine learning and statistical testing that takes correlation structures within the set of SNPs under investigation in a mathematically well-controlled manner into account. The novel two-step algorithm, COMBI, first trains a support vector machine to determine a subset of candidate SNPs and then performs hypothesis tests for these SNPs together with an adequate threshold correction. Applying COMBI to data from a WTCCC study (2007) and measuring performance as replication by independent GWAS published within the 2008-2015 period, we show that our method outperforms ordinary raw p-value thresholding as well as other state-of-the-art methods. COMBI presents higher power and precision than the examined alternatives while yielding fewer false (i.e. non-replicated) and more true (i.e. replicated) discoveries when its results are validated on later GWAS studies. More than 80\% of the discoveries made by COMBI upon WTCCC data have been validated by independent studies. Implementations of the COMBI method are available as a part of the GWASpi toolbox 2.0.}, language = {en} } @article{KellerMugnolo2016, author = {Keller, Matthias and Mugnolo, Delio}, title = {General Cheeger inequalities for p-Laplacians on graphs}, series = {Theoretical ecology}, volume = {147}, journal = {Theoretical ecology}, publisher = {Elsevier}, address = {Oxford}, issn = {0362-546X}, doi = {10.1016/j.na.2016.07.011}, pages = {80 -- 95}, year = {2016}, abstract = {We prove Cheeger inequalities for p-Laplacians on finite and infinite weighted graphs. Unlike in previous works, we do not impose boundedness of the vertex degree, nor do we restrict ourselves to the normalized Laplacian and, more generally, we do not impose any boundedness assumption on the geometry. This is achieved by a novel definition of the measure of the boundary which uses the idea of intrinsic metrics. For the non-normalized case, our bounds on the spectral gap of p-Laplacians are already significantly better for finite graphs and for infinite graphs they yield non-trivial bounds even in the case of unbounded vertex degree. We, furthermore, give upper bounds by the Cheeger constant and by the exponential volume growth of distance balls. (C) 2016 Elsevier Ltd. All rights reserved.}, 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} }