TY - JOUR A1 - Hedayat Mahmoudi, Mahdi A1 - Schulze, Bert-Wolfgang T1 - Corner boundary value problems JF - Asian-European journal of mathematics N2 - The paper develops some crucial steps in extending the first-order cone or edge calculus to higher singularity orders. We focus here on order 2, but the ideas are motivated by an iterative approach for higher singularities. KW - Mellin operators KW - Mellin oscillatory integrals KW - exit calculus KW - weighted Sobolev spaces Y1 - 2016 U6 - https://doi.org/10.1142/S1793557117500541 SN - 1793-5571 SN - 1793-7183 VL - 10 IS - 1 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Antonini, Paolo A1 - Azzali, Sara A1 - Skandalis, Georges T1 - Bivariant K-theory with R/Z-coefficients and rho classes of unitary representations JF - Journal of functional analysis N2 - 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. KW - Operator algebras KW - Bivariant K-theory KW - Rho invariants Y1 - 2016 U6 - https://doi.org/10.1016/j.jfa.2015.06.017 SN - 0022-1236 SN - 1096-0783 VL - 270 SP - 447 EP - 481 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Kollosche, David T1 - Criticising with Foucault: towards a guiding framework for socio-political studies in mathematics education JF - Educational studies in mathematics : an international journal N2 - Socio-political studies in mathematics education often touch complex fields of interaction between education, mathematics and the political. In this paper I present a Foucault-based framework for socio-political studies in mathematics education which may guide research in that area. In order to show the potential of such a framework, I discuss the potential and limits of Marxian ideology critique, present existing Foucault-based research on socio-political aspects of mathematics education, develop my framework and show its use in an outline of a study on socio-political aspects of calculation in the mathematics classroom. KW - Critique KW - Marx KW - Foucault KW - Critical mathematics education KW - Calculation Y1 - 2016 U6 - https://doi.org/10.1007/s10649-015-9648-5 SN - 0013-1954 SN - 1573-0816 VL - 91 SP - 73 EP - 86 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Nehring, Benjamin A1 - Rafler, Mathias A1 - Zessin, Hans T1 - Splitting-characterizations of the Papangelou process JF - Mathematische Nachrichten N2 - For point processes we establish a link between integration-by-parts-and splitting-formulas which can also be considered as integration-by-parts-formulas of a new type. First we characterize finite Papangelou processes in terms of their splitting kernels. The main part then consists in extending these results to the case of infinitely extended Papangelou and, in particular, Polya and Gibbs processes. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim KW - Papangelou processes KW - characterization of point processes KW - independent splittings KW - Gibbs processes Y1 - 2016 U6 - https://doi.org/10.1002/mana.201400384 SN - 0025-584X SN - 1522-2616 VL - 289 SP - 85 EP - 96 PB - Wiley-VCH CY - Weinheim ER - TY - JOUR A1 - Klein, Markus A1 - Rosenberger, Elke T1 - Agmon estimates for the difference of exact and approximate Dirichlet eigenfunctions for difference operators JF - Asymptotic analysis N2 - We analyze a general class of difference operators H-epsilon = T-epsilon + V-epsilon on l(2)(((epsilon)Z)(d)), where V-epsilon is a multi-well potential and epsilon is a small parameter. We construct approximate eigenfunctions in neighbourhoods of the different wells and give weighted l(2)-estimates for the difference of these and the exact eigenfunctions of the associated Dirichlet-operators. Y1 - 2016 U6 - https://doi.org/10.3233/ASY-151343 SN - 0921-7134 SN - 1875-8576 VL - 97 SP - 61 EP - 89 PB - IOS Press CY - Amsterdam ER - TY - JOUR A1 - Zöller, Gert A1 - Holschneider, Matthias T1 - The Earthquake History in a Fault Zone Tells Us Almost Nothing about m(max) JF - Seismological research letters N2 - In the present study, we summarize and evaluate the endeavors from recent years to estimate the maximum possible earthquake magnitude m(max) from observed data. In particular, we use basic and physically motivated assumptions to identify best cases and worst cases in terms of lowest and highest degree of uncertainty of m(max). In a general framework, we demonstrate that earthquake data and earthquake proxy data recorded in a fault zone provide almost no information about m(max) unless reliable and homogeneous data of a long time interval, including several earthquakes with magnitude close to m(max), are available. Even if detailed earthquake information from some centuries including historic and paleoearthquakes are given, only very few, namely the largest events, will contribute at all to the estimation of m(max), and this results in unacceptably high uncertainties. As a consequence, estimators of m(max) in a fault zone, which are based solely on earthquake-related information from this region, have to be dismissed. Y1 - 2016 U6 - https://doi.org/10.1785/0220150176 SN - 0895-0695 SN - 1938-2057 VL - 87 SP - 132 EP - 137 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Menne, Ulrich T1 - Weakly Differentiable Functions on Varifolds JF - Indiana University mathematics journal N2 - 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. KW - Rectifiable varifold KW - (generalised) wealdy differentiable function KW - distributional boundary KW - decomposition KW - relative isoperimetric inequality KW - Sobolev Poincare inequality KW - approximate differentiability KW - coarea formula KW - geodesic distance KW - curvature varifold Y1 - 2016 U6 - https://doi.org/10.1512/iumj.2016.65.5829 SN - 0022-2518 SN - 1943-5258 VL - 65 SP - 977 EP - 1088 PB - Indiana University, Department of Mathematics CY - Bloomington ER - TY - JOUR A1 - Gregory, A. A1 - Cotter, C. J. A1 - Reich, Sebastian T1 - MULTILEVEL ENSEMBLE TRANSFORM PARTICLE FILTERING JF - SIAM journal on scientific computing N2 - 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. KW - multilevel Monte Carlo KW - sequential data assimilation KW - optimal transport Y1 - 2016 U6 - https://doi.org/10.1137/15M1038232 SN - 1064-8275 SN - 1095-7197 VL - 38 SP - A1317 EP - A1338 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Tinpun, Kittisak A1 - Koppitz, Jörg T1 - Generating sets of infinite full transformation semigroups with restricted range JF - Acta scientiarum mathematicarum N2 - 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. KW - generating sets KW - transformation semigroups KW - restricted range KW - relative ranks Y1 - 2016 U6 - https://doi.org/10.14232/actasm-015-502-4 SN - 0001-6969 VL - 82 SP - 55 EP - 63 PB - Institutum Bolyaianum Universitatis Szegediensis CY - Szeged ER - TY - JOUR A1 - Bomanson, Jori A1 - Janhunen, Tomi A1 - Schaub, Torsten H. A1 - Gebser, Martin A1 - Kaufmann, Benjamin T1 - Answer Set Programming Modulo Acyclicity JF - Fundamenta informaticae N2 - 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. Y1 - 2016 U6 - https://doi.org/10.3233/FI-2016-1398 SN - 0169-2968 SN - 1875-8681 VL - 147 SP - 63 EP - 91 PB - IOS Press CY - Amsterdam ER - TY - JOUR A1 - Pornsawad, Pornsarp A1 - Böckmann, Christine T1 - Modified Iterative Runge-Kutta-Type Methods for Nonlinear Ill-Posed Problems JF - Numerical functional analysis and optimization : an international journal of rapid publication N2 - This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under a Holder-type sourcewise condition if the Frechet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt, Lobatto, and Radau methods. KW - Nonlinear ill-posed problems KW - Runge-Kutta methods KW - regularization methods KW - Holder-type source condition KW - stopping rules Y1 - 2016 U6 - https://doi.org/10.1080/01630563.2016.1219744 SN - 0163-0563 SN - 1532-2467 VL - 37 SP - 1562 EP - 1589 PB - Wiley-VCH CY - Philadelphia ER - TY - JOUR A1 - Chang, D. -C. A1 - Viahmoudi, M. Hedayat A1 - Schulze, Bert-Wolfgang T1 - PSEUDO-DIFFERENTIAL ANALYSIS WITH TWISTED SYMBOLIC STRUCTURE JF - Journal of nonlinear and convex analysis : an international journal N2 - 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. KW - Pseudo-differential operators KW - boundary value problems KW - operator valued symbols KW - Fourier transform Y1 - 2016 SN - 1345-4773 SN - 1880-5221 VL - 17 SP - 1889 EP - 1937 PB - Yokohama Publishers CY - Yokohama ER - TY - JOUR A1 - Blanchard, Gilles A1 - Flaska, Marek A1 - Handy, Gregory A1 - Pozzi, Sara A1 - Scott, Clayton T1 - Classification with asymmetric label noise: Consistency and maximal denoising JF - Electronic journal of statistics N2 - 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. KW - Classification KW - label noise KW - mixture proportion estimation KW - surrogate loss KW - consistency Y1 - 2016 U6 - https://doi.org/10.1214/16-EJS1193 SN - 1935-7524 VL - 10 SP - 2780 EP - 2824 PB - Institute of Mathematical Statistics CY - Cleveland ER - TY - JOUR A1 - Levy, Cyril A1 - Jimenez, Carolina Neira A1 - Paycha, Sylvie T1 - THE CANONICAL TRACE AND THE NONCOMMUTATIVE RESIDUE ON THE NONCOMMUTATIVE TORUS JF - Transactions of the American Mathematical Society N2 - Using a global symbol calculus for pseudodifferential operators on tori, we build a canonical trace on classical pseudodifferential operators on noncommutative tori in terms of a canonical discrete sum on the underlying toroidal symbols. We characterise the canonical trace on operators on the noncommutative torus as well as its underlying canonical discrete sum on symbols of fixed (resp. any) noninteger order. On the grounds of this uniqueness result, we prove that in the commutative setup, this canonical trace on the noncommutative torus reduces to Kontsevich and Vishik's canonical trace which is thereby identified with a discrete sum. A similar characterisation for the noncommutative residue on noncommutative tori as the unique trace which vanishes on trace-class operators generalises Fathizadeh and Wong's characterisation in so far as it includes the case of operators of fixed integer order. By means of the canonical trace, we derive defect formulae for regularized traces. The conformal invariance of the $ \zeta $-function at zero of the Laplacian on the noncommutative torus is then a straightforward consequence. Y1 - 2016 U6 - https://doi.org/10.1090/tran/6369 SN - 0002-9947 SN - 1088-6850 VL - 368 SP - 1051 EP - 1095 PB - American Mathematical Soc. CY - Providence ER - TY - JOUR A1 - Tarkhanov, Nikolai Nikolaevich T1 - Deformation quantization and boundary value problems JF - International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis & topology N2 - We describe a natural construction of deformation quantization on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator. KW - Symplectic manifold KW - star product KW - trace KW - index Y1 - 2016 U6 - https://doi.org/10.1142/S0219887816500079 SN - 0219-8878 SN - 1793-6977 VL - 13 SP - 176 EP - 195 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Eichmair, Michael A1 - Metzger, Jan T1 - JENKINS-SERRIN-TYPE RESULTS FOR THE JANG EQUATION JF - Journal of differential geometry N2 - Let (M, g, k) be an initial data set for the Einstein equations of general relativity. We show that a canonical solution of the Jang equation exists in the complement of the union of all weakly future outer trapped regions in the initial data set with respect to a given end, provided that this complement contains no weakly past outer trapped regions. The graph of this solution relates the area of the horizon to the global geometry of the initial data set in a non-trivial way. We prove the existence of a Scherk-type solution of the Jang equation outside the union of all weakly future or past outer trapped regions in the initial data set. This result is a natural exterior analogue for the Jang equation of the classical Jenkins Serrin theory. We extend and complement existence theorems [19, 20, 40, 29, 18, 31, 11] for Scherk-type constant mean curvature graphs over polygonal domains in (M, g), where (M, g) is a complete Riemannian surface. We can dispense with the a priori assumptions that a sub solution exists and that (M, g) has particular symmetries. Also, our method generalizes to higher dimensions. Y1 - 2016 U6 - https://doi.org/10.4310/jdg/1453910454 SN - 0022-040X SN - 1945-743X VL - 102 SP - 207 EP - 242 PB - International Press of Boston CY - Somerville ER - TY - JOUR A1 - Shtrakov, Slavcho A1 - Koppitz, Jörg T1 - Stable varieties of semigroups and groupoids JF - Algebra universalis N2 - 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. KW - composition of terms KW - essential position in terms KW - stable variety Y1 - 2016 U6 - https://doi.org/10.1007/s00012-015-0359-7 SN - 0002-5240 SN - 1420-8911 VL - 75 SP - 85 EP - 106 PB - Springer CY - Basel ER - TY - JOUR A1 - Acevedo, Walter A1 - Reich, Sebastian A1 - Cubasch, Ulrich T1 - Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques JF - Climate dynamics : observational, theoretical and computational research on the climate system N2 - 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. KW - Proxy forward modeling KW - Data assimilation KW - Fuzzy logic KW - Ensemble Kalman filter KW - Paleoclimate reconstruction Y1 - 2016 U6 - https://doi.org/10.1007/s00382-015-2683-1 SN - 0930-7575 SN - 1432-0894 VL - 46 SP - 1909 EP - 1920 PB - Springer CY - New York ER - TY - JOUR A1 - Hack, Thomas-Paul A1 - Hanisch, Florian A1 - Schenkel, Alexander T1 - Supergeometry in Locally Covariant Quantum Field Theory JF - Communications in mathematical physics N2 - In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor U : SLoc -> S*Alg to the category of super-*-algebras, which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct superquantum field theories in terms of enriched functors eU : eSLoc -> eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the enriched framework. As examples we analyze the superparticle in 1 vertical bar 1-dimensions and the free Wess-Zumino model in 3 vertical bar 2-dimensions. Y1 - 2016 U6 - https://doi.org/10.1007/s00220-015-2516-4 SN - 0010-3616 SN - 1432-0916 VL - 342 SP - 615 EP - 673 PB - Springer CY - New York ER - TY - JOUR A1 - Schroeter, M-A A1 - Ritter, M. A1 - Holschneider, Matthias A1 - Sturm, H. T1 - Enhanced DySEM imaging of cantilever motion using artificial structures patterned by focused ion beam techniques JF - Journal of micromechanics and microengineering N2 - We use a dynamic scanning electron microscope (DySEM) to map the spatial distribution of the vibration of a cantilever beam. The DySEM measurements are based on variations of the local secondary electron signal within the imaging electron beam diameter during an oscillation period of the cantilever. For this reason, the surface of a cantilever without topography or material variation does not allow any conclusions about the spatial distribution of vibration due to a lack of dynamic contrast. In order to overcome this limitation, artificial structures were added at defined positions on the cantilever surface using focused ion beam lithography patterning. The DySEM signal of such high-contrast structures is strongly improved, hence information about the surface vibration becomes accessible. Simulations of images of the vibrating cantilever have also been performed. The results of the simulation are in good agreement with the experimental images. KW - FIB patterning KW - structured cantilever KW - AFM KW - modal analysis KW - DySEM Y1 - 2016 U6 - https://doi.org/10.1088/0960-1317/26/3/035010 SN - 0960-1317 SN - 1361-6439 VL - 26 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Bärenzung, Julien A1 - Holschneider, Matthias A1 - Lesur, Vincent T1 - constraints JF - Journal of geophysical research : Solid earth N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1002/2015JB012464 SN - 2169-9313 SN - 2169-9356 VL - 121 SP - 1343 EP - 1364 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Cattiaux, Patrick A1 - Fradon, Myriam A1 - Kulik, Alexei M. A1 - Roelly, Sylvie T1 - Long time behavior of stochastic hard ball systems JF - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability N2 - 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. KW - hard core interaction KW - local time KW - Lyapunov function KW - normal reflection KW - Poincare inequality KW - reversible measure KW - stochastic differential equations Y1 - 2016 U6 - https://doi.org/10.3150/14-BEJ672 SN - 1350-7265 SN - 1573-9759 VL - 22 SP - 681 EP - 710 PB - International Statistical Institute CY - Voorburg ER - TY - JOUR A1 - Benini, Marco T1 - Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies JF - Journal of mathematical physics N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1063/1.4947563 SN - 0022-2488 SN - 1089-7658 VL - 57 SP - 1249 EP - 1279 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Holschneider, Matthias A1 - Lesur, Vincent A1 - Mauerberger, Stefan A1 - Baerenzung, Julien T1 - Correlation-based modeling and separation of geomagnetic field components JF - Journal of geophysical research : Solid earth N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1002/2015JB012629 SN - 2169-9313 SN - 2169-9356 VL - 121 SP - 3142 EP - 3160 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Hermann, Andreas A1 - Humbert, Emmanuel T1 - About the mass of certain second order elliptic operators JF - Advances in mathematics N2 - Let (M, g) be a closed Riemannian manifold of dimension n >= 3 and let f is an element of C-infinity (M), such that the operator P-f := Delta g + f is positive. If g is flat near some point p and f vanishes around p, we can define the mass of P1 as the constant term in the expansion of the Green function of P-f at p. In this paper, we establish many results on the mass of such operators. In particular, if f := n-2/n(n-1)s(g), i.e. if P-f is the Yamabe operator, we show the following result: assume that there exists a closed simply connected non-spin manifold M such that the mass is non-negative for every metric g as above on M, then the mass is non-negative for every such metric on every closed manifold of the same dimension as M. (C) 2016 Elsevier Inc. All rights reserved. KW - Yamabe operator KW - Surgery KW - Positive mass theorem Y1 - 2016 U6 - https://doi.org/10.1016/j.aim.2016.03.008 SN - 0001-8708 SN - 1090-2082 VL - 294 SP - 596 EP - 633 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Kistner, Saskia A1 - Vollmeyer, Regina A1 - Burns, Bruce D. A1 - Kortenkamp, Ulrich T1 - Model development in scientific discovery learning with a computer-based physics task JF - Computers in human behavior N2 - Based on theories of scientific discovery learning (SDL) and conceptual change, this study explores students' preconceptions in the domain of torques in physics and the development of these conceptions while learning with a computer-based SDL task. As a framework we used a three-space theory of SDL and focused on model space, which is supposed to contain the current conceptualization/model of the learning domain, and on its change through hypothesis testing and experimenting. Three questions were addressed: (1) What are students' preconceptions of torques before learning about this domain? To do this a multiple-choice test for assessing students' models of torques was developed and given to secondary school students (N = 47) who learned about torques using computer simulations. (2) How do students' models of torques develop during SDL? Working with simulations led to replacement of some misconceptions with physically correct conceptions. (3) Are there differential patterns of model development and if so, how do they relate to students’ use of the simulations? By analyzing individual differences in model development, we found that an intensive use of the simulations was associated with the acquisition of correct conceptions. Thus, the three-space theory provided a useful framework for understanding conceptual change in SDL. KW - Scientific discovery learning KW - Multiple problem spaces KW - Computer simulations KW - Physics concepts KW - Misconceptions KW - Conceptual change Y1 - 2016 U6 - https://doi.org/10.1016/j.chb.2016.02.041 SN - 0747-5632 SN - 1873-7692 VL - 59 SP - 446 EP - 455 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Kretschmer, Marlene A1 - Coumou, Dim A1 - Donges, Jonathan Friedemann A1 - Runge, Jakob T1 - Using Causal Effect Networks to Analyze Different Arctic Drivers of Midlatitude Winter Circulation JF - Journal of climate N2 - In recent years, the Northern Hemisphere midlatitudes have suffered from severe winters like the extreme 2012/13 winter in the eastern United States. These cold spells were linked to a meandering upper-tropospheric jet stream pattern and a negative Arctic Oscillation index (AO). However, the nature of the drivers behind these circulation patterns remains controversial. Various studies have proposed different mechanisms related to changes in the Arctic, most of them related to a reduction in sea ice concentrations or increasing Eurasian snow cover. Here, a novel type of time series analysis, called causal effect networks (CEN), based on graphical models is introduced to assess causal relationships and their time delays between different processes. The effect of different Arctic actors on winter circulation on weekly to monthly time scales is studied, and robust network patterns are found. Barents and Kara sea ice concentrations are detected to be important external drivers of the midlatitude circulation, influencing winter AO via tropospheric mechanisms and through processes involving the stratosphere. Eurasia snow cover is also detected to have a causal effect on sea level pressure in Asia, but its exact role on AO remains unclear. The CEN approach presented in this study overcomes some difficulties in interpreting correlation analyses, complements model experiments for testing hypotheses involving teleconnections, and can be used to assess their validity. The findings confirm that sea ice concentrations in autumn in the Barents and Kara Seas are an important driver of winter circulation in the midlatitudes. Y1 - 2016 U6 - https://doi.org/10.1175/JCLI-D-15-0654.1 SN - 0894-8755 SN - 1520-0442 VL - 29 SP - 4069 EP - 4081 PB - American Meteorological Soc. CY - Boston ER - TY - JOUR A1 - Becker, Christian T1 - Cheeger-Chern-Simons Theory and Differential String Classes JF - Annales de l'Institut Henri Poincaré N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1007/s00023-016-0485-6 SN - 1424-0637 SN - 1424-0661 VL - 17 SP - 1529 EP - 1594 PB - Springer CY - Basel ER - TY - JOUR A1 - Lyu, Xiaojing A1 - Schulze, Bert-Wolfgang T1 - Mellin Operators in the Edge Calculus JF - Complex analysis and operator theory N2 - A manifold M with smooth edge Y is locally near Y modelled on X-Delta x Omega for a cone X-Delta := ( (R) over bar (+) x X)/({0} x X) where Xis a smooth manifold and Omega subset of R-q an open set corresponding to a chart on Y. Compared with pseudo-differential algebras, based on other quantizations of edge-degenerate symbols, we extend the approach with Mellin representations on the r half-axis up to r = infinity, the conical exit of X-boolean AND = R+ x X (sic) (r, x) at infinity. The alternative description of the edge calculus is useful for pseudo-differential structures on manifolds with higher singularities. KW - Edge degenerate operators KW - Mellin and Green operators edge symbols Y1 - 2016 U6 - https://doi.org/10.1007/s11785-015-0511-6 SN - 1661-8254 SN - 1661-8262 VL - 10 SP - 965 EP - 1000 PB - Springer CY - Basel ER - TY - JOUR A1 - Kistner, Saskia A1 - Burns, Bruce D. A1 - Vollmeyer, Regina A1 - Kortenkamp, Ulrich T1 - The importance of understanding: Model space moderates goal specificity effects JF - The quarterly journal of experimental psychology N2 - The three-space theory of problem solving predicts that the quality of a learner's model and the goal specificity of a task interact on knowledge acquisition. In Experiment 1 participants used a computer simulation of a lever system to learn about torques. They either had to test hypotheses (nonspecific goal), or to produce given values for variables (specific goal). In the good- but not in the poor-model condition they saw torque depicted as an area. Results revealed the predicted interaction. A nonspecific goal only resulted in better learning when a good model of torques was provided. In Experiment 2 participants learned to manipulate the inputs of a system to control its outputs. A nonspecific goal to explore the system helped performance when compared to a specific goal to reach certain values when participants were given a good model, but not when given a poor model that suggested the wrong hypothesis space. Our findings support the three-space theory. They emphasize the importance of understanding for problem solving and stress the need to study underlying processes. KW - Goal specificity KW - Problem solving KW - Three-space theory KW - Scientific discovery learning Y1 - 2016 U6 - https://doi.org/10.1080/17470218.2015.1076865 SN - 1747-0218 SN - 1747-0226 VL - 69 SP - 1179 EP - 1196 PB - Optical Society of America CY - Abingdon ER - TY - JOUR A1 - Kröncke, Klaus T1 - Rigidity and Infinitesimal Deformability of Ricci Solitons JF - The journal of geometric analysis N2 - 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. KW - Ricci solitons KW - Moduli space KW - Linearized equation KW - Integrability Y1 - 2016 U6 - https://doi.org/10.1007/s12220-015-9608-4 SN - 1050-6926 SN - 1559-002X VL - 26 SP - 1795 EP - 1807 PB - Springer CY - New York ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - The partial clone of linear terms JF - Siberian Mathematical Journal N2 - 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. KW - linear term KW - clone KW - partial clone KW - linear hypersubstitution KW - linear identity KW - linear hyperidentity Y1 - 2016 U6 - https://doi.org/10.1134/S0037446616040030 SN - 0037-4466 SN - 1573-9260 VL - 57 SP - 589 EP - 598 PB - Pleiades Publ. CY - New York ER - TY - JOUR A1 - Stolle, Claudia A1 - Michaelis, Ingo A1 - Rauberg, Jan T1 - The role of high-resolution geomagnetic field models for investigating ionospheric currents at low Earth orbit satellites JF - Earth, planets and space N2 - Low Earth orbiting geomagnetic satellite missions, such as the Swarm satellite mission, are the only means to monitor and investigate ionospheric currents on a global scale and to make in situ measurements of F region currents. High-precision geomagnetic satellite missions are also able to detect ionospheric currents during quiet-time geomagnetic conditions that only have few nanotesla amplitudes in the magnetic field. An efficient method to isolate the ionospheric signals from satellite magnetic field measurements has been the use of residuals between the observations and predictions from empirical geomagnetic models for other geomagnetic sources, such as the core and lithospheric field or signals from the quiet-time magnetospheric currents. This study aims at highlighting the importance of high-resolution magnetic field models that are able to predict the lithospheric field and that consider the quiet-time magnetosphere for reliably isolating signatures from ionospheric currents during geomagnetically quiet times. The effects on the detection of ionospheric currents arising from neglecting the lithospheric and magnetospheric sources are discussed on the example of four Swarm orbits during very quiet times. The respective orbits show a broad range of typical scenarios, such as strong and weak ionospheric signal (during day- and nighttime, respectively) superimposed over strong and weak lithospheric signals. If predictions from the lithosphere or magnetosphere are not properly considered, the amplitude of the ionospheric currents, such as the midlatitude Sq currents or the equatorial electrojet (EEJ), is modulated by 10-15 % in the examples shown. An analysis from several orbits above the African sector, where the lithospheric field is significant, showed that the peak value of the signatures of the EEJ is in error by 5 % in average when lithospheric contributions are not considered, which is in the range of uncertainties of present empirical models of the EEJ. KW - Geomagnetic field KW - Ionospheric current KW - Geomagnetic models Y1 - 2016 U6 - https://doi.org/10.1186/s40623-016-0494-1 SN - 1880-5981 VL - 68 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Sinclair, Nathalie A1 - Bussi, Maria G. Bartolini A1 - de Villiers, Michael A1 - Jones, Keith A1 - Kortenkamp, Ulrich A1 - Leung, Allen A1 - Owens, Kay T1 - Recent research on geometry education: an ICME-13 survey team report JF - ZDM : The International Journal on Mathematics Education N2 - This survey on the theme of Geometry Education (including new technologies) focuses chiefly on the time span since 2008. Based on our review of the research literature published during this time span (in refereed journal articles, conference proceedings and edited books), we have jointly identified seven major threads of contributions that span from the early years of learning (pre-school and primary school) through to post-compulsory education and to the issue of mathematics teacher education for geometry. These threads are as follows: developments and trends in the use of theories; advances in the understanding of visuo spatial reasoning; the use and role of diagrams and gestures; advances in the understanding of the role of digital technologies; advances in the understanding of the teaching and learning of definitions; advances in the understanding of the teaching and learning of the proving process; and, moving beyond traditional Euclidean approaches. Within each theme, we identify relevant research and also offer commentary on future directions. KW - Geometry KW - Technology KW - Diagrams KW - Definitions KW - Gestures KW - Proving KW - Digital technology KW - Visuospatial reasoning Y1 - 2016 U6 - https://doi.org/10.1007/s11858-016-0796-6 SN - 1863-9690 SN - 1863-9704 VL - 48 SP - 691 EP - 719 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Flad, H. -J. A1 - Harutyunyan, Gohar A1 - Schulze, Bert-Wolfgang T1 - Asymptotic parametrices of elliptic edge operators JF - Journal of pseudo-differential operators and applications N2 - We study operators on singular manifolds, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. We introduce asymptotic parametrices, using tools from cone and edge pseudo-differential algebras. Our structures are motivated by models of many-particle physics with singular Coulomb potentials that contribute higher order singularities in Euclidean space, determined by the number of particles. KW - Cone and edge pseudo-differential operators KW - Ellipticity of edge-degenerate operators KW - Meromorphic operator-valued symbols KW - Asymptotics of solutions Y1 - 2016 U6 - https://doi.org/10.1007/s11868-016-0159-7 SN - 1662-9981 SN - 1662-999X VL - 7 SP - 321 EP - 363 PB - Springer CY - Basel ER - TY - JOUR A1 - Beinrucker, Andre A1 - Dogan, Urun A1 - Blanchard, Gilles T1 - Extensions of stability selection using subsamples of observations and covariates JF - Statistics and Computing N2 - 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. KW - Variable selection KW - Stability selection KW - Subsampling Y1 - 2016 U6 - https://doi.org/10.1007/s11222-015-9589-y SN - 0960-3174 SN - 1573-1375 VL - 26 SP - 1059 EP - 1077 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Keller, Matthias A1 - Münch, Florentin A1 - Pogorzelski, Felix T1 - Geometry and spectrum of rapidly branching graphs JF - Mathematische Nachrichten N2 - 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 KW - Graph Laplacians KW - discrete spectrum KW - eigenvalue asymptotics KW - isoperimetric estimates KW - stochastic completeness Y1 - 2016 U6 - https://doi.org/10.1002/mana.201400349 SN - 0025-584X SN - 1522-2616 VL - 289 SP - 1636 EP - 1647 PB - Wiley-VCH CY - Weinheim ER - TY - JOUR A1 - Kortenkamp, Ulrich A1 - Monaghan, John A1 - Trouche, Luc T1 - Jonathan M Borwein (1951-2016): exploring, experiencing and experimenting in mathematics - an inspiring journey in mathematics JF - Educational studies in mathematics : an international journal Y1 - 2016 U6 - https://doi.org/10.1007/s10649-016-9729-0 SN - 0013-1954 SN - 1573-0816 VL - 93 SP - 131 EP - 136 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Ly, Ibrahim A1 - Tarkhanov, Nikolai Nikolaevich T1 - A Rado theorem for p-harmonic functions JF - Boletin de la Sociedad Matemática Mexicana N2 - Let A be a nonlinear differential operator on an open set X subset of R-n and S a closed subset of X. Given a class F of functions in X, the set S is said to be removable for F relative to A if any weak solution of A(u) = 0 in XS of class F satisfies this equation weakly in all of X. For the most extensively studied classes F, we show conditions on S which guarantee that S is removable for F relative to A. KW - Quasilinear equations KW - Removable sets KW - p-Laplace equation Y1 - 2016 U6 - https://doi.org/10.1007/s40590-016-0109-7 SN - 1405-213X SN - 2296-4495 VL - 22 SP - 461 EP - 472 PB - Springer CY - Basel ER - TY - JOUR A1 - Müller, Detlef A1 - Böckmann, Christine A1 - Kolgotin, Alexei A1 - Schneidenbach, Lars A1 - Chemyakin, Eduard A1 - Rosemann, Julia A1 - Znak, Pavel A1 - Romanov, Anton T1 - Microphysical particle properties derived from inversion algorithms developed in the framework of EARLINET JF - Atmospheric measurement techniques : an interactive open access journal of the European Geosciences Union N2 - 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. Y1 - 2016 U6 - https://doi.org/10.5194/amt-9-5007-2016 SN - 1867-1381 SN - 1867-8548 VL - 9 SP - 5007 EP - 5035 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Bär, Christian A1 - Strohmaier, Alexander T1 - A Rigorous Geometric Derivation of the Chiral Anomaly in Curved Backgrounds JF - Communications in mathematical physics N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1007/s00220-016-2664-1 SN - 0010-3616 SN - 1432-0916 VL - 347 SP - 703 EP - 721 PB - Springer CY - New York ER - TY - JOUR A1 - Blanchard, Gilles A1 - Kraemer, Nicole T1 - Convergence rates of Kernel Conjugate Gradient for random design regression JF - Analysis and applications N2 - 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. KW - Nonparametric regression KW - reproducing kernel Hilbert space KW - conjugate gradient KW - partial least squares KW - minimax convergence rates Y1 - 2016 U6 - https://doi.org/10.1142/S0219530516400017 SN - 0219-5305 SN - 1793-6861 VL - 14 SP - 763 EP - 794 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Mieth, Bettina A1 - Kloft, Marius A1 - Rodriguez, Juan Antonio A1 - Sonnenburg, Soren A1 - Vobruba, Robin A1 - Morcillo-Suarez, Carlos A1 - Farre, Xavier A1 - Marigorta, Urko M. A1 - Fehr, Ernst A1 - Dickhaus, Thorsten A1 - Blanchard, Gilles A1 - Schunk, Daniel A1 - Navarro, Arcadi A1 - Müller, Klaus-Robert T1 - Combining Multiple Hypothesis Testing with Machine Learning Increases the Statistical Power of Genome-wide Association Studies JF - Scientific reports N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1038/srep36671 SN - 2045-2322 VL - 6 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Keller, Matthias A1 - Mugnolo, Delio T1 - General Cheeger inequalities for p-Laplacians on graphs JF - Theoretical ecology N2 - 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. KW - Cheeger inequalities KW - Spectral theory of graphs KW - Intrinsic metrics for Dirichlet forms Y1 - 2016 U6 - https://doi.org/10.1016/j.na.2016.07.011 SN - 0362-546X SN - 1873-5215 VL - 147 SP - 80 EP - 95 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Wichitsa-Nguan, Korakot A1 - Läuter, Henning A1 - Liero, Hannelore T1 - Estimability in Cox models JF - Statistical Papers N2 - 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. KW - Cox model KW - Estimability KW - Asymptotic variance of maximum partial likelihood estimate Y1 - 2016 U6 - https://doi.org/10.1007/s00362-016-0755-x SN - 0932-5026 SN - 1613-9798 VL - 57 SP - 1121 EP - 1140 PB - Springer CY - New York ER - TY - JOUR A1 - Zöller, Gert A1 - Holschneider, Matthias T1 - The Maximum Possible and the Maximum Expected Earthquake Magnitude for Production-Induced Earthquakes at the Gas Field in Groningen, The Netherlands JF - Bulletin of the Seismological Society of America N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1785/0120160220 SN - 0037-1106 SN - 1943-3573 VL - 106 SP - 2917 EP - 2921 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Keller, Matthias A1 - Lenz, Daniel A1 - Münch, Florentin A1 - Schmidt, Marcel A1 - Telcs, Andras T1 - Note on short-time behavior of semigroups associated to self-adjoint operators JF - Bulletin of the London Mathematical Society N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1112/blms/bdw054 SN - 0024-6093 SN - 1469-2120 VL - 48 SP - 935 EP - 944 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Menne, Ulrich T1 - Sobolev functions on varifolds JF - Proceedings of the London Mathematical Society N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1112/plms/pdw023 SN - 0024-6115 SN - 1460-244X VL - 113 SP - 725 EP - 774 PB - Oxford Univ. Press CY - Oxford ER - TY - THES A1 - Cheng, Yuan T1 - Recursive state estimation in dynamical systems Y1 - 2016 ER - TY - THES A1 - Samaras, Stefanos T1 - Microphysical retrieval of non-spherical aerosol particles using regularized inversion of multi-wavelength lidar data T1 - Retrieval der Mikrophysik von nichtkugelförmigen Aerosolpartikeln durch regularisierte Inversion von Mehrwellenlängen-Lidardaten N2 - Numerous reports of relatively rapid climate changes over the past century make a clear case of the impact of aerosols and clouds, identified as sources of largest uncertainty in climate projections. Earth’s radiation balance is altered by aerosols depending on their size, morphology and chemical composition. Competing effects in the atmosphere can be further studied by investigating the evolution of aerosol microphysical properties, which are the focus of the present work. The aerosol size distribution, the refractive index, and the single scattering albedo are commonly used such properties linked to aerosol type, and radiative forcing. Highly advanced lidars (light detection and ranging) have reduced aerosol monitoring and optical profiling into a routine process. Lidar data have been widely used to retrieve the size distribution through the inversion of the so-called Lorenz-Mie model (LMM). This model offers a reasonable treatment for spherically approximated particles, it no longer provides, though, a viable description for other naturally occurring arbitrarily shaped particles, such as dust particles. On the other hand, non-spherical geometries as simple as spheroids reproduce certain optical properties with enhanced accuracy. Motivated by this, we adapt the LMM to accommodate the spheroid-particle approximation introducing the notion of a two-dimensional (2D) shape-size distribution. Inverting only a few optical data points to retrieve the shape-size distribution is classified as a non-linear ill-posed problem. A brief mathematical analysis is presented which reveals the inherent tendency towards highly oscillatory solutions, explores the available options for a generalized solution through regularization methods and quantifies the ill-posedness. The latter will improve our understanding on the main cause fomenting instability in the produced solution spaces. The new approach facilitates the exploitation of additional lidar data points from depolarization measurements, associated with particle non-sphericity. However, the generalization of LMM vastly increases the complexity of the problem. The underlying theory for the calculation of the involved optical cross sections (T-matrix theory) is computationally so costly, that would limit a retrieval analysis to an unpractical point. Moreover the discretization of the model equation by a 2D collocation method, proposed in this work, involves double integrations which are further time consuming. We overcome these difficulties by using precalculated databases and a sophisticated retrieval software (SphInX: Spheroidal Inversion eXperiments) especially developed for our purposes, capable of performing multiple-dataset inversions and producing a wide range of microphysical retrieval outputs. Hybrid regularization in conjunction with minimization processes is used as a basis for our algorithms. Synthetic data retrievals are performed simulating various atmospheric scenarios in order to test the efficiency of different regularization methods. The gap in contemporary literature in providing full sets of uncertainties in a wide variety of numerical instances is of major concern here. For this, the most appropriate methods are identified through a thorough analysis on an overall-behavior basis regarding accuracy and stability. The general trend of the initial size distributions is captured in our numerical experiments and the reconstruction quality depends on data error level. Moreover, the need for more or less depolarization points is explored for the first time from the point of view of the microphysical retrieval. Finally, our approach is tested in various measurement cases giving further insight for future algorithm improvements. N2 - Zahlreiche Berichte von relativ schnellen Klimaveränderungen im vergangenen Jahrhundert liefern überzeugende Argumente über die Auswirkungen von Aerosolen und Wolken auf Wetter und Klima. Aerosole und Wolken wurden als Quellen größter Unsicherheit in Klimaprognosen identifiziert. Die Strahlungsbilanz der Erde wird verändert durch die Partikelgröße, ihre Morphologie und ihre chemische Zusammensetzung. Konkurrierende Effekte in der Atmosphäre können durch die Bestimmung von mikrophysikalischen Partikeleigenschaften weiter untersucht werden, was der Fokus der vorliegenden Arbeit ist. Die Aerosolgrößenverteilung, der Brechungsindex der Partikeln und die Einzel-Streu-Albedo sind solche häufig verwendeten Parameter, die mit dem Aerosoltyp und dem Strahlungsantrieb verbunden sind. Hoch entwickelte Lidare (Light Detection and Ranging) haben die Aerosolüberwachung und die optische Profilierung zu einem Routineprozess gemacht. Lidar-Daten wurden verwendet um die Größenverteilung zu bestimmen, was durch die Inversion des sogenannten Lorenz-Mie-Modells (LMM) gelingt. Dieses Modell bietet eine angemessene Behandlung für sphärisch angenäherte Partikeln, es stellt aber keine brauchbare Beschreibung für andere natürlich auftretende beliebig geformte Partikeln -wie z.B. Staubpartikeln- bereit. Andererseits stellt die Einbeziehung einer nicht kugelförmigen Geometrie –wie z.B. einfache Sphäroide- bestimmte optische Eigenschaften mit verbesserter Genauigkeit dar. Angesichts dieser Tatsache erweitern wir das LMM durch die Approximation von Sphäroid-Partikeln. Dazu ist es notwendig den Begriff einer zweidimensionalen Größenverteilung einzuführen. Die Inversion einer sehr geringen Anzahl optischer Datenpunkte zur Bestimmung der Form der Größenverteilung ist als ein nichtlineares schlecht gestelltes Problem bekannt. Eine kurze mathematische Analyse wird vorgestellt, die die inhärente Tendenz zu stark oszillierenden Lösungen zeigt. Weiterhin werden Optionen für eine verallgemeinerte Lösung durch Regularisierungsmethoden untersucht und der Grad der Schlechtgestelltheit quantifiziert. Letzteres wird unser Verständnis für die Hauptursache der Instabilität bei den berechneten Lösungsräumen verbessern. Der neue Ansatz ermöglicht es uns, zusätzliche Lidar-Datenpunkte aus Depolarisationsmessungen zu nutzen, die sich aus der Nicht-sphärizität der Partikeln assoziieren. Die Verallgemeinerung des LMMs erhöht erheblich die Komplexität des Problems. Die zugrundeliegende Theorie für die Berechnung der beteiligten optischen Querschnitte (T-Matrix-Ansatz) ist rechnerisch so aufwendig, dass eine Neuberechnung dieser nicht sinnvoll erscheint. Darüber hinaus wird ein zweidimensionales Kollokationsverfahren für die Diskretisierung der Modellgleichung vorgeschlagen. Dieses Verfahren beinhaltet Doppelintegrationen, die wiederum zeitaufwendig sind. Wir überwinden diese Schwierigkeiten durch Verwendung vorgerechneter Datenbanken sowie einer hochentwickelten Retrieval-Software (SphInX: Spheroidal Inversion eXperiments). Diese Software wurde speziell für unseren Zweck entwickelt und ist in der Lage mehrere Datensatzinversionen gleichzeitig durchzuführen und eine große Auswahl von mikrophysikalischen Retrieval-Ausgaben bereitzustellen. Eine hybride Regularisierung in Verbindung mit einem Minimierungsverfahren wird als Grundlage für unsere Algorithmen verwendet. Synthetische Daten-Inversionen werden mit verschiedenen atmosphärischen Szenarien durchgeführt, um die Effizienz verschiedener Regularisierungsmethoden zu untersuchen. Die Lücke in der gegenwärtigen wissenschaftlichen Literatur gewisse Unsicherheiten durch breitgefächerte numerische Fälle bereitzustellen, ist ein Hauptanliegen dieser Arbeit. Motiviert davon werden die am besten geeigneten Verfahren einer gründlichen Analyse in Bezug auf ihr Gesamtverhalten, d.h. Genauigkeit und Stabilität, unterzogen. Der allgemeine Trend der Anfangsgrößenverteilung wird in unseren numerischen Experimenten erfasst. Zusätzlich hängt die Rekonstruktionsqualität vom Datenfehler ab. Darüber hinaus wird die Anzahl der notwendigen Depolarisationspunkte zum ersten Mal aus der Sicht des mikrophysikalischen Parameter-Retrievals erforscht. Abschließend verwenden wir unsere Software für verschiedene Messfälle, was weitere Einblicke für künftige Verbesserungen des Algorithmus gibt. KW - microphysics KW - retrieval KW - lidar KW - aerosols KW - regularization KW - ill-posed KW - inversion KW - Mikrophysik KW - Retrieval KW - Lidar KW - Aerosole KW - Regularisierung KW - schlecht gestellt KW - Inversion Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-396528 ER -