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 -