@article{PornsawadBoeckmann2016, author = {Pornsawad, Pornsarp and B{\"o}ckmann, Christine}, title = {Modified Iterative Runge-Kutta-Type Methods for Nonlinear Ill-Posed Problems}, series = {Numerical functional analysis and optimization : an international journal of rapid publication}, volume = {37}, journal = {Numerical functional analysis and optimization : an international journal of rapid publication}, publisher = {Wiley-VCH}, address = {Philadelphia}, issn = {0163-0563}, doi = {10.1080/01630563.2016.1219744}, pages = {1562 -- 1589}, year = {2016}, abstract = {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.}, language = {en} } @article{ChangViahmoudiSchulze2016, author = {Chang, D. -C. and Viahmoudi, M. Hedayat and Schulze, Bert-Wolfgang}, title = {PSEUDO-DIFFERENTIAL ANALYSIS WITH TWISTED SYMBOLIC STRUCTURE}, series = {Journal of nonlinear and convex analysis : an international journal}, volume = {17}, journal = {Journal of nonlinear and convex analysis : an international journal}, publisher = {Yokohama Publishers}, address = {Yokohama}, issn = {1345-4773}, pages = {1889 -- 1937}, year = {2016}, abstract = {This paper is devoted to pseudo-differential operators and new applications. We establish necessary extensions of the standard calculus to specific classes of operator-valued symbols occurring in principal symbolic hierarchies of operators on manifolds with singularities or stratified spaces.}, language = {en} } @article{BlanchardFlaskaHandyetal.2016, author = {Blanchard, Gilles and Flaska, Marek and Handy, Gregory and Pozzi, Sara and Scott, Clayton}, title = {Classification with asymmetric label noise: Consistency and maximal denoising}, series = {Electronic journal of statistics}, volume = {10}, journal = {Electronic journal of statistics}, publisher = {Institute of Mathematical Statistics}, address = {Cleveland}, issn = {1935-7524}, doi = {10.1214/16-EJS1193}, pages = {2780 -- 2824}, year = {2016}, abstract = {In many real-world classification problems, the labels of training examples are randomly corrupted. Most previous theoretical work on classification with label noise assumes that the two classes are separable, that the label noise is independent of the true class label, or that the noise proportions for each class are known. In this work, we give conditions that are necessary and sufficient for the true class-conditional distributions to be identifiable. These conditions are weaker than those analyzed previously, and allow for the classes to be nonseparable and the noise levels to be asymmetric and unknown. The conditions essentially state that a majority of the observed labels are correct and that the true class-conditional distributions are "mutually irreducible," a concept we introduce that limits the similarity of the two distributions. For any label noise problem, there is a unique pair of true class-conditional distributions satisfying the proposed conditions, and we argue that this pair corresponds in a certain sense to maximal denoising of the observed distributions. Our results are facilitated by a connection to "mixture proportion estimation," which is the problem of estimating the maximal proportion of one distribution that is present in another. We establish a novel rate of convergence result for mixture proportion estimation, and apply this to obtain consistency of a discrimination rule based on surrogate loss minimization. Experimental results on benchmark data and a nuclear particle classification problem demonstrate the efficacy of our approach.}, language = {en} } @article{LevyJimenezPaycha2016, author = {Levy, Cyril and Jimenez, Carolina Neira and Paycha, Sylvie}, title = {THE CANONICAL TRACE AND THE NONCOMMUTATIVE RESIDUE ON THE NONCOMMUTATIVE TORUS}, series = {Transactions of the American Mathematical Society}, volume = {368}, journal = {Transactions of the American Mathematical Society}, publisher = {American Mathematical Soc.}, address = {Providence}, issn = {0002-9947}, doi = {10.1090/tran/6369}, pages = {1051 -- 1095}, year = {2016}, abstract = {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.}, language = {en} } @article{Tarkhanov2016, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Deformation quantization and boundary value problems}, series = {International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis \& topology}, volume = {13}, journal = {International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis \& topology}, publisher = {World Scientific}, address = {Singapore}, issn = {0219-8878}, doi = {10.1142/S0219887816500079}, pages = {176 -- 195}, year = {2016}, abstract = {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.}, language = {en} } @article{EichmairMetzger2016, author = {Eichmair, Michael and Metzger, Jan}, title = {JENKINS-SERRIN-TYPE RESULTS FOR THE JANG EQUATION}, series = {Journal of differential geometry}, volume = {102}, journal = {Journal of differential geometry}, publisher = {International Press of Boston}, address = {Somerville}, issn = {0022-040X}, doi = {10.4310/jdg/1453910454}, pages = {207 -- 242}, year = {2016}, abstract = {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.}, language = {en} } @article{ShtrakovKoppitz2016, author = {Shtrakov, Slavcho and Koppitz, J{\"o}rg}, title = {Stable varieties of semigroups and groupoids}, series = {Algebra universalis}, volume = {75}, journal = {Algebra universalis}, publisher = {Springer}, address = {Basel}, issn = {0002-5240}, doi = {10.1007/s00012-015-0359-7}, pages = {85 -- 106}, year = {2016}, abstract = {The paper deals with Sigma-composition and Sigma-essential composition of terms which lead to stable and s-stable varieties of algebras. A full description of all stable varieties of semigroups, commutative and idempotent groupoids is obtained. We use an abstract reduction system which simplifies the presentations of terms of type tau - (2) to study the variety of idempotent groupoids and s-stable varieties of groupoids. S-stable varieties are a variation of stable varieties, used to highlight replacement of subterms of a term in a deductive system instead of the usual replacement of variables by terms.}, language = {en} } @article{AcevedoReichCubasch2016, author = {Acevedo, Walter and Reich, Sebastian and Cubasch, Ulrich}, title = {Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques}, series = {Climate dynamics : observational, theoretical and computational research on the climate system}, volume = {46}, journal = {Climate dynamics : observational, theoretical and computational research on the climate system}, publisher = {Springer}, address = {New York}, issn = {0930-7575}, doi = {10.1007/s00382-015-2683-1}, pages = {1909 -- 1920}, year = {2016}, abstract = {This paper investigates the applicability of the Vaganov-Shashkin-Lite (VSL) forward model for tree-ring-width chronologies as observation operator within a proxy data assimilation (DA) setting. Based on the principle of limiting factors, VSL combines temperature and moisture time series in a nonlinear fashion to obtain simulated TRW chronologies. When used as observation operator, this modelling approach implies three compounding, challenging features: (1) time averaging, (2) "switching recording" of 2 variables and (3) bounded response windows leading to "thresholded response". We generate pseudo-TRW observations from a chaotic 2-scale dynamical system, used as a cartoon of the atmosphere-land system, and attempt to assimilate them via ensemble Kalman filtering techniques. Results within our simplified setting reveal that VSL's nonlinearities may lead to considerable loss of assimilation skill, as compared to the utilization of a time-averaged (TA) linear observation operator. In order to understand this undesired effect, we embed VSL's formulation into the framework of fuzzy logic (FL) theory, which thereby exposes multiple representations of the principle of limiting factors. DA experiments employing three alternative growth rate functions disclose a strong link between the lack of smoothness of the growth rate function and the loss of optimality in the estimate of the TA state. Accordingly, VSL's performance as observation operator can be enhanced by resorting to smoother FL representations of the principle of limiting factors. This finding fosters new interpretations of tree-ring-growth limitation processes.}, language = {en} } @article{HackHanischSchenkel2016, author = {Hack, Thomas-Paul and Hanisch, Florian and Schenkel, Alexander}, title = {Supergeometry in Locally Covariant Quantum Field Theory}, series = {Communications in mathematical physics}, volume = {342}, journal = {Communications in mathematical physics}, publisher = {Springer}, address = {New York}, issn = {0010-3616}, doi = {10.1007/s00220-015-2516-4}, pages = {615 -- 673}, year = {2016}, abstract = {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.}, language = {en} } @article{SchroeterRitterHolschneideretal.2016, author = {Schroeter, M-A and Ritter, M. and Holschneider, Matthias and Sturm, H.}, title = {Enhanced DySEM imaging of cantilever motion using artificial structures patterned by focused ion beam techniques}, series = {Journal of micromechanics and microengineering}, volume = {26}, journal = {Journal of micromechanics and microengineering}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0960-1317}, doi = {10.1088/0960-1317/26/3/035010}, pages = {7}, year = {2016}, abstract = {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.}, language = {en} }