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- ItemCanonical sets of best L1-approximation(New York, NY : Hindawi, 2012) Dryanov, D.; Petrov, P.In mathematics, the term approximation usually means either interpolation on a point set or approximation with respect to a given distance. There is a concept, which joins the two approaches together, and this is the concept of characterization of the best approximants via interpolation. It turns out that for some large classes of functions the best approximants with respect to a certain distance can be constructed by interpolation on a point set that does not depend on the choice of the function to be approximated. Such point sets are called canonical sets of best approximation. The present paper summarizes results on canonical sets of best L1-approximation with emphasis on multivariate interpolation and best L1-approximation by blending functions. The best L1-approximants are characterized as transfinite interpolants on canonical sets. The notion of a Haar-Chebyshev system in the multivariate case is discussed also. In this context, it is shown that some multivariate interpolation spaces share properties of univariate Haar-Chebyshev systems. We study also the problem of best one-sided multivariate L 1-approximation by sums of univariate functions. Explicit constructions of best one-sided L1-approximants give rise to well-known and new inequalities.
- ItemAdaptive smoothing of digital images: The R package adimpro(Los Angeles, Calif. : UCLA, Dept. of Statistics, 2007) Polzehl, J.; Tabelow, K.Digital imaging has become omnipresent in the past years with a bulk of applications ranging from medical imaging to photography. When pushing the limits of resolution and sensitivity noise has ever been a major issue. However, commonly used non-adaptive filters can do noise reduction at the cost of a reduced effective spatial resolution only. Here we present a new package adimpro for R, which implements the propagationseparation approach by (Polzehl arid Spokoiriy 2006) for smoothing digital images. This method naturally adapts to different structures of different size in the image and thus avoids oversmoothing edges and fine structures. We extend the method for imaging data with spatial correlation. Furthermore we show how the estimation of the dependence between variance and mean value can be included. We illustrate the use of the package through some examples.
- ItemStatistical methods for the qualitative assessment of dynamic models with time delay (R package qualV)(Los Angeles, CA : Foundation for Open Access Statistics, 2007) Jachner, S.; Van Den Boogaart, K.G.; Petzoldt, T.Results of ecological models differ, to some extent, more from measured data than from empirical knowledge. Existing techniques for validation based on quantitative assessments sometimes cause an underestimation of the performance of models due to time shifts, accelerations and delays or systematic differences between measurement and simulation. However, for the application of such models it is often more important to reproduce essential patterns instead of seemingly exact numerical values. This paper presents techniques to identify patterns and numerical methods to measure the consistency of patterns between observations and model results. An orthogonal set of deviance measures for absolute, relative and ordinal scale was compiled to provide informations about the type of difference. Furthermore, two different approaches accounting for time shifts were presented. The first one transforms the time to take time delays and speed differences into account. The second one describes known qualitative criteria dividing time series into interval units in accordance to their main features. The methods differ in their basic concepts and in the form of the resulting criteria. Both approaches and the deviance measures discussed are implemented in an R package. All methods are demonstrated by means of water quality measurements and simulation data. The proposed quality criteria allow to recognize systematic differences and time shifts between time series and to conclude about the quantitative and qualitative similarity of patterns.
- ItemTopology identification of complex network via chaotic ant swarm algorithm(New York, NY : Hindawi Publishing Corporation, 2013) Peng, H.; Li, L.; Kurths, J.; Li, S.; Yang, Y.Nowadays, the topology of complex networks is essential in various fields as engineering, biology, physics, and other scientific fields. We know in some general cases that there may be some unknown structure parameters in a complex network. In order to identify those unknown structure parameters, a topology identification method is proposed based on a chaotic ant swarm algorithm in this paper. The problem of topology identification is converted into that of parameter optimization which can be solved by a chaotic ant algorithm. The proposed method enables us to identify the topology of the synchronization network effectively. Numerical simulations are also provided to show the effectiveness and feasibility of the proposed method.
- ItemA reconfigurable logic cell based on a simple dynamical system(New York, NY : Hindawi Publishing Corporation, 2013) Li, L.; Yang, C.; Hui, S.; Yu, W.; Kurths, J.; Peng, H.; Yang, Y.This paper introduces a new scheme to achieve a dynamic logic gate which can be adjusted flexibly to obtain different logic functions by adjusting specific parameters of a dynamical system. Based on graphical tools and the threshold mechanism, the distribution of different logic gates is studied, and a transformation method between different logics is given. Analyzing the performance of the dynamical system in the presence of noise, we discover that it is resistant to system noise. Moreover, we find some part of the system can be considered as a leaky integrator which has been already widely applied in engineering. Finally, we provide a proof-of-principle hardware implementation of the proposed scheme to illustrate its effectiveness. With the proposed scheme in hand, it is convenient to build the flexible, robust, and general purpose computing devices such as various network coding routers, communication encoders or decoders, and reconfigurable computer chips.
- ItemAdvanced Computational Engineering(Zürich : EMS Publ. House, 2012) Carstensen, Carsten; Schröder, Jörg; Wriggers, PeterThe finite element method is the established simulation tool for the numerical solution of partial differential equations in many engineering problems with many mathematical developments such as mixed finite element methods (FEMs) and other nonstandard FEMs like least-squares, nonconforming, and discontinuous Galerkin (dG) FEMs. Various aspects on this plus related topics ranging from order-reduction methods to isogeometric analysis has been discussed amongst the pariticpants form mathematics and engineering for a large range of applications.
- ItemAlgorithmische Graphentheorie(Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 2002) Jansen, Klaus; Schiermeyer, Ingo[no abstract available]
- ItemAnalysis of Boundary Element Methods(Zürich : EMS Publ. House, 2008) Stephan, Ernst P.[no abstract available]
- ItemAlgebraic K-theory and Motivic Cohomology(Zürich : EMS Publ. House, 2013) Huber-Klawitter, Annette; Jannsen, Uwe; Levine, MarcAlgebraic K-theory and motivic cohomology are strongly related tools providing a systematic way of producing invariants for algebraic or geometric structures. The definition and methods are taken from algebraic topology, but there have been particularly fruitful applications to problems of algebraic geometry, number theory or quadratic forms. 19 one-hour talks presented a wide range of latest results on the theory and its applications.
- ItemActions and Invariants of Residually Finite Groups: Asymptotic Methods(Zürich : EMS Publ. House, 2010) Gaboriau, Damien; Grunewald, FritzThe workshop brought together experts in finite group theory, L2-cohomology, measured group theory, the theory of lattices in Lie groups, probability and topology. The common object of interest was residually finite groups, that each field investigates from a different angle.