On one-sided filters for spectral Fourier approximations of discontinuous functions

The existence of one-sided filters, for spectral Fourier approximations of discontinuous functions, which can recover spectral accuracy up to discontinuity from one side, was proved. A least square procedure was also used to construct such a filter and test it on several discontinuous functions numerically

Non-oscillatory spectral Fourier methods for shock wave calculations

A non-oscillatory spectral Fourier method is presented for the solution of hyperbolic partial differential equations. The method is based on adding a nonsmooth function to the trigonometric polynomials which are the usual basis functions for the Fourier method. The high accuracy away from the shock is enhanced by using filters. Numerical results confirm that no oscillations develop in the solution. Also, the accuracy of the spectral solution of the inviscid Burgers equation is shown to be higher than a fixed order

Detrended fluctuation analysis on the correlations of complex networks under attack and repair strategy

We analyze the correlation properties of the Erdos-Renyi random graph (RG) and the Barabasi-Albert scale-free network (SF) under the attack and repair strategy with detrended fluctuation analysis (DFA). The maximum degree k_max, representing the local property of the system, shows similar scaling behaviors for random graphs and scale-free networks. The fluctuations are quite random at short time scales but display strong anticorrelation at longer time scales under the same system size N and different repair probability p_re. The average degree , revealing the statistical property of the system, exhibits completely different scaling behaviors for random graphs and scale-free networks. Random graphs display long-range power-law correlations. Scale-free networks are uncorrelated at short time scales; while anticorrelated at longer time scales and the anticorrelation becoming stronger with the increase of p_re.Comment: 5 pages, 4 figure

Universal R-matrix Of The Super Yangian Double DY(gl(1|1))

Based on Drinfeld realization of super Yangian Double DY(gl(1|1)), its pairing relations and universal R-matrix are given. By taking evaluation representation of universal R-matrix, another realization $L^{\pm}(u)$ of DY(gl(1|1)) is obtained. These two realizations of DY(gl(1|1)) are related by the supersymmetric extension of Ding-Frenkel map.Comment: 6 pages, latex, no figure

Triangular Bézier sub-surfaces on a triangular Bézier surface

This paper considers the problem of computing the Bézier representation for a triangular sub-patch on a triangular Bézier surface. The triangular sub-patch is defined as a composition of the triangular surface and a domain surface that is also a triangular Bézier patch. Based on de Casteljau recursions and shifting operators, previous methods express the control points of the triangular sub-patch as linear combinations of the construction points that are constructed from the control points of the triangular Bézier surface. The construction points contain too many redundancies. This paper derives a simple explicit formula that computes the composite triangular sub-patch in terms of the blossoming points that correspond to distinct construction points and then an efficient algorithm is presented to calculate the control points of the sub-patch

SE-shapelets: Semi-supervised Clustering of Time Series Using Representative Shapelets

Shapelets that discriminate time series using local features (subsequences) are promising for time series clustering. Existing time series clustering methods may fail to capture representative shapelets because they discover shapelets from a large pool of uninformative subsequences, and thus result in low clustering accuracy. This paper proposes a Semi-supervised Clustering of Time Series Using Representative Shapelets (SE-Shapelets) method, which utilizes a small number of labeled and propagated pseudo-labeled time series to help discover representative shapelets, thereby improving the clustering accuracy. In SE-Shapelets, we propose two techniques to discover representative shapelets for the effective clustering of time series. 1) A \textit{salient subsequence chain} ($SSC$) that can extract salient subsequences (as candidate shapelets) of a labeled/pseudo-labeled time series, which helps remove massive uninformative subsequences from the pool. 2) A \textit{linear discriminant selection} ($LDS$) algorithm to identify shapelets that can capture representative local features of time series in different classes, for convenient clustering. Experiments on UCR time series datasets demonstrate that SE-shapelets discovers representative shapelets and achieves higher clustering accuracy than counterpart semi-supervised time series clustering methods