A Complex View of Barycentric Mappings

Barycentric coordinates are very popular for interpolating data values on polyhedral domains. It has been recently shown that expressing them as complex functions has various advantages when interpolating two‐dimensional data in the plane, and in particular for holomorphic maps. We extend and generalize these results by investigating the complex representation of real‐valued barycentric coordinates, when applied to planar domains. We show how the construction for generating real‐valued barycentric coordinates from a given weight function can be applied to generating complex‐valued coordinates, thus deriving complex expressions for the classical barycentric coordinates: Wachspress, mean value, and discrete harmonic. Furthermore, we show that a complex barycentric map admits the intuitive interpretation as a complex‐weighted combination of edge‐to‐edge similarity transformations, allowing the design of “home‐made” barycentric maps with desirable properties. Thus, using the tools of complex analysis, we provide a methodology for analyzing existing barycentric mappings, as well as designing new ones.     

Collision and intersection detection of two ruled surfaces using bracket method

Collision and intersection detection of surfaces is an important problem in computer graphics and robotic engineering. A key idea of our paper is to use the bracket method to derive the necessary and sufficient conditions for the collision of two ruled surfaces. Then the numerical intersection curve can be characterized. The cases for two bounded ruled surfaces are also discussed.     

Strong stability of the mono-tubular heat exchanger equation with output feedback

We investigate asymptotic behavior of the C₀-semigroup T(t) associated with the mono-tubular heat exchanger equation with output feedback by a perturbation method. It is shown that T(t) is bounded if a constraint is satisfied by the parameters and the spatial distribution function. Further, applying the Arendt-Batty-Lyubich-Vu theorem, a criterion is established to judge strong stability of T(t).     

Efficiently Testing Sparse <Emphasis Type="Italic">GF</Emphasis>(2) Polynomials

We give the first algorithm that is both query-efficient and time-efficient for testing whether an unknown function f:{0,1} ⁿ →{−1,1} is an s-sparse GF(2) polynomial versus ε-far from every such polynomial. Our algorithm makes poly(s,1/ε) black-box queries to f and runs in time n⋅poly(s,1/ε). The only previous algorithm for this testing problem (Diakonikolas et al. in Proceedings of the 48th Annual Symposium on Foundations of Computer Science, FOCS, pp. 549–558, 2007) used poly(s,1/ε) queries, but had running time exponential in s and super-polynomial in 1/ε.     

An Efficient Scaling Algorithm for the Minimum Weight Bibranching Problem

Let G=(VG,AG) be a digraph and let S ⊔ T be a bipartition of VG. A bibranching is a subset B⊆AG such that for each node s∈S there exists a directed s–T path in B and, vice versa, for each node t∈T there exists a directed S–t path in B.     

Sweeping Points

Given a set of points in the plane, and a sweep-line as a tool, what is best way to move the points to a target point using a sequence of sweeps? In a sweep, the sweep-line is placed at a start position somewhere in the plane, then moved orthogonally and continuously to another parallel end position, and then lifted from the plane. The cost of a sequence of sweeps is the total length of the sweeps. Another parameter of interest is the number of sweeps. Four variants are discussed, depending on whether the target is a hole or a pile, and whether the target is specified or freely selected by the algorithm. Here we present a ratio 4/π≈1.27 approximation algorithm in the length measure, which performs at most four sweeps. We also prove that, for the two constrained variants, there are sets of n points for which any sequence of minimum cost requires 3n/2?O(1) sweeps.     

一种基于码本聚类的低复杂度用户选择算法

现有块对角化(BD)预编码系统用户选择算法较少考虑利用已选用户与剩余用户之间的关系来排除不可选用户.针对这点不足,给出了一种采用码本聚类的低复杂度用户选择算法( CodeGreedy算法).该算法采用弦距离刻画用户信道的相关性,以此为依据将用户划分到不同码本空间中,聚集在同一码本空间的用户信道具有较强的相关性,形成互斥...     

BSPNN: boosted subspace probabilistic neural network for email security

In the modern age of Internet connectivity, advanced information systems have accumulated huge volumes of data. Such fast growing, tremendous amount of data, collected and stored in large databases has far exceeded our human ability to comprehend without proper tools. There has been a great deal of research conducted to explore the potential applications of Machine Learning technologies in Security Informatics. This article studies the Network Security Detection problems in which predictive models are constructed to detect network security breaches such as spamming. Due to overwhelming volume of data, complexity and dynamics of computer networks and evolving cyber threats, current security systems suffer limited performance with low detection accuracy and high number of false alarms. To address such performance issues, a novel Machine Learning algorithm, namely Boosted Subspace Probabilistic Neural Network (BSPNN), has been proposed which combines a Radial Basis Function Neural Network with an innovative diversity-based ensemble learning framework. Extensive empirical analyses suggested that BSPNN achieved high detection accuracy with relatively small computational complexity compared with other conventional detection methods.     

Orientation space filtering for multiple orientation linesegmentation

The goal of this paper is to present an appropriate method for the segmentation of lines at intersections (X-junctions) and branches (T-junctions), which can be regarded as local regions where lines occur at multiple orientations. A novel representation called “orientation space” is proposed, which is derived by adding the orientation axis to the abscissa and the ordinate of the image. The orientation space representation is constructed by treating the orientation parameter, to which Gabor filters can be tuned, as a continuous variable. The problem of segmenting lines at multiple orientations is dealt with by thresholding 3D images in the orientation space and then detecting the connected components therein. In this way, X-junctions and T-junctions can be separated effectively. Curve grouping can also be accomplished. The segmentation of mathematically modeled X-, T-, and L-junctions is demonstrated and analyzed. The sensitivity limits of the method are also discussed. Experimental results using both synthesized and real images show the method to be effective for junction segmentation and curve grouping     

Solvability conditions and solutions to perfect regulation problem under measurement output feedback

The problem of perfect regulation is to design a family of control laws for a given plant such that the resulting overall closed-loop system is internally stable and its controlled output can be reduced to zero arbitrarily fast from any initial condition. Such a problem was heavily studied by many researchers in the 1970s and early 1980s. However, to the best of our knowledge, all of the earlier results deal only with the problem under full state feedback. In this paper, we solve the long-standing problem of perfect regulation via measurement output feedback for general linear time-invariant multivariable systems. In particular, we derive necessary and sufficient conditions under which the problem of perfect regulation via measurement output feedback is solvable for general systems, and, under these conditions, construct two families of feedback laws, one of full order and the other reduced order, that solve the problem.