Multi-degree reduction of triangular Bézier surfaces with boundary constraints

Given a triangular Bézier surface of degree n, the problem of multi-degree reduction by a triangular Bézier surface of degree m with boundary constraints is investigated. This paper considers the continuity of triangular Bézier surfaces at the three corners, so that the boundary curves preserve endpoints continuity of any order . The l₂- and L₂-norm combined with the constrained least-squares method are used to get the matrix representations for the control points of the degree reduced surfaces. Both methods can be applied to piecewise continuous triangular patches or to only a triangular patch with the combination of surface subdivision. And the resulting piecewise approximating patches are globally C⁰ continuous. Finally, error estimation is given and numerical examples demonstrate the effectiveness of our methods.     

A minimal representation of Markov arrival processes and a moments matching method

The paper investigates the problem of minimal representation of Markov arrival processes of order n (MAP(n)). The minimal representation of MAPs is crucial for developing effective fitting methods. It seems that all existing MAP fitting methods are based on the , representation which is known to be redundant. We present the minimal number of parameters to define a MAP(n) and provide a numerical moments-matching method based on a minimal representation.

The discussion starts with a characterization of phase type (PH) distributions and then the analysis of MAPs follows a similar pattern. This characterization contains essential results on the identity of stationary behaviour of MAPs and on the number of parameters required to describe the stationary behaviour.

The proposed moments matching method is also applicable for PH distributions. In this case it is a unique method that fits a general PH distribution of order n based on 2n−1 parameters.     

The two-equal-disjoint path cover problem of Matching Composition Network

Embedding of paths have attracted much attention in the parallel processing. Many-to-many communication is one of the most central issues in various interconnection networks. A graph G is globally two-equal-disjoint path coverable if for any two distinct pairs of vertices (u,v) and (w,x) of G, there exist two disjoint paths P and Q satisfied that (1) P (Q, respectively) joins u and v (w and x, respectively), (2) |P|=|Q|, and (3) V(PQ)=V(G). The Matching Composition Network (MCN) is a family of networks which two components are connected by a perfect matching. In this paper, we consider the globally two-equal-disjoint path cover property of MCN. Applying our result, the Crossed cube CQ_n, the Twisted cube TQ_n, and the Möbius cube MQ_n can all be proven to be globally two-equal-disjoint path coverable for n5.     

Fibonacci mean and golden section mean

In this paper we show that there is a mapping D:M→DM on means such that if M is a Fibonacci mean so is DM, that if M is the harmonic mean, then DM is the arithmetic mean, and if M is a Fibonacci mean, then lim_n→∞DⁿM is the golden section mean.     

set membership identification: A survey

Robustness had become in past years a central issue in system and control theory, focusing the attention of researchers from the study of a single model to the investigation of a set of models, described by a set of perturbations of a “nominal” model. Such a set, often indicated as an uncertainty model set or model set for short, has to be suitably constructed to describe the inherent uncertainty about the system under consideration and to be used for analysis and design purposes. H_∞ identification methods deliver uncertainty model sets in a suitable form to be used by well-established robust design techniques, based on H_∞ or μ optimization methods. The literature on H_∞ identification is now very extensive. In this paper, some of the most relevant contributions related to assumption validation, evaluation of bounds on unmodeled dynamics, convergence analysis and optimality properties of linear, two-stage and interpolatory algorithms are surveyed from a deterministic point of view.     

Hamiltonian-connected graphs

For a simple graph G, let . In this paper, we prove that if NCD(G)≥|V(G)|, then either G is Hamiltonian-connected, or G belongs to a well-characterized class of graphs. The former results by Dirac, Ore and Faudree et al. are extended.     

output feedback control design for uncertain fuzzy singularly perturbed systems: an LMI approach

This paper examines the problem of designing a robust H_∞ output feedback controller for a class of singularly perturbed systems described by a Takagi–Sugeno fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain singularly perturbed nonlinear systems to have an H_∞ performance are derived. To eliminate the ill-conditioning caused by the interaction of slow and fast dynamic modes, solutions to the problem are presented in terms of LMIs which are independent of the singular perturbation . The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard singularly perturbed nonlinear systems. A numerical example is provided to illustrate the design developed in this paper.     

A parallel method for large sparse generalized eigenvalue problems using a GridRPC system

In this paper we present a master–worker type parallel method for finding several eigenvalues and eigenvectors of a generalized eigenvalue problem , where A and B are large sparse matrices. A moment-based method that finds all of the eigenvalues that lie inside a given domain is used. In this method, a small matrix pencil that has only the desired eigenvalues is derived by solving large sparse systems of linear equations constructed from A and B. Since these equations can be solved independently, we solve them on remote servers in parallel. This approach is suitable for master–worker programming models. We have implemented and tested the proposed method in a grid environment using a grid RPC (remote procedure call) system called OmniRPC. The performance of the method on PC clusters that were used over a wide-area network was evaluated.     

Fast algorithms for finding disjoint subsequences with extremal densities

We derive fast algorithms for the following problem: given a set of n points on the real line and two parameters s and p, find s disjoint intervals of maximum total length that contain at most p of the given points. Our main contribution consists of algorithms whose time bounds improve upon a straightforward dynamic programming algorithm, in the relevant case that input size n is much bigger than parameters s and p. These results are achieved by selecting a few candidate intervals that are provably sufficient for building an optimal solution via dynamic programming. As a byproduct of this idea we improve an algorithm for a similar subsequence problem of Chen et al. [Disjoint segments with maximum density, in: International Workshop on Bioinformatics Research and Applications IWBRA 2005, (within ICCS 2005), Lecture Notes in Computer Science, vol. 3515, Springer, Berlin, pp. 845–850]. The problems are motivated by the search for significant patterns in biological data. Finally, we propose several heuristics that further reduce the time complexity in typical instances. One of them leads to an apparently open subsequence sum problem of independent interest.     

A new algebra of Toeplitz-plus-Hankel matrices and applications

We introduce a new simultaneously diagonalizable real algebra of symmetrical centrosymmetrical matrices having a Toeplitz-plus-Hankel structure. We give the corresponding orthonormal basis of eigenvectors which are alternately symmetrical and skewsymmetrical vectors. An application is the construction of a symmetrical Toeplitz-plus-centrosymmetrical Hankel matrix of equal row sums having a prescribed real spectrum. This matrix can be used as the starting matrix for symmetrical centrosymmetrical isospectral flows. In particular, for the isospectral flow corresponding to the construction of a regular Toeplitz matrix having prescribed eigenvalues. Moreover, if A is a noise representation of an unknown matrix in of rank k then we give a procedure to approximate A by a matrix in of rank k.     

Improved construction for universality of determinant and permanent

Valiant [L. Valiant, Completeness classes in algebra, in: Proc. 11th Annual ACM Symposium on the Theory of Computing, Atlanta, GA, 1979, pp. 249–261] proved that every polynomial of formula size e is a projection of the (e+2)×(e+2) determinant polynomial. We improve “e+2” to “e+1”, also for a definition of formula size that does not count multiplications by constants as gates. Our proof imitates the “2e+2” proof of von zur Gathen [J. von zur Gathen, Feasible arithmetic computations: Valiant's hypothesis, Journal of Symbolic Computation 4 (1987) 137–172], but uses different invariants and a tighter set of base cases.     

Hermite interpolation with simple planar PH curves by speed reparametrization

We introduce a new method of solving C¹ Hermite interpolation problems, which makes it possible to use a wider range of PH curves with potentially better shapes. By characterizing PH curves by roots of their hodographs in the complex representation, we introduce PH curves of type K(t−c)²ⁿ⁺¹+d. Next, we introduce a speed reparametrization. Finally, we show that, for C¹ Hermite data, we can use PH curves of type K(t−c)²ⁿ⁺¹+d or strongly regular PH quintics satisfying the G¹ reduction of C¹ data, and use these curves to solve the original C¹ Hermite interpolation problem.     

Fault-tolerant and progressive transmission of images

A fault-tolerant progressive image transmission method is proposed. The advantages include the following: (1) Unlike most progressive methods, the image is divided into n parts with equal importance to avoid worrying about which part is lost or transmitted first. (2) If the image is a secret image, then the transmission can use n distinct channels (one shared result per channel), and intercepting up to r₁-1 channels by the enemy (r₁r_kn are all pre-set constants) will not reveal any secret. Meanwhile, the disconnection up to n-r_k channels will not affect the lossless recovery of the secret image.     

Reconstruction of convergent smooth B-spline surfaces

Recently, there have been improvements on reconstruction of smooth B-spline surfaces of arbitrary topological type, but the most important problem of smoothly stitching B-spline surface patches (the continuity problem of B-spline surface patches) in surface reconstruction has not been solved in an effective way. Therefore, the motivation of this paper is to study how to better improve and control the continuity between adjacent B-spline surfaces.

In this paper, we present a local scheme of constructing convergent G¹ smooth bicubic B-spline surface patches with single interior knots over a given arbitrary quad partition of a polygonal model. Unlike previous work which only produces (non-controllable) toleranced G¹ smooth B-spline surfaces, our algorithm generates convergent G¹ smooth B-spline surfaces, which means the continuity of the B-spline surfaces tends to G¹ smoothness as the number of control points increases. The most important feature of our algorithm is, in the meaning of convergent approximation order, the ability to control the continuity of B-spline surfaces within the given tolerance and capture the geometric details presented by the given data points.     

A novel lossless data compression scheme based on the error correcting Hamming codes

This paper introduces a novel lossless binary data compression scheme that is based on the error correcting Hamming codes, namely the HCDC scheme. In this scheme, the binary sequence to be compressed is divided into blocks of n bits length. To utilize the Hamming codes, the block is considered as a Hamming codeword that consists of p parity bits and d data bits (n=d+p). Then each block is tested to find if it is a valid or a non-valid Hamming codeword. For a valid block, only the d data bits preceded by 1 are written to the compressed file, while for a non-valid block all n bits preceded by 0 are written to the compressed file. These additional 1 and 0 bits are used to distinguish the valid and the non-valid blocks during the decompression process. An analytical formula is derived for computing the compression ratio as a function of block size, and fraction of valid data blocks in the sequence. The performance of the HCDC scheme is analyzed, and the results obtained are presented in tables and graphs. Finally, conclusions and recommendations for future works are pointed out.     

Analysis of input-to-state stability for discrete time nonlinear systems via dynamic programming

The input-to-state stability (ISS) property for systems with disturbances has received considerable attention over the past decade or so, with many applications and characterizations reported in the literature. The main purpose of this paper is to present analysis results for ISS that utilize dynamic programming techniques to characterize minimal ISS gains and transient bounds. These characterizations naturally lead to computable necessary and sufficient conditions for ISS. Our results make a connection between ISS and optimization problems in nonlinear dissipative systems theory (including L₂-gain analysis and nonlinear H_∞ theory). As such, the results presented address an obvious gap in the literature.     

Multimodal logic programming

We give a framework for developing the least model semantics, fixpoint semantics, and SLD-resolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. ) and some classical first-order Horn clauses. Our approach is direct and no special restriction on occurrences of □_i and _i is required. We apply our framework for a large class of basic serial multimodal logics, which are parameterized by an arbitrary combination of generalized versions of axioms T, B, 4, 5 (in the form, e.g. 4:□_i→□_j□_k) and I:□_i→□_j. Another part of the work is devoted to programming in multimodal logics intended for reasoning about multidegree belief, for use in distributed systems of belief, or for reasoning about epistemic states of agents in multiagent systems. For that we also use the framework, and although these latter logics belong to the mentioned class of basic serial multimodal logics, the special SLD-resolution calculi proposed for them are more efficient.     

Triple positive solutions for some second-order boundary value problem on a measure chain

In this paper, we study the existence of three positive solutions for the second-order two-point boundary value problem on a measure chain,

where f:[t₁,σ(t₂)]×[0,∞)×R→[0,∞) is continuous and p:[t₁,σ(t₂)]→[0,∞) a nonnegative function that is allowed to vanish on some subintervals of [t₁,σ(t₂)] of the measure chain. The method involves applications of a new fixed-point theorem due to Bai and Ge [Z.B. Bai, W.G. Ge, Existence of three positive solutions for some second order boundary-value problems, Comput. Math. Appl. 48 (2004) 699–707]. The emphasis is put on the nonlinear term f involved with the first order delta derivative x^Δ(t).     

Hybrid method for a general optimal sensor scheduling problem in discrete time

In this paper, we consider a general class of optimal sensor scheduling problems in discrete time. There are N₁ sensors available for acquiring data so as to estimate the needed but unknown signal. Only N₂ out of the N₁ sensors can be turned on at any moment, while different weights can be assigned to different sensors. This problem is formulated as a discrete time deterministic optimal control problem involving both discrete and continuous valued controls. A computational method is developed for solving this discrete time deterministic optimal control problem based on a branch and bound method in conjunction with a gradient-based method. The branch and bound method is used to determine the optimal schedule of sensors, where a sequence of lower bound dynamic systems is introduced so as to provide effective lower bounds for the construction of the branching rules. Each of the branches is an optimal weight vector assignment problem and a gradient-based method is developed for solving this optimal control problem. For illustration, two numerical examples are solved.     

Tuning and auto-tuning of fractional order controllers for industry applications

This paper deals with the design of fractional order PI^λD^μ controllers, in which the orders of the integral and derivative parts, λ and μ, respectively, are fractional. The purpose is to take advantage of the introduction of these two parameters and fulfill additional specifications of design, ensuring a robust performance of the controlled system with respect to gain variations and noise. A method for tuning the PI^λD^μ controller is proposed in this paper to fulfill five different design specifications. Experimental results show that the requirements are totally met for the platform to be controlled. Besides, this paper proposes an auto-tuning method for this kind of controller. Specifications of gain crossover frequency and phase margin are fulfilled, together with the iso-damping property of the time response of the system. Experimental results are given to illustrate the effectiveness of this method.