Some new preconditioned generalized AOR methods for generalized least-squares problems

Some new preconditioned GAOR methods for solving generalized least-squares problems and their comparison results are given. Comparison results show that the convergence rates of the new preconditioned GAOR methods are better than those of the preconditioned GAOR methods presented by Shen et al. [Preconditioned iterative methods for solving weighted linear least squares problems, Appl. Math. Mech. – Engl. Ed. 33(3) (2012), pp. 375–384] whenever these methods are convergent. Lastly, numerical experiments are provided to confirm the theoretical results.     

Projection-detecting filter for video cut detection

This paper discusses a video cut detection method. Cut detection is an important technique for making videos easier to handle. First, this paper analyzes the distribution of the image differenceV to clarify the characteristics that makeV suitable for cut detection. We propose a cut detection method that uses a projection (an isolated sharp peak) detecting filter. A motion sensitiveV is used to stabilizeV projections at cuts, and cuts are detected more reliably with this filter. The method can achieve high detection rates without increasing the rate of misdetection. Experimental results confirm the effectiveness of the filter.     

An acceleration of preconditioned generalized accelerated over relaxation methods for systems of linear equations

In this paper, a new type of preconditioners are proposed to accelerate the preconditioned generalized accelerated over relaxation methods presented by Zhou et al. [Preconditioned GAOR methods for solving weighted linear least squares problems, J. Comput. Appl. Math. 224 (2009), pp. 242–249] for the linear system of the generalized least-squares problem. The convergence and comparison results are obtained. The comparison results show that the convergence rates of the proposed methods are better than those of the original methods. Finally, numerical experiments are provided to confirm the results obtained in this paper.     

The superconvergence of composite trapezoidal rule for Hadamard finite-part integral on a circle and its application

The quadrature method for Hadamard finite-part integral on a circle is discussed and the emphasis is placed on the pointwise superconvergence phenomenon of the composite trapezoidal rule, i.e. when the singular point coincides with some a priori known points, the accuracy can be better than what is globally possible. The existence and uniqueness of the superconvergence points are proved and the correspondent superconvergence estimate is obtained. An indirect method is introduced and then applied to solve the integral equation of the second kind containing finite-part kernels, including that arising in the scattering theory. Some numerical results are also presented to confirm the theoretical results and to show the efficiency of the algorithms.     

Comparison results on the preconditioned GAOR method for generalized least squares problems

Recently, Zhou et al. [Preconditioned GAOR methods for solving weighted linear least squares problems, J. Comput. Appl. Math. 224 (2009), pp. 242–249] have proposed the preconditioned generalized accelerated over relaxation (GAOR) methods for solving generalized least squares problems and studied their convergence rates. In this paper, we propose a new type of preconditioners and study the convergence rates of the new preconditioned GAOR methods for solving generalized least squares problems. Comparison results show that the convergence rates of the new preconditioned GAOR methods are better than those of the preconditioned GAOR methods presented by Zhou et al. whenever these methods are convergent. Lastly, numerical experiments are provided in order to confirm the theoretical results studied in this paper.     

Stabilised hp-Finite Element Approximation of Partial Differential Equations with Nonnegative Characteristic Form

This paper is devoted to the a priori error analysis of the hp-version of a streamline-diffusion finite element method for partial differential equations with nonnegative characteristic form. This class of equations includes second-order elliptic and parabolic problems, first-order hyperbolic problems and second-order problems of mixed elliptic-parabolic-hyperbolic type. We derive error bounds which are simultaneously optimal in both the mesh size h and the spectral order p. Numerical examples are presented to confirm the theoretical results. Received October 28, 1999; revised May 26, 2000     

Adaptive control of Hammerstein–Wiener nonlinear systems

The Hammerstein–Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein–Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.     

Fast multilevel augmentation method for nonlinear integral equations

In this study, we extend the multilevel augmentation method for Hammerstein equations established in Chen et al. [Fast multilevel augmentation methods for solving Hammerstein equations, SIAM J. Numer. Anal. 47 (2009), pp. 2321–2346] to solve nonlinear Urysohn integral equations. Under certain differentiability assumptions on the kernel function, we show that the method enjoys the optimal convergence order and linear computational complexity. Finally, numerical experiments are presented to confirm the theoretical results and illustrate the efficiency of the method.     

The asymptotic behaviour of the θ-methods with constant stepsize for the generalized pantograph equation

This paper is concerned with the long-time behaviour of the numerical solutions to a class of linear non-autonomous neutral delay differential equation with proportional delays. Our purpose is to give some asymptotic estimates of the θ-methods with constant stepsize discretization and formulate their upper bounds. Asymptotic estimate not only describes more accurate than asymptotic stability, but also gives an upper bound estimate of the solution for the long-time behaviour. We also compare the known results and show that our formulae improve and generalize these results. Some numerical examples are given in the end of this paper to confirm the theoretical results.     

A Fully Automatic hp-Adaptivity

We present an algorithm, and a 2D implementation for a fully automatic hp-adaptive strategy for elliptic problems. Given a mesh, the next, optimally refined mesh, is determined by maximizing the rate of decrease of the hp-interpolation error for a reference solution. Numerical results confirm optimal, exponential convergence rates predicted by the theory of hp methods.     

Finite‐time stabilization for a class of switched stochastic nonlinear systems with dead‐zone input nonlinearities

This paper studies the finite‐time stabilizing control problem for a class of switched stochastic nonlinear systems (SSNSs) in p‐normal form. The switched systems under consideration possess the powers of different positive rational numbers and the dead‐zone input nonlinearities. Based on the improving finite‐time stability theorem for SSNSs established in this paper, a general framework to address common state feedback for SSNSs is developed by adopting the common Lyapunov function–based adding a power integrator technique. It is proved that the proposed controller renders the trivial solution of the closed‐loop system uniformly finite‐time stable in probability under arbitrary switchings. Finally, simulation results are given to confirm the validity of the proposed approach.     

h-p Spectral Element Method for Elliptic Problems on Non-smooth Domains Using Parallel Computers

We propose a new h-p spectral element method to solve elliptic boundary value problems with mixed Neumann and Dirichlet boundary conditions on non-smooth domains. The method is shown to be exponentially accurate and asymptotically faster than the standard h-p finite element method. The spectral element functions are fully non-conforming for pure Dirichlet problems and conforming only at the vertices of the elements for mixed problems, and hence, the dimension of the resulting Schur complement matrix is quite small. The method is a least-squares collocation method and the resulting normal equations are solved using preconditioned conjugate gradient method with an almost optimal preconditioner. The algorithm is suitable for a distributed memory parallel computer. The numerical results of a number of model problems are presented, which confirm the theoretical estimates.     

A split least-squares characteristic mixed element method for nonlinear nonstationary convection–diffusion problem

In this paper, a split least-squares characteristic mixed finite element method is proposed for solving nonlinear nonstationary convection–diffusion problem. By selecting the least-squares functional property, the resulting least-squares procedure can be split into two independent symmetric positive definite sub-schemes. The first sub-scheme is for the unknown variable u, which is the same as the standard characteristic Galerkin finite element approximation. The second sub-scheme is for the unknown flux σ. Theoretical analysis shows that the method yields the approximate solutions with optimal accuracy in L ²(Ω) norm for the primal unknown and in H(div; Ω) norm for the unknown flux, respectively. Some numerical examples are given to confirm our theory results.     

Statistical properties analysis of real world tournament selection in genetic algorithms

Genetic algorithms (GAs) are probabilistic optimization methods based on the biological principle of natural evolution. One of the important operators in GAs is the selection strategy for obtaining better solutions. Specifically, finding a balance between the selection pressure and diversity is a critical issue in designing an efficient selection strategy. To this extent, the recently proposed real world tournament selection (RWTS) method has showed good performance in various benchmark problems. In this paper, we focus on analyzing characteristics of RWTS from the viewpoint of both the selection probabilities and stochastic sampling properties in order to provide a rational explanation for why RWTS provides improved performance. Statistical experimental results show that RWTS has a higher selection pressure with a relatively small loss of diversity and higher sampling accuracy than conventional tournament selection. The performance tests in a traveling salesman problem further confirm that the comparatively higher pressure and sampling accuracy, which are inherent in RWTS, can enhance the performance in the selection strategy.     

Efficient parallel edge-centric approach for relaxed graph pattern matching

Prior algorithms on graph simulation for distributed graphs are not scalable enough as they exhibit heavy message passing. Moreover, they are dependent on the graph partitioning quality that can be a bottleneck due to the natural skew present in real-world data. As a result, their degree of parallelism becomes limited. In this paper, we propose an efficient parallel edge-centric approach for distributed graph pattern matching. We design a novel distributed data structure called ST that allows a fine-grain parallelism, and hence guarantees linear scalability. Based on ST, we develop a parallel graph simulation algorithm called PGSim. Furthermore, we propose PDSim, an edge-centric algorithm that efficiently evaluates dual simulation in parallel. PDSim combines ST and PGSim in a Split-and-Combine approach to accelerate the computation stages. We prove the effectiveness and efficiency of these propositions through theoretical guarantees and extensive experiments on massive graphs. The achieved results confirm that our approach outperforms existing algorithms by more than an order of magnitude.

     

Multiple-valued feedback and recurrent correlation neural networks

In this paper we consider two kinds of neural networks in which the activation function of each neuron is a multiple valued, piecewised-constant function. The main advantages of the proposed models are that they can store patterns with different grey levels, and that they can store binary patterns with much fewer neurons than the existing models. We prove theoretically the convergence property of the proposed models. Different synthesis methods are developed to guarantee the storage of desired patterns as asymptotic equilibria. Simulation results confirm the effectiveness of the new models.     

A centroid based vector quantization reversible data hiding technique

In this paper, we propose a reversible data hiding scheme that exploits the centroid formula. Specifically, we use it to define a centroid boundary vector and a centroid state codebook CSCB. Initially, our centroid boundary vectors and CSCBs are the same as the side match vector quantization (SMVQ) algorithm’s boundary vectors and state codebooks SCBs. For each VQ index, the proposed scheme exploits the centroid formula to update its centroid boundary vector and the corresponding CSCB. The updating is coupled with a heuristic to select the best state codebook (i.e., either SCB or CSCB) for each VQ index, which generates a highly compressible distribution of index values. Our experimental results show that the proposed scheme can embed n = 1, 2, 3, and 4 bit per index (bpi) at bit rates of 0.332, 0.394, 0.457, and 0.519 bit per pixel (bpp), respectively, for the main codebook size N = 256. These results confirm that the proposed scheme improves recent VQ and SMVQ based reversible data hiding schemes.

     

Variational multiscale method based on the Crank–Nicolson extrapolation scheme for the non-stationary Navier–Stokes equations

In this report, a variational multiscale (VMS) method based on the Crank–Nicolson extrapolation scheme of time discretization for the turbulent flow is analysed. The flow is modelled by the fully evolutionary Navier–Stokes problem. This method has two differences compared to the standard VMS method: (i) For the trilinear term, we use the extrapolation skill to linearize the scheme; (ii) for the projection term, we lag it onto the previous time level to simplify the construction of the projection. These modifications make the algorithm more efficient and feasible. An unconditionally stability and an a priori error estimate are given for a case with rather general linear (cellwise constant) viscosity of the turbulent models. Moreover, numerical tests for both linear viscosity and nonlinear Smagorinsky-type viscosity are performed, they confirm the theoretical results and indicate the schemes are effective.     

Data quality awareness: a case study for cost optimal association rule mining

The quality of discovered association rules is commonly evaluated by interestingness measures (commonly support and confidence) with the purpose of supplying indicators to the user in the understanding and use of the new discovered knowledge. Low-quality datasets have a very bad impact over the quality of the discovered association rules, and one might legitimately wonder if a so-called “interesting” rule noted LHS→ RHS is meaningful when 30% of the LHS data are not up-to-date anymore, 20% of the RHS data are not accurate, and 15% of the LHS data come from a data source that is well-known for its bad credibility. This paper presents an overview of data quality characterization and management techniques that can be advantageously employed for improving the quality awareness of the knowledge discovery and data mining processes. We propose to integrate data quality indicators for quality aware association rule mining. We propose a cost-based probabilistic model for selecting legitimately interesting rules. Experiments on the challenging KDD-Cup-98 datasets show that variations on data quality have a great impact on the cost and quality of discovered association rules and confirm our approach for the integrated management of data quality indicators into the KDD process that ensure the quality of data mining results.     

Back pain in the nursing profession I. Epidemiology and pilot methodology

Abstract

A survey of 3912 nurses suggests that 750,000 working days are lost annually from back pain and that 1 in 6.(159 per-1000 at risk) attributes the onset of pain to a patient-handling incident. Attempts to identify risk areas within nursing using point prevalence data have failed to confirm previous results using historical data (Stubbs et al 1980). Evidence is presented that suggests the conditions being assessed in each case are different. The need for further epidemiological data is emphasized together with ergonomic assessment of the tasks performed throughout the nursing profession. Such an assessment will form the foundation for safer systems of work within the National Health Service and, it is hoped, a reduction in the magnitude of the back pain problem.