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Context: The accuracy of estimated breeding values (EBVs) is an important metric in genetic evaluation systems in Australia. With reduced costs for DNA genotyping due to advances in molecular technology, more and more animals have been genotyped for EBVs. The rapid increase in genotyped animals has grown beyond the capacity of the current genomic best linear unbiased prediction (GBLUP) method. Aims: This study aimed to implement and evaluate a new single-nucleotide polymorphism (SNP)–BLUP model for the computation of prediction error variances (PEVs) to accommodate the increasing number of genotyped animals in beef and sheep single-step genetic evaluations in Australia. Methods: First, the equivalence of PEV estimates obtained from both GBLUP and SNP-BLUP models was demonstrated. Second, the computing resources required by each model were compared. Third, within the SNP-BLUP model, the PEVs obtained from subsets of SNP were evaluated against those from the complete dataset. Fourth, the new model was tested in the Australian Merino sheep and Angus beef cattle datasets. Key results: The PEVs of genotyped animals calculated from the SNP–BLUP model were equivalent to the PEVs derived from the GBLUP model. The SNP–BLUP model used much less time than did the GBLUP model when the number of genotyped animals was larger than the number of SNPs. Within the SNP–BLUP model, the running time could be further reduced using a subset of SNPs makers, with high correlations (>0.97) observed between the PEVs obtained from the complete dataset and subsets. However, it is important to exercise caution when selecting the size of the subsets in the SNP–BLUP model, as reducing the subset size may result in an increase in the bias of the PEVs. Conclusions: The new SNP-BLUP model for PEV calculation for genotyped animals outperforms the current GBLUP model. A new accuracy program has been developed for the Australian genetic evaluation system which uses much less memory and time to compute accuracies. Implications: The new model has been implemented in routine sheep and beef genetic evaluation systems in Australia. This development ensures that the calculation of accuracies is sustainable, with increasing numbers of animals with genotypes. The accuracy of estimated breeding values is routinely provided to breeders as part of genetic evaluations in Australia. A new method to approximate accuracies using genomic information has been developed and is presented in this paper. The new model has been implemented in Australia's routine sheep and beef genetic evaluation systems. This development ensures that the calculation of accuracies is sustainable with increasing numbers of animals with genotypes. [ABSTRACT FROM AUTHOR]

Spectral-type subspace clustering algorithms have attracted wide attention because of their excellent performance displayed in a great deal of applications in machine learning domain. It is critical for spectral-type subspace clustering algorithms to obtain suitable coefficient matrices which could reflect the subspace structures of data sets. In this paper, we propose a latent block diagonal representation clustering algorithm (LBDR). For a data set, the goal of LBDR is to construct a block diagonal and dense coefficient matrix and settle the noise adaptively within the original data set by using dimension reduction technique concurrently. In brief, by seeking the solution of a joint optimization problem, LBDR is capable of finding a suitable coefficient matrix and a projection matrix. Furthermore, a series of experiments conducted on several benchmark databases show that LBDR dominates the related methods. [ABSTRACT FROM AUTHOR]

The existing graph-based RGBT tracking methods mainly focus on assigning a weight to each local image patch to suppress background influence in target bounding box, but the influences of background clutter might limit the improvement of tracking performance. To solve this problem, we propose a new algorithm, called cooperative low-rank graph model, to suppress background clutter. Specifically, the proposed feature decomposition module decomposes input dual-modal features into low-rank components and sparse noisy components, which could be used collaboratively by regularizing graph learning by combining modal weights. Besides, to avoid SVD (Singular Value Decomposition) operations we have designed an efficient solver based on ADMM (Alternating Direction Methods of Multipliers), which could factorize the low-rank matrix into two low-dimensional submatrices. Extensive experiments on four RGBT tracking benchmark data sets show that our method performs favorably against other state-of-the-art tracking algorithms, and achieves more robust tracking performance. [ABSTRACT FROM AUTHOR]

In coal mine engineering, numerical software is used to analyze the behavior of coal rock damage and fluid migration. The order of the coefficient matrix used in numerical calculations is increasing, and this increases the computation steps in obtaining the coefficient matrix solution. The storage and solution of the coefficient matrix are key factors influencing the efficiency of the numerical software. Therefore, to save storage space and reduce the computation steps, the coefficient matrix must be effectively compressed and stored. In this work, the structural characteristics of different coefficient matrices are analyzed in detail, and we find that for different computational regions, as long as the nodes are numbered according to certain rules, the corresponding coefficient matrices will have similar structural characteristics. The nonzero elements are symmetrically distributed in the diagonal band, and all the elements on both sides outside the band are zero. Based on this, the coefficient matrix is compressed by a pivoting scheme, and the compressed matrix is directly eliminated by dislocation Gaussian elimination. Thus, a compressed storage method that integrates the compression and solution of the coefficient matrix is established. The compressed storage and calculation module is incorporated into our self-developed simulation software COMBUSS-3D to simulate the evolution of the temperature field in the goaf of Luling Coal Mine. Compared with the conventional method, the compressed storage module can significantly improve the computing rate of the simulation, by approximately 80%. [ABSTRACT FROM AUTHOR]

Advances in information technology have harnessed the application of Quick Response (QR) codes in day-to-day activities, simplifying information exchange. QR codes are witnessed almost everywhere, on consumables, newspapers, information bulletins, etc. The simplicity of QR code creation and ease of scanning with free software have tremendously influenced their wide usage, and since QR codes place information on an object they are a tool for the IoT. Many healthcare IoT applications are deployed with QR codes for data-labeling and quick transfer of clinical data for rapid diagnosis. However, these codes can be duplicated and tampered with easily, attributed to open- source QR code generators and scanners. This paper presents a novel (n,n) secret-sharing scheme based on Nonnegative Matrix Factorization (NMF) for secured transfer of QR codes as multiple shares and their reconstruction with a regularized Super Resolution Convolutional Neural Network (SRCNN). This scheme is an alternative to the existing polynomial and visual cryptography-based schemes, exploiting NMF in part-based data representation and structural regularized SRCNN to capture the structural elements of the QR code in the super-resolved image. The experimental results and theoretical analyses show that the proposed method is a potential solution for secured exchange of QR codes with different error correction levels. The security of the proposed approach is evaluated with the difficulty in launching security attacks to recover and decode the secret QR code. The experimental results show that an adversary must try 258 additional combinations of shares and perform 3 × 288 additional computations, compared to a representative approach, to compromise the proposed system. [ABSTRACT FROM AUTHOR]

To improve the ability of the acoustic computed tomography (CT) temperature field reconstruction system for reconstructing various temperature distributions in the measured area, square and circular layouts of transducers were studied. In case of the square layout, the focus was on the placement of the transducers, and in case of the circular layout, the focus was on the division of grids. We proposed the coefficient matrix theory and indexes for studying and evaluating transducers layout. Four typical temperature field models were simulated and reconstructed. Simulation results showed that in a square layout, optimizing the position of transducers can result in better reconstruction quality. In a circular layout, a regular hexagonal grid division was better than an equal-area division, and better reconstruction quality was obtained by choosing the appropriate number of grids. For a small number of transducers, the circular layout of nine transducers with 27 acoustic rays and 91 regular hexagonal grids resulted in better reconstruction quality than the square and circular layout of eight transducers; in each reconstruction, the error was ≤ 5.07%. [ABSTRACT FROM AUTHOR]

Aiming at the poor prediction performance of the traditional GM(1,N) model, this paper proposes the GM(1,N) model with expression optimization: firstly, unknown parameters are introduced into the coefficient matrix of the traditional GM(1,N) model to obtain the model expression with unknown parameters: Then the average relative error function with unknown parameters is constructed: Finally, the particle swarm optimization algorithm is used to obtain the parameter column with the smallest average relative error. Taking the carbon emission of the logistics industry in Hubei Province as an example, this paper forecasts the carbon emission by using the traditional GM(1,N) model, GM(1, N) model with background value optimization, and GM(1, N) model with expression optimization. By comparing and analyzing the prediction results of the three models, it is concluded that GM(1,N) model with expression optimization has better prediction performance. [ABSTRACT FROM AUTHOR]

Surface location error (SLE) caused by the forced vibration is one of the main factors limiting machining accuracy in stable milling. This paper presents a novel scheme with high precision and high efficiency to predict SLE based on the Newton polynomial-Chebyshev nodes. The dynamic model embodying the forced and regenerative excitations is first derived from the simplified milling process. After describing the response of the system with the direct integration format, the Newton polynomial frame is chosen to spread the self-excited and forced-excited elements successively in each equidistant time interval to obtain the separate output of tool vibration displacements with a close form. Then, the coefficient matrix which is not affected by the change of time is established in each spindle speed location to calculate SLE. Three examples which have been verified by the experiments are introduced to capture the optimal approximated order with exhibiting the characteristic of the proposed methods. It is observed that the prediction accuracy of the high-order methods drop seriously for the absence of Runge effect. In order to avoid this unwanted phenomenon, the origin uniform time joints are modified by a nonlinear sampling technique based on Chebyshev nodes to establish the novel coefficient matrix with fewer calculated loads for SLE prediction, and a series of comparisons illuminate the proposed modified method performs satisfactorily. [ABSTRACT FROM AUTHOR]

The change of electrodes' conductivity is a crucial parameter during battery aging process, non-contact detection of battery electrodes' defects through conductivity reconstruction is an innovative technology. In this paper, the magnetic induction tomography (MIT) was applied to reconstruct the conductivity of electrodes, the simplified battery models with complete and broken electrodes were chosen as target A and target Brespectively, and an eight-channel MIT system was designed to measure the change of mutual induced voltage. A method of computing the forward problem called 'A·E' was adopted to compute the coefficient matrix for the forward problem and the frequency 12.665kHz was chosen as the excitation frequency. Based on the conductivity reconstruction images, relative errors of reconstructed conductivity and objective function, 'A·E' method exhibited advantages in terms of computation time and accuracy compared to coefficient sensitivity method with the simulation data. In order to test the accuracy of 'A·E' method, data measured by MIT system was applied in the inverse problem with four regularization parameter selection methods. L-curve criterion and generalized cross-validation criterion identified defects successfully as they were more sensitive to the change of conductivity. [ABSTRACT FROM AUTHOR]

In this article, a fast numerical approach is proposed for finding the solution of nonlinear delay differential equations by using hybrid Taylor and Block-pulse Functions (HTBPFs). Firstly, some features of hybrid functions which are a combination of Block-Pulse functions and Taylor polynomials on the interval are introduced [0; 1) . In this spectral approach, the operational matrices of stretch, derivation and coefficient matrices are utilized. Based on these piecewise functions, we transfer delay differential equations (DDEs) into a system of linear or nonlinear algebraic equations. Also, in this numerical approach, it is shown that these operational matrices are sparse which is an effective advantage of the fast implementation of numerical computation. Then, error analysis is done. Finally, three examples are solved to show that the new proposed approach is comparable with other methods of high accuracy and efficiency. [ABSTRACT FROM AUTHOR]

The observation errors of independent variables in model prediction are typically neglected in traditional regression models, which leads to the decreased prediction accuracy. In this paper, a new regression prediction method that is based on the partial errors-in-variables (partial EIV) model is proposed, which takes into account the observation errors of all variables. It observes that each element of the coefficient matrix is an expression or a function. The partial EIV model is transformed into a linear model and constructed in the form of indirect adjustment for iterative solution. By considering the errors in the independent variables when predicting the corresponding dependent variables with the partial EIV model, the proposed method can achieve higher prediction accuracy. [ABSTRACT FROM AUTHOR]

The coefficient matrix and local unitary (LU) transformation invariant of three-qubit states are studied in this paper. There is general relation between the coefficient matrix and independent LU transformation invariant existing which is shown. Especially, the three coefficient matrix can completely determine six algebraically independent local invariants for three-qubit pure states. [ABSTRACT FROM AUTHOR]

In order to calculate eddy current testing (ECT) signals due to a complex natural crack by using a regular mesh, the multi-media element (MME) was proposed by authors. In this paper, a new high-precision method for calculating the MME coefficient matrices is proposed and implemented in the finite-element method (FEM)–BEM hybrid code for ECT of narrow cracks. Through the comparison of the new MME solutions with those of the conventional FEM–BEM method, validity and efficiency of the new method and the corresponding numerical code are demonstrated. Eddy current perturbations and distributions of the magnetic flux density affected by a narrow crack of different directions are also numerically analyzed by using the new MME. In addition, the measurement results from the experiments give further support to the validity of the new MME method. [ABSTRACT FROM AUTHOR]

Structural health monitoring (SHM) is a multidisciplinary damage detection technique that incorporates various mechanisms, of which guided waves (GWs) -based damage detection is one of the critical fields of research. To realize the complete process of SHM, research on GWs has concentrated on diagnosis and localization. GWs-based damage detection technology is widely used in plate structure, combining different sensor placement algorithms and equipment such as scanning laser doppler vibrometry (SLDV) to achieve accurate damage location. Simultaneously, developing the finite element method (FEM) allows for precise simulation in discontinuous media and complex sharp structures. Therefore, this paper combines the theoretical calculation approach of elastic wave propagation with the orthogonal matching pursuit (OMP) algorithm, using the excitation signal and signal reflected by damage as the input matrix and target matrix, respectively. Thus, the reflection-waves coefficient matrix (RCM) containing damage information could be obtained after calculation by the OMP algorithm. Besides, a prediction approach of reference reflected signal based on four-layers recurrent neural networks (RNNs) is proposed with experiments data to reduce the difficulty of expanding a dictionary matrix in a plate with multiple defects, which allows for predicting the damage reflection signal under different distances with 88.14% accuracy. And finally, considering the aluminum plate with hole damage as an example, the experiment results show that the proposed approaches are effective for the localization of single damage and muti-damage. Meanwhile, the prospects and limitations of the algorithm for precise localization are also addressed in the last. [ABSTRACT FROM AUTHOR]

In sparse subspace clustreing (SSC), non‐zero coefficients in the sparse representations are transformed to positive values to construct the affinity matrix. However, negative coefficients are not supposed to cause positive correlation in nature, so that the clustering performance may be undermined. In this Letter, non‐negative SSC by orthogonal matching pursuit (nSSCOMP) with a negative re‐purpose module is introduced for a reasonable clustering graph to improve the clustering performance, also an assemble negatives of negatives algorithm is proposed to strengthen the effectiveness of affinity matrix. The analysis indicates that the authors' approach can make the coefficient matrix contains only non‐negative values and bring additional positive correlations. Their approach is the first to process negative values after sparse representations are already calculated, without specify non‐negativity constraints beforehand. Experimental results demonstrate with the nSSCOMP not only the clustering accuracy and subspace‐preserving property can be improved, but also time complexity be kept. [ABSTRACT FROM AUTHOR]

Aiming at the situation of errors in observation data and coefficient matric in GPS Height anomaly, a robust total least squares (RTLS) is proposed with a IGGIII weight function based on standardized residuals. The method only takes the parts containing deviation in coefficient matrix into consideration. Taking the 80 groups GPS observation of benchmark as an example, the feasibility and accuracy of TRLS is analyzed compared with two kinds of experiment including 43 groups of data for fitting (4 groups of data with gross error) and 37 groups of data for testing. If the data have no robust, the result of RTLS is equal with robust LS. If the data have robust, the result of RTLS is better than robust LS. The experiment shows that the method of RTLS is the best choice when fitting GPS height anomaly. [ABSTRACT FROM AUTHOR]

This paper describes a set of solution-set-invariant coefficient matrices of the fuzzy relation equation with max-min composition A ⊙ x = b or ⋁ j ∈ { 1 , 2 , ⋯ , n } ( a ij ∧ x j ) = b i for all i ∈ { 1 , 2 , ⋯ , m } with 1 ≥ b 1 ≥ b 2 ≥ ⋯ ≥ b m > 0. An algorithm is given for determining the set scripfontA = {B ∣ {x ∣ B ⊙ x = b} = {x ∣ A ⊙ x = b}} completely. [ABSTRACT FROM AUTHOR]

This study presents a graphical presentation of the harmonic operating principles in voltage source converter (VSC) with sparse vector methods and provides a visualisation method for analysing the harmonic operations of VSC. Based on the dynamic phasor sequence components model of the VSC, the operation analysis of VSC has been transformed into a solution of an algebraic equations. With the sparse characteristics of the vectors and coefficient matrix, the sparse vector method is applied into solving equations. The coupling from the ac‐side to the dc‐side can be represented by the forward substitution operations and the coupling from the dc‐side to the ac‐side can be represented by the back solution operations in the sparse vector method correspondingly. Therefore, the factorisation paths which describe the forward substitution and the back solution operations can describe the harmonic operating principles of VSC too. When the set of factorisation paths are presented as the weighted directed graphs based on graph theory, the harmonic operating principles of VSC can be displayed as the graphs, which is direct and clear. Finally, the simulation results testify the correctness of the studies. [ABSTRACT FROM AUTHOR]

In a recent paper (J. Phys. A: Math. Theor 45, 075308 (2012)), Li et al. established the coefficient matrix of six-qubit entangled states. With an emphasis on six qubits, we present a new criterion for maximally six-qubit entangled states via those coefficient matrices. By calculating the determinants of coefficient matrix, one use the criterion that characterize these states. Moreover, the criterion via the coefficient matrices gives rise to the combination of maximally multi-qubit entangled state(MMES) and matrix, and we believe that the new criterion can play an important role in quantum information. [ABSTRACT FROM AUTHOR]

The detection of entanglement is one of the most important problem in quantum information theory. Many separability criteria for bipartite system are hard to understand and calculate, or apply to multipartite system. This paper proposed a separability criterion based on the coefficient matrix for an arbitrary multipartite state. It could tell whether a state is a separable state or entangled state according to the rank of coefficient matrix. It demonstrates that this method can find the specifically separable form of a multipartite state by some explicit examples. Finally the proposed separability criterion is easy to understand and calculate. [ABSTRACT FROM AUTHOR]

The problem of fault estimation for a class of non‐linear systems with Lipschitzian non‐linearities and faults is studied. In most of the existing fault estimation methods, the coefficient matrix of the fault vector is required to be full column rank, which leads to that the corresponding estimation approaches are conservative and unsuitable commonly for systems with multiple faults or/and subject to disturbances. In this study, this restriction is relaxed. A novel fault estimation method is proposed, where a full‐column‐rank state variable substitution is introduced so as to meet the requirement of fault estimation. The designed estimation observer guarantees the asymptotic stability of the overall error system with a prescribed H ∞ performance. The states and faults can be estimated with good accuracy simultaneously. Then, the proposed estimation approach is further extended to solve the problem of fault estimation for non‐linear systems with multiple faults or/and subject to disturbances. Finally, numerical examples illustrate the effectiveness and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

• Second-order displacement fields at liquid–solid interface. • Solution of wave equations based on velocity potentials. • Comparison between complete solution and special solution of displacements. • Sharply mutation of displacements at certain angle. • Different effect of interface on the second-order displacements. Based on the second-order harmonic potential theory, the characteristics of the second-order harmonic field generated at the solid–liquid interface induced by P wave incidence are analyzed. A planar model of the solid–liquid interface is established to study the variation of the second-order displacement field versus the incident angles. The homogeneous solution coefficient matrix, refraction and reflection coefficient matrix are introduced. According to the boundary conditions and Lagrange's various parameters method, the second-order displacement field is obtained, and its dependence on the solid–liquid interface is investigated. The different effects of boundary on the tangential displacement and normal displacement are demonstrated. Numerical simulation shows that the complete solution varies slightly at the incident angle, and the tangential displacement and the normal displacement change sharply at a mutation angle θ ω due to the boundary effect. [ABSTRACT FROM AUTHOR]

The Hankel matrix of type B Narayana polynomials was proved to be totally positive by Wang and Zhu, and independently by Sokal. Pan and Zeng raised the problem of giving a planar network proof of this result. In this paper, we present such a proof by constructing a planar network allowing negative weights, applying the Lindström-Gessel-Viennot lemma and establishing an involution on the set of nonintersecting families of directed paths. • Providing a combinatorial proof of the Hankel total positivity of type B Narayana polynomials. • Allowing negative weights in the construction of planar networks. • Establishing an elegant sign-reversing involution on families of nonintersecting lattice paths. [ABSTRACT FROM AUTHOR]

In this article, we obtain monomial bases for littleq-Schur algebras at even roots of unity. [ABSTRACT FROM PUBLISHER]

Solvers for linear systems with tridiagonal coefficient matrices sometimes employ direct methods such as the Gauss elimination method or the cyclic reduction method. In each step of the cyclic reduction method, nonzero offdiagonal entries in the coefficient matrix move incrementally away from diagonal entries and eventually vanish. The steps of the cyclic reduction method are generalized as forms of the stride reduction method. For example, the 2-stride reduction method coincides with the 1st step of the cyclic reduction method which transforms tridiagonal linear systems into pentadiagonal systems. In this paper, we explain arbitrary-stride reduction for linear systems with coefficient matrices with three nonzero bands. We then show that arbitrary-stride reduction is equivalent to a combination of 2-stride reduction and row and column permutations. We thus clarify eigenvalue clustering of coefficient matrices in the step-by-step process of the stride reduction method. We also provide two examples verifying this property. [ABSTRACT FROM AUTHOR]

By defining the coefficient matrix, a new quantum teleportation scheme in quantum wireless multi-hop network is proposed. With the help of intermediate nodes, an unknown qubit state can be teleported between two distant nodes which do not share entanglement in advance. Arbitrary Bell pairs and entanglement swapping are utilized for establishing quantum channel among intermediate nodes. Using collapsed matrix, the initial quantum state can be perfectly recovered at the destination. [ABSTRACT FROM AUTHOR]

Consider an infinite dimensional vector linear process. Under suitable assumptions on the parameter space, we provide consistent estimators of the autocovariance matrices. In particular, under causality, this includes the infinite-dimensional vector autoregressive (IVAR) process. In that case, we obtain consistent estimators for the parameter matrices. An explicit expression for the estimators is obtained for IVAR(1), under a fairly realistic parameter space. We also show that under some mild restrictions, the consistent estimator of the marginal large dimensional variance-covariance matrix has the same convergence rate as that in case of i.i.d. samples. [ABSTRACT FROM AUTHOR]

A common mesh smoothing method strives to improve the shape quality of all elements. Generally a mesh consisting of only well-shaped elements is desired in finite element analysis. Although a perfect-shaped element yields short computation time, even a well-shaped element, whose shape is close to a regular polygon, sometimes prolongs the computation time of solving the system of equations derived with the edge-based finite element method. In this paper, we propose a new smoothing scheme of improving a convergence property of the system of equations by applying a common mesh smoothing method to some elements, which cause long computation time of the iterative solver. The proposed smoothing scheme utilizes the condition number of submatrices, into which coefficient matrix derived with the edge-based finite element method is subdivided, in order to choose ill-conditioned elements to be smoothed. As a result, the computation time is shortened applying a smoothing process only to the chosen ill-conditioned elements. [ABSTRACT FROM AUTHOR]

This study presents a quadratic optimal reactive power flow (ORPF) models for ac‐dc hybrid power system. In the ac system, the load tap changing transformer is represented by an ideal transformer and its series impedance with an artificial node located between them. The ideal transformer is further replaced by the current injections at the two terminal nodes. The artificial node voltage and the current injections are used to express the relationship between the quantities at both sides. For the dc system, some variables are introduced to formulate the dc equations. Finally, utilising their couplings, the ac and dc equations expressed in different coordinates can be integrated into a unified quadratic ac‐dc ORPF model, which is simply expressed in the block form. The predictor‐corrector primal‐dual interior‐point method is used to solve the optimisation problem. The quadratic model results in the constant Hessians that all have elements of 1 or −1, and mostly being zero and multiplication is not required to form the full Hessian, thereby accelerating the entire optimal process significantly. Extensive numerical simulations have shown the validity and superior performance of the proposed model than the conventional one. [ABSTRACT FROM AUTHOR]

Abstract: State analysis of linear time-varying descriptor systems via hybrid functions are proposed in this paper. Based upon some useful properties of hybrid functions, a special product matrix and a related coefficient matrix are applied to solve the descriptor systems. The unknown coefficient matrix will be in generalized Lyapunov equation form, which is solved via the Kronecker product method. The advantages of hybrid functions are not only the values of n and m are adjustable but also it can yield more accurate numerical solutions than orthogonal functions and orthogonal polynomials to the problems of solving the descriptor systems. We propose that the available optimal values of n and m can minimize the relative errors in the numerical solutions. The high accuracy and the wide applicability of hybrid function approach will be demonstrated with numerical examples. [Copyright &y& Elsevier]

Abstract: In this paper, first, some disadvantages of original partial least squares method of independent component analysis (ICA-PLS) are analyzed. Then ICA-PLS is modified for regression purpose. Disadvantages of the original ICA-PLS algorithm are as follows: 1) the regression coefficient matrix and residual matrix cannot been given so that the computation time may increase with the number of samples; and 2) ICA-PLS lacks the ability to give better monitoring performance when the correlation structure of measured variables is nonlinear, which is often the case for industrial processes. To solve the above problems, we modified the original algorithm in following aspects: 1) the regression coefficient matrix and residual matrix in ICA-PLS are given so that the computation time is decreased; and 2) to solve the nonlinear problem, ICA-PLS and kernel trick is first combined for nonlinear regression purpose, which is called iterative ICA-KPLS in this paper. The iterative calculation of ICA-KPLS will be time consuming when the sample number becomes larger. Hence, the regression coefficient matrix and residual matrix in ICA-KPLS are given to avoid the expensive computation time when the number of samples is huge. The proposed methods are applied to the quality prediction in fermentation process and Tennessee Eastman process. Applications indicate that the proposed approach effectively captures the relations in the process variables and use of ICA-KPLS instead of ICA-PLS improves the predictive ability. The expensive computation time is avoided by using the coefficient matrix and residual matrix. [Copyright &y& Elsevier]

Abstract: Numerical solutions of Fredholm and Volterra integral equations of the second kind via hybrid functions, are proposed in this paper. Based upon some useful properties of hybrid functions, integration of the cross product, a special product matrix and a related coefficient matrix with optimal order, are applied to solve these integral equations. The main characteristic of this technique is to convert an integral equation into an algebraic; hence, the solution procedures are either reduced or simplified accordingly. The advantages of hybrid functions are that the values of and are adjustable as well as being able to yield more accurate numerical solutions than the piecewise constant orthogonal function, for the solutions of integral equations. We propose that the available optimal values of and can minimize the relative errors of the numerical solutions. The high accuracy and the wide applicability of the hybrid function approach will be demonstrated with numerical examples. The hybrid function method is superior to other piecewise constant orthogonal functions [W.F. Blyth, R.L. May, P. Widyaningsih, Volterra integral equations solved in Fredholm form using Walsh functions, Anziam J. 45 (E) (2004) C269–C282; M.H. Reihani, Z. Abadi, Rationalized Haar functions method for solving Fredholm and Volterra integral equations, J. Comp. Appl. Math. 200 (2007) 12–20] for these problems. [Copyright &y& Elsevier]

In this paper, an improved procedure for imposing displacement boundary conditions in the direct stiffness method of the finite element analysis is presented. The proposed procedure neither changes the original order of the master stiffness matrix, nor does it require the rearrangement of the coefficient matrix. Consequently, it is easy to be implemented. Especially, the condition numbers of coefficient matrices of the improved procedure are remarkably reduced; hence the sensitivity of the solution to perturbations is considerably lowered. Numerical examples are used to demonstrate the validity of the proposed procedure. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We provide explicit representations of the null space S of adjoints of companion-related matrices and of certain rectangular generalized Vandermonde matrices of block Toeplitz type which are encountered in the Fisher information matrix of time series processes. A formula for the right-inverse of this class of matrices A is provided which allows one to express the solution of the system Ax = b as x = A-b+ S. The formulas can be easily turned into solution algorithms. [ABSTRACT FROM AUTHOR]

Abstract: Reduced-rank restrictions can add useful parsimony to coefficient matrices of multivariate models, but their use is limited by the daunting complexity of the methods and their theory. The present work takes the easy road, focusing on unifying themes and simplified methods. For Gaussian and non-Gaussian (GLM, GAM, mixed normal, etc.) multivariate models, the present work gives a unified, explicit theory for the general asymptotic (normal) distribution of maximum likelihood estimators (MLE). MLE can be complex and computationally hard, but we show a strong asymptotic equivalence between MLE and a relatively simple minimum (Mahalanobis) distance estimator. The latter method yields particularly simple tests of rank, and we describe its asymptotic behavior in detail. We also examine the method''s performance in simulation and via analytical and empirical examples. [Copyright &y& Elsevier]

The matrix forms for curves and surfaces were largely promoted in CAD/CAM. In this paper we have presented two matrix representation formulations for arbitrary degree NURBS curves and surfaces explicitly other than recursively. The two approaches are derived from the computation of divided difference and the Marsden identity respectively. The explicit coefficient matrix of B-spline with equally spaced knot and Be´zier curves and surfaces can be obtained by these formulae. The coefficient formulae and the coefficient matrix formulae developed in this paper express non-uniform B-spline functions of arbitrary degree in explicit polynomial and matrix forms. They are useful for the evaluation and the conversion of NURBS curves and surfaces in CAD/CAM systems. [Copyright &y& Elsevier]

Weighted nonnegative matrix factorization (WNMF) is a technology for feature extraction, which can extract the feature of face dataset, and then the feature can be recognized by the classifier. To improve the performance of WNMF for feature extraction, a new iteration rule is proposed in this paper. Meanwhile, the base matrix U is sparse based on the threshold, and the new method is named sparse weighted nonnegative matrix factorization (SWNMF). The new iteration rules are based on the smaller iteration steps, thus, the search is more precise, therefore, the recognition rate can be improved. In addition, the sparse method based on the threshold is adopted to update the base matrix U, which can make the extracted feature more sparse and concentrate, and then easier to recognize. The SWNMF method is applied on the ORL and JAFEE datasets, and from the experiment results we can find that the recognition rates are improved extensively based on the new iteration rules proposed in this paper. The recognition rate of new SWNMF method reached 98% for ORL face database and 100% for JAFEE face database, respectively, which are higher than the PCA method, the sparse nonnegative matrix factorization (SNMF) method, the convex non-negative matrix factorization (CNMF) method and multi-layer NMF method. [ABSTRACT FROM AUTHOR]

In this paper, the non-ideal factors, which include spatial noise and temporal noise, are analyzed and suppressed in the high-speed spike-based image sensor, which combines the high-speed scanning sequential format with the method that uses the interspike time interval to indicate the scene information. In this imager, spatial noise contains device mismatch, which results in photo response non-uniformity (PRNU) and the non-uniformity of dark current. By multiplying the measured coefficient matrix the photo response non-uniformity is suppressed, and the non-uniformity of dark current is suppressed by correcting the interspike time interval based on the time interval of dark current. The temporal noise is composed of the shot noise and thermal noise. This kind of noise can be eliminated when using the spike frequency to restore the image. The experimental results show that, based on the spike frequency method, the standard deviation of the image decreases from 18.4792 to 0.5683 in the uniform bright light by using the calibration algorithm. While in the relatively uniform dark condition, the standard deviation decreases from 1.5812 to 0.4516. Based on interspike time interval method, because of time mismatch and temporal noise, the standard deviation of the image changes from 27.4252 to 27.4977 in the uniform bright light by using the calibration algorithm. While in the uniform dark condition, the standard deviation decreases from 2.361 to 0.3678. [ABSTRACT FROM AUTHOR]