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Abstract: In this paper, we focus on the proposed algorithms to solve a linear programming problem with the convex combination of the max–min and the max–average composition and the max–star composition, respectively. They have been proposed by Ghodousian and Khorram [A. Ghodousian, E. Khorram, Solving a linear programming problem with the convex combination of the max–min and the max–average fuzzy relation equations, Appl. Math. Comput. 180 (2006) 411–418] and Khorram et al. [E. Khorram, A. Ghodousian, A. Abbasi Molai, Solving linear optimization problems with max–star composition equation constraints, Appl. Math. Comput. 179 (2006) 654–661], respectively. Firstly, we show that the “Tabular method algorithm” in the first paper and the “First procedure” in the second paper may not lead to the optimal solutions of the two models in some cases. Secondly, we generalize the proposed algorithm by Abbasi Molai and Khorram [A. Abbasi Molai, E. Khorram, A modified algorithm for solving the proposed models by Ghodousian and Khorram and Khorram and Ghodousian, Appl. Math. Comput. 190 (2007) 1161–1167] to solve the two models. In fact, it modifies the presented algorithms in the two papers. Finally, some numerical examples are given to illustrate the purposes. [Copyright &y& Elsevier]

Abstract: The aim of this note is to show that the optimization algorithm proposed in may not lead to the optimal solution in some cases. In fact, the optimization problem remains open if we do not apply the branch-and-bound method to solve it or compute all the objective values of minimal solutions of the feasible domain. [Copyright &y& Elsevier]

Abstract: In abstract of the paper [A. Rafiq, A note on “A family of methods for solving nonlinear equations”, Appl. Math. Comput. 195 (2008) 819–821] we can find the following sentences. We cite: Ujević et al. introduced a family of methods for solving nonlinear equations. However the main Algorithm 1 put forward by Ujević et al. (p. 7) is wrong. This is the main aim of this note. We also point out some major bugs in the results of Ujević et al. – the end of the citation. Here it is shown that all of the mentioned assertions are not true. In other words, the Algorithm 1 is correct (up to an obvious misprint, which is not mentioned in the above paper) and there are no major bugs in the paper by Ujević et al. In fact, these observations, which will be given in this note, show that the main aim of the paper by Rafiq is wrong. [Copyright &y& Elsevier]

Abstract: The aim of this short note is to show on a numerical example that one of the two optimization algorithms proposed in [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886] may not lead to the optimal solution in some cases. Besides it will be pointed out that the other algorithm (correct, but unfortunately ineffective for larger problems) proposed in [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886] can be extended to a wider class of non-convex optimization problems. [Copyright &y& Elsevier]

In recent years, the reduced biquaternion algebras have been widely used in color image processing problems and in the field of electromagnetism. This paper studies eigen-problems of reduced biquaternion matrices by means of a complex representation of a reduced biquaternion matrix and derives new algebraic algorithms to find the eigenvalues and eigenvectors of reduced biquaternion matrices. This paper also concludes that the number of eigenvalues of an n × n reduced biquaternion matrix is infinite. In addition, the proposed algebraic algorithms are shown to be effective in application to a color face recognition problem. • The eigen-problems of reduced biquaternion matrices are further studied based on the complex representation form. • Propose new algebraic algorithms for finding the eigenvalues and the eigenvectors of a reduced biquaternion matrix. • An n × n reduced biquaternion matrix has infinite eigenvalues. • There are multiple eigenvalues corresponding to the same eigenvector of a reduced biquaternion matrix. • The proposed method is more comprehensive and can find more eigenvalues of a reduced biquaternion matrix. [ABSTRACT FROM AUTHOR]

Abstract: Phylogenetic trees are an important tool to help in the understanding of relationships between objects that evolve through time, in particular molecular sequences. In this paper, we efficiently solve two subtree-comparison problems on a set of phylogenetic trees which have practical applications to analyze the evolution and co-evolution genes clustering of genomic sequences. Let be a set of k phylogenetic trees such that the leaves of each tree are drawn from and the leaves for two arbitrary trees are not necessary the same, where n is the maximum number of the leaves among the k trees. We present a linear-time algorithm to find all the leaf-agreement descendant subtrees. By further extending this result, we present a linear-time algorithm to find all the leaf-agreement isomorphic descendant subtrees. Based on our algorithms, a web-based system using input tree files from TreeBASE is also implemented. [Copyright &y& Elsevier]

• The algorithm proposed in this paper is simpler and easier to understand compared to the algorithms in references [3] and [8]. • The paper focuses on the power domination problem on trees and presents a linear-time algorithm to solve it using the labeling method. In this paper, the power domination problem on trees is studied and we give a linear-time algorithm to it by using the labeling method. Our algorithm is simpler and easier to understand than those in [3,7]. [ABSTRACT FROM AUTHOR]

This Editorial paper provides an overview of a selection of contributions from researchers working in the fields of Subdivision, Applied Geometric and Algebraic Methods, Isogeometric Analysis, Refinability and Geometric Deep Learning, with special emphasis on numerical computation, advanced algorithms, their analysis, and their applications. [ABSTRACT FROM AUTHOR]

In the theory and applications of graphs, it is a basic problem to compute the numbers of independent sets and matchings of given sizes. Since the problem of computing the total number of independent sets and that of matchings of graphs is #P-complete, it is unlikely to give efficient algorithms to find the numbers of independent sets and matchings of given sizes. In this paper, for graphs with order n and treewidth at most p , we present two dynamic algorithms to compute the numbers of independent sets of all sizes with runtime O (2 p  ·  pn 3 ) and the numbers of matchings of all sizes with runtime O (2 2 p  ·  pn 3 ), respectively. By the algorithms presented in this paper, for graphs with small treewidths, the numbers of independent sets and matchings of all possible sizes can be computed efficiently. [ABSTRACT FROM AUTHOR]

This paper presents an efficient and concise double fast algorithm to solve high dimensional time-space fractional diffusion problems with spectral fractional Laplacian. We first establish semi-discrete scheme of time-space fractional diffusion equation, which uses linear finite element or fourth-order compact difference method combining with matrix transfer technique to approximate spectral fractional Laplacian. Then we introduce a fast time-stepping L1 scheme for time discretization. The proposed scheme can exactly evaluate fractional power of matrix and perform matrix-vector multiplication at per time level by using discrete sine transform, which doesn't need to resort to any iteration method and can significantly reduce computation cost and memory requirement. Further, we address stability and convergence analyses of full discrete scheme based on fast time-stepping L1 scheme on graded time mesh. Our error analysis shows that the choice of graded mesh factor ω = (2 − α) / α shall give an optimal temporal convergence O (N − (2 − α)) with N denoting the number of time mesh. Finally, ample numerical examples are delivered to illustrate our theoretical analysis and the efficiency of the suggested scheme. • Efficient spatial semi-discretization using matrix transfer technique for time-space fractional diffusion problem is established. • Stability and error bounds of full discrete scheme based on fast time-stepping L1 method on graded time meshes are discussed. • Fast and accurate solver for system of equations is designed by discrete sine transform at per time level. • Commendably concise and implementation-friendly double fast algorithm is proposed. [ABSTRACT FROM AUTHOR]

The Fantope-constrained sparse principal subspace estimation problem is initially proposed by Vu et al. (Vu et al., 2013). This paper investigates a semismooth Newton based proximal point (Ppassn) algorithm for solving the equivalent form of this problem, where a semismooth Newton (Ssn) method is utilized to optimize the inner problems involved in the Ppassn algorithm. Under standard conditions, the Ppassn algorithm is proven to achieve global convergence and an asymptotic superlinear convergence rate. Computationally, we derive nontrivial expressions for the Fantope projection and its generalized Jacobian, which are key ingredients for the Ppassn algorithm. Some numerical results on synthetic and real data sets are presented to illustrate the effectiveness of the proposed Ppassn algorithm for large-scale problems and superiority over the alternating direction method of multipliers (ADMM). [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel methodology for constructing incoherent unit norm tight frames, termed block coordinate descent-based alternating projection. In the proposed approach, the underlying min-max problem was reformulated in a block-wise fashion by taking a fixed number of columns as a block and adding a spectral constraint, and it was approximately solved via an alternating projection method with Nesterov accelerated gradient technique. Numerical experiments demonstrate that the resulting algorithm is particularly efficient for the construction of incoherent unit norm tight frames with high redundancy and has great advantages in running efficiency. • Incoherent unit-norm tight frame design method. • A block coordinate descent-based alternating projection framework. • An approach for ℓ ∞ -minimization problem with constraints of row orthogonality. [ABSTRACT FROM AUTHOR]

This paper is intended as a companion to [12] and focuses on the numerical implementations of the method in the context of insurance problems with mixed controls: reinsurance acting as continuous control, and capital injection and dividend payment acting as singular ones. The aim is twofold. On the one hand, we provide a comparison of the output of our method in terms of the optimal value against two benchmarks. The first benchmark is provided by [4] in the no-reinsurance setting and when the claims are exponentially distributed. The second benchmark refers to [8] where capital injections are not permitted, but different claim distributions can be employed. On the other hand, we illustrate the improvement of the models in [8] when capital injection is allowed. We also look into the effect of reinsurance in the model [4]. Several cases for the equity cost parameter are discussed as are the boundary (or limit) situations. • We provide a validation of the Dual Linear Programming algorithm by showcasing its performance on two benchmarks. • With a relatively modest order of moments (4), the relative errors are of at most 3%. • Leveraging this algorithm reveals significant enhancements in the expected dividends, advocating for capital injections. [ABSTRACT FROM AUTHOR]

In this paper, two new algorithms for computing the Weighted Moore–Penrose inverse A M , N † of a general matrix A for weights M and N which are based on elementary row and column operations on two appropriate block partitioned matrices are introduced and investigated. The computational complexity of the introduced two algorithms is analyzed in detail. These two algorithms proposed in this paper are always faster than those in Sheng and Chen (2013) and Ji (2014), respectively, by comparing their computational complexities. In the end, an example is presented to demonstrate the two new algorithms. [ABSTRACT FROM AUTHOR]

This paper deals with the stability analysis of Linear Time-Invariant (LTI) systems in the presence of a bounded and time-invariant delay parameter. The paper extends the theory of characteristic quasi-polynomial to derive equivalent stability conditions. Based on the quasi-polynomial, a two-variate polynomial is defined and it is proved that system stability is equivalently guaranteed if all roots of the new polynomial are not allocated in a certain region of the right half plane (RHP). Moreover, the algorithm uses the proposed equivalent stability conditions to develop a set of implementable stability conditions based on the exposed edges theorem. The algorithm is applied to three simulation examples that admit some novel results for these systems. The first example shows the step-by-step procedure for the proposed algorithm. The second and the third ones compare various aspects of the proposed algorithm with some existing methods. Two hundred and fifty delay systems are randomly generated and the proposed algorithm is compared with them in terms of conservativeness and computational burden. The results reveal the superiority of the proposed method over the existing ones. [ABSTRACT FROM AUTHOR]

• Two new computational algorithms are proposed for estimating the Lyapunov exponents from time series data in order to test the null hypothesis of a chaotic behavior. • The results obtained provide robust evidence that the Jacobian indirect methods provide better estimates than traditional direct methods in all the experiments we have conducted. • We have shown empirically that the algorithms proposed are robust to the presence of (small) measurement errors because the results obtained are comparable to those which are noise free. • The empirical size of the algorithms proposed decreased and the empirical power increased as the sample size increased which means that our hypothesis tests are consistent and reliable. • This paper opens a new research line where new contributions may appear considering new machine learning methods and deep learning algorithms for estimating the Lyapunov exponents from time series data. Most of the existing methods and techniques for the detection of chaotic behaviour from empirical time series try to quantify the well-known sensitivity to initial conditions through the estimation of the so-called Lyapunov exponents corresponding to the data generating system, even if this system is unknown. Some of these methods are designed to operate in noise-free environments, such as those methods that directly quantify the separation rate of two initially close trajectories. As an alternative, this paper provides two nonlinear indirect regression methods for estimating the Lyapunov exponents on a noisy environment. We extend the global Jacobian method, by using local polynomial kernel regressions and local neural net kernel models. We apply such methods to several noise-contaminated time series coming from different data generating processes. The results show that in general, the Jacobian indirect methods provide better results than the traditional direct methods for both clean and noisy time series. Moreover, the local Jacobian indirect methods provide more robust and accurate fit than the global ones, with the methods using local networks obtaining more accurate results than those using local polynomials. [ABSTRACT FROM AUTHOR]

In this paper, we consider the eigenvalue bounds for real symmetric matrices whose entries are in a given interval. Based on some matrix computation theories, a new algorithm and some theorems are presented which provide ways for solving the left problems in former papers and obtain satisfying results. Furthermore, the ideas are spread to general symmetric interval matrices. Finally, numerical examples are presented which show the validity of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper focuses on linearisation techniques for a class of mixed singular/continuous control problems and ensuing algorithms. The motivation comes from (re)insurance problems with reserve-dependent premiums with Cramér-Lundberg claims, by allowing singular dividend payments and capital injections. Using variational techniques and embedding the trajectories in an appropriate family of occupation measures, we provide the linearisation of such problems in which the continuous control is given by reinsurance policies and the singular one by dividends and capital injections. The linearisation translates into a dual dynamic programming (DDP) algorithm. An important part of the paper is dedicated to structural considerations allowing reasonable implementation. We also hint connections to methods relying on moment sum of squares and LMI (linear matrix inequality)-relaxations to approximate the optimal candidates. [ABSTRACT FROM AUTHOR]

The n -dimensional HSDC with the logic graph H n is one of the most attractive server-centric data center networks for high incremental scalability. The routing design in network topology is very important for information transmission. In particular, the application of disjoint path covers can solve various problems such as program code optimization and mapping parallel programs to parallel structures. H n consists of 2 n cliques and each two vertices in a clique are adjacent. For any vertex sets { x , u } and { y , v } in W and B , respectively, and any two disjoint vertex sets A 1 , A 2 in some clique, where (W , B) is a bipartition of H n , in this paper, we prove that, when | A i | ≠ 1 and A i ∩ { x , y , u , v } = ∅ for i = 1 , 2 , if | A 1 ∪ A 2 | ≤ n − 3 , then there exists an (x , y) -path P 1 and a (u , v) -path P 2 in H n passing through A 1 and A 2 , respectively, such that P 1 and P 2 have no common vertices and P 1 ∪ P 2 contains all vertices of H n. Then P 1 ∪ P 2 is called the 2-disjoint path cover in H n and we propose the efficient algorithms for the path design. Furthermore, we prove that our main result is optimal. • In the problem of data harvest and information transmission, it is very important to design the disjoint path cover in the logic graph of Data Center Network. • We consider the construction of 2-disjoint path cover such that each path should contain all prescribe vertices which have low probability of failure. • The efficient algorithms have been given and we prove that the number of prescribed vertices is not more than n − 3 and explain that this upper bound is sharp. [ABSTRACT FROM AUTHOR]

Analogs of balls in n -dimensional Euclidean space are defined in the monoid of strings composed of letters of an alphabet if a metric is defined on the monoid. These analogs are not only balls in the monoid of strings but also regular languages. Since the Levenshtein distance, a reasonable metric between strings, was introduced in 1965, researchers have aimed to determine a formula for computing the volumes of balls of strings under this distance and their growth rate. However, this problem remains open. In this paper, we first derive a formula for the volumes of balls of strings under a metric obtained by extending the Hamming distance as a metric on the whole monoid and subsequently reveal the growth rate of balls of strings under the Levenshtein distance using this formula. Furthermore, we describe a conjecture on the formula for the volumes of spheres of strings under the Levenshtein distance. Next, we construct an efficient randomized algorithm that computes estimates of the volumes of the balls whose estimation errors are less than a given value with a probability greater than a specified value. Finally, we examine the validity of the proposed conjecture, using the (true) volumes obtained by exhaustive searches for small spheres and estimates of the volumes obtained by this algorithm for large ones. [ABSTRACT FROM AUTHOR]

• Algebra matrix method integrates the structural factor and the state information of social networks. • Monte Carlo simulation experiments verify the effectiveness of the algebra matrix evaluation. • The evaluation deviations of diffusion threshold are shown best performance comparing with three popular mean field methods. • The weighted average strategy is proposed as applications. Tacit knowledge is the knowledge existing in human brain which is not easy to be recorded or quantified, and often is learned in the face-to-face interactions. The tacit knowledge diffusion depends on the decision-making of tacit knowledge owners, and the expression of explicit knowledge carriers. However, the comprehensive influence of the tacit knowledge owners, explicit knowledge carriers and the relations of them were not attracted enough attention. In this paper, an algebra matrix method is used to integrate the multidimensional information of network structures and the nodes' states. By the algebra matrix method, the diffusion threshold of the tacit knowledge is calculated, which is called algebra matrix evaluation. This evaluation method is proven to be effective by comparing with Monte Carlo simulations on three types of artificial networks and five reals. With applications of the algebra matrix evaluation, we construct a co-author network according the data of the academic papers from 1980 to 2017 on Aminer platform, and define states of tacit knowledge owners and the explicit knowledge carriers by the scholar's career lengths and the paper's cited quantities respectively. It is found that the thresholds of tacit knowledge diffusion are decreasing with the expansions of the scale of the largest connected components, whether tacit knowledge diffuses in the co-author networks or in the largest connected components. And with the evolution of cumulative co-author network, the diffusion thresholds of tacit knowledge in the largest connected component decrease in ladder-like with unequal steps. Furthermore, it is find ignoring the state factor will lead to the deviation in the evaluation of tacit knowledge diffusion thresholds, which is 16.33% in the largest connected components and 45.07% in the whole network. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new iterative method that is the combination of the proximal point algorithm, viscosity approximation method and alternating resolvent method for finding the common zeros of two accretive operators in Banach spaces. And we will prove the strong convergence theorems for the iterative algorithms and give the example of the main theorems. The results of this paper are improvements and extensions of the corresponding ones announced by many others. [ABSTRACT FROM AUTHOR]

In this paper, we provide a novel fractional particle swarm optimization (FPSO) algorithm. The traditional PSO is one of the most well-known bio-inspired algorithms used in optimization problems, which basically consists of a number of particles that collectively move in search of the global optimum. Nevertheless, despite its success over the past 20 years, the PSO is also known to be unable to converge, and even stagnate, in many complex problems with multiple local optima. In order to overcome this drawback, this paper proposes a modified version of the PSO algorithm, considering a fractional calculus approach. Stability results evaluation is carried out to analytically prove the convergence of the fractional extensions. This is naturally followed by simulation results to test the fractional-based PSOs under several well-known objective functions, thus highlighting the relationship between the fractional order velocity and position of particles with the convergence of the algorithm. Experimental results show that the FPSO and its variants significantly outperform the traditional PSO. [ABSTRACT FROM AUTHOR]

This paper investigates the Pareto optimization scheduling problem on a single machine with two competing agents A and B in which agent A wants to minimize the number of tardy A -jobs and agent B wants to minimize the maximum cost of B -jobs. In the literature, the constrained optimization problem of minimizing the number of tardy A -jobs under the restriction that the maximum cost of B -jobs is bounded is solved in polynomial time. This implies that the corresponding Pareto optimization scheduling problem can be solved in a weakly polynomial time. In this paper, by presenting a new algorithm for the constrained optimization problem, we provide a strongly polynomial-time algorithm for the corresponding Pareto optimization scheduling problem. Experimentation results show that the proposed algorithm for the considered problem is efficient. [ABSTRACT FROM AUTHOR]

Air pollution models plays a critical role in atmospheric environment research. Chemical kinetic equations is an important component of air pollution models. The chemical equations is numerically sticky because of its stiffness, nonlinearity, coupling and nonnegativity of the exact solutions. Over the past decades, numerous papers about chemical equation solvers have been published. However, these solvers cannot preserve the nonnegativity of the exact solutions. Therefore, in the calculation, the negative numerical concentration values are usually set to zero artificially, which may cause simulation errors. To obtain real nonnegative numerical concentration values, very small step-size has to be adopted. Then enormous amount of CPU time is consumed to solve the chemical equations. In this paper, we revisit this topic and derive a new algorithm. Our algorithm Modified-Backward-Euler (MBE) Method can unconditionally preserve the nonnegativity of the exact solutions. MBE is a simple, robust and efficient solver. It is much faster and more precise than the traditional solvers such as LSODE and QSSA. The numerical results and parameter suggestions are shown at the end of the paper. MBE is based on the P-L structure of the chemical equations and a deeper view into the nature of Euler Methods. It cannot only be used to solve chemical equations, but can also be applied to conquer ordinary differential equations (ODEs) with similar P-L structure. [ABSTRACT FROM AUTHOR]

In this paper, we give some necessary and sufficient conditions for the consistence of the system of quaternion matrix equations A 1 X = C 1 , Y B 1 = D 1 , A 2 W = C 2 , Z B 2 = D 2 , A 3 V = C 3 , V B 3 = C 4 , A 4 V B 4 = C 5 , A 5 X + Y B 5 + C 6 W + Z D 6 + E 6 V F 6 = G 6 , and constitute an expression of the general solution to the system when it is solvable. The outcomes of this paper encompass some recognized results in the collected works. In addition, we establish an algorithm and a numerical example to illustrate the theory constructed in the paper. [ABSTRACT FROM AUTHOR]

Uncertain differential equation is a type of differential equation driven by canonical Liu process. How to obtain the analytic solution of uncertain differential equation has always been a thorny problem. In order to solve uncertain differential equation, early researchers have proposed two numerical algorithms based on Euler method and Runge–Kutta method. This paper will design another numerical algorithm for solving uncertain differential equations via Adams–Simpson method. Meanwhile, some numerical experiments are given to illustrate the efficiency of the proposed numerical algorithm. Furthermore, this paper gives how to calculate the expected value, the inverse uncertainty distributions of the extreme value and the integral of the solution of uncertain differential equation with the aid of Adams–Simpson method. [ABSTRACT FROM AUTHOR]

First of all, by characterizing solutions of the quaternion equation a x = x ˜ b , this paper studies consimilarity of quaternions and some related consequences. For the important role of coneigenvalues in consimilarity tranformations of quaternion matrices, this paper further derives the relations between principle right coneigenvalues of a quaternion matrix and eigenvalues of the corresponding real representation matrix. Then, based on the real representation matrix, an effective algorithm is presented to calculate all coneigenvalues and the associated coneigenvectors of a quaternion matrix. Finally, two numerical examples are given to verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A given inventory problem consists of two parts: (1) the modeling part and (2) the solution procedure part. The modeling part can provide insight into the solution of the inventory problem and the solution procedure part involves the implementation of the inventory model. Both the modeling part and the solution procedure part of the inventory problem are equally important. Recently, Ouyang et al. [17] developed an integrated inventory model with a price-sensitive demand rate and determined both the economic lot size of the buyer’s ordering and the supplier’s production batch in order to maximize the total profit per unit time. Basically, their modeling is correct and interesting. They developed an algorithm based upon the first-order condition and the second-order condition to locate the optimal solution. However, the fundamentals of mathematics and the numerical examples which are considered in this paper illustrate that their algorithm based upon the first-order condition and the second-order condition to locate the optimal solution has several shortcomings. These shortcomings are shown here to influence the accuracy of the implementation of the inventory model. Since there exist reasons and motivations to present the correct solution procedures to the targeted readers, the main purpose of this paper is to adopt the rigorous methods of mathematical analysis in order to develop the complete solution procedures to locate the optimal solution for removing shortcomings in the earlier investigation by Ouyang et al. [17]. [ABSTRACT FROM AUTHOR]

This paper presents two conformance indexes that can be used to measure a similarity between two delineated structures. The authors use the presented conformance indexes for rating the results of Poisson Surface Reconstruction algorithm on real patient datasets. The rating is based on three delineations: original contours created during a standard procedure, reconstructed contours and reference contours created with an extra care by another physician. The chosen conformance indexes compare the delineations in two different forms: as a voxel grid and as a surface mesh. In this paper each of the conformance indexes is calculated in three different modes: the standard mode where all differences between datasets are taken into account and two more measuring how much one dataset exceeds the other. The last two modes are not symmetrical. The proposed conformance indexes allowed us to compare efficiently two delineations. The presented results also allow to state that the use of mesh reconstruction algorithms can improve delineations prepared within a limited time frame. [ABSTRACT FROM AUTHOR]

The paper deals with the problem of power quality and its solution. Passive or active compensators are usually used to reduce distortions of voltage and current waveforms. Active power filters seem to be the best choice if the effect of compensation is the only criterion. However, the financial cost of such a solution put the potential investors off. The paper shows that the cost could be reduced considerably if the optimization of active power filter allocation, as well as their nominal currents, is carried out. Two cases have been considered – active power filters with a classical control algorithm, which operates locally and aims at obtaining sinusoidal shape of waveforms in the point of installation, and active power filters with a modified control algorithm, which aims at reduction of waveform distortions in all nodes of an analyzed power system. Goal functions and optimization problems for both cases have been defined. [ABSTRACT FROM AUTHOR]

In this paper, neural algorithms, including the multi-layered perceptron (MLP) differential approximator, generalized hybrid power series, discrete Hopfield neural network, and the hybrid numerical, are used for constructing models that incorporate a priori knowledge in the form of differential equations for dynamic engineering processes. The properties of these approaches are discussed and compared to each other in terms of efficiency and accuracy. The presented algorithms have a number of advantages over other traditional mesh-based methods such as reduction of the computational cost, speed up of the execution time, and data integration with the a priori knowledge. Furthermore, the presented techniques are applicable when the differential equations governing a system or dynamic engineering process are not fully understood. The proposed algorithms learn to compute the unknown or free parameters of the equation from observations of the process behavior, hence a more precise theoretical description of the process is obtained. Additionally, there will be no need to solve the differential equation each time the free parameters change. The parallel nature of the approaches outlined in this paper make them attractive for parallel implementation in dynamic engineering processes. [ABSTRACT FROM AUTHOR]

In this paper, we present a new modified method for solving multi-level multi objective linear fractional programming problems (ML-MOLFPPs) based on fuzzy goal programming (FGP) approach with some modifications in the algorithm suggested by Baky (2010) [18] which dealt with multi-level multi objective linear programming problem (ML-MOLPP). In proposed modified approach, numerator and denominator function of each objective at each level are individually transformed into fuzzy goals and their aspiration levels are determined using individual best solutions. Different linear membership functions are defined for numerator and denominator function of each objective function. Then highest degree of each of these membership goals is achieved by minimising the sum of negative deviational variables. The proposed algorithm simplifies the ML-MOLFPP by eliminating solution preferences by the decision makers at each level, thereby avoiding difficulties associate with multi-level programming problems and decision deadlock situations. The aim of this paper is to present simple and efficient technique to obtain compromise optimal solution of ML-MOLFP problems. Numerical examples are illustrated in order to support the proposed modified FGP technique. [ABSTRACT FROM AUTHOR]

• In Section 5 Preconditioned BiCOR and TCORS Algorithms are added, i.e., "PBiCOR" and "PTCORS", which are two main methods obtained by introducing the preconditioner based on the nearest Kronecker product in Loan and Pitsianis [28] to accelerate the proposed TBiCOR and TCORS methods in the previous version. • In "Numerical Experiments" section, we added "PBiCOR" and "PTCORS" and compared with other methods. Numerical examples show that PTCORS converges fastest among all methods listed, and PBiCOR converges a bit slower than PTCORS does. • We have added an acknowledgements part. Other sections, such as the title/ introduction/abstract/Numerical experiments/Conclusions section, are all updated. • We have checked the English usage of the revised paper carefully. In this paper, the preconditioned TBiCOR and TCORS methods are presented for solving the Sylvester tensor equation. A tensor Lanczos L -Biorthogonalization algorithm (TLB) is derived for solving the Sylvester tensor equation. Two improved TLB methods are presented. One is the biconjugate L -orthogonal residual algorithm in tensor form (TBiCOR), which implements the L U decomposition for the triangular coefficient matrix derived by the TLB method. The other is the conjugate L -orthogonal residual squared algorithm in tensor form (TCORS), which introduces a square operator to the residual of the TBiCOR algorithm. A preconditioner based on the nearest Kronecker product is used to accelerate the TBiCOR and TCORS algorithms, and we obtain the preconditioned TBiCOR algorithm (PTBiCOR) and preconditioned TCORS algorithm (PTCORS). The proposed algorithms are proved to be convergent within finite steps of iteration without roundoff errors. Several examples illustrate that the preconditioned TBiCOR and TCORS algorithms present excellent convergence. [ABSTRACT FROM AUTHOR]

The hybridization of Differential Evolution (DE) and Particle Swarm Optimization (PSO) have been well preferred over their individual effort in solving optimization problems. The way of applying DE and PSO in the hybridization process is a big deal to achieve promising solutions. Recently, they have been used simultaneously (i.e. in parallel) on different sub-populations of the same population, instead of applying them alternatively in series over the generation. An attempt is made in this paper to hybrid DE and PSO in parallel, under a ‘tri-population’ environment. Initially, the whole population (in increasing order of fitness) is divided into three groups – inferior group, mid group and superior group. Based on their inherent ability, DE is employed in the inferior and superior groups whereas PSO is used in the mid-group. This proposed method is named as DPD as it uses DE–PSO–DE on the sub-populations of the same population. Two more strategies namely Elitism (to retain the best obtained values so far) and Non Redundant Search (to improve the solution quality) have been incorporated in DPD cycle. The paper is designed with three major aims: (i) investigation of suitable DE-mutation strategies to support DPD, (ii) performance comparison of DPD over state-of-the-art algorithms through a set of benchmark functions and (iii) application of DPD to real life problems. Numerical, statistical and graphical analysis in this paper finally concludes the robustness of the proposed DPD. [ABSTRACT FROM AUTHOR]

Let G = (V , E) be a graph. The weak rupture degree of G is defined as r w (G) = max { ω (G − X) − | X | − m e (G − X) : ω (G − X) > 1 } , where the maximum is taken over all X , the subset of V (G), ω (G − X) is the number of components in G − X , and m e (G − X) is the size (edge number) of a largest component in G − X. This is an important parameter to quantitatively describe the invulnerability of networks. In this paper, based on a study of relationship between network structure and the weak rupture degree, a polynomial algorithm for computing the weak rupture degree of trees is given. [ABSTRACT FROM AUTHOR]

In this paper we employ the Euclidean division for polynomials to recover uniquely a Jacobi matrix in terms of the mixed spectral data consisting of its partial entries and the information given on its full spectrum together with a subset of eigenvalues of its truncated matrix obtained by deleting the last row and last column, or its rank-one modification matrix modified by adding a constant to the last element. A necessary and sufficient condition is provided for the existence of the inverse problem. A numerical algorithm and a numerical example are given. [ABSTRACT FROM AUTHOR]

This paper proposes numerical quadrature rules for two-dimensional Cauchy principal-value integrals of the forms ∫ ∫ Ω f (x , y) (x − s) 2 + (y − t) 2 d y d x and ∫ ∫ Ω f (x , y) (x − s) (y − t) d y d x. The derivation of these quadrature rules is based on the Euler–Maclaurin error expansion of a modified trapezoidal rule for one-dimensional Cauchy singular integrals. The corresponding error estimations are investigated, and the convergence rates O (h m 2 μ + h n 2 μ) are obtained for the proposed quadrature rules, where h m and h n are partition sizes in x and y directions, μ is a positive integer determined by integrand. To further improve accuracy, a splitting extrapolation algorithm is developed based on the asymptotic error expansions. Several numerical tests are performed to verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In computer aided geometric design a polynomial is usually represented in Bernstein form. This paper presents a family of compensated algorithms to accurately evaluate a polynomial in Bernstein form with floating point coefficients. The principle is to apply error-free transformations to improve the traditional de Casteljau algorithm. At each stage of computation, round-off error is passed on to first order errors, then to second order errors, and so on. After the computation has been "filtered" (K − 1) times via this process, the resulting output is as accurate as the de Casteljau algorithm performed in K times the working precision. Forward error analysis and numerical experiments illustrate the accuracy of this family of algorithms. [ABSTRACT FROM AUTHOR]

Highlights • To fill a low-rank Toeplitz matrix from a small subset of its entries. • Definition of "Toeplitz structure smoothing operator". • The augmented Lagrange multiplier algorithm with smoothing for TMC problem. • Approximation matrices may hold on Toeplitz structure throughout the iteration. Abstract Toplitz matrix completion (TMC) is to fill a low-rank Toeplitz matrix from a small subset of its entries. Based on the augmented Lagrange multiplier (ALM) algorithm for matrix completion, in this paper, we propose a new algorithm for the TMC problem using the smoothing technique of the approximation matrices. The completion matrices generated by the new algorithm are of Toeplitz structure throughout iteration, which save computational cost of the singular value decomposition (SVD) and approximate well the solution. Convergence results of the new algorithm are proved. Finally, the numerical experiments show that the augmented Lagrange multiplier algorithm with smoothing is more effective than the original ALM and the accelerated proximal gradient (APG) algorithms. [ABSTRACT FROM AUTHOR]

• A novel fractional gradient descent method with adaptive momentum is presented for training BP neural networks. • The convergence of the proposed algorithm is proved. • The proposed fractional algorithm can effectively improve the training performance and expand the selection range of learning rate. A novel fractional gradient descent method with adaptive momentum is presented in this paper to improve the convergence speed and stability for BP neural network training. The fractional Grünwald-Letnikov derivative is used for the fractional gradient. The coefficient of the momentum term is set as an adaptive variable, depending on the fractional gradient of the current step and the weight change of the previous step. We give a detailed convergence proof of the proposed method. Experiments on MNIST data sets and XOR problem demonstrate that the fractional gradient descent method with adaptive momentum term can effectively improve convergence speed, maintain stability of BP neural network training, help escape from local minimum points, and enlarge the selection range of the learning rate. [ABSTRACT FROM AUTHOR]

• Discrete time Consensus Based Optimization (CBO) algorithm on a convex set is introduced. • The error between optimal value and consensus value is rigorously calculated and further extended from previous paper. • Portfolio optimization problem was solved using our proposed constrained CBO algorithm. In this paper, we propose a predictor-corrector type Consensus Based Optimization(CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the global minima of the non-convex function defined on a convex domain. As a practical application of the proposed algorithm, we study the portfolio optimization problem in finance. In this application, we introduce an objective function to choose the optimal weight on each asset in an asset-bundle, which yields the maximal expected returns given a certain level of risks. Simulation results show that our proposed predictor-corrector type model is successful in finding the optimal value. [ABSTRACT FROM AUTHOR]

• Active fault-tolerant strategy is introduced to distributed state estimation scheme. • Intermittent fault (IF) detector is designed and the detectability of IF is analyzed. • Estimation errors can remain the prescribed performance under the influence of IF. In this paper, the problem of distributed fault-tolerant state estimation is studied for stochastic systems over sensor networks with intermittent sensor faults. Compared with the traditional state estimation algorithms, the distinct advantage of fault-tolerant state estimation is that the estimator can keep good performance whether sensor faults occur or not. Different from the previous literature concerning with distributed fault diagnosis, the distributed fault diagnosis problem is investigated in this paper for intermittent faults, whose appearing time, disappearing time and magnitude are all nondeterministic. The distributed fault-tolerant state estimation scheme is constructed, in which the appearing time and disappearing time of intermittent faults are detected, intermittent faults are estimated and compensated. By means of the matrix inequality technique, the H ∞ performance of state estimation errors is guaranteed by properly choosing the estimator parameters. Finally, two examples are provided to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

• In this paper, the nonlinear fault detection observer is constructed and the observer gain function is derivated by choosing the novel Lyapunov functions. The predetermined estimation accuracy-dependent nonnegative function is introducing in the last step of recursive algorithm. • The threshold design problem is solved by suppressing the residual within the predetermined output estimation accuracy range during the implementation process of observer. • The tight thresholds ϵ and ϵ are predetermined under strategic designing scheme. It is straightforward to implement by comparison with the existing empirical or calculation methods of threshold. This paper presents an fault detection (FD) method for a class of uncertain nonlinear systems with unmatched nonlinear fault functions and disturbances. A recursive FD observer is designed with predetermined and small output estimation error. The nonlinear observer gain function is achieved by introducing predetermined output estimation accuracy-dependent nonnegative functions. Combining Lyapunov functions, it is shown that the absolute value of the residual signal is equal or lesser than tight threshold before fault occurrence. The FD scheme is proposed following fault detectability analysis, simulation example indicates the validity of the proposed method. [ABSTRACT FROM AUTHOR]

• Firstly, a robust discrete-time non-smooth consensus protocol solves that consensus problem for the first-order leaderless multi-agent systems with external disturbance and discrete-time feedback. • Then, a discrete-time super-twisting observer is proposed to estimate the multi-agent systems disturbance. Combining the robust discrete-time non-smooth consensus protocol and discrete-time super-twisting observer, we get a new consensus protocol. The superiorities of this method contains two aspects, i.e., the disturbance rejection ability and a smaller consensus error. To the best authors' knowledge, the presented results in this paper are novel in the literature. In this paper, we firstly consider the consensus problems of first-order leaderless multi-agent systems with external disturbance. Then, we propose a robust discrete-time non-smooth (RDTNS) consensus protocol, which makes agents reach consensus within a region. Besides, we design a disturbance observer based on the discrete-time super-twisting algorithm (DTSTA), which can improve the disturbance rejection ability and decrease the consensus error for the multi-agent systems. At last, we get a robust discrete-time disturbance rejection control consensus protocol by combining the RDTNS consensus protocol with the discrete-time super-twisting observer (DTSTO). The simulation results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• It is the first time to investigate the problem of decentralized finite-time tracking control with prescribed settling time for a class of p -normal form stochastic large-scale systems with output interconnections existing in both the drift and diffusion terms. • It is the first time to investigate the connective stability problem for stochastic large-scale systems when the system structure changes. • Differing from the existing results, this paper proposes a new mathematical treatment algorithm to deal with the interconnections of stochastic large-scale systems, such that the decentralized tracking control is achieved. • The proposed control strategy is more convenient for practical application than the general finite-time control. • Due to the complexity of the system mathematics model, this paper can better reflect the application of mathematics. This paper aims to solve the decentralized finite-time connective tracking control problem for p -normal form stochastic large-scale systems with output interconnections existing in both the drift and diffusion terms. By means of the stochastic system theory and a prescribed finite-time performance function (PFTPF), a novel design scheme is presented for the decentralized finite-time connective tracking controllers with an arbitrarily prescribed settling time. The connective stability problem of stochastic large-scale systems is investigated for the first time. In addition, a new solution for the decentralized tracking control problem of stochastic large-scale systems is presented via a novel mathematical treatment algorithm. The proposed controllers can ensure that the tracking errors converge to a predetermined region within an arbitrarily prescribed settling time and the controlled system is connectively bounded stable in probability. Three simulation examples are presented to exhibit the performance and the superiority of the new control strategy. [ABSTRACT FROM AUTHOR]

• A novel online mode-free integral reinforcement learning algorithm is proposed to solve the mutiplayer non-zero sum games. • The online learning is used to compute the corresponding N coupled algebraic Riccati equations. • The policy iterative algorithm is applied to solve the coupled algebraic Riccati equations corresponding to the multiplayer nonzero sum games. In this paper, a novel online mode-free integral reinforcement learning algorithm is proposed to solve the multiplayer non-zero sum games. We first collect and learn the subsystems information of states and inputs; then we use the online learning to compute the corresponding N coupled algebraic Riccati equations. The policy iterative algorithm proposed in this paper can solve the coupled algebraic Riccati equations corresponding to the multiplayer non-zero sum games. Finally, the effectiveness and feasibility of the design method of this paper is proved by simulation example with three players. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates single-machine scheduling problems with piece-rate machine maintenance and interval constrained actual processing time. The actual processing time of a job is a general function of the normal job processing time and the position in job sequence, and it is required to restrict in given interval otherwise earliness or tardiness penalty should be paid. The maintenance duration studied in the paper is a time-dependent linear function. The objective is to find jointly the optimal frequency to perform maintenances and the optimal job sequence to minimize the total cost, which is a linear function of the makespan, total earliness and total tardiness. There is shown that the problem can be optimally solved in O(n 4) time. There is also shown that two special cases of the problem can be optimally solved by lower order algorithms. [Copyright &y& Elsevier]

Abstract: Multipoint iterative methods belong to the class of the most efficient methods for solving nonlinear equations. Recent interest in the research and development of this type of methods has arisen from their capability to overcome theoretical limits of one-point methods concerning the convergence order and computational efficiency. This survey paper is a mixture of theoretical results and algorithmic aspects and it is intended as a review of the most efficient root-finding algorithms and developing techniques in a general sense. Many existing methods of great efficiency appear as special cases of presented general iterative schemes. Special attention is devoted to multipoint methods with memory that use already computed information to considerably increase convergence rate without additional computational costs. Some classical results of the 1970s which have had a great influence to the topic, often neglected or unknown to many readers, are also included not only as historical notes but also as genuine sources of many recent ideas. To a certain degree, the presented study follows in parallel main themes shown in the recently published book (Petković et al., 2013) [53], written by the authors of this paper. [Copyright &y& Elsevier]

Abstract: In this paper we provide an extension of the classical Chaos game for IFSP. The paper is divided into two parts: in the first one, we discuss how to determine the integral with respect to a measure which is a combination of a self-similar measure from an IFSP along with a density given by an IFSM. In the second part, we prove a version of the Ergodic Theorem for the integration of a continuous multifunction with respect to the invariant measure of an IFSP. These results are in line with some recent extensions of IFS theory to multifunctions. [Copyright &y& Elsevier]