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This paper proposes a capacity estimation algorithm for Li-ion batteries (LIBs) using the successive approximation method. Model-based capacity estimation method can be applied to a variety of current profiles because the capacity is calculated from state of charge (SOC) estimated accurately using the functional relationship between open circuit voltage (OCV) and the SOC. However, with aging, the OCV-SOC table changes, which worsens the estimation accuracy. Therefore, additional experiments are necessary to compensate the errors whenever the capacity should be identified. To overcome this restriction, this paper proposes an algorithm for estimating both the capacity and the corresponding OCV-SOC table based on the preliminary OCV-SOC tables obtained from other batteries. The capacity and the table are updated successively based on the prior capacity estimate. This work proposes two algorithms for voltage characteristics: OCV measurement and SOC estimation cases. The former uses the measured OCV to calculate the SOCs directly, while the latter estimates the SOCs using a dual extended Kalman filter (DEKF). Aging data from five LIB packs are analyzed, and the capacity estimation errors are less than 2.2% for the OCV measurement case and 3.06% until 20% loss of capacity estimate for SOC estimation case. [ABSTRACT FROM AUTHOR]

Meshfree approximation schemes possess a high potential in computer aided engineering due to their large flexibility. Especially the tremendous progress in processor technology within recent years relativizes the increase in computation time due to the inherent search algorithm. Nevertheless meshfree approximation schemes are still faced with some challenges, like imposition of Dirichlet boundary conditions, robustness of the algorithm and accuracy. The recent developed Optimal Transportation Meshfree (OTM) method seemed to overcome most of these problems. In this paper the OTM solution scheme is combined with a standard search algorithm in order to allow a simple and flexible computation. However this scheme is not stable for some examples of application. Hence an investigation is conducted which shows that the reason for this instability is due to underintegration. Based on this investigation a remedy to stabilize the algorithm is suggested which is based on well known concepts to control the hourglass effects in the Finite Element Method. In contrast to the original publication, the OTM algorithm is derived here from the principle of virtual work. Local maximum entropy shape functions are used which possess a weak Kronecker- δ property. This enables a direct imposition of Dirichlet boundary conditions if the boundary is convex. The limitations of this basis function are also addressed in this paper. Additionally, the search algorithm presented fulfills basic topological requirements. Several examples are investigated demonstrating the improved behavior of the stabilized OTM algorithm. [ABSTRACT FROM AUTHOR]

Evolutionary multi-objective optimization (EMO) algorithms are actively used for answering optimization problems with multiple contradictory objectives and scheming interpretable and precise real-time applications. A majority of existing EMO algorithms performs better on two or three objectives non-dominated problems; however, they meet complications in managing and maintaining a set of optimal solutions to multi-objective optimization problems. This paper proposes a search space-based multi-objective evolutionary algorithm (SSMOEA) for multi-objective optimization problems. To accomplish the potential of the search space-based method for solving multi-objective optimization problems and to reinforce the selection procedure toward the ideal direction while sustaining an extensive and uniform distribution of solutions is our key objective. To the best of our knowledge, this paper is the first attempt to propose a search space-based multi-objective evolutionary algorithm for multi-objective optimization. The experimental setup used showed that the proposed algorithm is good and competitive in comparison to the existing EMO algorithms from the viewpoint of finding a scattered and estimated solution set in multi-objective optimization problems. SSMOEA can achieve a good trade-off between search space convergence and search space diversity in the appropriate experimental setup. [ABSTRACT FROM AUTHOR]

This paper is motivated by recent results in the design of signal plans for Manhattan that highlight the importance of providing signal control algorithms with an analytical description of between-link dependencies. This is particularly important for congested networks prone to the occurrence of spillbacks. This paper formulates a probabilistic network model that proposes an aggregate description of the queue-length, and then approximates the joint aggregate queue-length distribution of subnetworks. The goal is to model between-queue dependencies beyond first-order moments, yet to do so in a tractable manner such that these techniques can be used for optimization purposes. This paper models an urban road network as a finite space capacity Markovian queueing network. Exact evaluation of the stationary joint queue-length distribution of such a network with arbitrary size and topology can be obtained numerically. Nonetheless, the main challenge to such an approach remains the dimensionality of the network state space, which is exponential in the number of queues. This paper proposes to address the dimensionality issue by: 1) describing the state of the network aggregately, and 2) decomposing the network into overlapping subnetworks. We propose an analytical approximation of the stationary aggregate joint queue-length distribution of a subnetwork. The model consists of a system of nonlinear equations with a dimension that is linear, instead of exponential, in the number of queues and that is independent of the space capacity of the individual queues. The method is derived for tandem Markovian finite capacity queueing networks. The proposed model is computationally tractable and scalable, it can be efficiently used for the higher-order distributional analysis of large-scale networks. The model is validated versus simulation estimates and versus other decomposition methods. We then use it to address an urban traffic control problem. We show the added value of accounting for higher-order spatial between-queue dependency information in the control of congested urban networks. [ABSTRACT FROM AUTHOR]

During the last decade, the paradigm of compressed sensing has gained significant importance in the signal processing community. While the original idea was to utilize sparsity assumptions to design powerful recovery algorithms of vectors x ∈ R d , the concept has been extended to cover many other types of problems. A noteable example is low-rank matrix recovery. Many methods used for recovery rely on solving convex programs. A particularly nice trait of compressed sensing is its geometrical intuition. In recent papers, a classical optimality condition has been used together with tools from convex geometry and probability theory to prove beautiful results concerning the recovery of signals from Gaussian measurements. In this paper, we aim to formulate a geometrical condition for stability and robustness, i.e. for the recovery of approximately structured signals from noisy measurements. We will investigate the connection between the new condition with the notion of restricted singular values , classical stability and robustness conditions in compressed sensing, and also to important geometrical concepts from complexity theory. We will also prove the maybe somewhat surprising fact that for many convex programs, exact recovery of a signal x 0 immediately implies some stability and robustness when recovering signals close to x 0 . [ABSTRACT FROM AUTHOR]

In this paper we consider the problem of computing the 2-vertex-connected components of directed graphs. We present a new algorithm for solving this problem in O ( n m ) time. Furthermore, we show that the old algorithm of Erusalimskii and Svetlov runs in O ( n m 2 ) time. In this paper, we investigate the relationship between 2-vertex-connected components and dominator trees. We also consider three applications of our new algorithm, which are approximation algorithms for problems that are generalization of the problem of approximating the smallest 2-vertex-connected spanning subgraph of 2-vertex-connected directed graph. [ABSTRACT FROM AUTHOR]

Particle-based methods based on material models using spheres can provide good approximations for many physical phenomena at both the micro and macroscales. The point of departure for the simulations, in general, is a dense arrangement of spherical particles (sphere pack) inside a given container. For generic domains, the generation of a sphere pack may be complex and time-consuming, especially if the pack must comply with a prescribed sphere size distribution and the stability requirements of the simulation. The primary goal of this paper is to present an efficient algorithm that is capable of producing packs with millions of spheres following a statistical sphere size distribution inside complex arbitrary domains. This algorithm uses a new strategy to ensure that the sphere size distribution is preserved even when large particles are rejected in the growing process. The paper also presents numerical results that enable an evaluation of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper we present an efficient framework for the evaluation of subdivision schemes with polynomial reproduction property. For all interested rational parameters between 0 and 1 with the same denominator, their exact limit positions on the subdivision curve can be obtained by solving a system of linear equations. When the framework is applied to binary and ternary 4-point interpolatory subdivision schemes, we find that the corresponding coefficient matrices are strictly diagonally dominant, and so the evaluation processes are robust. For any individual irrational parameters between 0 and 1, its approximate value is computed by a recursive algorithm which can attain an arbitrary error bound. For surface schemes generalizing univariate subdivision schemes with polynomial reproduction property, exact evaluation methods can also be derived by combining Stam’s method with that of this paper. [ABSTRACT FROM AUTHOR]

This paper aims to develop a data-driven approximate causal inference model using the newly-proposed evidential reasoning (ER) rule. The ER rule constitutes a generic conjunctive probabilistic reasoning process and generalises Dempster’s rule and Bayesian inference. The belief rule based (BRB) methodology was developed to model complicated nonlinear causal relationships between antecedent attributes and consequents on the basis of the ER algorithm and traditional IF-THEN rule-based systems, and in essence it keeps methodological consistency with Bayesian Network (BN). In this paper, we firstly introduce the ER rule and then analyse its inference patterns with respect to the bounded sum of individual support and the orthogonal sum of collective support from multiple pieces of independent evidence. Furthermore, we propose an approximate causal inference model with the kernel mechanism of data-based approximate causal modelling and optimal learning. The exploratory approximate causal inference model inherits the main strengths of BN, BRB and relevant techniques, and can potentially extend the boundaries of applying approximate causal inference to complex decision and risk analysis, system identification, fault diagnosis, etc. A numerical study on the practical pipeline leak detection problem demonstrates the applicability and capability of the proposed data-driven approximate causal inference model. [ABSTRACT FROM AUTHOR]

In this paper, a three-term conjugate gradient algorithm is developed for solving large-scale unconstrained optimization problems. The search direction at each iteration of the algorithm is determined by rectifying the steepest descent direction with the difference between the current iterative points and that between the gradients. It is proved that such a direction satisfies the approximate secant condition as well as the conjugacy condition. The strategies of acceleration and restart are incorporated into designing the algorithm to improve its numerical performance. Global convergence of the proposed algorithm is established under two mild assumptions. By implementing the algorithm to solve 75 benchmark test problems available in the literature, the obtained results indicate that the algorithm developed in this paper outperforms the existent similar state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Empirical evidence shows that repositories of business process models used in industrial practice contain significant amounts of duplication. This duplication arises for example when the repository covers multiple variants of the same processes or due to copy-pasting. Previous work has addressed the problem of efficiently retrieving exact clones that can be refactored into shared subprocess models. This paper studies the broader problem of approximate clone detection in process models. The paper proposes techniques for detecting clusters of approximate clones based on two well-known clustering algorithms: DBSCAN and Hierarchical Agglomerative Clustering (HAC). The paper also defines a measure of standardizability of an approximate clone cluster, meaning the potential benefit of replacing the approximate clones with a single standardized subprocess. Experiments show that both techniques, in conjunction with the proposed standardizability measure, accurately retrieve clusters of approximate clones that originate from copy-pasting followed by independent modifications to the copied fragments. Additional experiments show that both techniques produce clusters that match those produced by human subjects and that are perceived to be standardizable. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the discrete multitone multiple input, multiple output interference channel (DMT MIMO IC) in DSL networks. The scenario consists of a number of users, each with a given number of transceivers, that share the same channel in multiple tones. Our goal is to maximize the weighted rate sum of the users subject to power constraints. A recent paper has treated this problem with per-user power constraints. In this paper we focus on per-transceiver power constraints. We propose two different algorithms. First, we straightforwardly adapt the previously proposed DMT-WMMSE algorithm. Second, we adapt the WMMSE-GDSB, in which we separate the problem in signal and spectrum coordination parts. For the spectrum coordination part, we show that the problem can be solved more efficiently with a change of variables: we use a coordinate system consisting of a radius and a direction vector with ℓ1 norm equal to 1. This can be interpreted as spherical coordinates in taxicab geometry. It is observed that for the radial dimension the problem can be made concave after approximations and it is thus easy to solve. The remaining dimensions are solved with a sequence of line searches. Simulation results show that the WMMSE-GDSB converges faster. [Copyright &y& Elsevier]

Abstract: In some recent papers, some procedures based on some weighted empirical measures related to decreasing-step Euler schemes have been investigated to approximate the stationary regime of a diffusion (possibly with jumps) for a class of functionals of the process. This method is efficient but needs the computation of the function at each step. To reduce the complexity of the procedure (especially for functionals), we propose in this paper to study a new scheme, called the mixed-step scheme, where we only keep some regularly time-spaced values of the Euler scheme. Our main result is that, when the coefficients of the diffusion are smooth enough, this alternative does not change the order of the rate of convergence of the procedure. We also investigate a Richardson–Romberg method to speed up the convergence and show that the variance of the original algorithm can be preserved under a uniqueness assumption for the invariant distribution of the “duplicated” diffusion, condition which is extensively discussed in the paper. Finally, we conclude by giving sufficient “asymptotic confluence” conditions for the existence of a smooth solution to a discrete version of the associated Poisson equation, condition which is required to ensure the rate of convergence results. [Copyright &y& Elsevier]

Highlights: [•] Aiming at the problem that how to classify T-splines this paper gives a mathematical analysis, and a sufficient condition of standard T-splines is also given. [•] Then this paper presents an algorithm of determining the T-spline classification, and we can get the inherently mathematical properties of T-splines by the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose a two-stage algorithm utilizing the Cauchy integral and the matrix-valued adaptive Fourier decomposition (abbreviated as matrix AFD) to identify transfer functions of linear time-invariant (LTI) multi-input multi-output (MIMO) systems in the continuous time case. In recent work of Alpay et al. (2017), a theory of adaptive rational approximation to matrix-valued Hardy space functions on the unit disk was established. The matrix-valued function theory has great potential in applications, in views of the practice of its scalar-valued counterparts. The algorithm and application aspects of the mentioned theory of Alpay et al. (2017) have not been developed. The theory was only written for the unit disk case corresponding to the discrete time systems. The contributions of the present paper are 3-fold. First, we construct an analogous adaptive approximation theory for complex matrix-valued Hardy space functions defined on a half of the complex plane, corresponding to the Laplace transforms of signals of finite energy whose Fourier transforms are supported on a half of the frequency domain. The half plane model corresponds to signals defined in the whole axis range which is an alternative case to signals defined in a compact interval. The second fold contribution lays on maximal selection of the pair (a , P) where a is a point of the right-half plane and P is an orthogonal projection. We show that the optimal selection of P is dependent on a when a is first fixed, that is P = P (a) , where P : a → P (a) has an explicit corresponding relation. Due to this relation we reduce the maximal selection of the pair (a , P) to only that of the parameter a. This result can be extended to the compact intervals case as well. The third fold is, with the precise rule from a to P (a) , we develop a practical algorithm for the adaptive approximation to the transfer function. Through an example we show that the proposed algorithm is effective in both the noise-free and noisy cases. [ABSTRACT FROM AUTHOR]

Abstract: Although the rough set and intuitionistic fuzzy set both capture the same notion, imprecision, studies on the combination of these two theories are rare. Rule extraction is an important task in a type of decision systems where condition attributes are taken as intuitionistic fuzzy values and those of decision attribute are crisp ones. To address this issue, this paper makes a contribution of the following aspects. First, a ranking method is introduced to construct the neighborhood of every object that is determined by intuitionistic fuzzy values of condition attributes. Moreover, an original notion, dominance intuitionistic fuzzy decision tables (DIFDT), is proposed in this paper. Second, a lower/upper approximation set of an object and crisp classes that are confirmed by decision attributes is ascertained by comparing the relation between them. Third, making use of the discernibility matrix and discernibility function, a lower and upper approximation reduction and rule extraction algorithm is devised to acquire knowledge from existing dominance intuitionistic fuzzy decision tables. Finally, the presented model and algorithms are applied to audit risk judgment on information system security auditing risk judgement for CISA, candidate global supplier selection in a manufacturing company, and cars classification. [Copyright &y& Elsevier]

Abstract: The topic of this paper is the estimation of modal parameters from nonstationary ambient vibration data by applying the random decrement algorithm. If the ambient excitation can be modeled as a nonstationary white noise in the form of a product model, then the nonstationary cross randomdec signatures of structural response evaluated at any fixed time instant are shown theoretically to be proportional to the nonstationary cross-correlation functions, which is of the same form as the free-vibration decay or impulse response of the original system. The practical problem of insufficient data samples available for evaluating nonstationary randomdec signatures can be approximately resolved by first extracting the amplitude-modulating function from the response and then transforming the nonstationary responses into stationary ones. However, the error involved in the approximate free-decay response would generally lead to a distortion in the modal identification. In the present paper, we also further propose that, if the ambient excitation can be modeled as a zero-mean nonstationary process, without any additional treatment of transforming the original nonstationary responses, the nonstationary cross randomdec signatures of structural response are shown in the same mathematical form as that of free vibration of a structure, from which modal parameters of the original system can thus be identified. Numerical simulations, including one example of using the practical excitation data, confirm the validity of the proposed method for identification of modal parameters from nonstationary ambient response data only. [Copyright &y& Elsevier]

Abstract: This paper reports on improvements to recent work on the computation of a structured low rank approximation of the Sylvester resultant matrix of two inexact polynomials and . Specifically, it has been shown in previous work that these polynomials must be processed before a structured low rank approximation of is computed. The existing algorithm may still, however, yield a structured low rank approximation of , but not a structured low rank approximation of , which is unsatisfactory. Moreover, a structured low rank approximation of must be equal to, apart from permutations of its columns, a structured low rank approximation of , but the existing algorithm does not guarantee the satisfaction of this condition. This paper addresses these issues by modifying the existing algorithm, such that these deficiencies are overcome. Examples that illustrate these improvements are shown. [Copyright &y& Elsevier]

Abstract: In this paper, we develop the adaptive data fitting algorithms by virtue of the local property of the Progressive-iterative approximation (abbr. PIA), which generates the fitting curve (patch) by adjusting the control points of a blending curve (patch) iteratively. In the adaptive data fitting algorithms, the control points are classified into two classes, namely, active and fixed control points, and only the active control points need to be adjusted in each iteration, thus saving computation greatly. Lots of examples and experimental data are presented to demonstrate the efficiency of the adaptive data fitting algorithm. Since the PIA method can be made parallel easily, the adaptive data fitting algorithm developed in this paper has important applications in parallel large scale data fitting. [Copyright &y& Elsevier]

Abstract: This paper addresses the toll design problem of finding the toll locations and levels in a congestion pricing scheme, which minimize the total travel time and the toll-point cost (set-up and operational costs of the toll collecting facilities). Road users in the network are assumed to be distributed according to the principle of user equilibrium, with the demand assumed to be fixed and given a priori. The toll design problem is commonly formulated as a non-linear program, which in general is non-convex and non-smooth, and thus difficult to solve for a global optimum. In this paper, the toll design problem is approximated by a mixed integer linear program (MILP), which can be solved to its globally optimal solution. The MILP also gives a lower bound estimation of the original non-linear problem, and the accuracy of the approximation is improved by iteratively updating the MILP. To demonstrate the approach, we apply the algorithm to two networks: a smaller network with 18 links and 4 OD-pairs to illustrate the properties of the approach, and the Sioux Falls network with 87 links and 30 OD-pairs to demonstrate the applicability of the approach. [Copyright &y& Elsevier]

Abstract: The sampling theory describes ways of reconstructing signals from their uniform or nonuniform samples associated with the traditional Fourier transform (FT). Most of the published papers about the sampling theory require signals to be bandlimited in the FT domain and assume that the sample locations and the band width are all known. However, the sample locations are not always known and most of the signals are non-stationary in practical applications. In order to overcome these shortcomings, this paper provides an algorithm for approximating signals from nonuniform samples at unknown locations. These signals are not necessarily bandlimited in the FT domain, however bandlimited in the LCT domain. The experimental results are given to verify the accuracy of the algorithm. [Copyright &y& Elsevier]

Abstract: This paper considers the problem of finding architectures with sufficient multi-objective Pareto optimality and maximum diversity of their design-variable values. This problem has been exclusively addressed to date by Evolutionary Algorithms, which are known to be powerful, and yet, the optimality of their solutions cannot be guaranteed. This paper defines two somewhat dual Maximal Design Diversity (MDD) problems, namely, (1) Primal -MDD: maximizing a design-variable diversity metric between architectures given a margin for compromising Pareto optimality, and (2) Dual -MDD: minimizing the compromise of Pareto optimality of architectures given a lower bound for design-variable diversity. Greedy algorithms for computing both Primal and Dual -MDD are presented. For the Primal -MDD the proposed greedy algorithm is proven to be a -approximation of the optimal algorithm and an upper bound for the optimality violation is computed, with respect to the efficient frontier in the objective space. For the Dual -MDD the optimality violation of the proposed greedy algorithm is proven to be at least as good as that of the optimal algorithm when the lower bound on the distance between the solutions in the design-variable space is doubled. Finally, a real-world mixed-integer non-linear programming model with two objectives, dozens of variables and hundreds of constraints is considered as the main use case, taken from the domain of aircraft-engine design. The results validate the fidelity of the algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, a method for telecommunications fraud detection is proposed. The method is based on the user profiling utilizing the Latent Dirichlet Allocation (LDA). Fraudulent behavior is detected with use of a threshold-type classification algorithm, allocating the telecommunication accounts into one of two classes: fraudulent account and non-fraudulent account. The paper provides also a method for automatic threshold computation. The accounts are classified with use of the Kullback–Leibler divergence (KL-divergence). Therefore, we also introduce three methods for approximating the KL-divergence between two LDAs. Finally, the results of experimental study on KL-divergence approximation and fraud detection in telecommunications are reported. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the projection algorithm studied by Iiduka and Takahashi (2008) for finding a solution of the variational inequality problem for an inverse strongly monotone operator in a Banach space. We first remark that, under the assumptions imposed on the operator in their paper, the iterative sequence converges weakly to a zero of the operator, not just a solution of the variational inequality problem. In our proof, slightly modified from the original, we do not assume the uniform smoothness of a space as was the case there. Finally, using Halpern’s type method, we modify this algorithm to obtain the strong convergence to a zero of an inverse strongly monotone operator which is nearest to the initial element of the algorithm in the sense of the Bergman distance associated with the function . [Copyright &y& Elsevier]

Abstract: The linear complementarity problem is to find a vector in satisfying , ,, where and are given. In this paper, we use the fact that solving is equivalent to solving the nonlinear equation where is a function from into itself defined by . We build a sequence of smooth functions which is uniformly convergent to the function . We show that, an approximation of the solution of the (when it exists) is obtained by solving for a parameter large enough. Then we give a globally convergent hybrid algorithm which is based on vector divisions and the secant method for solving . We close our paper with some numerical simulations to illustrate our theoretical results, and to show that this method can solve efficiently large-scale linear complementarity problems. [Copyright &y& Elsevier]

Abstract The shift and invert Arnoldi (SIA) method is a numerical algorithm for approximating the product of Toeplitz matrix exponential with a vector. In this paper, we extend the SIA method to chemical master equation (CME) and propose a SIA algorithm based on the strategy of reorthogonalization (SIRA). We establish a theoretical error of the resulting approximation of SIRA algorithm. Numerical experiments show that the SIRA algorithm is more efficient than the Krylov FSP algorithm in terms of finite models, and the error estimate can be used to determine whether this result obtained by SIRA algorithm is acceptable or not. [ABSTRACT FROM AUTHOR]

Highlights • A method for radar HRRP target recognition is proposed based on Conditional VAE. • The model is regularized through the average HRRP for robust representations. • The label information is introduced by a three-way weight conditional model. • Weight factorization is utilized to effectively reduce model parameters. • Our method performs well under the low SNR and small amount of training data. Abstract In this paper, we propose a conditional generative model for radar high resolution range profile (HRRP) target recognition to learn the discriminative representations and sufficiently encode the observed feature variability by taking the multi-layer perception (MLP) as the sufficient statistics of posterior approximation distribution, thus offering the potential to improve the overall recognition performance. Considering the target-aspect sensitivity of HRRP, the model is regularized through reconstructing the average profiles. Then we introduce three-way weight tensors for MLPs to capture the multiplicative interactions between label information and HRRP samples, which are then further factorized to effectively reduce model parameters. The extensive experimental results on the measured HRRP data demonstrate that the proposed algorithm achieves the promising target recognition and reconstruction performance. [ABSTRACT FROM AUTHOR]

Highlights • New method to improve the linear measurement range of Four-quadrant detector. • The new proposed method effectively enhances the accuracy of light spot position. • The light spot detection sensitivity of detector was analyzed and calculated. • The measuring range of detector from 20 μm up to 60 μm with the resolution is 20 nm. Abstract In this paper, we propose new method to improve the linear measurement range of four-quadrant detector (4QD) in micro-displacement measuring system. Based combines the central approximation method and polynomial fitting algorithm due to their opposite error characteristics of the spot position measurements, the voltage-displacement curves of four spot models, circular spot with flat energy distribution, circular spot with Gaussian energy, a novel method is designed to analyze the detecting the linear measurement range on a 4QD. The experimental results show that the proposed algorithm improves the detecting sensitivity and effective measure ranges of the 4QD, which the measuring range of 4QD is extend from 20 μm up to 60 μm, and the resolution is 20 nm. Finally, the proposed method was designed to ensure the most efficient use of the detecting sensitivity and effective measure ranges of the 4QD. [ABSTRACT FROM AUTHOR]

Abstract We are interested by an alternating method for an inverse Cauchy problem. Our main results of this paper consists in exhibiting local error indicators, based on a posteriori analysis, with respect to both space approximation and iterative algorithms. In contrast to existing results, the choice of adaptive finite element meshes will be considered after a comparison between the two kinds of indicators. This lead to an efficient method which have the ability to dramatically reduce the computational cost comparing with uniform grid refinement. Some numerical experiments support these results. [ABSTRACT FROM AUTHOR]

Highlights • The SAX algorithm is improved by investigating from multi-domain to extract comprehensive fault information. • The fault pattern is firstly presented to investigate the fault information. • The Shannon entropy is applied into symbol sequences based on local structure analysis for feature extraction. • A new machinery fault diagnosis framework based on ISAX, Shannon entropy technique and KPCA is proposed and validated. Abstract Feature extraction from vibration signals is considerably significant for condition monitoring and fault diagnosis. The Symbolic Aggregate approXimation (SAX) technique essentially transforming a real-valued time series into a symbol sequence, has been proven as a potential tool of feature extraction for machinery intelligent diagnosis. However, challenge still exists that the SAX cannot fulfill feature extraction tasks well since it is carried out only on the basis of mean value in time domain. To overcome this limitation, an improved SAX (ISAX) is proposed in this paper. This new method substitutes the feature of mean value in time domain with multiple features extracted from time, frequency and time-frequency domains in order to obtain comprehensive fault information. With the ISAX transformation, a vibration signal can be transformed into various symbol sequences according to the multi-domain features. Next the Shannon entropy technique is conducted on a symbol sequence to capture sequential patterns in local signals and then the Shannon entropy value is used as the eigenvalue of the symbol sequence. Various eigenvalues are obtained to describe a vibration signal from different perspectives, which leads to a better feature extraction. These eigenvalues are then fed into the Kernel Principal Component Analysis (KPCA) to reduce dimensions and extract principal features for classification tasks. Compared with SAX, the most significant advantage of ISAX is extracting comprehensive signal characteristics from multi-domain. Moreover, the ISAX captures fault information better considering the local fault patterns. The effectiveness and superiority of ISAX were validated by experimental studies using the fault signals of rolling bearings and reciprocating compressor valves with remarkably high classification rates. [ABSTRACT FROM AUTHOR]

Abstract In this paper we show that it is possible to estimate the backward error for the approximation of the matrix exponential on-the-fly , without the need to precompute in high precision quantities related to specific accuracies. In this way, the scaling parameter s and the degree m of the truncated Taylor series (the underlying method) are adapted to the input matrix and not to a class of matrices sharing some spectral properties, such as with the classical backward error analysis. The result is a very flexible method which can approximate the matrix exponential at any desired accuracy. Moreover, the risk of overscaling, that is the possibility to select a value s larger than necessary, is mitigated by a new choice as the sum of two powers of two. Finally, several numerical experiments in MATLAB with data in double and variable precision and with different tolerances confirm that the method is accurate and often faster than available good alternatives. [ABSTRACT FROM AUTHOR]

Highlights • Two new Taylor algorithms for the computation of the matrix exponential are proposed. • They are based on matrix polynomial evaluation methods more efficient than Paterson–Stockmeyer method. • In tests they showed higher efficiency and accuracy than state-of-the-art Padé based methods. • They also showed a higher efficiency than state-of-the-art Taylor methods, and higher accuracy in some tests. Abstract This paper presents new Taylor algorithms for the computation of the matrix exponential based on recent new matrix polynomial evaluation methods. Those methods are more efficient than the well known Paterson–Stockmeyer method. The cost of the proposed algorithms is reduced with respect to previous algorithms based on Taylor approximations. Tests have been performed to compare the MATLAB implementations of the new algorithms to a state-of-the-art Padé algorithm for the computation of the matrix exponential, providing higher accuracy and cost performances. [ABSTRACT FROM AUTHOR]

Abstract This paper mainly investigates the numerical implementation issue of fractional order systems. First, a pattern of fixed pole schemes are developed to approximate fractional integrator/differentiator, whose common is that the poles keep constant for different α. Then, two solutions are proposed to improve the approximation performance around α = 0. Afterwards, the simulation schemes are introduced for two kinds of fractional order systems. In those schemes, the configuration problem of nonzero initial value is considered. Finally, a fair and solid comparison to the classical approximation methods is presented, demonstrating the effectiveness and efficiency of the elaborated algorithms. Highlights • A universal fixed pole approximation algorithm is derived for fractional integrator/differentiator. • The improvement is made to achieve a better performance with smaller order. • Two approximation schemes are presented for implementing fractional transfer function model. • Three approximation schemes are proposed for implementing fractional state space model. • The configuration of nonzero initial system state is discussed for fractional order system. [ABSTRACT FROM AUTHOR]

Abstract: Combinatorial discrepancy theory is the theory of coloring hypergraphs in a balanced way, generalizing graph coloring, is an important field in combinatorics with applications to algorithms and complexity, such as efficient sampling, randomization and derandomization. One of the most celebrated and deep theorems in discrepancy theory says that the 2-color discrepancy of the hypergraph of arithmetic progressions in the first n integers is (lower bound by Roth (1964), upper bound Matoušek, Spencer (1996)). In this paper we consider the problem of finding the c-color discrepancy, , of arithmetic progressions and centered arithmetic progressions resp. in . It is notable that the problem of approximating the discrepancy of centered arithmetic progressions in the natural numbers is certainly one of the most difficult problems posed by P. Erdös, with almost no progress over the last 30 years. The problem considered in this paper can be seen as a kind of non-trivial relaxation of the Erdös problem. It is easy to prove that for the discrepancy of the arithmetic progressions in is exactly and it is 1 for any p and for the centered arithmetic progressions. But no matching upper and lower bounds were known beyond these special cases. We show that for both hypergraphs the lower bound is tight up to a logarithmic factor in p: the lower bound is and the upper bound is . The main work is the proof of the lower bounds with Fourier analysis on . We consider the result for the centered arithmetic progressions as our main achievement because here due to the lack of translation-invariance of the hypergraph Fourier analysis alone does not work, and has to be combined with a new decomposition of such progressions. Techniques of this type may be usefull also in other areas where lower bounds for combinatorial functions are sought. [Copyright &y& Elsevier]

Abstract: Many simulation algorithms (chemical reaction systems, differential systems arising from the modelling of transient behaviour in the process industries etc.) contain the numerical solution of systems of differential equations. For the efficient solution of the above mentioned problems, linear multistep methods or Runge–Kutta single-step methods are used. For the simulation of chemical procedures the radial Schrödinger equation is used frequently. In the present paper we will study a class of linear multistep methods. More specifically, the purpose of this paper is to develop an efficient algorithm for the approximate solution of the radial Schrödinger equation and related problems. This algorithm belongs in the category of the multistep methods. In order to produce an efficient multistep method the phase-lag property and its derivatives are used. Hence the main result of this paper is the development of an efficient multistep method for the numerical solution of systems of ordinary differential equations with oscillating or periodical solutions. The reason of their efficiency, as the analysis proved, is that the phase-lag and its derivatives are eliminated. Another reason of the efficiency of the new obtained methods is that they have high algebraic order [Copyright &y& Elsevier]

Abstract: In this paper, we proposed an algorithm for solving the linear systems of matrix equations over the generalized -reflexive matrix (). According to the algorithm, the solvability of the problem can be determined automatically. When the problem is consistent over the generalized -reflexive matrix , for any generalized -reflexive initial iterative matrices , the generalized -reflexive solution can be obtained within finite iterative steps in the absence of roundoff errors. The unique least-norm generalized -reflexive solution can also be derived when the appropriate initial iterative matrices are chosen. A sufficient and necessary condition for which the linear systems of matrix equations is inconsistent is given. Furthermore, the optimal approximate solution for a group of given matrices can be derived by finding the least-norm generalized -reflexive solution of a new corresponding linear system of matrix equations. Finally, we present a numerical example to verify the theoretical results of this paper. [Copyright &y& Elsevier]

Abstract: Extreme learning machine (ELM) is one of the most popular and important learning algorithms. It comes from single-hidden-layer feedforward neural networks. It has been proved that ELM can achieve better performance than support vector machine (SVM) in regression and classification. In this paper, mathematically, with regression problem, the step 3 of ELM is studied. First of all, the equation are reformulated as an optimal model. With the optimality, the necessary conditions of optimal solution are presented. The equation is replaced by . We can prove that the latter must have one solution at least. Second, optimal approximation solution is discussed in cases of is column full rank, row full rank, neither column nor row full rank. In the last case, the rank-1 and rank-2 methods are used to get optimal approximation solution. In theory, this paper present a better algorithm for ELM. [Copyright &y& Elsevier]

Abstract: In this paper, the factor of safety for a prescribed slip surface will be determined from an equivalent lower bound method (extremum principle), which can satisfy all equilibrium conditions without an interslice force function. This approach will give an overall factor of safety close to that from the classical methods for normal problems, while the thrust line, the local factor of safety for individual slice/block and the progressive yielding phenomenon can be estimated, which will be useful for some special cases. The force and moment equilibrium of every slice will be satisfied, while the location of the thrust line will always be acceptable in the present formulation. To solve the difficult optimisation problem, an innovative coupled particle swarm/harmony search algorithm is proposed in this paper, and a practical engineering problem for which the factor of safety is close to 1.0 is used to illustrate the consideration of the residual strength in the limit equilibrium slope stability analysis. [Copyright &y& Elsevier]

Abstract: In this paper, some existence theorems for the mixed quasi-variational-like inequalities problem in a reflexive Banach space are established. The auxiliary principle technique is used to suggest a novel and innovative iterative algorithm for computing the approximate solution for the mixed quasi-variational-like inequalities problem. Consequently, not only the existence of theorems of the mixed quasi-variational-like inequalities is shown, but also the convergence of iterative sequences generated by the algorithm is also proven. The results proved in this paper represent an improvement of previously known results. [Copyright &y& Elsevier]

Abstract: In this paper, we study the following minimization problem where is a bounded linear operator, is some constant, is a potential function for , is the set of fixed points of nonexpansive mapping and is the solution set of an equilibrium problem. This paper introduces two new algorithms (one implicit and one explicit) that can be used to find the solution of the above minimization problem. [Copyright &y& Elsevier]

Abstract: Rough k-means clustering describes uncertainty by assigning some objects to more than one cluster. Rough cluster quality index based on decision theory is applicable to the evaluation of rough clustering. In this paper we analyze rough k-means clustering with respect to the selection of the threshold, the value of risk for assigning an object and uncertainty of objects. According to the analysis, clusters presented as interval sets with lower and upper approximations in rough k-means clustering are not adequate to describe clusters. This paper proposes an interval set clustering based on decision theory. Lower and upper approximations in the proposed algorithm are hierarchical and constructed as outer-level approximations and inner-level ones. Uncertainty of objects in out-level upper approximation is described by the assignment of objects among different clusters. Accordingly, ambiguity of objects in inner-level upper approximation is represented by local uniform factors of objects. In addition, interval set clustering can be improved to obtain a satisfactory clustering result with the optimal number of clusters, as well as optimal values of parameters, by taking advantage of the usefulness of rough cluster quality index in the evaluation of clustering. The experimental results on synthetic and standard data demonstrate how to construct clusters with satisfactory lower and upper approximations in the proposed algorithm. The experiments with a promotional campaign for the retail data illustrates the usefulness of interval set clustering for improving rough k-means clustering results. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes our methodology for building conformant planners, which is based on recent advances in the theory of action and change and answer set programming. The development of a planner for a given dynamic domain starts with encoding the knowledge about fluents and actions of the domain as an action theory of some action language. Our choice in this paper is – an action language with dynamic and static causal laws and executability conditions. An action theory of defines a transition diagram containing all the possible trajectories of the domain. A transition belongs to iff the execution of the action a in the state s may move the domain to the state . The second step in the planner development consists in finding a deterministic transition diagram such that nodes of are partial states of , its arcs are labeled by actions, and a path in from an initial partial state to a partial state satisfying the goal corresponds to a conformant plan for and in . The transition diagram is called an ‘approximation’ of . We claim that a concise description of an approximation of can often be given by a logic program under the answer sets semantics. Moreover, complex initial situations and constraints on plans can be also expressed by logic programming rules and included in . If this is possible then the problem of finding a parallel or sequential conformant plan can be reduced to computing answer sets of . This can be done by general purpose answer set solvers. If plans are sequential and long then this method can be too time consuming. In this case, is used as a specification for a procedural graph searching conformant planning algorithm. The paper illustrates this methodology by building several conformant planners which work for domains with complex relationship between the fluents. The efficiency of the planners is experimentally evaluated on a number of new and old benchmarks. In addition we show that for a subclass of action theories of our planners are complete, i.e., if in we cannot get from to a state satisfying the goal then there is no conformant plan for and in . [Copyright &y& Elsevier]

Abstract The goal of affine matrix rank minimization problem is to reconstruct a low-rank or approximately low-rank matrix under linear constraints. In general, this problem is combinatorial and NP-hard. In this paper, a nonconvex fraction function is studied to approximate the rank of a matrix and translate this NP-hard problem into a transformed affine matrix rank minimization problem. The equivalence between these two problems is established, and we proved that the uniqueness of the global minimizer of transformed affine matrix rank minimization problem also solves affine matrix rank minimization problem if some conditions are satisfied. Moreover, we also proved that the optimal solution to the transformed affine matrix rank minimization problem can be approximately obtained by solving its regularization problem for some proper smaller λ > 0. Lastly, the DC algorithm is utilized to solve the regularization transformed affine matrix rank minimization problem and the numerical experiments on image inpainting problems show that our method performs effectively in recovering low-rank images compared with some state-of-art algorithms. [ABSTRACT FROM AUTHOR]

The detection of community structure for dynamic social networks is significant for understanding evolution features of collective behaviors. In this paper, we present community detection method based on nonnegative matrix factorization for dynamic networks considering the strength between nodes. The basic idea of this algorithm is that node pairs with stronger connection strength have more possibility to be grouped into the same community. Firstly, we build weighted networks by calculating the embeddedness E t and dispersion D t between each pair of nodes to measure the strength of the relationships at each timestamp t . Then we construct a node strength matrix in which each element represents the connection strength of a pair of nodes. Combining the structural information at previous timestamp, the nonnegative matrix factorization method is used to detect the community structure for the dynamic networks. Finally, the experiments for two synthetic networks show that when considering the previous information, the accuracy of our algorithm improve 0.3425, 0.5191 for the first synthetic networks. For the second synthetic networks, the accuracy of our algorithm is also improved. Furthermore, we compare the other two algorithms, the results show that our algorithms perform better than other algorithms on the both synthetic networks. Our work may be helpful for providing a new perspective that we detect community structures for dynamic networks. [ABSTRACT FROM AUTHOR]