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We consider the problem of generating balanced training samples from an unlabeled data set with an unknown class distribution. While random sampling works well when the data are balanced, it is very ineffective for unbalanced data. Other approaches, such as active learning and cost-sensitive learning, are also suboptimal as they are classifier-dependent and require misclassification costs and labeled samples, respectively. We propose a new strategy for generating training samples, which is independent of the underlying class distribution of the data and the classifier that will be trained using the labeled data. Our methods are iterative and can be seen as variants of active learning, where we use semi-supervised clustering at each iteration to perform biased sampling from the clusters. We provide several strategies to estimate the underlying class distributions in the clusters and to increase the balancedness in the training samples. Experiments with both highly skewed and balanced data from the UCI repository and a private data set show that our algorithm produces much more balanced samples than random sampling or uncertainty sampling. Further, our sampling strategy is substantially more efficient than active learning methods. The experiments also validate that, with more balanced training data, classifiers trained with our samples outperform classifiers trained with random sampling or active learning. [ABSTRACT FROM AUTHOR]

Many complex systems in the real world such as social networks can be modeled by complex networks. The complex network analysis and especially community detection is an important research topic in graph analysis that aims to identify the structure of a graph and its similar groups of nodes. In recent years, various algorithms such as Girvan and Newman's method (GN) is introduced which is based on a divisive approach for graph clustering. Although GN is a highly popular and widely used method, it suffers from scalability and computational complexity. GN needs O(m3) and O(m3 + m3logm) time to detects communities in unweighted and weighted graphs respectively. Hence, in this paper, a faster method is suggested that detects communities in O(m2) for both weighted and unweighted graphs. In this paper, firstly, we define degree for each edge and then we propose a new and fast approach for the calculation of edges betweenness that is based on edge degree centrality. Furthermore, in order to boost the speed of the algorithm, we suggest instead of just one edge, multiple edges can be removed in each iteration. Since the proposed method wants to enhance the GN method, in the evaluation section the quality of detected communities, the accuracy and speed of the suggested method are assessed by the comparison with the GN method. Results prove that our proposed method is extremely faster than plain GN and the detected communities often have better quality than the plain GN method. Furthermore, we compare our proposed method with meta-heuristic algorithms which are a novel approach for community detection. Results clarify that the suggested method is notably faster, scalable, stable, reliable, and efficient than meta-heuristic algorithms. [ABSTRACT FROM AUTHOR]

In view of the difficulty of accurate online detection for massive data collecting real-timely in a strong noise environment during control process, an order self-learning Autoregressive Hidden Markov Model (ARHMM) algorithm is proposed to carry out online outlier detection in industrial control process. The algorithm utilizes AR model to fit the time series and makes use of HMM as basic detection tool, which can avoid the deficiency of presetting the threshold in traditional detection methods. In order to update parameters of ARHMM online, the structure of traditional Brockwell-Dahlhaus-Trindade (BDT) algorithm is improved to be a double-iterative structure in which iterative calculation from both time and order is applied respectively. With the purpose of reducing the influence of outlier on parameter update of ARHMM, the strategies of detection-before-update and detection-based-update are adopted, which also improve the robustness of algorithm. Subsequent simulation by model data and practical application verify the accuracy, robustness and property of online detection of the algorithm. According to the result, it is obvious that new algorithm proposed in this paper is more suitable for outlier detection of control process data in process industry. [ABSTRACT FROM AUTHOR]

For solving nonlinear monotone equations with convex constraints, Liu and Feng (Numer. Algoritm. 82(1):245–262, 2019) suggested a derivative-free iterative technique. Although they assert that the direction d k satisfies inequality (2.1), however, this is not true, as the derivation of the parameter θ k given by equation (2.7) is not correct. This led to Lemma 2.2, Lemma 3.1 and Theorem 3.1 in Liu and Feng (Numer. Algoritm. 82(1):245–262, 2019) not holding. In addition, Theorem 3.1 is still invalid as the bound for ‖ F (x k + α k ′ d k) ‖ was not established by the authors, instead the authors used the bound for ‖ F (x k + α k d k) ‖ as the bound for ‖ F (x k + α k ′ d k) ‖ . In this paper, We first describe the necessary adjustments and establish the bound for ‖ F (x k + α k ′ d k) ‖ , after which the proposed approach by Liu and Feng continues to converge globally. In addition, we provide some numerical results to support the adjustments. [ABSTRACT FROM AUTHOR]

The rigid motion involving both rotation and translation in the 3D space can be simultaneously described by a unit dual quaternion. Considering this excellent property, the paper constructs the Helmert transformation (seven-parameter similarity transformation) model based on a unit dual quaternion and then presents a rigid iterative algorithm of Helmert transformation using a unit dual quaternion. Because of the singularity of the coefficient matrix of the normal equation, the nine parameter (including one scale factor and eight parameters of a dual quaternion) Helmert transformation model is reduced into five parameter (including one scale factor and four parameters of a unit quaternion which can represent the rotation matrix) Helmert transformation one. Besides, a good start estimate of parameter is required for the iterative algorithm, hence another algorithm employed to compute the initial value of parameter is put forward. The numerical experiments involving a case of small rotation angles i.e. geodetic coordinate transformation and a case of big rotation angles i.e. the registration of LIDAR points are studied. The results show the presented algorithms in this paper are correct and valid for the two cases, disregarding the rotation angles are big or small. And the accuracy of computed parameter is comparable to the classic Procrustes algorithm from Grafarend and Awange (J Geod 77:66-76, 2003), the orthonormal matrix algorithm from Zeng (Earth Planets Space 67:105, 2015), and the algorithm from Wang et al. (J Photogramm Remote Sens 94:63-69, 2014). [ABSTRACT FROM AUTHOR]

A novel approach to generation of parallel synchronization-free tiled code for the loop nest is presented. It is derived via a combination of the Polyhedral and Iteration Space Slicing frameworks. It uses the transitive closure of loop nest dependence graphs to carry out corrections of original rectangular tiles so that all dependences of the original loop nest are preserved under the lexicographic order of target (corrected) tiles. Then parallel synchronization-free tiled code is generated on the basis of valid (corrected) tiles applying the transitive closure of dependence graphs. The main contribution of the paper is demonstrating that the presented technique is able to generate parallel synchronization-free tiled code, provided that the exact transitive closure of a dependence graph can be calculated and there exist synchronization-free slices on the statement instance level in the loop nest. We show that the presented approach extracts such a parallelism when well-known techniques fail to extract it. Enlarging the scope of loop nests, for which synchronization-free tiled code can be generated, is achieved by means of applying the intersection of extracted slices and generated valid tiles, in contrast to forming slices of valid tiles as suggested in previously published techniques based on the transitive closure of a dependence graph. The presented approach is implemented in the publicly available TC optimizing compiler. Results of experiments demonstrating the effectiveness of the approach and the efficiency of parallel programs generated by means of it are discussed. [ABSTRACT FROM AUTHOR]

The common spatial patterns (CSP) technique is an effective strategy for the classification of multichannel electroencephalogram (EEG) signals. However, the objective function expression of the conventional CSP algorithm is based on the L2-norm, which makes the performance of the method easily affected by outliers and noise. In this paper, we consider a new extension to CSP, which is termed capped L21-norm-based common spatial patterns (CCSP-L21), by using the capped L21-norm rather than the L2-norm for robust modeling. L21-norm considers the L1-norm sum which largely alleviates the influence of outliers and noise for the sake of robustness. The capped norm is further used to mitigate the effects of extreme outliers whose signal amplitude is much higher than that of the normal signal. Moreover, a non-greedy iterative procedure is derived to solve the proposed objective function. The experimental results show that the proposed method achieves the highest average recognition rates on the three real data sets of BCI competitions, which are 91.67%, 85.07%, and 82.04%, respectively. Capped L21-norm-based common spatial patterns—a robust model for EEG signals classification [ABSTRACT FROM AUTHOR]

We study iterative methods for solving a set of sparse non-negative tensor equations (multivariate polynomial systems) arising from data mining applications such as information retrieval by query search and community discovery in multi-dimensional networks. By making use of sparse and non-negative tensor structure, we develop Jacobi and Gauss-Seidel methods for solving tensor equations. The multiplication of tensors with vectors are required at each iteration of these iterative methods, the cost per iteration depends on the number of non-zeros in the sparse tensors. We show linear convergence of the Jacobi and Gauss-Seidel methods under suitable conditions, and therefore, the set of sparse non-negative tensor equations can be solved very efficiently. Experimental results on information retrieval by query search and community discovery in multi-dimensional networks are presented to illustrate the application of tensor equations and the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper considers the distributed compressed sensing (DCS), where each node has a common component and an innovation component. Most existing reconstruction methods for this DCS model are actually centralized, where the measurements of each signal are utilized together at a certain node. In this paper, we propose a decentralized reconstruction algorithm that works in an iterative manner, where each node implements the reconstruction in each iteration only with its own measurements and some estimations in the previous iteration from other nodes. Simulation results show that the proposed algorithm has better performance than separate recovery. [ABSTRACT FROM AUTHOR]

This paper deals with the irregular binary low-density parity-check (LDPC) codes and two iterative low-complexity decoding algorithms. The first one is the majority error-correcting decoding algorithm, and the second one is iterative erasure-correcting decoding algorithm. The lower bounds on correcting capabilities (the guaranteed corrected error and erasure fraction respectively) of irregular LDPC code under decoding (error and erasure correcting respectively) algorithms with low-complexity were represented. These lower bounds were obtained as a result of analysis of Tanner graph representation of irregular LDPC code. The numerical results, obtained at the end of the paper for proposed lower-bounds achieved similar results for the previously known best lower-bounds for regular LDPC codes and were represented for the first time for the irregular LDPC codes. [ABSTRACT FROM AUTHOR]

Algebraic Riccati equations with indefinite quadratic terms play an important role in applications related to robust controller design. While there are many established approaches to solve these in case of small-scale dense coefficients, there is no approach available to compute solutions in the large-scale sparse setting. In this paper, we develop an iterative method to compute low-rank approximations of stabilizing solutions of large-scale sparse continuous-time algebraic Riccati equations with indefinite quadratic terms. We test the developed approach for dense examples in comparison to other established matrix equation solvers, and investigate the applicability and performance in large-scale sparse examples. [ABSTRACT FROM AUTHOR]

In this paper, we continue to study a non-local free boundary problem arising in financial bubbles. We focus on the parabolic counterpart of the bubble problem and suggest an iterative algorithm which consists of a sequence of parabolic obstacle problems at each step to be solved, that in turn gives the next obstacle function in the iteration. The convergence of the proposed algorithm is proved. Moreover, we consider the finite difference scheme for this algorithm and obtain its convergence. At the end of the paper, we present and discuss computational results. [ABSTRACT FROM AUTHOR]

Random Sample Consensus (RANSAC) is an iterative algorithm for robust model parameter estimation from observed data in the presence of outliers. First proposed by Fischler and Bolles back in 1981, it still is a very popular algorithm in the computer vision community. The primary objective of their paper was to find an effective strategy for excluding outliers from estimation process, but it did not consider the presence of noise among the inliers. A common practice among implementations of RANSAC is to take a few samples extra than the minimum required for estimation problem, but implications of this heuristic are lacking in the literature. In this paper, we present a probabilistic analysis of this common heuristic and explore the possibility of finding an optimal size for the randomly sampled data points per iteration of RANSAC. We also improve upon the lower bound for the number of iterations of RANSAC required to recover the model parameters. On the basis of this analysis, we propose an improvement in the hypothesis step of RANSAC algorithm. Since this step is shared (unchanged) by many of the variants of RANSAC, their performance can also be improved upon. The paper also presents the improvements achieved by incorporating the findings of our analysis in two of the popular variants of RANSAC. [ABSTRACT FROM AUTHOR]

In modern software development, much time is devoted and much attention is paid to the activity of data modeling and the translation of data models into databases. This has motivated the proposal of different approaches and tools to support this activity, such as semiautomatic approaches that generate data models from requirements artifacts using text analysis and sets of heuristics, among other techniques. However, these approaches still suffer from important limitations, including the lack of support for requirements traceability, the poor support for detecting and solving conflicts in domain-specific requirements, and the considerable effort required for manually checking the generated models. This paper introduces DataMock, an Agile approach that enables the iterative building of data models from requirements specifications, while supporting traceability and allowing inconsistencies detection in data requirements and specifications. The paper also describes how the approach effectively allows improving traceability and reducing errors and effort to build data models in comparison with traditional, state-of-the-art, data modeling approaches. [ABSTRACT FROM AUTHOR]

Selecting the most discriminative features is a challenging problem in many applications. Bio-inspired optimization algorithms have been widely applied to solve many optimization problems including the feature selection problem. In this paper, the most discriminating features were selected by a new Chaotic Dragonfly Algorithm (CDA) where chaotic maps embedded with searching iterations of the Dragonfly Algorithm (DA). Ten chaotic maps were employed to adjust the main parameters of dragonflies' movements through the optimization process to accelerate the convergence rate and improve the efficiency of DA. The proposed algorithm is employed for selecting features from the dataset that were extracted from the Drug bank database, which contained 6712 drugs. In this paper, 553 drugs that were bio-transformed into liver are used. This data have four toxic effects, namely, irritant, mutagenic, reproductive, and tumorigenic effect, where each drug is represented by 31 chemical descriptors. The proposed model is mainly comprised of three phases; data pre-processing, features selection, and the classification phase. In the data pre-processing phase, Synthetic Minority Over-sampling Technique (SMOTE) was used to solve the problem of the imbalanced dataset. At the features selection phase, the most discriminating features were selected using CDA. Finally, the selected features from CDA were used to feed Support Vector Machine (SVM) classifier at the classification phase. Experimental results proved the capability of CDA to find the optimal feature subset, which maximizing the classification performance and minimizing the number of selected features compared with DA and the other meta-heuristic optimization algorithms. Moreover, the experiments showed that Gauss chaotic map was the appropriate map to significantly boost the performance of DA. Additionally, the high obtained value of accuracy (81.82-96.08%), recall (80.84-96.11%), precision (81.45-96.08%) and F-Score (81.14-96.1%) for all toxic effects proved the robustness of the proposed model. [ABSTRACT FROM AUTHOR]

This paper introduces a novel iterative approach for interactive single or multiple foreground co-segmentation using semantic information. A quadratic cost function based on a graph model is proposed. The cost function includes a ‘smoothness’ and a ‘label-information’ terms. The ‘label-information’ term propagates the feature-level and contextual information. This information is updated based on the features and neighborhood patterns of all the images after each iteration. The approach can be easily implemented with a few scribbles on a few random images. The paper also proposes a model called Neighborhood Pattern Model (NPM) for contextual information. Along with feature level information, NPM helps to give semantic meanings to the labels (i.e., foreground(s) and background). Moreover, in the case of insufficient features (i.e., same features for different labels), NPM can be effective to distinct the labels. Experimental results on two benchmark datasets, iCoseg and FlickrMFC, illustrate the better performance of the proposed approach over the current state-of-the-art co-segmentation methods.Workflow of the proposed algorithm. The left images are samples of the ’Hot-Balloons’ group in iCoseg dataset [1]. It is the only image of the group which is scribbled by user. Green and red scribbles indicate label1 (i.e., background) and label2 (i.e., foreground), respectively. The final results are illustrated in the right [ABSTRACT FROM AUTHOR]

In Panaite [Iterated crossed products, J. Algebra Appl. 13(7), 14580036 (2014)], Panaite studied iterated crossed product construction from the point of algebraic structures. In this paper, we study iterated crossed product from the point of Combinatorial Group Theory and define a new version of the crossed product of groups. First, we give some conditions for this new product to be a group, then we obtain a presentation for iterated crossed product of cyclic groups. Additionally, using this presentation, we find a complete rewriting system and thus we obtain normal form structure of elements of this new group construction. This gives us the solvability of the word problem for this product. [ABSTRACT FROM AUTHOR]

The paper concerns with an inertial-like algorithm for approximating solutions of equilibrium problems in Hilbert spaces. The algorithm is a combination around the relaxed proximal point method, inertial effect and the Krasnoselski-Mann iteration. The using of the proximal point method with relaxations has allowed us a more flexibility in practical computations. The inertial extrapolation term incorporated in the resulting algorithm is intended to speed up convergence properties. The main convergence result is established under mild conditions imposed on bifunctions and control parameters. Several numerical examples are implemented to support the established convergence result and also to show the computational advantage of our proposed algorithm over other well known algorithms. [ABSTRACT FROM AUTHOR]

Supernode transformation is a technique to decrease the communication overhead by partitioning and scheduling a loop nest to a multi-processor system. This is achieved by grouping a number of iterations in a perfectly nested loop with regular dependences as a $$supernode$$ . Previous work has been focusing on finding the optimal supernode size and shape as well as an optimal execution schedule for multi-processor systems with unbounded resources. This paper emphasizes on the actual implementation strategies of supernode transformations on multi-core systems with limited resources. Using an example, the longest common subsequence (LCS) problem, we present and compare three different multithreading implementations. A formula for the total execution time of each method is presented. The techniques are benchmarked on a 12-core and a 4-core machine. On the 12-core machine our first technique, which yields increased data locality, speeds up the unaltered sequential loop nest 16.7 times. Combining this technique with skewing the loop by changing the linear schedule scores a 42.6 speedup. A more sophisticated method that executes entire rows of the loop nest in one thread scores a 59.5 speedup. Concepts presented and discussed in this paper on the LCS problem serve as basic foundation for implementations at regular dependence algorithms. [ABSTRACT FROM AUTHOR]

Many real-life problems using mathematical modeling can be reduced to scalar and system of nonlinear equations. In this paper, we develop a family of three-step sixth-order method for solving nonlinear equations by employing weight functions in the second and third step of the scheme. Furthermore, we extend this family to the multidimensional case preserving the same order of convergence. Moreover, we have made numerical comparisons with the efficient methods of this domain to verify the suitability of our method. [ABSTRACT FROM AUTHOR]

This paper first introduces a new iterative method for weak and strong convergence theorem to demonstrate the estimation potential for a fixed point of the cutter and the finite general split feasibility problem. Consequently, the set of fixed points of a quasi-nonexpansive mapping and the finite general split feasibility problem, the constrained minimization problem, and the general constrained minimization problems are proved using our main results. Finally, we give two numerical examples to advocate our main results. [ABSTRACT FROM AUTHOR]

The analytical solution of 3D datum transformation with an isotropic weight has been elegantly presented based on Procrustes algorithm (singular value decomposition). But the existence of analytical solution of 3D datum transformation with a non-isotropic weight needs further investigation. Based on the Lagrangian extremum law, the paper derives the analytical formula for translation parameter and scale factor, but because the rotation matrix is unsolved, the analytical solution does not exist. For this reason, the paper presents two kinds of iterative approach of 3D datum transformation with a non-isotropic weight. One is the iterative approach dependent on the objective function value, which uses the Lagrangian minimum function in the variable of rotation matrix as the objective function, and the other is the iterative approach dependent on the derivative of function, which uses the 3D datum transformation model that eliminates the translation parameter. In order to improve the speed and reliability of iterative computation, the form of rotation matrix represented by Rodrigues matrix instead of rotation angles or unit quaternion is adopted for the two iterative approaches. A numerical experiment is demonstrated, and comparison analysis of the two iterative approaches is carried out. The result shows from the view of computing speed and reliability, the iterative approach based on derivatives is preferred. [ABSTRACT FROM AUTHOR]

With the development of manufacture, more and more 3D models are generated by users and many differnet factories. 3D model retrieval has been receiving more and more attention in computer vision and the field of data analysis. In this paper, we propose a novel 3D model retrieval algorithm by cross-modal feature mapping (CMFM), which utilize one single image as query information to address 3D model retrieval problem. Specifically, in this paper, we first proposed to leverage 2D image to handle 3d model retrieval problem, which is one new problem in this field. The proposed feature learning method can benefit: 1) avoiding the interference of query image recorded by different visual sensor; 2) handling cross-modal data retrieval by simple computer vision technologies, which can guarantee the performance of retrieval and also control that the retrieval time hold a low level; 3) the low complexity of this method can guarantee that this method can be applied in many fields. Finally, we validate the retrieval method on three popular datasets. Extensive comparison experiments show the superiority of the proposed mehtod. To the best of our knowledge, it is the first method to handle 3D model retreival based on one single 2D image. [ABSTRACT FROM AUTHOR]

This paper is a continuation of the author’s previous papers [Front. Math. China, 2016, 11(6): 1379-1418; 2017, 12(5): 1023-1043], where the linear case was studied. A shifted inverse iteration algorithm is introduced, as an acceleration of the inverse iteration which is often used in the non-linear context (the p-Laplacian operators for instance). Even though the algorithm is formally similar to the Rayleigh quotient iteration which is well-known in the linear situation, but they are essentially different. The point is that the standard Rayleigh quotient cannot be used as a shift in the non-linear setup. We have to employ a different quantity which has been obtained only recently. As a surprised gift, the explicit formulas for the algorithm restricted to the linear case (p = 2) is obtained, which improves the author’s approximating procedure for the leading eigenvalues in different context, appeared in a group of publications. The paper begins with p-Laplacian, and is closed by the non-linear operators corresponding to the well-known Hardy-type inequalities. [ABSTRACT FROM AUTHOR]

The paper surveys articles that construct and investigate direct and iterative methods for computing weighted pseudoinverses and weighted normal pseudosolutions with singular weights. The methods considered in the paper are mainly constructed based on the authors’ articles devoted to the development of the theory of weighted pseudoinversion aimed at investigating the characteristics of both weighted pseudoinverses and weighted normal pseudosolutions with singular weights. The paper uses the following results obtained and investigated by the authors: expansions of weighted pseudoinverses into matrix power series and products, limit representations of such matrices, and determination of decompositions of weighted pseudoinverses based on weighted singular value decompositions of matrices with singular weights. [ABSTRACT FROM AUTHOR]

With the dense deployment of small cell networks, low-cost backhaul schemes for small cell base stations (SBSs) have attracted great attentions. Self-backhaul using cellular communication technology is considered as a promising solution. Although some excellent works have been done on self-backhaul in small cell networks, most of them do not consider the recent advances of full-duplex (FD) and massive multiple-input and multiple-output (MIMO) technologies. In this paper, we propose a self-backhaul scheme for small cell networks by combining FD and massive MIMO technologies. In our proposed scheme, the macro base station (MBS) is equipped with massive MIMO antennas, and the SBSs have the FD communication ability. By treating the SBSs as special macro users, we can achieve the simultaneous transmissions of the access link of users and the backhaul link of SBSs in the same frequency. Furthermore, considering the existence of inter-tier and intra-tier interference, we formulate the power allocation problem of the MBS and SBSs as an optimization problem. Because the formulated power allocation problem is a non-convex problem, we transform the original problem into a difference of convex program by successive convex approximation method and variable transformation, and then solve it using a constrained concave convex procedure based iterative algorithm. Finally, extensive simulations are conducted with different system configurations to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we present a generalization approach of an algebraic existing method to estimate stability regions for discrete nonlinear polynomial systems of degree 3. The existing method is based on the enlargement of a guaranteed stability region by applying various steps of a proposed algorithm. Its main limitation is that the initial result has only been subsequently developed in a particular case of a single iteration. The stability domain obtained is consequently not the widest one. Our main contribution in this paper is to develop generalized functions that allow the enlargement of the guaranteed stability region after k iterations, for any value of k. A required fundamental tool is developed and consists in a general formula allowing to give the result of the Kronecker power calculation of two matrices sum. The advantages of this generalization are to reach a larger region of asymptotic stability and to improve the existing methods results. Two application examples illustrate the proposed method. [ABSTRACT FROM AUTHOR]

The paper introduces and analyzes the convergence of a new iterative algorithm for approximating solutions of equilibrium problems involving strongly pseudomonotone and Lipschitz-type bifunctions in Hilbert spaces. The algorithm uses a stepsize sequence which is non-increasing, diminishing, and non-summable. This leads to the main advantage of the algorithm, namely that the construction of solution approximations and the proof of its convergence are done without the prior knowledge of the modulus of strong pseudomonotonicity and Lipschitz-type constants of bifunctions. The strongly convergent theorem is established under suitable assumptions. The paper also discusses the assumptions used in the formulation of the convergent theorem. Several numerical results are reported to illustrate the behavior of the algorithm with different sequences of stepsizes and also to compare it with others. [ABSTRACT FROM AUTHOR]

Based on the in-depth analysis of the essence and key features of vague phenomena, this paper focuses on establishing the axiomatical foundation of membership degree theory using for modeling vague phenomena, presents an axiomatic system to govern membership degrees and their interconnections. The concept of vague partition is introduced, on this basis, the concept of fuzzy set in Zadeh’s sense is redefined based on vague partition from the perspective of axiomatization. The thesis defended in this paper is that the mutual constraint relationship among vague attribute values in a vague partition should be the starting point to recognize and model vague phenomena by the quantitative analysis method. [ABSTRACT FROM AUTHOR]

The key challenges in real time voice communication in long term evolution mobile are reduction in complexity and latency. Efficient encoding and decoding algorithms can cater to these. The implementation of such polar code based efficient algorithms is proposed in this paper. The overall latency of 3.8 ms is needed to process 8 bit block length. The novel sub-matrix near to identity matrix is presented. This resulted into minimization of loops among least reliable bits due to iterated parity check matrix. Look-up table based memory mapping is used in encoder to reduce latency while Euclidian decoding technique is used in decoder. The number of iterations is reduced by 50%. The experimentation is performed with additive white Gaussian noise and QPSK modulation. The proposed modified iterative decoding algorithm requires SNR of 5.5 dB and 192 computations for targeted bit error rate of 10. The second proposed method needs 9 dB, 2 iterations for 384 computations. The penalty paid is quantization error of 0.63% due to restricting computations to fourth order series of hyperbolic function with same 8 bit block length. [ABSTRACT FROM AUTHOR]

This paper presents a method to conceptually model sacrificing non-critical sub-systems, or components, in a failure scenario to protect critical system functionality through a functional failure modeling technique. Understanding the potential benefits and drawbacks of choosing how a failure is directed in a system away from critical sub-systems and toward sub-systems that can be sacrificed to maintain core functionality can help system designers to design systems that are more likely to complete primary mission objectives despite failure events. Functional modeling techniques are often used during the early stage of conceptual design for complex systems to provide a better understanding of system architecture. A family of methods exists that focuses on the modeling of failure initiation and propagation within a functional model of a system. Modeling failure flow provides an opportunity to understand system failure propagation and inform system design iteration for improved survivability and robustness. Currently, the ability to model failure flow decision-making is missing from the family of function failure and flow methodologies. The failure flow decision function (FFDF) methodology presented in this paper enables system designers to model failure flow decision-making problems where functions and flows that are critical to system operation are protected through the sacrifice of less critical functions and flow exports. The sacrifice of less critical system functions and flows allows for mission critical functionality to be preserved, leading to a higher rate of mission objective completion. An example of FFDF application in a physical design is a non-critical peripheral piece of electrical hardware being sacrificed during an electrical surge condition to protect critical electronics necessary for the core functionality of the system. In this paper, a case study of the FFDF method is presented based on a Sojourner class Mars Exploration Rover (MER) platform. [ABSTRACT FROM AUTHOR]

Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically, with inequalities. In this paper, we present a geometric approach to analyzing contractive and nonexpansive fixed point iterations with a new tool called the scaled relative graph. The SRG provides a correspondence between nonlinear operators and subsets of the 2D plane. Under this framework, a geometric argument in the 2D plane becomes a rigorous proof of convergence. [ABSTRACT FROM AUTHOR]

Ambartsumian equation and its generalizations are some of the main integral equations of astrophysics, which have found wide application in many areas of physics and technology. An analytical solution to this equation is currently unknown, and the development of approximate methods is urgent. To solve the Ambartsumian equation, several iterative methods are proposed that are used in solving practical problems. Methods of collocations and mechanical quadratures have also been constructed and substantiated under rather severe conditions. It is of considerable interest to construct an iterative method adapted to the coefficients and kernels of the equation. This paper is devoted to the construction of such method. The construction of the iterative method is based on a continuous method for solving nonlinear operator equations. The method is based on the Lyapunov stability theory and is stable against perturbation of the initial conditions, coefficients, and kernels of the equations being solved. An additional advantage of the continuous method for solving nonlinear operator equations is that its implementation does not require the reversibility of the Gateaux derivative of the nonlinear operator. An iterative method for solving the Ambartsumian equation is constructed and substantiated. Model examples were solved to illustrate the effectiveness of the method. Equations generalizing the classical Ambartsumian equation are considered. To solve them, computational schemes of collocation and mechanical quadrature methods are constructed, which are implemented by a continuous method for solving nonlinear operator equations. [ABSTRACT FROM AUTHOR]

Finite Element Methods (FEM) are widely used in academia and industry, especially in the fields of mechanical engineering, civil engineering, aerospace, and electrical engineering. These methods usually convert partial difference equations into large sparse linear systems. For complex problems, solving these large sparse linear systems is a time consuming process. This paper presents a parallelized iterative solver for large sparse linear systems implemented on a GPGPU cluster. Traditionally, these problems do not scale well on GPGPU clusters. This paper presents an approach to reduce the communications between cluster compute nodes for these solvers. Additionally, computation and communication are overlapped to reduce the impact of data exchange. The parallelized system achieved a speedup of up to 15.3 times on 16 NVIDIA Tesla GPUs, compared to a single GPU. An analytical evaluation of the algorithm is conducted in this paper, and the analytical equations for predicting the performance are presented and validated. [ABSTRACT FROM AUTHOR]

This paper proposes a nonlinear controlling model in three-level supply chain. The proposed model consists of a manufacturer, a warehouse and two retailers. As nonlinear multi level programming problems are much more difficult to solve, the proposed model was converted to two nonlinear bilevel programming problems in order to make the model easier both to solve and to describe. The first model consists of warehouse's objective function at its first level and the manufacturer at the second level. In the second model, retailers are the leader and warehouse is the follower. Bilevel programming has been investigated to be NP-hard problem. Numerous algorithms have been developed so far for solving bilevel programming problem; however, algorithm proposed in this paper is easier than other algorithms for solving this type of problems. In this paper, we proposed a modified randomly iterated search and statistical competency approach in genetic algorithm to provide precise and reliable optimal solutions for manufacturer, warehouse and retailers' value in situations with no empirical observations and we presented confidence interval as solution. [ABSTRACT FROM AUTHOR]

This paper analyzes the problem of selecting a set of items whose prices are to be updated in the next iteration in so called simple ascending auctions with unit-demand bidders. A family of sets called “sets in excess demand” is introduced, and the main result demonstrates that a simple ascending auction always terminates at the minimum Walrasian equilibrium prices if and only if the selection belongs to this family. [ABSTRACT FROM AUTHOR]

This paper is a continuation of our previous work [Front. Math. China, 2016, 11(6): 1379-1418] where an efficient algorithm for computing the maximal eigenpair was introduced first for tridiagonal matrices and then extended to the irreducible matrices with nonnegative off-diagonal elements. This paper introduces mainly two global algorithms for computing the maximal eigenpair in a rather general setup, including even a class of real (with some negative off-diagonal elements) or complex matrices. [ABSTRACT FROM AUTHOR]

Since the traditional classic hash function structure (MD structure) is suffering from all kinds of attacks, the research of new hash function structure becomes hot issue. This paper analyses these attacks, based on MD structure, this paper brings in two security parameters and improves the message padding scheme, and then designs a Double-Serial iterative structure. In this structure, since there are more message blocks affecting the chaining variables, it can not only avoid the traditional second collision attack, multicollision attack and second preimage attack of long message, but also accelerate the message diffusion and enhance the avalanche effect. According to the efficiency analysis and security authentication, this proposed structure improves security and has the same efficiency of Double-Pipe structure. [ABSTRACT FROM AUTHOR]

This paper conduct a quantitative experiment to assess the effectiveness of a hybrid perturbation-projection (HPP) method to solve dynamic stochastic general equilibrium (DSGE) asset pricing models. We employ a macro-based asset pricing model to compare HPP method and value function iteration (VFI) method based on the same reasonable calibrations. This DSGE asset pricing model in the paper incorporates nonlinearities in both household preferences and firm production technologies. Additionally, the market for debt introduces its own type of nonlinearity; leverage can force a nonlinear wedge between asset rates. In the paper, we first show how to apply the HPP method and then assess its accuracy and speed compared with the old VFI method. Accuracy of solutions is demonstrated by comparing standard deviations of the logged values of first order conditions errors of important financial assets. Speed of the solution methods is shown by comparing the computational time. By comparing the results from applying the same DSGE asset pricing model to the competing methods, we find that the HPP method is not only feasible but also robust to the extreme nonlinearities in the asset pricing model. [ABSTRACT FROM AUTHOR]

The optical projection using speckles is one of the structured light methods that have been applied to three-dimensional (3-D) range sensors. This paper investigates the design and fabrication of diffractive optical elements (DOEs) for generating the light field with uniformly distributed speckles. Based on the principles of computer generated holograms, the iterative Fourier transform algorithm was adopted for the DOE design. It was used to calculate the phase map for diffracting the incident laser beam into a goal pattern with distributed speckles. Four patterns were designed in the study. Their phase maps were first examined by a spatial light modulator and then fabricated on glass substrates by microfabrication processes. Finally, the diffraction characteristics of the fabricated devices were verified. The experimental results show that the proposed methods are applicable to the DOE design of 3-D range sensors. Furthermore, any expected diffraction area and speckle density could be possibly achieved according to the relations presented in the paper. [ABSTRACT FROM AUTHOR]

The problem of automated video categorization in large datasets is considered in the paper. A new Iterative Multi-label Propagation (IMP) algorithm for relational learning in multi-label data is proposed. Based on the information of the already categorized videos and their relations to other videos, the system assigns suitable categories-multiple labels to the unknown videos. The MapReduce approach to the IMP algorithm described in the paper enables processing of large datasets in parallel computing. The experiments carried out on 5-million videos dataset revealed the good efficiency of the multi-label classification for videos categorization. They have additionally shown that classification of all unknown videos required only several parallel iterations. [ABSTRACT FROM AUTHOR]

This paper suggests a data envelopment analysis (DEA) model for selecting the most efficient alternative in advanced manufacturing technology in the presence of both cardinal and ordinal data. The paper explains the problem of using an iterative method for finding the most efficient alternative and proposes a new DEA model without the need of solving a series of LPs. A numerical example illustrates the model, and an application in technology selection with multi-inputs/multi-outputs shows the usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper analyzes the iteration-complexity of a generalized alternating direction method of multipliers (G-ADMM) for solving separable linearly constrained convex optimization problems. This ADMM variant, first proposed by Bertsekas and Eckstein, introduces a relaxation parameter α into the second ADMM subproblem in order to improve its computational performance. It is shown that, for a given tolerance ε>0, the G-ADMM with α∈(0,2) provides, in at most O(1/ε2) iterations, an approximate solution of the Lagrangian system associated to the optimization problem under consideration. It is further demonstrated that, in at most O(1/ε) iterations, an approximate solution of the Lagrangian system can be obtained by means of an ergodic sequence associated to a sequence generated by the G-ADMM with α∈(0,2]. Our approach consists of interpreting the G-ADMM as an instance of a hybrid proximal extragradient framework with some special properties. Some preliminary numerical experiments are reported in order to confirm that the use of α>1 can lead to a better numerical performance than α=1 (which corresponds to the standard ADMM). [ABSTRACT FROM AUTHOR]

In this paper we will consider the tetration, defined by the equation F(z + 1) = bF(z) in the complex plane with F(0) = 1, for the case where b is complex. A previous paper determined conditions for a unique solution the case where b is real and b > e1/e. In this paper we extend these results to find conditions which determine a unique solution for complex bases. We also develop iteration methods for numerically approximating the function F(z), both for bases inside and outside the Shell-Thron region. [ABSTRACT FROM AUTHOR]

In this paper, we develop an efficient explicit method based on the spectral parametric iteration method and quasilinearization scheme, which can be used for the efficient numerical solution of nonlinear stiff/nonstiff two-point boundary value problems. The method derived here has the advantage that it does not require the solution of nonlinear systems of equations. We derive the method, which requires one evaluation of the Jacobian and one LU decomposition per step. Some numerical experiments on nonlinear stiff/nonstiff problems show the efficiency and accuracy of the method. Moreover, the method provides us a simple way to control and modify the convergence rate of the solution. [ABSTRACT FROM AUTHOR]

Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this relatively low degree of popularity is the lack of a well developed system of theory and algorithms to support the applications, as is the case for its convex counterpart. This paper aims to take one step in the direction of disciplined nonconvex and nonsmooth optimization. In particular, we consider in this paper some constrained nonconvex optimization models in block decision variables, with or without coupled affine constraints. In the absence of coupled constraints, we show a sublinear rate of convergence to an ϵ-stationary solution in the form of variational inequality for a generalized conditional gradient method, where the convergence rate is dependent on the Hölderian continuity of the gradient of the smooth part of the objective. For the model with coupled affine constraints, we introduce corresponding ϵ-stationarity conditions, and apply two proximal-type variants of the ADMM to solve such a model, assuming the proximal ADMM updates can be implemented for all the block variables except for the last block, for which either a gradient step or a majorization-minimization step is implemented. We show an iteration complexity bound of O(1/ϵ2) to reach an ϵ-stationary solution for both algorithms. Moreover, we show that the same iteration complexity of a proximal BCD method follows immediately. Numerical results are provided to illustrate the efficacy of the proposed algorithms for tensor robust PCA and tensor sparse PCA problems. [ABSTRACT FROM AUTHOR]

In this paper, we present an iterative method for finding the least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint. We prove that if the constrained matrix equations are consistent, the solution can be obtained within finite iterative steps in the absence of round-off errors; if constrained matrix equations are inconsistent, the least squares solution can be obtained within finite iterative steps in the absence of round-off errors. Finally, numerical examples are provided to illustrate the efficiency of the proposed method and testify the conclusions suggested in this paper. [ABSTRACT FROM AUTHOR]

For a class of nonlinear multi-agent systems under switching topologies with disturbances, we propose a distributed H∞ consensus control protocol based on relative output feedback and utilize an iterative algorithm for solving nonlinear matrix inequality in this paper. Firstly, a consensus control protocol via relative output feedback is designed. Then, an iterative algorithm is utilized to calculate nonlinear matrix inequality. By this, the output feedback gain is designed but not chosen, which increases the design degree of freedom and meanwhile H∞ performance index γ is obtained. Finally, the proposed theory is applied to multiple simple-pendulums network systems driven by DC motors, and simulation results show the effectiveness of the designed consensus control protocol. [ABSTRACT FROM AUTHOR]

Multiobjective evolutionary algorithms based on decomposition (MOEA/D) decompose a multiobjective optimization problem (MOP) into a group of subproblems and optimizes them at the same time. The reproduction method in MOEA/D, which generates offspring solutions, has crucial effect on the performance of algorithm. As the difficulties of MOPs increases, it requires much higher efficiency for the reproduction methods in MOEA/D. However, for the complex optimization problems whose PS shape is complicated, the original reproduction method used in MOEA/D might not be suitable to generate excellent offspring solutions. In order to improve the property of the reproduction method for MOEA/D, this paper proposes an external archive matching strategy which selects solutions’ most matching archive solutions as parent solutions. The offspring solutions generated by this strategy can maintain a good convergence ability. To balance convergence and diversity, a perturbed learning scheme is used to extend the search space of the solutions. The experimental results on three groups of test problems reveal that the solutions obtained by MOEA/D-EAM have better convergence and diversity than the other four state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]