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Abstract: In 1.9 of the paper [A. Hahn, A Hermitian Morita theorem for algebras with anti-structure, J. Algebra 93 (1985) 215–235], should be replaced by . This leads to minor changes in the rest of the paper where the ring should be replaced by its opposite and vice versa. [Copyright &y& Elsevier]

Grey wolf optimization (GWO) algorithm is a new emerging algorithm that is based on the social hierarchy of grey wolves as well as their hunting and cooperation strategies. Introduced in 2014, this algorithm has been used by a large number of researchers and designers, such that the number of citations to the original paper exceeded many other algorithms. In a recent study by Niu et al., one of the main drawbacks of this algorithm for optimizing real‐world problems was introduced. In summary, they showed that GWO's performance degrades as the optimal solution of the problem diverges from 0. In this paper, by introducing a straightforward modification to the original GWO algorithm, that is, neglecting its social hierarchy, the authors were able to largely eliminate this defect and open a new perspective for future use of this algorithm. The efficiency of the proposed method was validated by applying it to benchmark and real‐world engineering problems. [ABSTRACT FROM AUTHOR]

Necessary conditions for the existence of a super‐simple, decomposable, near‐resolvable (v,4,6)‐balanced incomplete block design (BIBD) whose 2‐component subdesigns are both near‐resolvable (v,4,3)‐BIBDs are v≡1 (mod 4) and v≥17. In this paper, we show that these necessary conditions are sufficient. Using these designs, we also establish that the necessary conditions for the existence of a super‐simple near‐resolvable (v,4,3)‐RBIBD, namely v≡1 (mod 4) and v≥9, are sufficient. A few new pairwise balanced designs are also given. [ABSTRACT FROM AUTHOR]

It is a classic topic of social network analysis to evaluate the importance of nodes and identify the node that takes on the role of core or bridge in a network. Because a single indicator is not sufficient to analyze multiple characteristics of a node, it is a natural solution to apply multiple indicators that should be selected carefully. An intuitive idea is to select some indicators with weak correlations to efficiently assess different characteristics of a node. However, this paper shows that it is much better to select the indicators with strong correlations. Because indicator correlation is based on the statistical analysis of a large number of nodes, the particularity of an important node will be outlined if its indicator relationship doesn't comply with the statistical correlation. Therefore, the paper selects the multiple indicators including degree, ego-betweenness centrality and eigenvector centrality to evaluate the importance and the role of a node. The importance of a node is equal to the normalized sum of its three indicators. A candidate for core or bridge is selected from the great degree nodes or the nodes with great ego-betweenness centrality respectively. Then, the role of a candidate is determined according to the difference between its indicators' relationship with the statistical correlation of the overall network. Based on 18 real networks and 3 kinds of model networks, the experimental results show that the proposed methods perform quite well in evaluating the importance of nodes and in identifying the node role. [ABSTRACT FROM AUTHOR]

Bayesian network classifiers (BNCs) have demonstrated competitive classification performance in a variety of real-world applications. A highly scalable BNC with high expressivity is extremely desirable. This paper proposes Redundant Dependence Elimination (RDE) for improving the classification performance and expressivity of k-dependence Bayesian classifier (KDB). To demonstrate the unique characteristics of each case, RDE identifies redundant conditional dependencies and then substitute/remove them. The learned personalized k-dependence Bayesian Classifier (PKDB) can achieve high-confidence conditional probabilities, and graphically interpret the dependency relationships between attributes. Two thyroid cancer datasets and four other cancer datasets from the UCI machine learning repository are selected for our experimental study. The experimental results prove the effectiveness of the proposed algorithm in terms of zero-one loss, bias, variance and AUC. [ABSTRACT FROM AUTHOR]

Linear feedback shift registers (LFSRs) play a significant role in communications security and we investigate design of a selected class of word-based LFSRs known as σ -LFSRs. Both the search algorithm and the construction algorithm generate efficient primitive σ -LFSRs. The search algorithm first constructs the σ -polynomial and then checks the primitiveness of the σ -polynomial, whereas the construction algorithm for the σ -LFSR, first finds a primitive polynomial f ( x ) and then constructs the primitive σ -LFSR from f ( x ) . In this paper, we present some novel results pertaining to the search algorithm for primitive σ -LFSR along with the exhaustive search space complexity of the search algorithm for σ -LFSRs. Then we investigate and compare the performance of the construction algorithm with the search algorithm for the primitive σ -LFSR. Finally, the number of σ -LFSRs similar to the σ -LFSRs generated by the construction algorithm is provided. [ABSTRACT FROM AUTHOR]

In this paper, a unique and more distinctive encryption algorithm is proposed. This is based on the complexity of highly nonlinear S box in Flesnelet domain. The nonlinear pattern is transformed further to enhance the confusion in the dummy data using Fresnelet technique. The security level of the encrypted image boosts using the algebra of Galois field in Fresnelet domain. At first level, the Fresnelet transform is used to propagate the given information with desired wavelength at specified distance. It decomposes given secret data into four complex subbands. These complex sub-bands are separated into two components of real subband data and imaginary subband data. At second level, the net subband data, produced at the first level, is deteriorated to non-linear diffused pattern using the unique S-box defined on the Galois field . In the diffusion process, the permuted image is substituted via dynamic algebraic S-box substitution. We prove through various analysis techniques that the proposed scheme enhances the cipher security level, extensively. [ABSTRACT FROM AUTHOR]

This paper proposes a new measure for recommendation through integrating Triangle and Jaccard similarities. The Triangle similarity considers both the length and the angle of rating vectors between them, while the Jaccard similarity considers non co-rating users. We compare the new similarity measure with eight state-of-the-art ones on four popular datasets under the leave-one-out scenario. Results show that the new measure outperforms all the counterparts in terms of the mean absolute error and the root mean square error. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of sBCI/sBCK/eBCI/eBCK-algebras as a generalization of the notion of BCI/BCK-algebras. This structure is studied in detail. Also we introduce a way to make an eBCK-algebra from a BCK-algebra and vice versa. [ABSTRACT FROM AUTHOR]

Let A be any fixed cut-off restart algorithm running in parallel on multiple processors. If the algorithm is only allowed to run for up to time D, then it is no longer guaranteed that a result can be found. In this case, the probability of finding a solution within the time D becomes a measure for the quality of the algorithm. In this paper we address this issue and provide upper and lower bounds for the probability of A finding a solution before a deadline passes under varying assumptions. We also show that the optimal restart times for a fixed cut-off algorithm running in parallel is identical for the optimal restart times for the algorithm running on a single processor. Finally, we conclude that the odds of finding a solution scale superlinearly in the number of processors. [ABSTRACT FROM AUTHOR]

In this paper, we describe the BIBasis package designed for REDUCE and Macaulay2 computer algebra systems, which allows one to compute Boolean involutive bases and Gröbner bases. The implementations and user interfaces of the package for both systems are described in the respective sections of the paper. Also, we present results of comparisons of BIBasis with other packages and algorithms for constructing Boolean Gröbner bases available in the computer algebra systems. [ABSTRACT FROM AUTHOR]

In this paper, we consider approximation algorithms for optimizing a generic multi-variate homogeneous polynomial function, subject to homogeneous quadratic constraints. Such optimization models have wide applications, e.g., in signal processing, magnetic resonance imaging (MRI), data training, approximation theory, and portfolio selection. Since polynomial functions are non-convex, the problems under consideration are all NP-hard in general. In this paper we shall focus on polynomial-time approximation algorithms. In particular, we first study optimization of a multi-linear tensor function over the Cartesian product of spheres. We shall propose approximation algorithms for such problem and derive worst-case performance ratios, which are shown to be dependent only on the dimensions of the model. The methods are then extended to optimize a generic multi-variate homogeneous polynomial function with spherical constraint. Likewise, approximation algorithms are proposed with provable approximation performance ratios. Furthermore, the constraint set is relaxed to be an intersection of co-centered ellipsoids; namely, we consider maximization of a homogeneous polynomial over the intersection of ellipsoids centered at the origin, and propose polynomial-time approximation algorithms with provable worst-case performance ratios. Numerical results are reported, illustrating the effectiveness of the approximation algorithms studied. [ABSTRACT FROM AUTHOR]

A common thread in all of the recent results concerning the testing of dense graphs is the use of Szemerédi's regularity lemma. In this paper we show that in some sense this is not a coincidence. Our first result is that the property defined by having any given Szemerédi-partition is testable with a constant number of queries. Our second and main result is a purely combinatorial characterization of the graph properties that are testable with a constant number of queries. This characterization (roughly) says that a graph property P can be tested with a constant number of queries if and only if testing P can be reduced to testing the property of satisfying one of finitely many Szemerédi-partitions. This means that in some sense, testing for Szemerédi-partitions is as hard as testing any testable graph property. We thus resolve one of the main open problems in the area of property-testing, which was first raised by Goldreich, Goldwasser, and Ron [J. ACM, 45 (1998), pp. 653-750] in the paper that initiated the study of graph property-testing. This characterization also gives an intuitive explanation as to what makes a graph property testable. [ABSTRACT FROM AUTHOR]

The k-out-of-n system structure is a very popular type of redundancy in fault-tolerant systems, with wide applications in both industrial and military systems. In this paper, the modeling, application and reliability evaluation of k-out-of-n systems are studied for the case where the components and the system have multiple performance levels. A multi-state k-out-of-n system model is proposed that allows different requirements on the number of components for different state levels, and, very importantly, more practical engineering systems can fit into this model. The multiple states in the model can be interpreted in two ways: (i) multiple levels of capacity; and (ii) multiple failure modes. Application examples of the proposed multi-state k-out-of-n system model are given under each of the interpretations. An approach is presented for efficient reliability evaluation of multi-state k-out-of-n systems with identically and independently distributed components. A recursive algorithm is proposed for reliability evaluation of multi-state k-out-of-n systems with independent components. Efficiency investigations show that both of the reliability evaluation approaches are efficient. The multi-state k-out-of-n system model with a constant k value, which is a special case of the general multi-state k-out-of-n system model, has been studied for a long time, but only on the theoretical stage. A practical application of this model is presented in this paper as well. [ABSTRACT FROM AUTHOR]

Abstract: Quasimodules for vertex algebras are generalizations of modules for vertex algebras. These new objects arise from a generalization of locality for fields. Quasimodules tie together module theory and twisted module theory, and both twisted and untwisted modules feature Poincaré–Birkhoff–Witt-like spanning sets. This paper generalizes these spanning set results to quasimodules for certain Möbius vertex algebras. In particular this paper presents two spanning sets, one featuring a difference-zero ordering restriction on modes and another featuring a difference-one ordering restriction. [Copyright &y& Elsevier]

Abstract: Neighborhoods and neighborhood sequences play important roles in several branches of pattern analysis. In earlier papers in only certain special (e.g. periodic or octagonal) sequences were investigated. In this paper we study neighborhood sequences which are either ultimately periodic or allow at every neighborhood to do nothing at no cost. We give finite procedures and descriptive theoretical criteria for certain important (e.g. metrical) properties of the sequences. Our results are valid for several types of classical neighborhood sequences and for generated distance functions (e.g. octagonal and chamfer distances) which are widely applied in digital image processing. We conclude the paper by showing how our results contribute to the theory of distance transformations. [Copyright &y& Elsevier]

Abstract: This paper describes a generic software designed to implement meshing algorithms based on the Delaunay refinement paradigm. Such a meshing algorithm is generally described through a set of rules guiding the refinement of mesh elements. The central item of the software design is a generic class, called a mesher level, that is able to handle one of the rules guiding the refinement process. Several instantiations of the mesher level class can be stacked and tied together to implement the whole refinement process. As shown in this paper, the design is flexible enough to implement all currently known mesh generation algorithms based on Delaunay refinement. In particular it can be used to generate meshes approximating smooth or piecewise smooth surfaces, as well as to mesh three dimensional domains bounded by such surfaces. It also adapts to algorithms handling small input angles and various refinement criteria. This design highly simplifies the task of implementing Delaunay refinement meshing algorithms. It has been used to implemented several meshing algorithms in the Cgal library. [Copyright &y& Elsevier]

This paper proposes several globally convergent geometric optimization algorithms on Riemannian manifolds, which extend some existing geometric optimization techniques. Since any set of smooth constraints in the Euclidean space Rn (corresponding to constrained optimization) and the Rn space itself (corresponding to unconstrained optimization) are both special Riemannian manifolds, and since these algorithms are developed on general Riemannian manifolds, the techniques discussed in this paper provide a uniform framework for constrained and unconstrained optimization problems. Unlike some earlier works, the new algorithms have less restrictions in both convergence results and in practice. For example, global minimization in the one-dimensional search is not required. All the algorithms addressed in this paper are globally convergent. For some special Riemannian manifold other than Rn, the newalgorithms are very efficient. Convergence rates are obtained. Applications are discussed. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of minimization of a nonsmooth function under general nonsmooth constraints when no derivatives of the objective or constraint functions are available. We introduce the mesh adaptive direct search (MADS) class of algorithms which extends the generalized pattern search (GPS) class by allowing local exploration, called polling, in an asymptotically dense set of directions in the space of optimization variables. This means that under certain hypotheses, including a weak constraint qualification due to Rockafellar, MADS can treat constraints by the extreme barrier approach of setting the objective to infinity for infeasible points and treating the problem as unconstrained. The main GPS convergence result is to identify limit points x0302;, where the Clarke generalized derivatives are nonnegative in a finite set of directions, called refining directions. Although in the unconstrained case, nonnegative combinations of these directions span the whole space, the fact that there can only be finitely many GPS refining directions limits rigorous justification of the barrier approach to finitely many linear constraints for GPS. The main result of this paper is that the general MADS framework is flexible enough to allow the generation of an asymptotically dense set of refining directions along which the Clarke derivatives are nonnegative. We propose an instance of MADS for which the refining directions are dense in the hypertangent cone at x0302; with probability 1 whenever the iterates associated with the refining directions converge to a single x0302;. The instance of MADS is compared to versions of GPS on some test problems. We also illustrate the limitation of our results with examples. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a new definition of the filled function is given, it is different from the primary definition which was given by Ge in paper [R.P. Ge, A filled function method for finding a global minimzer of a function of several variables, Math. Program. 46 (1990) 191–204]. Based on the definition, a new filled function is proposed, and it has better properties. An algorithm for unconstrained global optimization is developed from the new filled function. The implementation of the algorithm on several test problems is reported with satisfactory numerical results. [Copyright &y& Elsevier]

The article informs that the no free lunch theorem says that there is no single evolutionary algorithm (EA) which can solve all possible optimization problems efficiently. Over the entire problem space, the performance of all EAs is equivalent. For a given optimization problem, people need to focus on designing problem-oriented algorithms in order to improve the algorithm's performance. For any NP-hard problem, people only have limited heuristic knowledge to use when designing EAs that solve it. This paper, aims to discover the role of heuristic knowledge in EAs. Through a comparative study of three different EAs for solving the node covering problem, the paper investigates the role of heuristic knowledge in EAs finding a feasible solution and the optimal solution.

This paper points out that meta-heuristics should have not only robustness and adaptability to problems with different structure but also adjustability of parameters included in their algorithms. Particle swarm optimization (PSO), whose concept began as a simulation of a simplified social milieu, is known as one of the most powerful optimization methods for solving nonconvex continuous optimization problems. Then, in order to improve adjustability, a new parameter is introduced into PSO on the basis of the proximate optimality principle (POP). In this paper, we propose adaptive PSO and the effectiveness and the feasibility of the proposed approach are demonstrated on simulations using some typical nonconvex optimization problems. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 151(3): 41–49, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20077 [ABSTRACT FROM AUTHOR]

This paper addresses the problem of discovering the structure of a fitness function from binary strings to the reals under the assumption of bounded epistasis. Two loci (string positions) are epistatically Linked if the effect of changing the allele (value) at one locus depends on the allele at the other locus. Similarly, a group of loci are epistatically linked if the effect of changing the allele at one locus depends on the alleles at all other loci of the group. Under the assumption that the size of such groups of loci are bounded, and assuming that the function is given only as a "black box function", this paper presents and analyzes a randomized algorithm that finds the complete epistatic structure of the function in the form of the Walsh coefficients of the function. [ABSTRACT FROM AUTHOR]

In this paper, a new sequential penalty algorithm, based on the L[sub ∞] exact penalty function, is proposed for a general nonlinear constrained optimization problem. The algorithm has the following characteristics: it can start from an arbitrary initial point; the feasibility of the subproblem is guaranteed; the penalty parameter is adjusted automatically; global convergence without any regularity assumption is proved. The update formula of the penalty parameter is new. It is proved that the algorithm proposed in this paper behaves equivalently to the standard SQP method after sufficiently many iterations. Hence, the local convergence results of the standard SQP method can be applied to this algorithm. Preliminary numerical experiments show the efficiency and stability of the algorithm. [ABSTRACT FROM AUTHOR]

This paper contains a new convergence analysis for the Lewis and Torczon generalized pattern search (GPS) class of methods for unconstrained and linearly constrained optimization. This analysis is motivated by a desire to understand the successful behavior of the algorithm under hypotheses that are satisfied by many practical problems. Specifically, even if the objective function is discontinuous or extended-valued, the methods find a limit point with some minimizing properties. Simple examples show that the strength of the optimality conditions at a limit point depends not only on the algorithm, but also on the directions it uses and on the smoothness of the objective at the limit point in question. The contribution of this paper is to provide a simple convergence analysis that supplies detail about the relation of optimality conditions to objective smoothness properties and to the defining directions for the algorithm, and it gives previous results as corollaries. [ABSTRACT FROM AUTHOR]

Community structure is considered one of the most interesting features in complex networks. Many real-world complex systems exhibit community structure, where individuals with similar properties form a community. The identification of communities in a network is important for understanding the structure of said network, in a specific perspective. Thus, community detection in complex networks gained immense interest over the last decade. A lot of community detection methods were proposed, and one of them is the label propagation algorithm (LPA). The simplicity and time efficiency of the LPA make it a popular community detection method. However, the LPA suffers from instability detection due to randomness that is induced in the algorithm. The focus of this paper is to improve the stability and accuracy of the LPA, while retaining its simplicity. Our proposed algorithm will first detect the main communities in a network by using the number of mutual neighbouring nodes. Subsequently, nodes are added into communities by using a constrained LPA. Those constraints are then gradually relaxed until all nodes are assigned into groups. In order to refine the quality of the detected communities, nodes in communities can be switched to another community or removed from their current communities at various stages of the algorithm. We evaluated our algorithm on three types of benchmark networks, namely the Lancichinetti-Fortunato-Radicchi (LFR), Relaxed Caveman (RC) and Girvan-Newman (GN) benchmarks. We also apply the present algorithm to some real-world networks of various sizes. The current results show some promising potential, of the proposed algorithm, in terms of detecting communities accurately. Furthermore, our constrained LPA has a robustness and stability that are significantly better than the simple LPA as it is able to yield deterministic results. [ABSTRACT FROM AUTHOR]

Waveform design is a pivotal component of the fully adaptive radar construct. In this paper, we consider waveform design for radar space time adaptive processing (STAP), accounting for the waveform dependence of the clutter correlation matrix. Due to this dependence, in general, the joint problem of receiver filter optimization and radar waveform design becomes an intractable, nonconvex optimization problem, Nevertheless, it is, however, shown to be individually convex either in the filter or in the waveform variables. We derive constrained versions of a) the alternating minimization algorithm, b) proximal alternating minimization, and c) the constant modulus alternating minimization, which, at each step, iteratively optimizes either the STAP filter or the waveform independently. A fast and slow time model permits waveform design in radar STAP, but the primary bottleneck is the computational complexity of the algorithms. [ABSTRACT FROM PUBLISHER]

Vector quantization is known widely as a highly efficient coding for image and speech signals. The algorithm proposed by Linde, Buzo, and Gray (the LBG algorithm) is the most fundamental design procedure for this kind of quantizer. However, the LBG algorithm usually gives only the local minimum of the distortion measure based on the quantization error. With such a background, this paper introduces the simulated annealing procedure into the design of the vector quantizer based on the LBG algorithm, which is known as the effective method for the NP-complete probabilistic combinational optimization problem. The widely employed mean-square error is adopted as the distortion measure. Various approaches are considered to derive the global minimum of the measure. In other words, this paper is based on the LBG algorithm and presents a design procedure for the vector quantizer (more generally, the vector quantizer considering the channel error) by introducing simulated annealing. By this approach, a vector quantizer with a better performance than the traditional design as well as a more ideal highly efficient coding is realized. A simulated experiment is executed for the standard image data (SIDBA), and it is demonstrated that the simulated annealing is useful in the design of the vector quantizer. [ABSTRACT FROM AUTHOR]

Fuzzy Number Ranking (FNR), plays a very important role in decision making and some other fuzzy application systems. Several strategies have been proposed for ranking Fuzzy Numbers (FNs). Each of these techniques has been shown to produce non-intuitive results in certain cases. In this paper, a new algorithm has been introduced for ranking FNs which considers both left and right (LR) sides. Through using several distinct points, this algorithm, provides the result with higher degree of certainty with respect methods which using one point. This algorithm, as shown by several examples, can be easily used for comparing triangular and trapezoidal FNs. [ABSTRACT FROM AUTHOR]

This paper deals with equilibrium problems with nonlinear constraints. Exploiting a gap function which relies on a polyhedral approximation of the feasible region, we propose two descent methods. They are both based on the minimization of a suitable exact penalty function, but they use different rules for updating the penalization parameter and they rely on different types of line search. The convergence of both algorithms is proved under standard assumptions. [ABSTRACT FROM AUTHOR]

In the paper, the Goursat problem-classification of nonlinear hyperbolic differential equations possessing two characteristic invariants-is considered. An algorithm for finding the characteristic invariants is described. On the basis of the algorithm implemented in REDUCE, the characteristic invariants of two Laine's equations are verified. One of them is shown to have invariants of the second and third orders. This equation shows that the Goursat problem, apparently, is still open. Computer calculations show that the characteristic invariants of the second Laine's equation given in his paper are incorrect. [ABSTRACT FROM AUTHOR]

Abstract: A sigraph is a graph in which each edge carries a value called its sign, denoted specially as . Given a sigraph , a new sigraph , called the common-edge sigraph of is that sigraph whose vertex-set is the set of pairs of adjacent edges in and two vertices of are adjacent if the corresponding pairs of adjacent edges of have exactly one edge in common, and the sign of the edge is the sign of the common edge. If all the edges of the sigraph carry + sign then is actually a graph and the corresponding common-edge sigraph is termed as the common-edge graph. In this paper, we characterize common-edge graph and common-edge sigraph and write an algorithm to obtain a corresponding common-edge root graph and common-edge root sigraph from a given common-edge graph and common-edge sigraph respectively. [Copyright &y& Elsevier]

Abstract: This paper describes an algorithm which produces all ideals compatible with a given surjective Frobenius near-splitting. [Copyright &y& Elsevier]

Abstract: This paper presents a study of the opportunities presented to students that allow them to learn different types of mathematical reasoning during teachers’ ordinary task solving presentations. The characteristics of algorithmic and creative reasoning that are seen in the presentations are analyzed. We find that most task solutions are based on available algorithms, often without arguments that justify the reasoning, which may lead to rote learning. The students are given some opportunities to see aspects of creative reasoning, such as reflection and arguments that are anchored in the mathematical properties of the task components, but in relatively modest ways. [Copyright &y& Elsevier]

Property testing is a rapid growing field in theoretical computer science. It considers the following task: given a function f over a domain D, a property ℘ and a parameter 0< ε<1, by examining function values of f over o(| D|) elements in D, determine whether f satisfies ℘ or differs from any one which satisfies ℘ in at least ε| D| elements. An algorithm that fulfills this task is called a property tester. We focus on tree-likeness of quartet topologies, which is a combinatorial property originating from evolutionary tree construction. The input function is f, which assigns one of the three possible topologies for every quartet over an n-taxon set S. We say that f satisfies tree-likeness if there exists an evolutionary tree T whose induced quartet topologies coincide with f. In this paper, we prove the existence of a set of quartet topologies of error number at least $c{n\choose 4}$ for some constant c>0, and present the first property tester for tree-likeness of quartet topologies. Our property tester makes at most O( n/ ε) queries, and is of one-sided error and non-adaptive. [ABSTRACT FROM AUTHOR]

Abstract: This paper concerns systems with small coherence parameter. Simple greedy-type algorithms perform well on these systems, which are also useful in the construction of compressed sensing matrices. We discuss the following problems for both and . How large can a dictionary be, if we prescribe the coherence parameter? How small could the resulting coherence parameter be, if we impose a size on the dictionary? How could we construct such a system? Several fundamental results from different areas of mathematics shed light on these important problems with far-reaching implications in approximation theory. [Copyright &y& Elsevier]

Abstract: In this paper an attempt is made to extend some standard results in set theory on the basis of soft set relations. Antisymmetric relation and transitive closure of a soft set relation are introduced and an analogue of Warshall’s algorithm is proposed for calculating the transitive closure of a soft set relation. Ordering on a soft set is defined and some set theoretical results based on this are proved. [Copyright &y& Elsevier]

MAX-2-SAT is one of the representative combinatorial problems and is known to be NP-hard. Given a set of m clauses on n propositional variables, where each clause contains at most two literals and is weighted by a positive real, MAX-2-SAT asks to find a truth assignment that maximizes the total weight of satisfied clauses. In this paper, we propose branch-and-bound exact algorithms for MAX-2-SAT utilizing three kinds of lower bounds. All lower bounds are based on a directed graph that represents conflicts among clauses, and two of them use a set covering representation of MAX-2-SAT. Computational comparisons on benchmark instances disclose that these algorithms are highly effective in reducing the number of search tree nodes as well as the computation time. [ABSTRACT FROM AUTHOR]

In this paper, an ancient Chinese algorithm is used to estimate the length constant of a long cooling fin, and an approximate solution formulation is obtained. The obtained results show that this method is a simple but promising method without any requirement for advanced calculus. [ABSTRACT FROM AUTHOR]

A novel algorithm for solving the classic Stefan problem is proposed in the paper. Instead of front tracking, we preset the moving interface locations and use these location coordinates as the grid points to find out the arrival time of moving interface respectively. Through this approach, the difficulty in mesh generation can be avoided completely. The simulation shows the numerical result is well coincident with the exact solution, implying the new approach performes well in solving this problem. [ABSTRACT FROM AUTHOR]

This paper presents a general and comprehensive description of Optimization Methods, and Algorithms from a novel viewpoint. It is shown, in particular, that Direct Methods, Iterative Methods, and Computer Science Algorithms belong to a well-defined general class of both Finite and Infinite Procedures, characterized by suitable descent directions. [ABSTRACT FROM AUTHOR]

Structure of data set is of critical importance in identifying clusters, especially the density difference feature. In this paper, we present a clustering algorithm based on density consistency, which is a filtering process to identify same structure feature and classify them into same cluster. This method is not restricted by the shapes and high dimension data set, and meanwhile it is robust to noises and outliers. Extensive experiments on synthetic and real world data sets validate the proposed the new clustering algorithm. [ABSTRACT FROM AUTHOR]

In elliptic curve cryptosystems, scalar multiplications performed on the curves have much effect on the efficiency of the schemes, and many efficient methods have been proposed. In particular, recoding methods of the scalars play an important role in the performance of the algorithm used. For integer radices, the non-adjacent form (NAF) and its generalizations (e.g., the generalized non-adjacent form (GNAF) and the radix- r non-adjacent form ( rNAF)) have been proposed for minimizing the non-zero densities in the representations of the scalars. On the other hand, for subfield elliptic curves, the Frobenius expansions of the scalars can be used for improving efficiency. Unfortunately, there are only a few methods apply the techniques of NAF or its analogue to the Frobenius expansion, namely τ-adic NAF techniques on Koblitz curves and hyperelliptic Koblitz curves. In this paper, we try to combine these techniques, namely recoding methods for reducing non-zero density and the Frobenius expansion, and propose two new efficient recoding methods of scalars on more general family of subfield elliptic curves in odd characteristic. We also prove that the non-zero densities for the new methods are same as those for the original GNAF and rNAF. We estimate scalar multiplication costs on the above subfield elliptic curves in terms of elliptic curve operations and finite field operations for several previous methods and the proposed methods. In addition, we implement scalar multiplication on an subfield elliptic curve belonging to the above family, for the previous methods and a proposed method. As a result, our estimation and implementation show that the speed of the proposed methods improve between 8% and 50% over that for the Frobenius expansion method. [ABSTRACT FROM AUTHOR]

In the paper we prove that the equational class $\mathcal{V}(bp\mathbb {BCK})$ generated by the class $bp\mathbb{BCK}$ of all bounded pseudo-BCK-algebras is generated by its simple members. As a matter of fact, we prove that simple members of $\mathcal {V}(bp\mathbb{BCK})$ just coincide with relative simple bounded pBCK-algebras. Moreover, as a byproduct we show that every simple bounded pBCK-algebra can be embedded into a simple integral residuated lattice. [ABSTRACT FROM AUTHOR]

Celebrating the sixtieth anniversary since the zeroth International Symposium on Mathematical Programming was held in 1949, this paper discusses several promising paradigms in mathematical programming that have gained momentum in recent years but have yet to reach the main stream of the field. These are: competition, dynamics, and hierarchy. The discussion emphasizes the interplay between these paradigms and their connections with existing subfields including disjunctive, equilibrium, and nonlinear programming, and variational inequalities. We will describe the modeling approaches, mathematical formulations, and recent results of these paradigms, and sketch some open mathematical and computational challenges arising from the resulting optimization and equilibrium problems. Our goal is to elucidate the need for a systematic study of these problems and to inspire new research in the field. [ABSTRACT FROM AUTHOR]

A novel filled function is given in this paper to find a global minima for a nonsmooth constrained optimization problem. First, a modified concept of the filled function for nonsmooth constrained global optimization is introduced, and a filled function, which makes use of the idea of the filled function for unconstrained optimization and penalty function for constrained optimization, is proposed. Then, a solution algorithm based on the proposed filled function is developed. At last, some preliminary numerical results are reported. The results show that the proposed approach is promising. [ABSTRACT FROM AUTHOR]

Recommender systems are now popular both commercially and in the research community, where many algorithms have been suggested for providing recommendations. These algorithms typically perform differently in various domains and tasks. Therefore, it is important from the research perspective, as well as from a practical view, to be able to decide on an algorithm that matches the domain and the task of interest. The standard way to make such decisions is by comparing a number of algorithms offline using some evaluation metric. Indeed, many evaluation metrics have been suggested for comparing recommendation algorithms. The decision on the proper evaluation metric is often critical, as each metric may favor a different algorithm. In this paper we review the proper construction of offline experiments for deciding on the most appropriate algorithm. We discuss three important tasks of recommender systems, and classify a set of appropriate well known evaluation metrics for each task. We demonstrate how using an improper evaluation metric can lead to the selection of an improper algorithm for the task of interest. We also discuss other important considerations when designing offline experiments. [ABSTRACT FROM AUTHOR]

Linearization of coupled second-order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper, we describe a simple and straightforward method to derive linearizing transformations for a class of two coupled SNODEs. Our procedure gives several new types of linearizing transformations of both invertible and non-invertible kinds. In both cases, we provide algorithms to derive the general solution of the given SNODE. We illustrate the theory with potentially important examples. [ABSTRACT FROM AUTHOR]

In this paper, we study algorithms for tiling problems. We show that the conditions (T1) and (T2) of Coven and Meyerowitz [E. Coven and A. Meyerowitz, Tiling the integers with translates of one finite set, J. Algebra 212(1) (1999), pp. 161-174], conjectured to be necessary and sufficient for a finite set A to tile the integers, can be checked in time polynomial in diam (A). We also give heuristic algorithms to find all non-periodic tilings of a cyclic group N. In particular, we carry out a full classification of all non-periodic tilings of 144. [ABSTRACT FROM AUTHOR]

We study the maximum edge-disjoint paths problem in undirected planar graphs: given a graph G and node pairs (demands) s1t1, s2t2, … , sktk, the goal is to maximize the number of demands that can be connected (routed) by edge-disjoint paths. The natural multicommodity flow relaxation has an Ω(√n) integrality gap, where n is the number of nodes in G. Motivated by this, we consider solutions with small constant congestion c > 1, that is, solutions in which up to c paths are allowed to use an edge (alternatively, each edge has a capacity of c). In previous work we obtained an O(log n) approximation with congestion 2 via the flow relaxation. This was based on a method of decomposing into well-linked subproblems. In this paper we obtain an O(1) approximation with congestion 4. To obtain this improvement we develop an alternative decomposition that is specific to planar graphs. The decomposition produces instances that we call Okamura-Seymour (OS) instances. These have the property that all terminals lie on a single face. Another ingredient we develop is a constant factor approximation for the all-or-nothing flow problem on OS instances via the flow relaxation. [ABSTRACT FROM AUTHOR]