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Variable (feature) selection plays an important role in data analysis and mathematical modeling. This paper aims to address the significant lack of formal evaluation benchmarks for feature selection algorithms (FSAs). To evaluate FSAs effectively, controlled environments are required, and the use of synthetic datasets offers significant advantages. We introduce a set of ten synthetically generated datasets with known relevance, redundancy, and irrelevance of features, derived from various mathematical, logical, and geometric sources. Additionally, eight FSAs are evaluated on these datasets based on their relevance and novelty. The paper first introduces the datasets and then provides a comprehensive experimental analysis of the performance of the selected FSAs on these datasets including testing the FSAs' resilience on two types of induced data noise. The analysis has guided the grouping of the generated datasets into four groups of data complexity. Lastly, we provide public access to the generated datasets to facilitate bench-marking of new feature selection algorithms in the field via our Github repository. The contributions of this paper aim to foster the development of novel feature selection algorithms and advance their study. [ABSTRACT FROM AUTHOR]

The generation of mathematical models for the analysis of buildings with multiple thermal zones is a large and complex task. Furthermore, the order and complexity of the dynamical model are increased by the number of included thermal zones. To overcome this problem, this paper presents an algorithm to define the mathematical model automatically, using the geometric and physics parameters as inputs. Additionally, the spatial position of each thermal zone must be recorded in an arrangement called a contact matrix. The algorithm for modeling systems with multiple thermal zones is the main contribution of this work. This algorithm is presented in pseudocode format and as an annex, an implementation in MATLAB software. One of the advantages of this methodology is that it allows us to work with parallelepipeds and not necessarily cubic thermal zones. The algorithm allows us to generate mathematical models with symbolic variables, starting from the knowledge of how many thermal zones compose the system and its geometric organization. This information must be organized in a matrix arrangement called a contact matrix. Different arrays of thermal zones were constructed with wooden boxes to verify the functionality of the models generated with the algorithm. Each case provided information that allowed us to adjust the mathematical models and their simulations, obtaining a range of errors between experimental and simulated temperatures from 2.08 to 5.6 , depending on the number of thermal zones studied. [ABSTRACT FROM AUTHOR]

This paper continues formalization in the Mizar system [2, 1] of basic notions of the composition-nominative approach to program semantics [14] which was started in [8, 12, 10]. The composition-nominative approach studies mathematical models of computer programs and data on various levels of abstraction and generality and provides tools for reasoning about their properties. In particular, data in computer systems are modeled as nominative data [15]. Besides formalization of semantics of programs, certain elements of the composition-nominative approach were applied to abstract systems in a mathematical systems theory [4, 6, 7, 5, 3]. In the paper we give a formal definition of the notions of a binominative function over given sets of names and values (i.e. a partial function which maps simple-named complex-valued nominative data to such data) and a nominative predicate (a partial predicate on simple-named complex-valued nominative data). The sets of such binominative functions and nominative predicates form the carrier of the generalized Glushkov algorithmic algebra for simple-named complex-valued nominative data [15]. This algebra can be used to formalize algorithms which operate on various data structures (such as multidimensional arrays, lists, etc.) and reason about their properties. In particular, we formalize the operations of this algebra which require a specification of a data domain and which include the existential quantifier, the assignment composition, the composition of superposition into a predicate, the composition of superposition into a binominative function, the name checking predicate. The details on formalization of nominative data and the operations of the algorithmic algebra over them are described in [11, 13, 9]. [ABSTRACT FROM AUTHOR]

This paper continues formalization in Mizar [2, 1] of basic notions of the composition-nominative approach to program semantics [13] which was started in [8, 11]. The composition-nominative approach studies mathematical models of computer programs and data on various levels of abstraction and generality and provides tools for reasoning about their properties. Besides formalization of semantics of programs, certain elements of the composition-nominative approach were applied to abstract systems in a mathematical systems theory [4, 6, 7, 5, 3]. In the paper we introduce a definition of the notion of a binominative function over a set D understood as a partial function which maps elements of D to D. The sets of binominative functions and nominative predicates [11] over given sets form the carrier of the generalized Glushkov algorithmic algebra [14]. This algebra can be used to formalize algorithms which operate on various data structures (such as multidimensional arrays, lists, etc.) and reason about their properties. We formalize the operations of this algebra (also called compositions) which are valid over uninterpretated data and which include among others the sequential composition, the prediction composition, the branching composition, the monotone Floyd-Hoare composition, and the cycle composition. The details on formalization of nominative data and the operations of the algorithmic algebra over them are described in [10, 12, 9]. [ABSTRACT FROM AUTHOR]

In this paper, the duality in differential form is developed between a 3D primal surface and its dual manifold formed by the surface's tangent planes, that is, each tangent plane of the primal surface is represented as a four-dimensional vector that constitutes a point on the dual manifold. The iterated dual theorem shows that each tangent plane of the dual manifold corresponds to a point on the original 3D surface, that is, the "dual" of the "dual" goes back to the "primal." This theorem can be directly used to reconstruct 3D surface from image edges by estimating the dual manifold from these edges. In this paper, we further develop the work in our original conference papers resulting in the robust differential dual operator. We argue that the operator makes good use of the information available in the image data by using both points of intensity discontinuity and their edge directions; we provide a simple physical interpretation of what the abstract algorithm is actually estimating and why it makes sense in terms of estimation accuracy; our algorithm operates on all edges in the images, including silhouette edges, self occlusion edges, and texture edges, without distinguishing their types (thus, resulting in improved accuracy and handling locally concave surface estimation if texture edges are present); the algorithm automatically handles various degeneracies; and the algorithm incorporates new methodologies for implementing the required operations such as appropriately relating edges in pairs of images, evaluating and using the algorithm's sensitivity to noise to determine the accuracy of an estimated 3D point. Experiments with both synthetic and real images demonstrate that the operator is accurate, robust to degeneracies and noise, and general for reconstructing free-form objects from occluding edges and texture edges detected in calibrated images or video sequences. [ABSTRACT FROM AUTHOR]

In the past decade the humanitarian supply chain (HSC) has attracted the attention of researchers due to the increasing frequency of disasters. The uncertainty in time, location, and severity of disaster during predisaster phase and poor conditions of available infrastructure during postdisaster phase make HSC operations difficult to handle. In order to overcome the difficulties during these phases, we need to assure that HSC operations are designed in an efficient manner to minimize human and economic losses. In the recent times, several mathematical optimization techniques and algorithms have been developed to increase the efficiency of HSC operations. These techniques and algorithms developed for the field of HSC motivate the need of a systematic literature review. Owing to the importance of mathematical modelling techniques, this paper presents the review of the mathematical contributions made in the last decade in the field of HSC. A systematic literature review methodology is used for this paper due to its transparent procedure. There are two objectives of this study: the first one is to conduct an up-to-date survey of mathematical models developed in HSC area and the second one is to highlight the potential research areas which require attention of the researchers. [ABSTRACT FROM AUTHOR]

This paper presents seven theorems which expand understanding of the theoretical structure of the Charnes­Cooper­Rhodes (CCR) model of Data Envelopment Analysis, especially with respect to slacks and the underlying structure of facets and faces. These theorems also serve as a basis for new algorithms which will provide optimal primal and dual solutions that satisfy the strong complementary slackness conditions (SCSC) for many (if not most) non-radially efficient DMUs; an improved procedure for identifying the set E of extreme efficient DMUs; and may, for many DEA domains, also settle in a single pass the existence or non-existence of input or output slacks in each of their DMUs. This paper also introduces the concept of a positive goal vector G, which is applied to characterize the set of all possible maximal optimal slack vectors. The appendix C presents an example which illustrates the need for a new concept, face regular, which focuses on the role of convexity in the intersections of radial efficient facets with the efficient frontier FR. The same example also illustrates flaws in the popular ‘sum of the slacks’ methodology. [ABSTRACT FROM AUTHOR]

This paper introduces orthogonal decision trees that offer an effective way to construct a redundancy-free, accurate, and meaningful representation of large decision-tree-ensembles often created by popular techniques such as Bagging, Boosting, Random Forests, and many distributed and data stream mining algorithms. Orthogonal decision trees are functionally orthogonal to each other and they correspond to the principal components of the underlying function space. This paper offers a technique to construct such trees based on the Fourier transformation of decision trees and eigen-analysis of the ensemble in the Fourier representation. It offers experimental results to document the performance of orthogonal trees on the grounds of accuracy and model complexity. [ABSTRACT FROM AUTHOR]

This paper describes a Boolean satisfiability checking (SAT)-based unbounded symbolic model-checking algorithm. The conjunctive normal form is used to represent sets of states and transition relation. A logical operation on state sets is implemented as an operation on conjunctive normal form formulas. A satisfy-all procedure is proposed to compute the existential quantification required in obtaining the preimage and fix point. The proposed satisfy-all procedure is implemented by modifying a SAT procedure to generate all the satisfying assignments of the input formula, which is based on new efficient techniques such as line justification to make an assignment covering more search space, excluding clause management, and two-level logic minimization to compress the set of found assignments. In addition, a cache table is introduced into the satisfy-all procedure. It is a difficult problem for a satisfy-all procedure to detect the case that a previous, result can be reused. This paper shows that the case can be detected by comparing sets of undetermined variables and clauses. Experimental results show that the proposed algorithm can check more circuits than binary decision diagram-based and previous SAT-based model-checking algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a review of the most relevant current techniques that deal with hole-filling in 3D models. Contrary to earlier reports, which approach mesh repairing in a sparse and global manner, the objective of this review is twofold. First, a specific and comprehensive review of hole-filling techniques (as a relevant part in the field of mesh repairing) is carried out. We present a brief summary of each technique with attention paid to its algorithmic essence, main contributions and limitations. Second, a solid comparison between 34 methods is established. To do this, we define 19 possible meaningful features and properties that can be found in a generic hole-filling process. Then, we use these features to assess the virtues and deficiencies of the method and to build comparative tables. The purpose of this review is to make a comparative hole-filling state-of-the-art available to researchers, showing pros and cons in a common framework. [ABSTRACT FROM AUTHOR]

This paper extends recent work on finding the stochastic queue median (SQM) on a network. The SQM is the optimal location of a single mobile server, when idle, who travels to customers in response to requests for service. Customer demands are limited to the nodes of the network and their requests for service arrive according to a time homogeneous Poisson process, independently from each node. When a service request finds the server busy with a previous customer, it is entered into an M/G/1 queue that is depleted in a first-in, first-out (FIFO) manner. The SQM is the point on the network at which the sum of mean queueing delay and mean travel time is minimized. In this paper the transportation network is restricted to be a tree. By discovering and exploiting convex properties of the objective function and related functions, an efficient finite-step algorithm is found for locating the SQM on a tree. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a collaborative filter that answers the simple question: What is popular amongst your “friends”? While this basic principle seems to be prevalent in many practical implementations, there does not appear to be much theoretical analysis of its performance. In this paper, we partly fill this gap. While recent works on this topic, such as the low-rank matrix completion literature, consider the probability of error in recovering the entire rating matrix, we consider probability of an error in an individual recommendation [bit error rate (BER)]. For a mathematical model introduced by Aditya in 2009 and 2011, we identify three regimes of operation for our algorithm (named Popularity Amongst Friends) in the limit as the matrix size grows to infinity. In a regime characterized by large number of samples and small degrees of freedom (defined precisely for the model in the paper), the asymptotic BER is zero; in a regime characterized by large number of samples and large degrees of freedom, the asymptotic BER is bounded away from 0 and 1/2 (and is identified exactly except for a special case); and in a regime characterized by a small number of samples, the algorithm fails. We then compare these results with the performance of the optimal recommender. We also present numerical results for the MovieLens and Netflix datasets. We discuss the empirical performance in light of our theoretical results and compare with an approach based on low-rank matrix completion. [ABSTRACT FROM AUTHOR]

This paper presents a developed algorithm for reliability sensitivity analysis of engineering networks. . Reliability Modeling is proposed for the Iraqi Kurdistan Regional Power Network (IKRPN) using Symbolic Reliability function of the model. The written Pascal code for the developed algorithm finds efficiently path sets and cut sets of the model. Reliability and Unreliability indices are found. The sensitivity of these indices are found with respect to the variation of the network's elements reliabilities [ABSTRACT FROM AUTHOR]

This paper explores the mathematical and algorithmic properties of two sample-based texture models: random phase noise (RPN) and asymptotic discrete spot noise (ADSN). These models permit to synthesize random phase textures. They arguably derive from linearized versions of two early Julesz texture discrimination theories. The ensuing mathematical analysis shows that, contrarily to some statements in the literature, RPN and ADSN are different stochastic processes. Nevertheless, numerous experiments also suggest that the textures obtained by these algorithms from identical samples are perceptually similar. The relevance of this study is enhanced by three technical contributions providing solutions to obstacles that prevented the use of RPN or ADSN to emulate textures. First, RPN and ADSN algorithms are extended to color images. Second, a preprocessing is proposed to avoid artifacts due to the nonperiodicity of real-world texture samples. Finally, the method is extended to synthesize textures with arbitrary size from a given sample. [ABSTRACT FROM AUTHOR]

The disassembly line is the best choice for automated disassembly of disposal products. Therefore, disassembly line should be designed and balanced so that it can work as efficiently as possible. In this paper, a mathematical model for the multi-objective disassembly line balancing problem is formalized firstly. Then, a novel multi-objective ant colony optimization (MOACO) algorithm is proposed for solving this multi-objective optimization problem. Taking into account the problem constraints, a solution construction mechanism based on the method of tasks assignment is utilized in the algorithm. Additionally, niche technology is used to embed in the updating operation to search the Pareto optimal solutions. Moreover, in order to find the Pareto optimal set, the MOACO algorithm uses the concept of Pareto dominance to dynamically filter the obtained non-dominated solution set. To validate the performance of algorithm, the proposed algorithm is measured over published results obtained from single-objective optimization approaches and compared with multi-objective ACO algorithm based on uniform design. The experimental results show that the proposed MOACO is well suited to multi-objective optimization in disassembly line balancing. [ABSTRACT FROM AUTHOR]

The GDPO algorithm for phase-1 of the dual simplex method developed by Maros possesses some interesting theoretical features that have potentially huge computational advantages. This paper gives account of a computational analysis of GDPO that has investigated how these features work in practice by exploring the internal operation of the algorithm. Experience of a systematic study involving 48 problems gives an insight how the predicted performance advantages materialize that ultimately make GDPO an indispensable tool for dual phase-1. [ABSTRACT FROM AUTHOR]

Reliability-Based impact (R-impact) factor, defined as the cited half-life multiplied by the citation impact factor, measures both the citation impact and long-lasting impact of published journals. Currently there are several different ways to calculate the citation rates, each with limitations to be improved. This paper provides a new analysis approach for the ranking and citation of published journals. Because cited half-life is the number of publication years from the current year that account for 50% of the current citations published by a journal in its article references, it can evaluate the age of the majority of cited articles. Through using the cited half-life as the sample time variable, we can seek the normalized value of citations and the citable items. This value can avoid the impacts from different journals or different fields. A more radical improvement is suggested in the impact factor, and relative impact factor, which can measure effectively not only the short-time performance of the journals but also the long-time performance. Based on this, relative R-impact (RRI) is proposed to improve R-impact effectively. [ABSTRACT FROM AUTHOR]

We present a new computational approach to the problem of placing n identical nonoverlapping disks in the unit square in such a way that their radii are maximized. The problem has been studied in a large number of papers, from both a theoretical and a computational point of view. In this paper, we conjecture that the problem possesses a so-called funneling landscape, a feature that is commonly found in molecular conformation problems. Based on this conjecture, we develop a stochastic search algorithm that displays excellent numerical performance. Thanks to this algorithm, we could improve over previously known putative optima in the range n ≤ 130 in as many as 32 instances, the smallest of which is n=53. [ABSTRACT FROM AUTHOR]

In this paper, we present an algorithm which, for a given compact orientable irreducible boundary irreducible 3-manifold M, verifies whether M contains an essential orientable surface (possibly, with boundary), whose genus is at most N. The algorithm is based on Haken’s theory of normal surfaces, and on a trick suggested by Jaco and consisting in estimating the mean length of boundary curves in an unknown essential surface of a given genus in the given manifold. [ABSTRACT FROM AUTHOR]

Let T = (V,E) be an edge-weighted tree with |V| = n vertices embedded in the Euclidean plane. Let IE denote the set of all points on the edges of T. Let X and Y be two subsets of IE and let r be a positive real number. A subset D ⊆ X is an X/Y/r-dominating set if every point in Y is within distance r of a point in D. The X/Y/r-dominating set problem is to find an X/Y/r-dominating set D* with minimum cardinality. Let p ≥ 1 be an integer. The X/Y/p-center problem is to find a subset C* ⊆ X of p points such that the maximum distance of any point in Y from C* is minimized. Let X and Y be either V or IE. In this paper, efficient parallel algorithms on the EREW PRAM are first presented for the X/Y/r-dominating set problem. The presented algorithms require O(log² n) time for all cases of X and Y. Parallel algorithms on the BREW PRAM are then developed for the X/Y/p-center problem. The presented algorithms require O(log³ n) time for all cases of X and Y. Previously, sequential algorithms for these two problems had been extensively studied in the literature. However, parallel solutions with polylogarithmic time existed only for their special cases. The algorithms presented in this paper are obtained by using an interesting approach which we call the dependency-tree approach. Our results are examples of parallelizing sequential dynamic-programming algorithms by using the approach. [ABSTRACT FROM AUTHOR]

This paper considers the problem of finding minimal length tree networks on the unit sphere Φ of a given point set (V) where distance is measured along great circular arcs. The related problems of finding a Steiner Minimal Tree SMT (V) and of finding a Minimum Spanning Tree MST(V) are treated through a simplicial decomposition technique based on computing the Delaunay Triangulation DT (V) and the Voronoi Diagram VD(V) of the given point set. O (N log N) algorithms for computing DT(V), VD(V), and WST(V) as well as an O(N log N) heuristic for finding a sub-optimal SMT(V) solution are presented, together with experimental results for randomly distributed points on Φ. [ABSTRACT FROM AUTHOR]

This paper proposes a novel optimization algorithm for grouping problems, the Grouping Coral Reefs Optimization algorithm, and describes its application to a Mobile Network Deployment Problem (MNDP) under four optimization criteria. These criteria include economical cost and coverage, and also electromagnetic pollution control and capacity constraints imposed at the base stations controllers, which are novel in this study. The Coral Reefs Optimization algorithm (CRO) is a recently-proposed bio-inspired approach for optimization, based on the simulation of the processes that occur in coral reefs, including reproduction, fight for space or depredation. This paper presents a grouping version of the CRO, which has not previously evaluated before. Grouping meta-heuristics are characterized by variable-length encoding solutions, and have been successfully applied to a number of different optimization and assignment problems. The GCRO proposed is a novel contribution to the intelligent systems field, which is able to improve results obtained by two alternative grouping algorithms such as grouping genetic algorithms and grouping Harmony Search. The performance of the proposed GCRO and the algorithms for comparison has been tested with real data in a case study of a MNDP in Alcalá de Henares, Madrid, Spain. [ABSTRACT FROM AUTHOR]

Our paper introduces a new methodology to solve group decision-making problems under fuzzy and dynamic environment. The methodology takes group members’ linguistically defined pair wise preferences of alternatives in different time intervals and aggregates them across the intervals to obtain each member's net preference levels. Each member's net preference levels are again aggregated across the members to obtain the group's preference. Our paper attaches higher importance to the members whose involvement in the decision process is more recent than the members who opined their views in the past. The fuzzy aggregation operator, IOWA (Induced Ordered Weighted Average) is used to aggregate their views in accordance to their importance in the group. The Ranked_List algorithm, introduced in our paper, inputs the aggregated views of the members in pair wise form and produces the set of sequences of ranked list of alternatives representing the group's consensus view as output. The Ranked_List algorithm is validated and analyzed through a series of synthetic data sets and its results are compared with a movie selection case study. The methodology is illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we first propose a weak convergence algorithm, called the linesearch algorithm, for solving a split equilibrium problem and nonexpansive mapping (SEPNM) in real Hilbert spaces, in which the first bifunction is pseudomonotone with respect to its solution set, the second bifunction is monotone, and fixed point mappings are nonexpansive. In this algorithm, we combine the extragradient method incorporated with the Armijo linesearch rule for solving equilibrium problems and the Mann method for finding a fixed point of an nonexpansive mapping. We then combine the proposed algorithm with hybrid cutting technique to get a strong convergence algorithm for SEPNM. Special cases of these algorithms are also given. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to study the proximal split feasibility problems. For solving the problems, we present new self-adaptive algorithms with the regularization technique. By using these algorithms, we give some strong convergence theorems for the proximal split feasibility problems. [ABSTRACT FROM AUTHOR]

It is commonly believed that real networks are scale-free and the fraction of nodes P(k) with degree k satisfies the power-law P(k) / k-γ for k > kmin > 0. Preferential attachment is the mechanism that has been considered responsible for such organization of these networks. In many real networks, degree distribution before the kmin varies very slowly to the extent of being uniform as compared to the degree distribution for k > kmin. In this paper, we propose a model that describes this particular degree distribution for the whole range of k > 0. We adopt a two step approach. In the first step, at every time stamp we add a new node to the network and attach it to an existing node using preferential attachment method. In the second step, we add edges between existing pairs of nodes with the node selection based on the uniform probability distribution. Our approach generates weakly scale-free networks that closely follow the degree distribution of real-world networks. We perform a comprehensive mathematical analysis of the model in the discrete domain and compare the degree distribution generated by this model with that of real-world networks. [ABSTRACT FROM AUTHOR]

The enumeration of inversion sequences avoiding a single pattern was initiated by Corteel, Martinez, Savage and Weselcouch, and Mansour and Shattuck, independently. Their work has sparked various investigations of generalized patterns in inversion sequences, including patterns of relation triples by Martinez and Savage, consecutive patterns by Auli and Elizalde, and vincular patterns by Lin and Yan. In this paper, we carried out the systematic study of inversion sequences avoiding two patterns of length 3. Our enumerative results establish further connections to the OEIS sequences and some classical combinatorial objects, such as restricted permutations, weighted ordered trees and set partitions. Since patterns of relation triples are some special multiple patterns of length 3, our results complement the work by Martinez and Savage. In particular, one of their conjectures regarding the enumeration of (021, 120)- avoiding inversion sequences is solved. [ABSTRACT FROM AUTHOR]

Abstract: This paper is to illustrate that the main result of the paper [R.U. Verma, Generalized over-relaxed proximal algorithm based on -maximal monotonicity framework and applications to inclusion problems, Mathematical and Computer Modelling 49 (2009) 1587–1594] is incorrect. The convergence rate of the over-relaxed proximal point algorithm should be greater than 1. Moreover, the strong convergence and the unique solution may not be proved accordingly in the paper by Verma. [Copyright &y& Elsevier]

In this paper, an unconditionally stable finite-difference time-domain algorithm is presented for analysis of lossy nonuniform multiconductor transmission line (MTL). The results of the proposed algorithm are confirmed by those of the Leap-Frog algorithm. The unconditionally stable algorithm alone cannot decrease the time consumption, especially when the MTL is excited by modulated signals. The complex phasor transformation approach is used to separate the modulating signal from the carrier signal when an MTL is excited by a modulated signal. A new set of equations is generated using this approach. The new equations are based on the modulating signal, and the carrier signal is eliminated in these equations. The derived equations are solved by Leap-Frog algorithm, and the results confirm the accuracy of these equations. Finally, the proposed equations are solved by the unconditionally stable algorithm at several temporal step sizes. The results indicate that this method has much lower CPU time compared with the conventional method and also has a very good accuracy. [ABSTRACT FROM AUTHOR]

Abstract: The mesh density has an important affect on finite element analysis of engineering problems. This paper studies the adaptive and local refinement techniques of hexahedral element meshes. A set of refinement templates and its converting rules of refinement fields are established. The refinement field propagation problem is solved using two corner templates and an isolated node template. A relative curvature criterion for constructing refinement source point fields is proposed by introducing the relative area of STL (stereo lithography) facets into the curvature criterion. The adaptive refinement of meshes can be easily realized using the constructed refinement source point fields. Examples show that the relative curvature criterion can more accurately capture the curvature features of solid models than the conventional curvature refinement criterion. To facilitate users and obtain the effective local refinement, this paper proposes a local refinement technique. The levels of local refinement can be self-controlled by users. The geometric features can be easily identified before each level of refinement. The effective refinement of nodes, elements, element-edges, element-surfaces, mesh-boundaries, mesh-faces and local regions can be realized. The accuracy and robustness of the adaptive and local refinement algorithms presented in this paper are demonstrated using several examples. The mesh refinement quality and flexibility are improved significantly. [Copyright &y& Elsevier]

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Time-varying GARCH-Mmodels are commonly used in econometrics and financial economics. Yet the recursive nature of the conditional variance makes exact likelihood analysis of these models computationally infeasible. This paper outlines the issues and suggests to employ a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a simulated Bayesian solution in only O(T) computational operations, where T is the sample size. Furthermore, the theoretical dynamic properties of a time-varying GQARCH(1,1)-M are derived. We discuss them and apply the suggested Bayesian estimation to three major stock markets. [ABSTRACT FROM AUTHOR]

In this paper, a new molecular alignment based recognition method for question answering from from the Web is proposed. This identifies locations using an molecular alignment sequence algorithm according to their similarity with a user natural-language question. Different experiments and results concerning questions on locations are discussed. The high accuracy of the proposed alignment strategy shows the promise of approach to effectively deal with questions extracted from natural-language corpus which contain many complex patterns. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate the minimax properties of Stein block thresholding in any dimension d with a particular emphasis on . Towards this goal, we consider a frame coefficient space over which minimaxity is proved. The choice of this space is inspired by the characterization provided in [L. Borup, M. Nielsen, Frame decomposition of decomposition spaces, J. Fourier Anal. Appl. 13 (1) (2007) 39–70] of family of smoothness spaces on , a subclass of so-called decomposition spaces [H.G. Feichtinger, Banach spaces of distributions defined by decomposition methods, II, Math. Nachr. 132 (1987) 207–237]. These smoothness spaces cover the classical case of Besov spaces, as well as smoothness spaces corresponding to curvelet-type constructions. Our main theoretical result investigates the minimax rates over these decomposition spaces, and shows that our block estimator can achieve the optimal minimax rate, or is at least nearly-minimax (up to a log factor) in the least favorable situation. Another contribution is that the minimax rates given here are stated for a noise sequence model in the transform coefficient domain satisfying some mild assumptions. This covers for instance the Gaussian case with frames where the noise is not white in the coefficient domain. The choice of the threshold parameter is theoretically discussed and its optimal value is stated for some noise models such as the (non-necessarily i.i.d.) Gaussian case. We provide a simple, fast and a practical procedure. We also report a comprehensive simulation study to support our theoretical findings. The practical performance of our Stein block denoising compares very favorably to the BLS-GSM state-of-the art denoising algorithm on a large set of test images. A toolbox is made available for download on the Internet to reproduce the results discussed in this paper. [Copyright &y& Elsevier]

Abstract  In this paper we present a word-level model checking method that attempts to speed up safety property checking of industrial netlists. Our aim is to construct an algorithm that allows us to check both bounded and unbounded properties using standard bit-level model checking methods as back-end decision procedures, while incurring minimum runtime penalties for designs that are unsuited to our analysis. We do this by combining modifications of several previously known techniques into a static abstraction algorithm which is guaranteed to produce bit-level netlists that are as small or smaller than the original bitblasted designs. We evaluate our algorithm on several challenging hardware components. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers Hotelling''s duopoly model on a tree with parametric service prices. Two competitors, the leader and the follower, sequentially place a server in a network. Users decide for a server according to the sum of distance and server price. The goal of the competitors is to maximize their profit induced by the total demand served. García and Pelegrín (2003) develop an algorithm with running time to compute the Stackelberg set, i.e., the set of all optimal leader positions. In this paper we first provide an algorithm to compute the Stackelberg set and the relaxed Simpson set with worst case running time . Second we suggest an algorithm to compute the optimal set for general monotonous gain functions. Its running time is and we prove that this bound is tight even for computing the security set. [Copyright &y& Elsevier]

Abstract: Threshold group testing first proposed by Damaschke is a generalization of classic group testing. Specifically, a group test is positive (negative) if it contains at least (at most ) positives, and if the number of positives is between and , the test outcome is arbitrary. Although sequential group testing algorithms have been proposed, it is unknown whether an efficient nonadaptive algorithm exists. In this paper, we give an affirmative answer to this problem by providing efficient nonadaptive algorithms for the threshold model. The key observation is that disjunct matrices, a standard tool for group testing designs, also work in this threshold model. This paper improves and extends previous results in three ways: 1. The algorithms we propose work in one stage, which saves time for testing. 2. The test complexity is lower than previous results, at least for the number of elements which need to be tested is sufficiently large. 3. A limited number of erroneous test outcomes are allowed. [Copyright &y& Elsevier]

Abstract: The effectiveness of the first entry of the original series by GM(1, 1) is researched in this paper. The results show that the modelling values and forecasts are independent of the first entry of the original series. The grey prediction model presented in this paper is called first-entry GM(1, 1), abbreviated as FGM(1, 1), which is based on the existing GM(1, 1) but modelled with data including the first-entry’s messages of the original series. A proof concerning this subject has been presented by other authors. However, the algorithm of their direct proof is too complicated. A more compact algorithm is presented in this paper to prove the first entry of the original series ineffective to the modelling values and forecasts by GM(1, 1). Then, an arbitrary number can be inserted in the front of the original series to extract the messages from its first entry. Only a few data (usually fewer than ten) are used for model building. This paper deals with the effectiveness of the first entry of the original series by GM(1, 1). [Copyright &y& Elsevier]

In this paper, we show how the construction of a trans-dimensional equivalent of the Gibbs sampler can be used to obtain a powerful suite of adaptive algorithms suitable for trans-dimensional MCMC samplers. These algorithms adapt at the local scale, optimizing performance at each iteration in contrast to the globally adaptive scheme proposed by others for the fixeddimensional problem. Our adaptive scheme ensures suitably high acceptance rates for MCMC and RJMCMC proposals without the need for (often prohibitively) time-consuming pilot-tuning exercises. We illustrate our methods using the problem of Bayesian model discrimination for the important class of autoregressive time series models and, through the use of a variety of prior and proposal structures, demonstrate their ability to provide powerful and effective adaptive sampling schemes. [ABSTRACT FROM AUTHOR]

Abstract  In this paper, we present several new implementable methods for solving a generalized fractional program with convex data. They are Dinkelbach-type methods where a prox-regularization term is added to avoid the numerical difficulties arising when the solution of the problem is not unique. In these methods, at each iteration a regularized parametric problem is solved inexactly to obtain an approximation of the optimal value of the problem. Since the parametric problem is nonsmooth and convex, we propose to solve it by using a classical bundle method where the parameter is updated after each ‘serious step’. We mainly study two kinds of such steps, and we prove the convergence and the rate of convergence of each of the corresponding methods. Finally, we present some numerical experience to illustrate the behavior of the proposed algorithms, and we discuss the practical efficiency of each one. [ABSTRACT FROM AUTHOR]

Abstract  A novel method for the convex underestimation of univariate functions is presented in this paper. The method is based on a piecewise application of the well-known αBB underestimator, which produces an overall underestimator that is piecewise convex. Subsequently, two algorithms are used to identify the linear segments needed for the construction of its $${{\mathcal C}^1}$$-continuous convex envelope, which is itself a valid convex underestimator of the original function. The resulting convex underestimators are very tight, and their tightness benefits from finer partitioning of the initial domain. It is theoretically proven that there is always some finite level of partitioning for which the method yields the convex envelope of the function of interest. The method was applied on a set of univariate test functions previously presented in the literature, and the results indicate that the method produces convex underestimators of high quality in terms of both lower bound and tightness over the whole domain under consideration. [ABSTRACT FROM AUTHOR]

Traditional stereo matching algorithms are limited in their ability to produce accurate results near depth discontinuities, due to partial occlusions and violation of smoothness constraints. In this paper, we use small baseline multiflash illumination to produce a rich set of feature maps that enable the acquisition of discontinuity preserving point correspondences. First, from a single multiflash camera, we formulate a qualitative depth map using a gradient domain method that encodes object relative distances. Then, in a multiview setup, we exploit shadows created by light sources to compute an occlusion map. Finally, we demonstrate the usefulness of these feature maps by incorporating them into two different dense stereo correspondence algorithms, the first based on local search and the second based on belief propagation. Experimental results show that our enhanced stereo algorithms are able to extract high-quality discontinuity preserving correspondence maps from scenes that are extremely challenging for conventional stereo methods. We also demonstrate that small baseline illumination can be useful to handle specular reflections in stereo imagery. Different from most existing active illumination techniques, our method is simple, inexpensive, and compact and requires no calibration of light sources. [ABSTRACT FROM AUTHOR]

This paper introduces an automatic robust nonlinear identification algorithm using the leave-one-out test score also known as the PRESS (Predicted REsidual Sums of Squares) statistic and regularised orthogonal least squares. The proposed algorithm aims to achieve maximised model robustness via two effective and complementary approaches, parameter regularisation via ridge regression and model optimal generalisation structure selection. The major contributions are to derive the PRESS error in a regularised orthogonal weight model, develop an efficient recursive computation formula for PRESS errors in the regularised orthogonal least squares forward regression framework and hence construct a model with a good generalisation property. Based on the properties of the PRESS statistic the proposed algorithm can achieve a fully automated model construction procedure without resort to any other validation data set for model evaluation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce obnoxious effects into obnoxious facility location games on a line, where each agent i has a private location x i on a closed interval [ 0 , 1 ] and one facility will be built on a location y in the interval according to the bids of all the agents. In addition, there are two thresholds d 1 and d 2 in the utility function of each agent, where 0 ≤ d 1 ≤ d 2 ≤ 1 . Denote d ( y , x i ) = | y − x i | to be the distance between agent i and the facility on the location y . The utility function of agent i is 0 if d ( y , x i ) is at most d 1 ; 1 if d ( y , x i ) is at least d 2 ; otherwise a linear increasing function between 0 and 1. Each agent attempts to get the largest utility while the social welfare is to maximize the sum of all the agents' utilities. The classic obnoxious facility game [4,11] is a special case of our problem when d 1 = 0 and d 2 = 1 . In this work, we first study the hardness of approximate mechanism design on this generalized problem, which states that our problem cannot admit any deterministic strategy-proof mechanism with bounded approximation ratio if d 1 ≥ 1 2 . Then we limit the thresholds to some ranges, both deterministic and randomized strategy-proof mechanisms are studied, and the approximation ratios vary with the specific values of d 1 and d 2 . [ABSTRACT FROM AUTHOR]

The Linear Programming Problem is by far the most widely used optimization model. Its impact on economic and government modeling is immense. The Simplex Method for solving the Linear Programming (LP) Problem, due to George Dantzig, has been an extremely efficient computational tool for almost four decades. The method has been the subject of intense investigations for many years, but some major aspects of its behavior are not fully understood yet. The purpose of this paper is to survey the body of knowledge on the efficiency of the Simplex Method, from both practical and theoretical points of view. Adopting the number of iterations (pivot steps) as the yardstick for efficiency, we survey four aspects of the issue: 1. Reports on practical experience of the method's performance on real-life LP problems. 2. Results on controlled (Monte-Carlo) experiments solving LP problems which were randomly generated according to some predetermined distributions. 3. Complexity results, including theoretical analyses on both upper and lower bounds for the performance of the Simplex as well as non-Simplex algorithms for LP. 4. Results of recent theoretical studies using probabilistic analysis to derive bounds on the average behavior of the Simplex Method. We discuss the consequences and limitations of the various studies. Special emphasis is given to open questions. [ABSTRACT FROM AUTHOR]

Planning languages and spreadsheet systems are very popular, and the number of new users is increasing dramatically. On larger computers, IFPS, System W, and FCS-EPS are among the most widely used systems; while on personal computers, Multiplan and 1-2-3 enjoy great popularity. Currently, such languages operate mainly as simulators, evaluating specific cases. In this paper, we propose methodology which is useful in designing an optimization capability for these languages. This capability permits the user to designate certain model variables as decisions, constraints, and the objective. Upper and lower limits on the decisions and constraints are also specified. The optimization interface then diagnoses the problem as linear or nonlinear, computes first partial derivatives needed by the solution algorithms, and invokes the appropriate "solver." Information regarding the optimal solution is obtained using the reporting and graphics capabilities of the planning language. Sensitivity analysis and "what if" features permit easy modification of the problem for further analysis. These ideas have been implemented in a system called IFPS/OPTIMUM, which provides an optimization capability to users of the widely-used planning language IFPS. A simple IFPS/OPTIMUM example is presented, and two applications are described. Endowing planning languages with an optimization capability promises to increase dramatically the use of optimization. There are already hundreds of thousands of users of planning languages and spreadsheet systems, most of whom are unfamiliar with optimization models or methods. Making optimization a natural extension of systems they understand and find very useful holds great promise, both for applications and for teaching optimization concepts. [ABSTRACT FROM AUTHOR]

Multiobjective mathematical programming has been one of the fastest growing areas of OR/MS during the last 15 years. This paper presents: 1. some reasons for the rapidly growing increase in interest in multiobjective mathematical programming. 2. a discussion of the advantages and disadvantages of the three general approaches (articulation of the decision maker's preference structure over the multiple objectives prior to, during, or after the optimization) towards multiobjective mathematical programming, 3. a nontechnical overview of many of the specific solution techniques for multiobjective mathematical programming, and 4. a discussion of important areas for further research. The overview concentrates on those techniques which require an articulation of the decision maker's preference structure either during or after the optimization, since these are the areas where most of the recent research has been conducted. It differs from previous overviews in that, in addition to the timing of the elicited preference information, the techniques are also classified according to the types of decision variables contained in the model (i.e., only continuous decision variables, or at least some discrete decision variables). In addition, the types of preference information (e.g., a ranking of outcomes) required of the various techniques are also discussed. [ABSTRACT FROM AUTHOR]

The global solvers are an attractive class of iterative solvers for solving linear systems with multiple right-hand sides. In this paper, first, a new global method for solving general linear systems with several right-hand sides is presented. This method is the global version of the LSMR algorithm presented by Fong and Saunders (2011). Then, some theoretical properties of the new method are discussed. Finally, numerical experiments from real applications are used to confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A BC-tree (block-cutpoint-tree) is a tree (with at least two vertices) where the distance between any two leaves is even. A BC-subtree is a subtree of a connected graph that is also a BC-tree. In this paper, we first consider subtrees containing a specific vertex with conditions on the parity of the distances from this vertex to the leaves and the enumeration of such subtrees of unicyclic and edge-disjoint bicyclic graphs. Using these results and through generating functions of BC-subtrees, we present graph-theoretical based algorithms for enumerating BC-subtrees, BC-subtrees containing a given vertex, and BC-subtrees containing two distinct vertices of unicyclic and edge-disjoint bicyclic graphs. These results also provide a novel perspective on exploring the structural properties of molecules. [ABSTRACT FROM AUTHOR]