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Stochastic cellular automata for rock-paper-scissors games are related to Lotka-Volterra model. Simulations are usually performed by two methods local and global interactions. It is well known that the population dynamics with local interaction is stable, where all species coexist. In contrast, global interaction leads to extinction. So far, theories such as mean-field theory and pair approximation have been presented, but they never explained the stable dynamics in local simulation. In the present article, we apply effective medium approximation (EMA) which has been developed in Physics. The effective medium is determined in a self-consistent way. The EMA theory well predicts the stability of population dynamics. Moreover, it fairly explains the aggregation of each species observed in the stationary state. [ABSTRACT FROM AUTHOR]

Abstract: A physical model of a continuous paper pulp digester is simplified and two subprocesses selected from the digester are modelled by coupled linear partial differential equations. This study focuses on the parameter identification of the simplified linear models. Finite-dimensional approximation of the model is made and a software package developed for identification of distributed parameter processes is applied. This identification system is developed for flexibility to allow identification for different choices of subprocesses and process variables. Unknown parameters of the subprocess models are estimated and the results are illustrated by process simulation and model validation. [Copyright &y& Elsevier]

Abstract: In this note, we point out an error in the recently published article [R.K. Mohanty, M.K. Jain, D. Dhall, A cubic spline approximation and application of TAGE iterative method for the solution of two-point boundary value problems with forcing function in integral form, Appl. Math. Model. 35 (2011) 3036–3047] and then correct it. [Copyright &y& Elsevier]

Abstract: Ahn, Lee, Park and Yoo proved that the best constrained degree reduction of a polynomial f in -norm equals the best weighted Euclidean approximation of the Bernstein–Bézier coefficients of f in a paper, published in the journal, Computer Aided Geometric Design 21 (2) (2004) 181–191. In this note, we point out an error in their paper and give the correct result. [Copyright &y& Elsevier]

Abstract: A comment on a recent paper about the combined effects of radiation and viscous dissipation on the convection in an annular porous enclosure has raised the problem of the role played by the viscous dissipation and the pressure work contributions in buoyant flows. The aim of this further comment is to show that the criticism expressed by Costa on the model of the viscous dissipation effect employed in the paper by Badruddin and co-workers is unjustified. [ABSTRACT FROM AUTHOR]

The paper is concerned with the mathematical theory and numerical approximation of systems of partial differential equations (pde) of hyperbolic, pseudo-parabolic type. Some mathematical properties of the initial-boundary-value problem (ibvp) with Dirichlet boundary conditions are first studied. They include the weak formulation, well-posedness and existence of traveling wave solutions connecting two states, when the equations are considered as a variant of a conservation law. Then, the numerical approximation consists of a spectral approximation in space based on Legendre polynomials along with a temporal discretization with strong stability preserving (SSP) property. The convergence of the semidiscrete approximation is proved under suitable regularity conditions on the data. The choice of the temporal discretization is justified in order to guarantee the stability of the full discretization when dealing with nonsmooth initial conditions. A computational study explores the performance of the fully discrete scheme with regular and nonregular data. [ABSTRACT FROM AUTHOR]

The transmission eigenvalue problem arising from the inverse scattering theory is of great importance in the theory of qualitative methods and in the practical applications. In this paper, we study the FEM for the transmission eigenvalue problem for anisotropic inhomogeneous media in Ω ⊂ R d (d = 2 , 3). Using the T -coercivity and the spectral approximation theory, we derive an a posteriori estimator of residual type and prove its effectiveness and reliability for eigenfunctions. In addition, we also prove the reliability of the estimator for transmission eigenvalues. The numerical experiments indicate our method is efficient and can reach the optimal order D o F − 2 m / d by using piecewise polynomials of degree m for real and complex eigenvalues. [ABSTRACT FROM AUTHOR]

In recent years, significant advancements have been made in neural beamforming, leveraging spectral and spatial cues to enhance their performance in multi-channel speech enhancement. When the frame-wise processing mechanism is required, there exists a trade-off between performance and algorithmic delay for existing all-neural beamformers. However, from the perspective of multi-source information fusion, the network is often encapsulated into a black box to entangle and fuse the spatial and spectral features into a non-linear feature space, which hinders our understanding of how they work collaboratively for target speech extraction. In this regard, this paper proposes to decouple the spatial and spectral domain processing inspired by Taylor's approximation theory. Specifically, we reformulate the time-variant beamforming defined in the spatial domain into the adaptive weighting and mixing of different beam components in the beamspace domain. This reformulation enables us to model the recovery of target speech as a weighted sum operation in the beamspace domain, where each beam component is associated with an introduced unknown term for residual interference cancellation. By virtue of Taylor's series expansion, the recovery process can be decomposed into the superimposition of the 0th-order non-derivative and high-order derivative terms, where the former acts as spatial filtering in the spatial domain, and the latter serves as a residual interference canceller in the spectral domain. We conduct extensive experiments on the spatialized LibriSpeech and L3DAS Challenge datasets. Experimental results show that, compared with existing advanced approaches, the proposed method not only achieves competitive performance in terms of multiple objective metrics but also provides feasible guidance in multi-channel speech enhancement pipeline design. • This paper proposes to decouple the spatial and spectral processing inspired by Taylor's approximation theory. • Beamforming in spatial domain is reformulated into the adaptive weighting of beamed components in the beamspace domain. • Speech recovery is decomposed into the superimposition of the 0th-order non-derivative and high-order derivative terms. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the application of reduced models of a distributed parameter system for robust process control and state estimation. We take the approach of integrating model reduction, parameter identification, and model uncertainty analysis, in purpose to find an appropriate trade-off between complexity and robust performance. The application example is the temperature system in a continuous paper pulp digester. Physical modeling of this process results in coupled linearized partial differential equations which are then reduced into low-order nominal process models using an orthogonal collocation approximation method. Two different approaches to obtaining a model uncertainty description are adapted for use on a distributed parameter system with low-order nominal model and shown to produce similar results when tested with measurement data. It is also demonstrated how this uncertainty description, in combination with the reduced model, may be used for robust control design and verification of the control performance on the distributed parameter system. Finally, the possibility of estimating the distributed process state using a state observer for the reduced process is demonstrated. Measurements of the process state in a certain position is available and is shown to agree with the estimated state at the same position. [Copyright &y& Elsevier]

In this paper we study a C 1 Virtual Element Method (VEM) on polyhedral meshes for bi-harmonic eigenvalue problems in three dimensions. Optimal order error estimates for the eigenfunctions and a double order for the eigenvalues are obtained by using the approximation theory of compact self-adjoint operators. Finally, a set of tests will numerically prove the theoretical result of the proposed scheme. [ABSTRACT FROM AUTHOR]

Approximation Fixpoint Theory (AFT) and Justification Theory (JT) are two frameworks to unify logical formalisms. AFT studies semantics in terms of fixpoints of lattice operators, and JT in terms of so-called justifications, which are explanations of why certain facts do or do not hold in a model. While the approaches differ, the frameworks were designed with similar goals in mind, namely to study the different semantics that arise in (mainly) non-monotonic logics. The first contribution of our current paper is to provide a formal link between the two frameworks. To be precise, we show that every justification frame induces an approximator and that this mapping from JT to AFT preserves all major semantics. The second contribution exploits this correspondence to extend JT with a novel class of semantics, namely ultimate semantics : we formally show that ultimate semantics can be obtained in JT by a syntactic transformation on the justification frame, essentially performing a sort of resolution on the rules. [ABSTRACT FROM AUTHOR]

Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to dealing with non-deterministic constructs that allow to handle indefinite information, represented e.g. by disjunctive formulas. This is done by generalizing the main constructions and corresponding results of AFT to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming. [ABSTRACT FROM AUTHOR]

Spatial tubes, known for their attributes of lightweight, large section modulus, and high strength, find extensive applications across various industries. Nevertheless, in the course of forming spatial tubes, springback poses a significant challenge in enhancing the forming quality. In this paper, the bound approximations for the combined bending and twisting of circular tubes employing the power-hardening material model are deduced innovatively. Drawing upon the boundary approximation theory, the interactive mechanism of bending and twisting is meticulously examined. The forming principles of the four-axis free-bending (FFB) are expounded. Concurrently, an innovative method for predicting springback, based on the established bound approximations within the framework of total plasticity theory, is introduced, which holds significant importance for addressing combined bending and torsion issues in engineering applications. Noteworthy findings reveal that the interaction between bending and twisting exhibits a predominant sensitivity to the hardening exponent n and the higher n the material has, the less pronounced the interaction will be. The augmentation of torsion contributes to mitigating the springback resulting from bending, and conversely, a similar effect is observed with the influence of bending on torsion. These findings contribute significantly to the understanding of combined bending and twisting problems. The proportionality coefficients of bending and twisting, denoted as λ M and λ T , are defined and investigated via comprehensive finite element (FE) simulations. Furthermore, this method of springback prediction is corroborated by FE simulations as well as the FFB experiments. • A novel deduction of bound approximations for combined bending and twisting. • The interactive mechanism of bending and twisting. • An innovative method for springback prediction. [ABSTRACT FROM AUTHOR]

Abstract In a previous paper (Hennink and Lathouwers, 2017) we developed a finite element discretization for the Boltzmann transport equation with forward peaked scatter modeled by the Fokker–Planck approximation. The discretization was based on the discontinuous Galerkin method in both space and angle. It was expected and found that the regular source iteration algorithm for the Boltzmann equation is not effective in solving the discretized system and becomes excessively expensive for problems with many angular degrees of freedom. The purpose of this paper is to develop a multigrid scheme as preconditioner for the above mentioned discretization. The method exploits the nested nature of the meshes and the natural prolongation/restriction between meshes by Galerkin projection. A set of test problems ranging from pure spherical diffusion to the complete Boltzmann transport problem in 3D are presented to illustrate that the method is very effective, resulting in iteration counts nearly independent of problem size even for highly non-isotropically refined angular meshes. [ABSTRACT FROM AUTHOR]

Highlights • A finite-buffer vacation queue with batch Markovian arrival process has been analyzed. • The server is subjected to serve under gated-limited service discipline. • Proposed analysis is based on the successive substitution and the supplementary variable method. • The results have been matched with the corresponding infinite-buffer queue. • Numerical results are presented for different service- and vacation-time distributions. Abstract This paper analyzes the finite-buffer single server queue with vacation(s). It is assumed that the arrivals follow a batch Markovian arrival process (BMAP) and the server serves customers according to a non-exhaustive type gated-limited service discipline. It has been also considered that the service and vacation distributions possess rational Laplace-Stieltjes transformation (LST) as these types of distributions may approximate many other distributions appeared in queueing literature. Among several batch acceptance/rejection strategies, the partial batch acceptance strategy is discussed in this paper. The service limit L (1 ≤ L ≤ N) is considered to be fixed, where N is the buffer-capacity excluding the one in service. It is assumed that in each busy period the server continues to serve until either L customers out of those that were waiting at the start of the busy period are served or the queue empties, whichever occurs first. The queue-length distribution at vacation termination/service completion epochs is determined by solving a set of linear simultaneous equations. The successive substitution method is used in the steady-state equations embedded at vacation termination/service completion epochs. The distribution of the queue-length at an arbitrary epoch has been obtained using the supplementary variable technique. The queue-length distributions at pre-arrival and post-departure epoch are also obtained. The results of the corresponding infinite-buffer queueing model have been analyzed briefly and matched with the previous model. Net profit function per unit of time is derived and an optimal service limit and buffer-capacity are obtained from a maximal expected profit. Some numerical results are presented in tabular and graphical forms. [ABSTRACT FROM AUTHOR]

Abstract G. Ramponi et al. introduced in Carrato et al. (1997,1998), Castagno and Ramponi (1996) and Ramponi (1995) a non linear rational interpolator of order two. In this paper we extend this result to get order four. We observe the Gibbs phenomenon that is obtained near discontinuities with its weights. With the weights we propose we obtain approximations of order four in smooth regions and three near discontinuities. We also introduce a rational nonlinear extrapolation which is also of order four in the smooth region of the given function. In the experiments we calculate numerically approximation orders for the different methods described in this paper and see that they coincide with those that have been obtained theoretically. We also present reconstructions in 1d and 2d with which we reach the same conclusions. [ABSTRACT FROM AUTHOR]

Abstract This paper is devoted to the construction of multiresolution frameworks related to general but linear subdivision schemes applied on sequences of finite length. Thanks to the flexible properties of subdivision schemes, a subdivision-based multiresolution is a promising powerful tool for compression, control and analysis of data. However, its construction is not straightforward either for non-interpolatory subdivisions, or for sequences of finite length. In this paper, given a subdivision for finite length sequences, we provide a first approach to construct compatible multiresolutions thanks to an extension of some classical wavelet results. As it will become clear that this type of approach can become computationally costly in practice, a new edge-adapted method that combines local consistent decimation is then developed to circumvent this limitation. An illustration in the case of the 4-point shifted Lagrange subdivision scheme, for which there is no available multiresolution up to now, is then provided. Finally, some properties of the new multiresolutions are analyzed and their performances are evaluated in the framework of image approximation. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the superconvergence properties of the quadratic finite volume method (FVM) on triangular meshes for elliptic equations. We proved the 3rd order superconvergence rate of the gradient approximation ‖ u h − u I ‖ 1 = O (h 3) and the 4th order superconvergence rate of the function value approximation ‖ u h − u I ‖ 0 = O (h 4) for the quadratic FVM on triangular meshes. Here u h is the FVM solution and u I is the piecewise quadratic Lagrange interpolation of the exact solution. It should be pointed out that the superconvergence phenomena of FVM strongly depends on the construction of dual mesh. Specially for quadratic FVMs, the scheme presented in this paper is the unique scheme which holds superconvergence. [ABSTRACT FROM AUTHOR]

Abstract Recently, sparse representation has attracted a great deal of interest in many of the image processing applications. However, the idea of self-similarity, which is inherently present in an image, has not been considered in standard sparse representation. Moreover, if the dictionary atoms are not constrained to be correlated, the redundancy present in the dictionary may not improve the performance of sparse coding. This paper addresses these issues by using orthogonal moments to extract the correlations among the atoms and group them together by extracting the characteristics of the noisy image patches. Most of the existing sparsity-based image denoising methods utilize an over-complete dictionary, for example, the K-SVD method that requires solving a minimization problem which is computationally challenging. In order to improve the computational efficiency and the correlation between the sparse coefficients, this paper employs the concept of overlapping group sparsity formulated for both convex and non-convex denoising frameworks. The optimization method used for solving the denoising framework is the well known majorization–minimization method, which has been applied successfully in sparse approximation and statistical estimations. Experimental results demonstrate that the proposed method offers, in general, a performance that is better than that of the existing state-of-the-art methods irrespective of the noise level and the image type. Highlights • We propose the use of Orthogonal moments as similarity measure in dictionary learning based image denoising. • The concept of overlapping group sparsity (OGS) is employed to promote strong correlation between sparse coding coefficients. Further, OGS is used in solving both convex and non-convex optimization problems. • The grouping of the similar patches in an image is proposed using L 2 norm-based similarity criterion evaluated using Krawtchouk and Tchebichef moments. The advantage of using moment domain-based similarity measure over L 2 norm is increased noise robustness. • The proposed image denoising framework is solved using majorization–minimization optimization framework used widely in signal processing. [ABSTRACT FROM AUTHOR]

Abstract Continuous-time Stochastic Game (CTSG) can be seen as a proper model to analyze probabilistic, non-deterministic, and competitive behaviors as found in Stochastic Multi-Player Game (SMG). The difference is that in an SMG the system under design is analyzed in the discrete-time setting. In comparison, in a CTSG, the system transitions occur in the continuous-time setting with exponentially distributed delays. This paper focuses on the model checking of CTSGs and presents a uniformization-based algorithm, called TPA, to approximate the time-bounded reachability probabilities with an arbitrary error bound. We concentrate on CTSGs with bounded transition rates. To illustrate the strength points of our algorithm, we have implemented it in Java, developed some large examples, and compared our results with the ones from an existing algorithm which is based on discretization. In order to express properties specifying these types of probabilities in the continuous-time setting, we adjusted the existing temporal logic, PATL. Thus, properties like the following can be stated and checked over a CTSG: " A coalition of players has a strategy to guarantee to reach the target states within time bound t ∈ Q ⩾ 0 with a probability equal to or greater than threshold P, regardless of the other players' behaviors." Highlights • This paper addresses the model checking of Continuous-Time Stochastic Games (CTSGs). • We propose a new algorithm to approximate time-bounded reachability probabilities over CTSGs. • In order to express properties over CTSGs, we introduce a temporal logic called Continuous-ATL. • We have illustrated the strength points of our algorithm by comparing its results with ones from an existing algorithm. [ABSTRACT FROM AUTHOR]

Hairer and Iserles (2016) presented a detailed study of skew-symmetric matrix approximation to a first derivative which is proved to be fundamental in ensuring stability of discretisation for evolutional partial differential equations with variable coefficients. An open problem is proposed in that paper which concerns about the existence and construction of the perturbed grid that supports high-order skew-symmetric differentiation matrix for a given grid and only the case p = 2 for this problem have been solved. This paper is an attempt to solve the problem for any p ⩾ 3 . We focus ourselves on the symmetric grid and prove the existence of the perturbed grid for arbitrarily high order p and give in detail the construction of the perturbed grid. Numerical experiments are carried out to illustrate our theory. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the rate of convergence in the normal approximation of the sequence { F n } , where each F n is a functional of an infinite-dimensional Gaussian field. We develop new and powerful techniques for computing the exact rate of convergence in distribution with respect to the Kolmogorov distance. As a tool for our works, the Edgeworth expansion of general orders, with an explicitly expressed remainder, will be obtained, and this remainder term will be controlled to find upper and lower bounds of the Kolmogorov distance in the case of an arbitrary sequence { F n }. As applications, we provide the optimal fourth moment theorem of the sequence { F n } in the case when { F n } is a sequence of random variables living in a fixed Wiener chaos or a finite sum of Wiener chaoses. In the former case, our results show that the conditions given in this paper seem more natural and minimal than ones appeared in the previous works. [ABSTRACT FROM AUTHOR]

This paper introduces a nonlinear multigrid solver for mixed finite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The AMGe coarse spaces with approximation properties used in this work enable us to overcome the difficulties in evaluating the nonlinear coarse operators and the degradation in convergence rates that characterized previous attempts to extend FAS to algebraic multilevel hierarchies on general unstructured grids. Specifically, the AMGe technique employed in this paper allows to derive stable and accurate coarse discretizations on general unstructured grids for a large class of nonlinear partial differential equations, including saddle point problems. The approximation properties of the coarse spaces ensure that our FAS approach for general unstructured meshes leads to optimal mesh-independent convergence rates similar to those achieved by geometric FAS on a nested hierarchy of refined meshes. In the numerical results, Newton’s method and Picard iterations with state-of-the-art inner linear solvers are compared to our FAS algorithm for the solution of a nonlinear saddle point problem arising from porous media flow applications. Our approach outperforms – both in terms of number of iterations and computational time – traditional methods in all the experiments. [ABSTRACT FROM AUTHOR]

In this paper, the unsteady isothermal flow of a gas through a semi-infinite micro–nano porous medium described by a non-linear two-point boundary value problem on a semi-infinite interval has been considered. We solve this problem by a nonstandard finite difference method defined on quasi-uniform grids in order to derive a new numerical approximation. By introducing a stencil that is constructed in such a way that the boundary conditions at infinity are exactly assigned, the proposed method is effectively used to determine the numerical solution. In addition, a mesh refinement and the Richardson’s extrapolation allow to improve the accuracy of the numerical solution and to define a posteriori estimator for the global error of the proposed numerical scheme. We determine the accurate initial slope d u d x ( 0 ) = − 1 . 1917906497194208 calculated for α = 0 . 5 with good capturing the essential behavior of u ( x ) . This clearly demonstrates that the numerical solutions presented in this paper result highly accurate and in excellent agreement with the existing solutions available in the literature. [ABSTRACT FROM AUTHOR]

This paper deals with solving the general random (Caputo) fractional linear differential equation under general assumptions on random input data (initial condition, forcing term and diffusion coefficient). Our contribution extends, in two directions, the results presented in a recent contribution by the authors. In that paper, a mean square random generalized power series solution has been constructed in the case that the fractional order, say α , of the Caputo derivative lies on the interval ] 0 , 1 ] and assuming that the diffusion coefficient belongs to a class, ℭ , of random variables that contains all bounded random variables. However, significant families of unbounded random variables, such as Gaussian and Exponential, for example, do not fall into class ℭ . Now, in this contribution we first enlarge the class of random variables to which the diffusion coefficient belongs and we prove that the constructed random generalized power series solution is mean square convergent too. We show that any bounded random variable and important unbounded random variables, including Gaussian and Exponential ones, are allowed to play the role of the diffusion coefficient as well. Secondly, we construct a mean square random generalized power series solution in the case that α parameter lies on the larger interval ] 0 , 2 ] . As a consequence, the results established in our previous contribution are fairly generalized. It is particularly enlightening, the numerical study of the convergence of the approximations to the mean and the standard deviation of the solution stochastic process in terms of α parameter and on the type of the probability distribution chosen for the diffusion coefficient. [ABSTRACT FROM AUTHOR]

In this paper, we study darning of general symmetric Markov processes by shorting some parts of the state space into singletons. A natural way to construct such processes is via Dirichlet forms restricted to the function spaces whose members take constant values on these collapsing parts. They include as a special case Brownian motion with darning, which has been studied in details in Chen (2012), Chen and Fukushima (2012) and Chen et al. (2016). When the initial processes have discontinuous sample paths, the processes constructed in this paper are the genuine extensions of those studied in Chen and Fukushima (2012). We further show that, up to a time change, these Markov processes with darning can be approximated in the sense of finite-dimensional distributions by introducing additional jumps with large intensity among these compact sets to be collapsed into singletons. For diffusion processes, it is also possible to get, up to a time change, diffusions with darning by increasing the conductance on these compact sets to infinity. To accomplish these, we give a version of the semigroup characterization of Mosco convergence to closed symmetric forms whose domain of definition may not be dense in the L 2 -space. The latter is of independent interest and potentially useful to study convergence of Markov processes having different state spaces. Indeed, we show in Section 5 of this paper that Brownian motion in a plane with a very thin flag pole can be approximated by Brownian motion in the plane with a vertical cylinder whose horizontal motion on the cylinder is a circular Brownian motion moving at fast speed. [ABSTRACT FROM AUTHOR]

The search for multivariate quadrature rules of minimal size with a specified polynomial accuracy has been the topic of many years of research. Finding such a rule allows accurate integration of moments, which play a central role in many aspects of scientific computing with complex models. The contribution of this paper is twofold. First, we provide novel mathematical analysis of the polynomial quadrature problem that provides a lower bound for the minimal possible number of nodes in a polynomial rule with specified accuracy. We give concrete but simplistic multivariate examples where a minimal quadrature rule can be designed that achieves this lower bound, along with situations that showcase when it is not possible to achieve this lower bound. Our second contribution is the formulation of an algorithm that is able to efficiently generate multivariate quadrature rules with positive weights on non-tensorial domains. Our tests show success of this procedure in up to 20 dimensions. We test our method on applications to dimension reduction and chemical kinetics problems, including comparisons against popular alternatives such as sparse grids, Monte Carlo and quasi Monte Carlo sequences, and Stroud rules. The quadrature rules computed in this paper outperform these alternatives in almost all scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the displacement of two incompressible phases in a Darcy–Brinkman flow in a porous media. The equations are obtained by the conservation of the mass and by considering the Brinkman regularization velocity of each phase. This model is treated in its general form with the whole nonlinear terms. This paper deals with construction and convergence analysis of a combined finite volume–nonconforming finite element scheme together with a phase-by-phase upstream according to the total velocity. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study the notion of low risk mechanisms . Intuitively, we say a mechanism is a low risk mechanism if the randomization of the mechanism does not affect the utility of agents by a lot. Specifically, we desire to design mechanisms in which the variances of the utility of agents are small . Inspired by this work, later, Procaccia et al. (0000) study the approximation–variance tradeoffs in mechanism design. In particular, here we present a low risk mechanism for the pairwise kidney exchange game . This game naturally appears in situations that some service providers benefit from pairwise allocations on a network, such as the kidney exchanges between hospitals. Ashlagi et al. (2013) present a 2-approximation randomized truthful mechanism for this problem. This is the best-known result in this setting with multiple players. However, we note that the variance of the utility of an agent in this mechanism may be as large as Ω ( n 2 ) , where n is the number of vertices. Indeed, this is not desirable in a real application. In this paper, we resolve this issue by providing a 2-approximation randomized truthful mechanism in which the variance of the utility of each agent is at most 2 + ϵ . As a side result, we apply our technique to design a deterministic mechanism such that, if an agent deviates from the mechanism, she does not gain more than 2 ⌈ log 2 m ⌉ , where m is the number of players. [ABSTRACT FROM AUTHOR]

In this paper we consider a family of high-order iterative methods which is more efficient than the Newton method to approximate a solution of symmetric algebraic Riccati equations. In fact, this paper is devoted to the convergence study of a k -steps iterative scheme with low operational cost and high order of convergence. We analyze their accessibility and computational efficiency. We also obtain results about the existence and localization of solution. Numerical experiments confirm the advantageous performance of the iterative scheme analyzed. [ABSTRACT FROM AUTHOR]

Nowadays, most of real world problems are complex and hence they cannot be solved by exact methods. So generally, we have to utilize approximate methods such as metaheuristics. So far, a significant amount of metaheuristic algorithms are proposed which are different with together in algorithm motivation and steps. Similarly, this paper presents the Tree Growth Algorithm (TGA) as a novel method with different approach to address optimization tasks. The proposed algorithm is inspired by trees competition for acquiring light and foods. Diversification and intensification phases and their tradeoff are detailed in the paper. Besides, the proposed algorithm is verified by using both mathematical and engineering benchmarks commonly used in this research area. This new approach in metaheuristic is compared and studied with well-known optimization algorithms and the comparison of TGA with standard versions of these employed algorithms showed the superiority of TGA in these problems. Also, convergence analysis and significance tests via some nonparametric technique are employed to confirm efficiency and robustness of the TGA. According to the results of conducted tests, the TGA can be considered as a successful metaheuristic and suitable for optimization problems. Therefore, the main purpose of providing this algorithm is achieving to better results, especially in continuous problems, due to the natural behavior inspired by trees. [ABSTRACT FROM AUTHOR]

Websites are one of the most widely distributed information resources. Educational institutions use this resource to ensure that the best quality of information transmission is achieved. As such, academic sites have become a very important aspect of academic institutions, one that affects their overall quality. Bearing in mind the importance of university websites’ quality, the authors of this paper presented a multi-criteria model for evaluating the quality of university websites. This paper presents the hybrid IR-AHP-MABAC (Interval Rough Analytic Hierarchy Process - MultiAttributive Border Approximation Area Comparison) model. The model is adapted to group decision making as based on the application of a new approach to treating uncertainties through the use of interval rough numbers (IRN). The modified IR-AHP method was used to determine the weight coefficients of the criteria in the group decision-making process. The results of the IR-AHP model are compared with results provided by the traditional AHP method and the fuzzy AHP approach. The IR-MABAC model was used for the evaluation of university websites. In order to verify the results of the IRN based approach, the IR-MABAC model was compared to the F-TOPSIS (Fuzzy Technique for Order of Preference by Similarity to Ideal Solution), F-VIKOR (Fuzzy MultiCriterion Optimization and Compromise Solution), F-COPRAS (Fuzzy COmpressed PRoportional ASsessment), F-MAIRCA (Fuzzy MultiAtributive Ideal-Real Comparative Analysis), and F-TODIM (an acronym of Interactive and Multi Criteria Decision Making in Portuguese) models. The credibility of the IR-AHP-MABAC model was demonstrated by comparing the results of different multi-criteria techniques and analyzing viability. The results of the IRN approach and fuzzy comparison have shown that the new approach to dealing with imprecision yields credible, reputable ranks. [ABSTRACT FROM AUTHOR]

This paper presents a computational scheme to solve nonlinear logarithmic singular boundary integral equations. These types of integral equations arise from boundary value problems of Laplace’s equations with nonlinear Robin boundary conditions. The discrete Galerkin method together with the (inverse) multiquadric radial basis functions established on scattered points is utilized to approximate the solution. The discrete Galerkin method for solving boundary integral equations results from the numerical integration of all integrals in the method. The proposed scheme uses a special accurate quadrature formula via the nonuniform Gauss–Legendre integration rule to compute logarithm-like singular integrals appeared in the scheme. Since the numerical method developed in the current paper does not require any mesh generations on the boundary of the domain, it is meshless and does not depend to the domain form. We also investigate the error analysis of the proposed method. Illustrative examples show the reliability and efficiency of the new scheme and confirm the theoretical error estimates. [ABSTRACT FROM AUTHOR]

In this paper, we establish sufficient conditions for the existence of optimal non-linear approximations to a linear subspace generated by a given weakly-closed (non-convex) cone of a Hilbert space. Most non-linear problems have difficulties to implement good projection-based algorithms due to the fact that the subsets, where we would like to project the functions, do not have the necessary geometric properties to use the classical existence results (such as convexity, for instance). The theoretical results given here overcome some of these difficulties. To see this we apply them to a fractional model for image deconvolution. In particular, we reformulate and prove the convergence of a computational algorithm proposed in a previous paper by some of the authors. Finally, some examples are given. [ABSTRACT FROM AUTHOR]

This paper presents a new family of methods for evaluating matrix polynomials more efficiently than the state-of-the-art Paterson–Stockmeyer method. Examples of the application of the methods to the Taylor polynomial approximation of matrix functions like the matrix exponential and matrix cosine are given. Their efficiency is compared with that of the best existing evaluation schemes for general polynomial and rational approximations, and also with a recent method based on mixed rational and polynomial approximants. For many years, the Paterson–Stockmeyer method has been considered the most efficient general method for the evaluation of matrix polynomials. In this paper we show that this statement is no longer true. Moreover, for many years rational approximations have been considered more efficient than polynomial approximations, although recently it has been shown that often this is not the case in the computation of the matrix exponential and matrix cosine. In this paper we show that in fact polynomial approximations provide a higher order of approximation than the state-of-the-art computational methods for rational approximations for the same cost in terms of matrix products. [ABSTRACT FROM AUTHOR]

This work is focused on the application of functional-type a posteriori error estimates and corresponding indicators to a class of time-dependent problems. We consider the algorithmic part of their derivation and implementation and also discuss the numerical properties of these bounds that comply with obtained numerical results. This paper examines two different methods of solution approximation for evolutionary models, i.e., a time-marching technique and a space–time approach. The first part of the study presents an algorithm for global minimisation of the majorant on each of discretisation time-cylinders (time-slabs), the effectiveness of this approach to error estimation is confirmed by extensive numerical tests. In the second part of the publication, the application of functional error estimates is discussed with respect to a space–time approach. It is followed by a set of extensive numerical tests that demonstrates the efficiency of proposed error control method. The numerical results obtained in this paper rely on the implementation carried out using open source software, which allows formulating the problem in a weak setting. To work in a variational framework appears to be very natural for functional error estimates due to their derivation method. The search for the optimal parameters for the majorant is done by a global functional minimisation, which to the authors’ knowledge is the first work using this technique in an evolutionary framework. [ABSTRACT FROM AUTHOR]

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

We study a combinatorial problem arising from the microarray synthesis. The objective of the Border Minimization Problem (BMP) is to place a set of sequences in the array and to find an embedding of these sequences into a common supersequence such that the sum of the “border length” is minimized. A variant of the problem, called P-BMP, is that the placement is given and the concern is simply to find the embedding. An exponential time algorithm has been proposed for the problem but it is unknown whether the problem is NP-hard or not. In this paper, we give a comprehensive study of different variations of BMP by presenting NP-hardness proofs and approximation algorithms. We show that BMP, P-BMP, and 1D-BMP are all NP-hard and 1D-BMP is polynomial time solvable. The interesting implications include (i) the BMP is NP-hard regardless of the dimension (1D or 2D) of the array; (ii) the array dimension differentiates the complexity of the P-BMP; and (iii) for 1D array, whether placement is given differentiates the complexity of the BMP. Another contribution of the paper is devising approximation algorithms, and in particular, we present a randomized approximation algorithm for BMP with approximation ratio O ( n 1 ∕ 4 log 2 n ) , where n is the total number of sequences. [ABSTRACT FROM AUTHOR]

This paper introduces the Δ N general solution to linear Fredholm integro-differential equations and sets its properties. The conditions for existence of classical general solution and solvability criteria for the equation are provided. Necessary and sufficient conditions for solvability of linear boundary value problems are established. Algorithms for construction of the Δ N general solutions are obtained. This paper also proposes approximate and numerical methods to solve the boundary value problems. [ABSTRACT FROM AUTHOR]

Oxygen evolution reaction (OER) is reconciled with the bottleneck in hydrogen production via photo- or electrocatalytic water splitting. One of the remedies to overcome this shortcoming is to develop catalytically efficient anode materials. Strontium titanate (STO) is a potential candidate for the OER by referring to recent experimental reports on enhanced photocatalytic activity of faceted nanoparticles. In this paper, we perform electronic structure calculations in the density functional theory approximation to study the OER on flat and stepped surfaces, such as encountered in nano-sized STO. We demonstrate that stepped surfaces reveal higher OER activity than flat surfaces, which is consistent with experimental data. We also observe partial breaking of OER scaling relation on stepped surfaces, albeit this does not necessarily cause higher catalytic activity. Finally, we propose recommendations for thorough implementation of zero-point energy calculations as the calculation method may impact the free-energy landscape of the OER. Demonstrating enhanced catalytic properties of a stepped strontium titanate surface toward oxygen evolution reaction. [Display omitted] • Stepped strontium titanate surfaces show increased OER catalytic activity. • The ridge of the step is the main contributor to the increased catalytic activity. • Different configurations of *O and *OOH adsorbates are possible. • The breaking of Δ G 2 + Δ G 3 scaling relation is observed. • The way of approximating the zero-point energy impacts conclusions in selected cases. [ABSTRACT FROM AUTHOR]

Design concept evaluation is a wide domain of research as the production process of new product development is mainly based on the evaluations of experts. As different types of uncertainties like vagueness, randomness, and diversity essentially exist in the evaluation information, the manipulation models that deal with just one type of uncertainty are not appropriate for ranking the design alternatives. The integration of multiple approaches into a single mathematical model to create an effective framework is more useful for uncertain information manipulation. This paper presents an innovative group decision-making approach to evaluate design concepts by integrating cloud rough numbers, analytic hierarchy process (AHP) and VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method to introduce a novel cloud rough AHP-VIKOR model. The concept of cloud rough numbers is utilized by fusing the merits of the cloud model theory and rough approximations in addressing randomness in experts' judgments and intrapersonal uncertainty for handling consensus inconsistency. Some new modified algebraic operations are introduced to remove the errors in already existing operations of cloud rough numbers. The cloud rough AHP technique is introduced to compute weights of design criteria by computing the cloud rough numbers of linguistic values and their reciprocals. Based on cloud rough values of positive and negative ideals, the individual regret, group utility values and evaluation indices are determined. Using the distance of evaluation indices from minimized cloud rough value, the design alternatives are ranked using different formulae. The significance of the proposed approach is illustrated with a real-world application in lithography tool manufacturing process. The out-performance and reliability of the proposed model is studied by a sensitivity analysis of different parameters in the method, and a comparison analysis with existing approaches. [ABSTRACT FROM AUTHOR]

The present paper focuses on the discretization and implementation of the Thick Level Set (TLS) approach for quasi-brittle failure when dealing with both local and non-local development of damage. The TLS damage model introduces a length scale and nonlocality in the Fracture Process Zone (FPZ) and it handles the continuous to discontinuous failure transition. The added nonlocality is limited to the FPZ and therefore the model is local away from the FPZ or before its emergence. It leads to concurrent development of local and nonlocal damage during simulations. This paper presents a space–time discretization that handles concurrent computations in a unified manner. It is based on an explicit time discretization written as a predictor–corrector scheme and a space discretization that uses specific approximation functions (modes) that embed nonlocality. It also uses an alternative implementation of the eXtended Finite Element Method (X-FEM) enrichment used in the TLS which is based on virtual nodes. [ABSTRACT FROM AUTHOR]

In Jung and Roh (2017), we investigated some properties of approximate solutions of the second-order inhomogeneous linear differential equations. In this paper as an application of above paper we will study the stability of the time independent Schrödinger equation with a potential box of finite walls. [ABSTRACT FROM AUTHOR]

A new weak Galerkin (WG) finite element method for solving the second-order elliptic problems on polygonal meshes by using polynomials of boundary continuity is introduced and analyzed. The WG method is utilizing weak functions and their weak derivatives which can be approximated by polynomials in different combination of polynomial spaces. Different combination gives rise to different weak Galerkin finite element methods, which makes WG methods highly flexible and efficient in practical computation. This paper explores the possibility of certain combination of polynomial spaces that minimize the degree of freedom in the numerical scheme, yet without losing the accuracy of the numerical approximation. Error estimates of optimal order are established for the corresponding WG approximations in both a discrete H 1 norm and the standard L 2 norm. In addition, the paper also presents some numerical experiments to demonstrate the power of the WG method. The numerical results show that the WG method achieves the optimal convergence order with a relatively low computational cost, which reveals a great promise of the flexibility and accuracy of the WG method. [ABSTRACT FROM AUTHOR]

The smooth and discontinuous oscillator with fractional derivative damping under combined harmonic and random excitations is investigated in this paper. The short memory principle is introduced so that the evolution process of the oscillator with fractional derivative damping can be described by the Markov chain. Then the stochastic generalized cell mapping method is used to obtain the steady-state probability density functions of the response. The stochastic response and bifurcation of the oscillator with fractional derivative damping are discussed in detail. We found that both the smoothness parameter, the noise intensity, the amplitude and frequency of the harmonic force can induce the occurrence of stochastic P-bifurcation in the system. Monte Carlo simulation verifies the effectiveness of the method we adopt in the paper. [ABSTRACT FROM AUTHOR]

Gradient averaging-type a posteriori error estimators applied to the finite element method enjoy great popularity in the engineering community. This is mainly because they are easy in their construction and computer implementation and usually provide constant-free and sharp error estimates on the expense of losing the bounding property. However, it proves difficult to transfer this error estimation procedure to Galerkin meshfree methods. One reason is that the meshfree gradient approximation is generally rather accurate per se and difficult to improve. Moreover, in many Galerkin meshfree methods the shape functions are no interpolants, as required in the original idea of constructing the recovered and thus smooth gradient field. In this paper, a novel error estimation procedure is presented that is based on the enhanced assumed strain (EAS) method and applied to the reproducing kernel particle method (RKPM) as a representative of Galerkin meshfree methods. The error estimator is naturally tailored to Galerkin meshfree methods if stabilized conforming nodal integration (SCNI) is employed, which provides two gradient fields: a globally smooth one (the compatible strain) and a cellwise constant one (the enhanced assumed strain). It is shown that the difference (the enhanced strain) can be used to derive an error estimator that follows the notion of gradient averaging-type error estimators and resolves its issues when applied to Galerkin meshfree methods. In addition, the enhanced-strain error estimator is even easier to implement and computationally less expensive than gradient averaging-type error estimators. Numerical examples of engineering interest illustrate the performance of the enhanced-strain error estimator presented in this paper. [ABSTRACT FROM AUTHOR]

The problem of similar code sequences search in executable binary files is explored in this paper. Within the scope of the previously proposed original search method outlined in this paper the impact on its efficiency of several ways of the program’s code initial description is investigated. The results of experimental researches of search efficiency for each of them are presented. The efficiency of the proposed method is also compared to known methods of similar code sequences search. [ABSTRACT FROM AUTHOR]

In this paper, the nonminimum phase problem of a flexible hypersonic vehicle is investigated. The main challenge of nonminimum phase is the prevention of dynamic inversion methods to nonlinear control design. To solve this problem, we make research on the relationship between nonminimum phase and backstepping control, finding that a stable nonlinear controller can be obtained by changing the control loop on the basis of backstepping control. By extending the control loop to cover the internal dynamics in it, the internal states are directly controlled by the inputs and simultaneously serve as virtual control for the external states, making it possible to guarantee output tracking as well as internal stability. Then, based on the extended control loop, a simplified control-oriented model is developed to enable the applicability of adaptive backstepping method. It simplifies the design process and releases some limitations caused by direct use of the no simplified control-oriented model. Next, under proper assumptions, asymptotic stability is proved for constant commands, while bounded stability is proved for varying commands. The proposed method is compared with approximate backstepping control and dynamic surface control and is shown to have superior tracking accuracy as well as robustness from the simulation results. This paper may also provide a beneficial guidance for control design of other complex systems. [ABSTRACT FROM AUTHOR]