Search

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 new two-dimensional network model is proposed as a micromechanics model to simulate paper’s failure process due to sequentially breakages of fibers and/or bonds. Paper is approximated as a network composed of fibers any two of which link to each other by their intersecting point, namely so-called bond. Fibers distribute along three particular directions, leading to network’s macro-level isotropy. In the framework of finite element method, nodes correspond to fiber-to-fiber bonds, while elements are fiber segments between every two neighboring nodes and described by Timoshenko beam theory. Element breaks when its equivalent internal tensile stress reaches the tensile strength of fiber. Strength of nodes, i.e. fiber-to-fiber bonds is assumed to be dependant on shearing interaction between fibers, considering the dominant interaction is shearing in a plane problem. Numerical examples show the model’s capacity of reflecting basic failure characteristic in paper. Influences of fiber length and the ratio of fiber strength to bond strength are analyzed in detail. [ABSTRACT FROM AUTHOR]

In the framework of a 1D cyclic competition model, the Rock-Paper-Scissors model, where three kinds of generic agents are allowed to mutate, to interact and to move in space, we study the formation of stochastic patterns, where all the agents do coexist. We modelled the problem using an individual-based setting and we used the system size van Kampen expansion to deal with the Master Equation. We have hence been able to characterise the spatio-temporal patterns using the power spectrum of the fluctuations. We proved that such patterns are robust against the intrinsic noise and they can be found for parameter values beyond the ones fixed by the deterministic approach (mean field approximation). We complement such analytical results with numerical simulations based on the Gillespie algorithm. [ABSTRACT FROM AUTHOR]

Abstract: We show that the main results in the recent paper [4] by Sadiq Basha (2012) are not real generalizations but particular cases of existing fixed point theorems in the literature. [Copyright &y& Elsevier]

Abstract: This paper proposes a multi-attribute comprehensive evaluation method of individual research output (IRO). It highlights the fact that a single index can never give more than a rough approximation to IRO, and the evaluation of IRO is a multi-attribute complex problem. Firstly, an evaluation index system is established by determining evaluation attributes and choosing the appropriate bibliometric indicators. To address the multiple authorship problem, this paper develops an improved number-of-papers-published indicator. Following this, TOPSIS method is used to conduct a comprehensive IRO evaluation. Then this paper uses a case study to test the feasibility of the methodology. Finally, this paper discusses the effectiveness of the proposed method. Compared with traditional single-indicator evaluation approaches, the proposed multi-attribute evaluation takes more aspects into consideration, therefore it is able to effectively overcome the one-sidedness of a single indicator. The proposed method also has significant advantages compared with other comprehensive IRO evaluation methods. [Copyright &y& Elsevier]

Abstract: We report on the fabrication and characterization of densified and transferred carbon nanotube forests for electronic interconnect application. A simple, low cost and quality method is developed for densifying vertically-aligned carbon nanotube (VA-CNTs) forests at room temperature. Commercially available paper is utilized in this work to serve as a solvent carrier. Highly densified CNT bundles are formed by the sorption of evaporative liquid from the paper into carbon nanotube forests. An average Young’s modulus increase from approximately 15.8 to 111.9MPa is extrapolated from the measured load–displacement curves in the compression tests of the as-densified VA-CNTs. Subsequent low temperature transfer method is used to transfer the VA-CNT bundles onto the target substrate. Four-probe measurement of the transferred VA-CNTs shows resistance of 3.70±0.04Ω of each CNT bundle. [Copyright &y& Elsevier]

Abstract: In the present paper we studied the Voronovskaya type theorem for modified Gamma operators presented by A. İzgi in the paper “Voronovskaya type asymptotic approximation by modified Gamma operators” [Applied Mathematics and Computation 217 (2011) 8061–8067]. We show that this theorem is not true. We present a correct form of this theorem and its proof. Furthermore, we obtain an error estimate for modified Gamma operators. [Copyright &y& Elsevier]

Abstract: presented a bias adjustment to the jackknife variance estimator of in the presence of non-response. In their paper, they obtained a second-order approximation of the bias of the Rao-Sitter variance estimator and then proposed a bias-adjusted estimator based on this approximation. To compare their proposed variance estimator to various other variance estimators, they performed a simulation study and showed that their variance estimator is superior to the Rao-Sitter variance estimator. In fact they showed that the Rao-Sitter variance estimator suffers from severe underestimation. These results contradict those in the literature, which indicate that the Rao-Sitter variance estimator suffers from a positive bias if the sampling fractions are not negligible; see , and . Because of this contradiction, we felt that a further investigation was warranted. In this paper, we attempt to recreate the results of and, in fact, show that their second order approximation to the bias of the Rao-Sitter variance estimator is incorrect and that their simulation results are also questionable. [Copyright &y& Elsevier]

Abstract: The paper presents the results of experimental investigations of paper–oil insulation samples from the point of view of the assessment of the influence of temperature on the parameters of the approximation method of the time characteristics analysis of depolarization current. Three types of equations: Debye’s function with a single relaxation time, Curie–von Schweidler’s function with triple Debye’s function (taking into account short, average and long relaxation times of paper–oil insulation), and Jonscher’s function with Debye’s function with a single relaxation time were selected as approximation functions, as recommended by literature. The investigated insulation samples were diversified with respect to the degree of dampness and aging. Summing up, the paper focuses on verification of the determined parameters of approximation equations in relation to the influence of insulation temperature and presents recommendations for their application in diagnostics carried out by the PDC (Polarization and Depolarization Current) Method. [Copyright &y& Elsevier]

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]

Abstract: A questionable approximation in the calculation of the period of revolution of a pair of extended bodies, appearing in the paper mentioned in the title, is pointed out. An exact method to perform this task is suggested. [Copyright &y& Elsevier]

This paper outlines Binomial and Poisson distributions which are both used to measure the occurrence of a number of random events within a certain period. [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 this paper, we present the virtual element approximation for the modified transmission eigenvalue problem. The eigenvalue problem arises in inverse scattering theory for artificial inhomogeneous media characterized as a metamaterial. By the shifting argument and spectral approximation theory of compact operators, we prove the correct spectral approximation of the virtual element scheme, and derive the optimal order error estimates for the eigenfunctions and the double order for the eigenvalues. Finally, we implement numerical experiments to illustrate behaviors of the standard and serendipity virtual element schemes, and the finite element scheme. [ABSTRACT FROM AUTHOR]

In recent years, deep neural networks have been employed to approximate nonlinear continuous functionals F defined on L p ( [ − 1 , 1 ] s) for 1 ≤ p ≤ ∞. However, the existing theoretical analysis in the literature either is unsatisfactory due to the poor approximation results, or does not apply to the rectified linear unit (ReLU) activation function. This paper aims to investigate the approximation power of functional deep ReLU networks in two settings: F is continuous with restrictions on the modulus of continuity, and F has higher order Fréchet derivatives. A novel functional network structure is proposed to extract features of higher order smoothness harbored by the target functional F. Quantitative rates of approximation in terms of the depth, width and total number of weights of neural networks are derived for both settings. We give logarithmic rates when measuring the approximation error on the unit ball of a Hölder space. In addition, we establish nearly polynomial rates (i.e., rates of the form exp − a (log M) b with a > 0 , 0 < b < 1) when measuring the approximation error on a space of analytic functions. [ABSTRACT FROM AUTHOR]

• Transmittance predictions based on pore scattering in transparent ceramics. • Mie theory and approximations (Rayleigh, Fraunhofer, van de Hulst, Rayleigh-Gans). • Different transparent ceramics (magnesium aluminum spinel, magnesia, YAG, yttria). • The Rayleigh-Gans approximation provides best predictions for small pore sizes. • Van de Hulst's approximation is useful for all pore sizes, including large pores. In this paper transmittance predictions based on residual pore scattering in transparent ceramics with cubic crystallites via Mie theory and its approximations (Rayleigh, Fraunhofer, van de Hulst and Rayleigh-Gans, including the small- and large-size limits) are recalled and systematically compared. Due to the high phase contrast, the difference between different types of ceramics is of secondary importance, so that the essential conclusions are of general validity for all types of transparent ceramics. It is shown that the Rayleigh-Gans approximation and its large-size limit provide surprisingly good transmittance predictions, although it has not often been used in the ceramic literature. The main conclusion of this paper is that, of all the approximations presented here and used in ceramic science so far, the van de Hulst approximation is the one that most closely approaches the exact Mie results, although it has been largely ignored in the literature on transparent ceramics so far. [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]

Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy and efficiency, the approaches available in the literature still lack a rigorous justification on their mathematical foundations. Motivated by this fact, in this paper we derive rigorous error bounds for the approximation of nonlinear operators by means of CNN models. More precisely, we address the case in which an operator maps a finite dimensional input μ ∈ R p onto a functional output u μ : [ 0 , 1 ] d → R , and a neural network model is used to approximate a discretized version of the input-to-output map. The resulting error estimates provide a clear interpretation of the hyperparameters defining the neural network architecture. All the proofs are constructive, and they ultimately reveal a deep connection between CNNs and the Fourier transform. Finally, we complement the derived error bounds by numerical experiments that illustrate their application. [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]

The evolution of ice conditions and wave patterns in polar water areas is complex, and studying the hydrodynamic response between sea ice and waves is crucial. In this study, the hydrodynamic response of sea ice in infinitely deep water is investigated by a sea ice scattering model based on linear potential flow and thin plate approximation theory. Building upon regular wave and sea ice scattering models, an irregular wave model was established and analyzed. This paper discusses the factors that influence sea ice resonance in a three-dimensional scattering model. It categorizes resonance phenomena into strong and weak based on mass and elasticity coefficients and provides a predictive function for identifying strong resonance points. Additionally, the study examines sea ice attenuation from an energy perspective. Research on sea ice in irregular waves indicates a negative correlation between the directional spreading parameter and wave attenuation. An increase in directional spreading parameter weakens the inhibitory effect on the high-frequency part of the waves. Increasing sea ice thickness enhances wave attenuation, exerting an inhibitory effect on waves in the high-frequency region. • A resonance study on three-dimensional elastic sea ice scattering model. • A new energy analysis criterion is proposed for sea ice wave attenuation. • A study on wave attenuation of sea ice in irregular waves. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of interpolation operators by using Lagrange polynomials of degree r , which can be regarded as feedforward neural networks with four layers. The approximation rate of the new operators can be estimated by the (r + 1) -th modulus of smoothness of the objective functions. By adding some smooth assumptions on the activation function, we establish two important inequalities of the derivatives of the operators. With these two inequalities, by using the K -functional and Berens–Lorentz lemma in approximation theory, we establish the converse theorem of approximation. We also give the Voronovskaja-type asymptotic estimation of the operators for smooth functions. Furthermore, we extend our operators to the multivariate case, and investigate their approximation properties for multivariate functions. Finally, some numerical examples are given to demonstrate the validity of the theoretical results obtained and the superiority of the operators. [ABSTRACT FROM AUTHOR]

Despite the successful use of Gaussian-binary restricted Boltzmann machines (GB-RBMs) and Gaussian-binary deep belief networks (GB-DBNs), little is known about their theoretical approximation capabilities to represent distributions of continuous random variables. In this paper, we address the expressive properties of GB-RBMs and GB-DBNs, contributing theoretical insights to the optimal number of hidden variables. We first treat the GB-RBM's unnormalized log-likelihood as a sum of a special two-layer feedforward neural network and a negative quadratic term. Then, a series of simulation results are established, which can be used to relate GB-RBMs to general two-layer feedforward neural networks whose expressive properties are much better understood. On this basis, we show that a two-layer ReLU network with all weights in the second layer being 1, along with a negative quadratic term, can approximate all continuous functions. In addition, we provide qualified lower bounds for the number of hidden variables of GB-RBMs required to approximate distributions whose log-likelihood are given by some classes of smooth functions. Moreover, we further study the universal approximation of GB-DBNs with two hidden layers by providing a sufficient number of hidden variables O (ɛ − 2) that are guaranteed to approximate any given strictly positive continuous distribution within a given error ɛ. Finally, numerical experiments are carried out to verify some of the proposed theoretical results. • The properties of GB-RBMs/GB-DBNs to approximate continuous distributions are studied. • Simulation results between GB-RBMs and 2-layer feedforward neural networks are built. • The lower bounds of the size of GB-RBMs to compute smooth functions are provided. • The universal approximation of GB-DBNs is studied on the number of hidden variables. [ABSTRACT FROM AUTHOR]

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]

Abstract In this paper, we extend a number of important results of the classical Chebyshev approximation theory to the case of simultaneous approximation of two or more functions. The need for this extension is application driven, since such kind of problems appears in the area of curve (signal) clustering. In this paper, we propose a new efficient algorithm for signal clustering and develop a procedure that allows one to reuse the results obtained at the previous iteration without recomputing the cluster centres from scratch. This approach is based on the extension of the classical de la Vallée-Poussin procedure originally developed for polynomial approximation. We also develop necessary and sufficient optimality conditions for two curve Chebyshev approximation, which is our core tool for curve clustering. These results are based on application of nonsmooth convex analysis. [ABSTRACT FROM AUTHOR]

Highlights • This paper deals with the decimations of the intrinsic mode functions. • This paper proposes an optimal adaptive nonuniform filter bank design approach. • The nonuniform filter bank design problem is formulated as a semi‐infinite programming problem. • The semi‐infinite programming problem is approximated by a semi‐definite programming problem. • Our proposed system could achieve a very small reconstruction error at a very small oversampling ratio. Abstract A signal can be represented as the sum of the intrinsic mode functions via performing the empirical mode decomposition. For the discrete time signals, the lengths of the intrinsic mode functions are equal to the lengths of the input signals. As there is usually more than one intrinsic mode function, the total numbers of discrete points of all the intrinsic mode functions are usually more than the lengths of the input signals. In other words, the empirical mode decomposition is an oversampled representation. For some applications such as the compression application, the oversampled representation is not preferred. Therefore, this paper proposes an optimal adaptive nonuniform filter bank design approach for performing the decimations on the intrinsic mode functions. In particular, the passbands of the intrinsic mode functions are estimated based on an adaptive gradient algorithm. Then, the intrinsic mode functions are nonuniformly downsampled and upsampled with the sampling integers derived based on their estimated passbands. Next, a bank of filters is employed to reconstruct the original signal. Here, the passbands of the filters are also derived based on those of the intrinsic mode functions. After that, the nonuniform filter bank design problem is formulated as a semi-infinite programming problem such that the total ripple energies of all the filters are minimized subject to the specifications on the absolute maximum values of both the real part and the imaginary part of the reconstruction error. The semi-infinite programming problem is approximated by a semi-definite programming problem. Computer numerical simulation results show that our proposed system could achieve a very small reconstruction error at a very small oversampling ratio. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we show that the univariate interpolatory subdivision schemes with the optimal approximation order, which are the D-D interpolatory ones, can be obtained from the cubic B-spline scheme. Such schemes are derived in this paper by suitably using the push-back operation, a connection between the approximating and interpolatory subdivision. Then, the process to obtain the D-D schemes is generalized to the bivariate case and bivariate interpolatory schemes with the optimal approximation order are generated based on the triangular meshes. Compared with the existing bivariate interpolatory schemes with the optimal approximation order, the newly constructed ones own some advantages, such as a better performance in terms of the number of nonzero coefficients in the mask. Several examples are given and explicitly computed. [ABSTRACT FROM AUTHOR]

Abstract This paper presents an approach to the efficient calculation of all or just one important part of the eigenvalues of the parameter dependent quadratic eigenvalue problem (λ 2 (v) M + λ (v) D (v) + K) x (v) = 0 , where M, K are positive definite Hermitian n × n matrices and D (v) is an n × n Hermitian semidefinite matrix which depends on a damping parameter vector v = [ v 1 ... v k ] ∈ R + k. With the new approach one can efficiently (and accurately enough) calculate all (or just part of the) eigenvalues even for the case when the parameters v i , which in this paper represent damping viscosities, are of the modest magnitude. Moreover, we derive two types of approximations with corresponding error bounds. The quality of error bounds as well as the performance of the achieved eigenvalue tracking are illustrated in several numerical experiments. [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 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]

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]

Highlights • For efficiently solving the radiative transfer equation with finite element methods, we develop a novel algorithm of angular mesh adaptation based on a posteriori calculation. • Our mesh adaptation algorithm leads to ad hoc angular discretizations which are optimized in such a way that they suit the particular physics under consideration. • The algorithm is drafted in such a way that it could be easily implemented using per-existing open-source mathematical libraries. • Finally, by means of numerical testing we prove that ad hoc angular discretizations with lesser number of directions out performers an ordinary uniform discretization with high number of direction. Consequently, we are able to reduce the computational cost of a radiative transfer simulation, while maintaining the accuracy of the solution. • novelties: We approximate the angular functional space using vertex-based piece-wise constant functions, while continuous piece-wise linear functions are chosen for the spatial functional space. • We developed an angular adaptivity algorithm based on an a posteriori error estimation using vertex-based P0 Lagrange functions built on a triangulation of a unit sphere without any other predefined rule. • The angular ad hoc discretization is performed on physical problems that include specular reflection on boundaries. Abstract Solving the radiative transfer equation (RTE) with the finite element method requires both angular and spatial discretizations. We develop a novel algorithm of angular mesh discretization based on a posteriori calculations. The obtained angular discretizations are optimized in such a way that they suit the particular physics under consideration. Such ad hoc angular discretizations are implemented to increase the finite element solution efficiency. Using comparative numerical tests based on the solution accuracy, the solutions provided by the obtained ad hoc discretizations are proven to be better than the ones provided by the standard uniform angular discretizations. The algorithm is drafted in such a way that it could be easily implemented using pre-existing open-source mathematical libraries. This paper is an extended version of a paper presented at the CTRPM-VI conference [1]. As an extension to the two-dimensional version presented at the conference, a three-dimensional adaptive ad hoc angular discretization of the RTE is addressed here. [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]

Highlights • The heat equation with nonlocal initial condition is considered. • Several finite difference schemes are constructed and analyzed. • The stability of the schemes is the main objective of investigation. • Time step size bound obtained in previous paper is revised. • Numerical experiments with linear and nonlinear problems confirm the theoretical results. Abstract In this paper, the two-level finite difference schemes for the one-dimensional heat equation with a nonlocal initial condition are analyzed. As the main result, we obtain conditions for the numerical stability of the schemes. In addition, we revise the stability conditions obtained in [21] for the Crank–Nicolson scheme. We present several numerical examples that confirm the theoretical results within linear, as well as nonlinear problems. In some particular cases, it is shown that for small regions of the time step size values, the explicit FTCS scheme is stable while certain implicit methods, such as Crank–Nicolson scheme, are not. [ABSTRACT FROM AUTHOR]

Highlights • To extract event information by exploiting historical data such as cable asset inventory. • To estimate the failure rate of every individual cables using PHM. • To demonstrate that, although many previous works make different approximations which are designed for non-repairable systems, the results of applying these approaches are misleading for repairable power cables. Abstract In this paper Weibull parametric proportional hazard model (PHM) is used to estimate the failure rate of every individual cable based on its age and a set of explanatory factors. The required information for the proposed method is obtained by exploiting available historical cable inventory and failure data. This data-driven method does not require any additional measurements on the cables, and allows the cables to be ranked for maintenance prioritization and repair actions. Furthermore, the results of reliability analysis of power cables are compared when the cables are considered as repairable or non-repairable components. The paper demonstrates that the methods which estimate the time-to-the-first failure (for non-repairable components) lead to incorrect conclusions about reliability of repairable power cables. The proposed method is used to evaluate the failure rate of each individual Paper Insulated Lead Cover (PILC) underground cables in a distribution grid in the south of Sweden. [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]

Highlights • The paper addresses the problem of spatial variability in the degradation process. • A spatio-temporal random field model is proposed to address this problem with the details of its construction and simulation. • Inference procedure is developed for such spatio-temporal model • Estimation of quantities of interest used in the reliability analysis and maintenance. • The model is applied to numerical examples in one and two dimensional case. • The results show that the uncertainties are reduced, the inference procedure is improved. Abstract The objective of this work is to propose a spatio-temporal random field for assessing the effect of spatial variability on the degradation process in structural reliability assessment. Our model extends the classical Gamma process which is usually developed for degradation temporal variability concerns to integrate spatial variability and heterogeneity issues. A log-normal distributed spatial random scale is then introduced in the Gamma process. Mathematical models for a structure degradation in space and time and estimation procedures are developed in this paper. Approximations and simulations are given to evaluate the failure time distribution and to characterize the residual lifetime after inspection. Simulation results are performed using pseudo-random data based on Monte-Carlo simulations to fit the model and the inference of their parameters. The two proposed estimation method – Method of Moments and Pseudo Maximum Likelihood – are numerically compared according to statistical measures. The accuracy of the methods are also discussed by numerical examples given the approximations of quantities of interests. [ABSTRACT FROM AUTHOR]