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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]

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 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]

Fuzzy coverings are a natural extension of the coverings by replacing crisp sets with fuzzy sets. Recently, an excellent introduction to the definition of a fuzzy β -covering is due to Ma and two fuzzy covering-based rough set models are presented. In this paper, by introducing some new definitions of fuzzy β -covering approximation spaces, the properties of fuzzy β -covering approximation spaces and Ma's fuzzy covering-based rough set models are studied. Furthermore, three new types of fuzzy covering-based rough set models as generalizations of Ma's models are first proposed in this paper. First, some properties of fuzzy β -covering and its fuzzy β -neighborhood family are proposed. We present a necessary and sufficient condition for fuzzy β -neighborhood family induced by a fuzzy β -covering to be equal to the fuzzy β -covering itself. Then we study the characterizations of Ma's fuzzy covering-based rough set models and give a necessary and sufficient condition for two fuzzy β -coverings to generate the same fuzzy covering lower approximation or the same fuzzy covering upper approximation. Finally, this paper proposes three new types of fuzzy covering-based rough set models by introducing a new notion of a fuzzy complementary β -neighborhood. [ABSTRACT FROM AUTHOR]

This paper presents an effective method to automatically construct trivariate tensor-product spline models of complicated geometry and arbitrary topology. Our method takes as input a solid model defined by its triangulated boundary surface. Using cuboid decomposition, an initial polycube approximating the input boundary mesh is built. This polycube serves as the parametric domain of the tensor-product spline representation required for isogeometric analysis. The polycube’s nodes and arcs decompose the input model’s boundary into quadrilateral patches, and these patches form hexahedral domains. Using aligned global parameterization, the nodes are re-positioned and the arcs are re-routed across the surface in a way to achieve low overall patch distortion, and alignment to principal curvature directions and sharp features. The optimization process is based on one of the main contributions of this paper: a novel way to design cross fields with topological (i.e., imposed singularities) and geometrical (i.e., imposed directions) constraints by solving only sparse linear systems. Based on the optimized polycube and parameterization, compatible B-spline boundary surfaces are reconstructed. Finally, the interior volumetric parameterization is computed using Coon’s interpolation. In the context of parametric studies based on geometrical parameters, this method can be used to compute the morphing required for reduced order modeling. For different parametric instances with the same topology but different geometries, this method allows to have the same representation: i.e., meshes (or parameterizations) with the same topology. The efficiency and the robustness of the proposed approach are illustrated by several examples. [ABSTRACT FROM AUTHOR]

In this paper, we present a new iterative method based on the hybrid viscosity approximation method and the hybrid steepest-descent method for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of common fixed points of a finite family of nonexpansive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative method has strong convergence under some mild conditions imposed on algorithm parameters. The results presented in this paper improve and extend the corresponding results reported by some authors recently. [ABSTRACT FROM AUTHOR]

This paper aims to develop a data-driven approximate causal inference model using the newly-proposed evidential reasoning (ER) rule. The ER rule constitutes a generic conjunctive probabilistic reasoning process and generalises Dempster’s rule and Bayesian inference. The belief rule based (BRB) methodology was developed to model complicated nonlinear causal relationships between antecedent attributes and consequents on the basis of the ER algorithm and traditional IF-THEN rule-based systems, and in essence it keeps methodological consistency with Bayesian Network (BN). In this paper, we firstly introduce the ER rule and then analyse its inference patterns with respect to the bounded sum of individual support and the orthogonal sum of collective support from multiple pieces of independent evidence. Furthermore, we propose an approximate causal inference model with the kernel mechanism of data-based approximate causal modelling and optimal learning. The exploratory approximate causal inference model inherits the main strengths of BN, BRB and relevant techniques, and can potentially extend the boundaries of applying approximate causal inference to complex decision and risk analysis, system identification, fault diagnosis, etc. A numerical study on the practical pipeline leak detection problem demonstrates the applicability and capability of the proposed data-driven approximate causal inference model. [ABSTRACT FROM AUTHOR]

This paper develops an analytical method to measure the performance of a multi-product unreliable production line with finite buffers between workstations. The performance measure used in this paper is Total Cycle Time. The proposed method is an approximation that generalizes the processing times to ease the variation of product types in a multi-product system. A decomposition method is then employed to approximate the production rate of a multi-product production line. The decomposition method considers generally distributed processing times as well as random failure and repair. A GI/G/1/N queuing model is also applied to obtain parameters such as blocking and starvation probabilities that are needed for the approximation procedure. Several numerical experiments under different scenarios are performed and results are validated by simulation models in order to assess the accuracy and strength of the proposed method. Consequent analysis and discussion of the results are also presented. [ABSTRACT FROM AUTHOR]

This paper presents a model to estimate the lifetime of degrading infrastructure systems subject to shocks based on the family of Phase-type (PH) distributions. In particular, the paper focuses on damage accumulation when both the inter-arrival time of shocks and their sizes are random. PH distributions are applied to approximate any probability distribution with positive support; furthermore, their matrix-geometric properties allow to handle problems involving the calculation of convolutions (e.g., sum of shock sizes). The proposed PH shock model relaxes the identically distributed assumption for the inter-arrival times and/or shock sizes. Besides, the model provides easy-to-evaluate expressions for important reliability quantities such as the density function and the moments of the lifetime, and the mean and moments of the cumulative shock deterioration at any time. In order to fit data or theoretical distributions to PH, the paper compares and discusses two PH fitting algorithms: the Moment Matching (MM) and the Expectation Maximization (EM) methods in terms of accuracy, computational efficiency and the available information of the random variables to fit. Then, it provides an algorithm for the reliability estimation of infrastructures along with a study of its accuracy and efficiency; the results show acceptable execution times for most practical applications. Finally, the use of PH to handle degradation is illustrated with several examples of engineering interest; i.e., deterioration due to crack growth, corrosion, aftershocks sequences, among others. [ABSTRACT FROM AUTHOR]

Motivated by a recent paper by the RBC–UKQCD Collaboration, which observes large violations of the naïve factorization hypothesis in K → π π decays, we study in this paper the accuracy of the Vacuum Insertion Approximation (VIA) for the matrix elements of the complete basis of four-fermion Δ F = 2 operators. We perform a comparison between the matrix elements in QCD, evaluated on the lattice, and the VIA predictions. We also investigate the dependence on the external meson masses by computing matrix elements for K , D s , B s and static mesons. In commonly used renormalization schemes, we find large violations of the VIA in particular for one of the two relevant Wick contractions in the kaon sector. These deviations, however, decrease significantly as the meson mass increases and the VIA predictions turn out to be rather well verified for B -meson matrix elements and, even better, in the infinite mass limit. [ABSTRACT FROM AUTHOR]

Abstract In this paper we study the approximation ratio of the solutions achieved after an ϵ -approximate one-round walk in non-atomic congestion games. Prior to this work, the solution concept of one-round walks had been studied for atomic congestion games with linear latency functions only (Christodoulou et al. [1] , Bilò et al. [2]). We give an explicit formula to determine the approximation ratio for non-atomic congestion games having general latency functions. In particular, we focus on polynomial latency functions, and, we prove that the approximation ratio is exactly ((1 + ϵ) (p + 1)) p + 1 for every polynomial of degree p. Then, we show that, by resorting to static (resp. dynamic) resource taxation, the approximation ratio can be lowered to (1 + ϵ) p + 1 (p + 1) p (resp. (1 + ϵ) p + 1 (p + 1) !). [ABSTRACT FROM AUTHOR]

Abstract In this paper, we address the Approximate Agreement problem in the Mobile Byzantine Fault model. Our contribution is three-fold. First, we refine the problem specification to adapt it to the Mobile Byzantine Fault environment. Then, we propose the first mapping from the existing variants of Mobile Byzantine models to the Mixed-mode Fault model. This mapping further help us to prove the correctness of MSR (Mean-Subsequence-Reduce) algorithms class in our context and it is of independent interest. We also prove lower bounds for solving Approximate Agreement under all existing Mobile Byzantine fault models. [ABSTRACT FROM AUTHOR]

Abstract This article deals with a backward diffusion problem for an inhomogeneous backward diffusion equation with fractional Laplacian in R : u t (x , t) + − Δ α u (x , t) = f (x , t) , (x , t) ∈ R × [ 0 , T ] , u (x , T) = g (x) , x ∈ R , lim x → ± ∞ u (x , t) = 0. This problem is an ill-posed problem due to the instability in solution. The goal of this paper is not only to provide a simple but effective regularization scheme to obtain the Hölder convergence rate, but also to give an approximation of solution of the equation with fractional diffusion to the one of the equation with Laplacian in both L 2 (R) and L p (R) setting. This result holds, in particular, when f (x , t) is spatially compactly supported, in which the difficulties due to the fractional Laplacian have been successfully overcome thanks to an additional condition on Fourier transform of f. We further study the convergence of solution of inhomogeneous problem to that of the homogeneous problem. Finally, numerical simulations, with finite difference schemes, based on Discrete Fourier Transform (DFT) algorithm are also presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract Dynamic traffic assignment models rely on a network performance module known as dynamic network loading (DNL), which expresses flow propagation, flow conservation, and travel delay at a network level. The DNL defines the so-called network delay operator , which maps a set of path departure rates to a set of path travel times (or costs). It is widely known that the delay operator is not available in closed form, and has undesirable properties that severely complicate DTA analysis and computation, such as discontinuity, non-differentiability, non-monotonicity, and computational inefficiency. This paper proposes a fresh take on this important and difficult issue, by providing a class of surrogate DNL models based on a statistical learning method known as Kriging. We present a metamodeling framework that systematically approximates DNL models and is flexible in the sense of allowing the modeler to make trade-offs among model granularity, complexity, and accuracy. It is shown that such surrogate DNL models yield highly accurate approximations (with errors below 8%) and superior computational efficiency (9 to 455 times faster than conventional DNL procedures such as those based on the link transmission model). Moreover, these approximate DNL models admit closed-form and analytical delay operators, which are Lipschitz continuous and infinitely differentiable, with closed-form Jacobians. We provide in-depth discussions on the implications of these properties to DTA research and model applications. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Mathematical model of a bioreactor with biofilm and axial dispersion of the liquid is presented. • Algorithm for the determination of steady-states was formulated. • Optimal Peclet number is influenced by biofilm detachment rate. • Peclet numbers which justify plug-flow and perfect-mixing approximation were obtained. Abstract The paper presents the method of modelling and numerical simulation of bioreactors with biofilm and axial dispersion of the liquid. Such bioreactors belong to systems with distributed state variables. The mathematical model was compared with a model assuming perfect mixing and a model assuming piston-flow of the liquid. According to calculations performed, the piston flow of the liquid can be assumed for Peclet numbers above 40. In turn, Peclet numbers below 0.5 justify perfect-mixing approximation. It was shown that there may exist an optimal value of Peclet number for which a maximum degree of conversion of the limiting substrate at the bioreactor outlet is obtained. The existence of the optimal Peclet number depends on the operating conditions of the bioreactor. [ABSTRACT FROM AUTHOR]

Variable selection methods have been widely used for system identification. However, there is still a major challenge in producing parsimonious models with optimal model structures as popular variable selection methods often produce suboptimal model with redundant model terms. In the paper, stability orthogonal regression (SOR) is proposed to build a more compact model with fewer or no redundant model terms. The main idea of SOR is that multiple intermediate models are produced by orthogonal forward regression (OFR) using sub-sampling technique and then the final model is a combination of these intermediate model terms but does not include infrequently selected terms. The effectiveness of the proposed methods is analyzed in theory and also demonstrated using two numerical examples in comparison with some popular algorithms. [ABSTRACT FROM AUTHOR]

In this paper, the H 2 -optimal approximation of a multi-input multi-output transfer function by a finite dimensional system including input/output delays, is addressed. This problem is of particular interest when the full order model represents a transport phenomenon. The contribution is twofold : firstly, based on the pole/residue decomposition, an H 2 -inner product formula in the presence of input/output delays is derived. Secondly, the underlying H 2 optimality conditions of the approximation problem are obtained as an extension of the tangential interpolatory conditions. It is also demonstrated that for fixed delay values, this problem can be recast as a rational function approximation one. An iterative algorithm is sketched out and numerical results assess the theoretical contributions. [ABSTRACT FROM AUTHOR]

In this paper analytical properties of solutions of a novel human papillomavirus (HPV) infected cells model is investigated. We show existence, uniqueness and stability of solutions by using standard techniques based on the energy method and the method of upper and lower solutions. For the numerical counterpart, we develop and implement one efficient numerical algorithm scheme which satisfies nonnegative conditions and dynamical consistency. Efficiency of this method is shown by its longtime approximations, which are of paramount importance for a slow process like the evolution of HPV infected cells. [ABSTRACT FROM AUTHOR]

In this paper, we define analysis-suitable++ (AS++) T-splines which include analysis-suitable (AS) T-splines as a special case and maintain all the good mathematical properties as AS T-splines. We prove that AS++ T-splines are always linear independent regardless of the knot values and show that the classical construction of the dual basis for tensor-product B-splines and AS T-splines can be generalized to AS++ T-spline spaces. We also discuss how all of these issues pave the way to a mathematical theory for AS++ T-splines. [ABSTRACT FROM AUTHOR]

Confined concrete has superior anti-penetration performance over unconfined concrete. A finite dynamic spherical cavity-expansion approximation model with radially elastic confinement is proposed to analyze the confinement on concrete targets and predict the depth of penetration (DOP), taking steel-tube-confined concrete (STCC) targets normally penetrated by rigid projectiles as an example. Firstly, the validity of a nonlinear failure criterion to describe strength feature of concrete in the comminuted region is demonstrated by triaxial compressible tested data and the reference range of dimensionless parameter m in the modified Griffith criterion is recommended. Secondly, the relationship between the stresses in concrete and cavity-expansion velocity is developed. Furthermore, the confinement effects on response modes of confined concrete, radial stress at cavity wall and stresses distribution in concrete are analyzed. Lastly, an engineering model is also established to predict the DOP of STCC targets normally penetrated by rigid projectiles. The results show that the radial stress at cavity wall is not a constant during the cavity-expansion process in finite concrete with radially elastic confinement, which is different from the steady spherical cavity-expansion of infinite material in which the radial stress at cavity wall is a constant with constant cavity-expansion velocity. The possible response phases of confined concrete targets normally penetrated by rigid projectiles include “elastic-cracked-comminuted”, “cracked-comminuted” and “full-comminuted”, depending on the relationship among cavity-expansion velocity, radial confining stiffness and radius ratio of cavity to target. The DOP data from the engineering model established in this paper agree well with those of experiments in the published references. [ABSTRACT FROM AUTHOR]

Recently a WENO scheme, with smoothness indicators constructed based on L 1 measure is introduced by Ha et al. (2013) and the improved version of this scheme is presented by Kim et al. (2016), referred to as WENO-NS and WENO-P schemes respectively. These schemes perform better than the existing many fifth-order WENO schemes for the problems which contain discontinuities and attain fifth-order accuracy at the critical points where the first derivative vanishes but not at the points where the second derivatives are zero. This paper deals with modification of the above said methods to obtain a new fifth-order weighted essentially non-oscillatory (WENO) scheme. A new global-smoothness indicator is proposed which shows an improved behavior over the solutions of WENO-NS and WENO-P schemes and the proposed scheme attains an optimal order of approximation, even at the critical points where the first and second derivatives vanish but not the third derivative. Examples are taken in the numeric section to check the robustness and accuracy of the proposed scheme for one and two-dimensional system of Euler equations. [ABSTRACT FROM AUTHOR]

In this paper, we present a new wavelet multigrid method for the numerical solution of elliptic type differential equations based on Daubechies (db4) high pass and low pass filter coefficients with modified intergrid operators. The proposed method is the robust technique for faster convergence with less computational cost which is justified through the error analysis and condition number of a system in comparison with integrated-RBF technique based on Galerkin formulation (Mai-Duy and Tran-Cong, 2009) and finite difference method. Some of the illustrative problems are presented to demonstrate the attractiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

The paper presents the numerical analysis of interaction of the vibrating simplified human vocal folds model with the incompressible viscous airflow in a channel modeling simplified subglottal and supraglottal spaces. The flow in the considered 2D computational fluid domain is governed by the Navier–Stokes equations written in the Arbitrary Lagrangian–Eulerian form. The stabilized finite element method is applied for numerical approximation and the choice of boundary conditions and their implementation is discussed. For the considered model problem the prescribed inlet velocity and prescribed pressure difference formulations were numerically analyzed. The prescribed inlet velocity formulation was successful in predicting of the flutter velocity value, whereas the prescribed pressure difference gave nonphysical results. Finally a modified inlet boundary condition motivated by the penalization approach is suggested. It is shown that this approach gives possibilities to optimize the inlet boundary condition related to a physical reality by changing smoothly the penalty parameter in the interval between the two extremes and to treat the complete closures of the channel. [ABSTRACT FROM AUTHOR]

It is well understood that during the pharmaceutical aqueous film coating process the amount of liquid water that interacts with the porous tablet core can affect the quality of the final product. Therefore, understanding and simulating the mechanisms of water droplet spreading, absorption and evaporation is crucial for controlling the process and optimising the shelf-life of the tablets. The purpose of the work presented in this paper is to define and describe the spreading, absorption and evaporation phenomena after droplet impingement on a tablet. We divided the droplet behaviour into three phases of different dynamics and duration: the kinematic, capillary and evaporation phases. To model the kinematic phase, we combined and modified 1-D spreading models from the literature which solve the kinetic energy balance equation for the first milliseconds of spreading. For the capillary phase, we simplified and solved the continuity and Navier-Stokes equations using the lubrication approximation theory. Finally, for the evaporation phase, we adopted a modelling approach for the second drying stage of slurry droplets inside a spray dryer. During this stage, one can no longer describe the droplet as a liquid system containing solids, having to regard it as a wet particle with a dry crust and a wet core. In our work, we represented in a novel way the crust as the dry surface of the tablet and the wet core as the wetted area inside the porous matrix. We implemented the mathematical model presented in this work in gPROMS, employing the Modelbuilder platform. Our numerical results (droplet height and spreading, wetting, evaporation front profiles) are in good agreement with recent experimental data that we found in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the hedging problem based on the CVaR in incomplete markets. As the superhedging is quite expensive in terms of initial capital, we construct a self-financing strategy that minimizes the CVaR of hedging risk under a budget constraint on the initial capital. In incomplete markets, no explicit solution can be provided. To approximate the problem, we apply the Neyman–Pearson lemma approach with a specific equivalent martingale measure. Afterwards, we explicit the solution for call options hedging under the exponential-Lévy class of price models. This approach leads to an efficient and easy to implement method using the fast Fourier transform. We illustrate numerical results for the Merton model. [ABSTRACT FROM AUTHOR]

The paper develops mathematical models for the analysis of the mutual interference of closely positioned ground electrodes in order to assess the safety risks that might appear in various circumstances often characteristic for urban areas. The potentially hazardous situation that might arise in open pit mines at the equipment grounded by connection with the common ground electrode is also investigated. In the scope of the analysis of possible dangerous circumstances the maximum touch – and step – voltages that appear at the sites protected by the grounding grids are calculated for various distances between the grids and in case of uniform and nonuniform two – layer soil. Approximate expressions for assessing some interference effects are also provided and successfully checked for various cases. Based upon the results of the conducted series of calculations, the safety risks are determined for all investigated cases. It was shown that the highest safety risks can appear in the case when the neighboring grids are unintentionally connected as well as in the case when the neighboring grid is connected with some grounded objects, which is characteristic for urban areas and for open pit mines with common ground electrodes. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate the Minimum Eccentricity Shortest Path (MESP) problem in unweighted graphs. It asks for a given graph to find a shortest path with minimum eccentricity. Let n and m denote the number of vertices and the number of edges of a given graph. We demonstrate that: • a minimum eccentricity shortest path plays a crucial role in obtaining the best to date approximation algorithm for a minimum distortion embedding of a graph into the line; • the MESP problem is NP-hard for planar bipartite graphs with maximum degree 3 and W[2]-hard for general graphs; • a shortest path of minimum eccentricity k can be computed in O ( n 2 k + 2 m ) time; • a 2-approximation, a 3-approximation, and an 8-approximation for the MESP problem can be computed in O ( n 3 ) time, in O ( n m ) time, and in O ( m ) time, respectively; • in a graph with a shortest path of eccentricity k , a k -dominating set can be found in n O ( k ) time. [ABSTRACT FROM AUTHOR]

In deep sea environment, the quality of underwater imagery is primarily affected with low contrast, blur and color cast due to the absorption and scattering. In order to deal with these discrepancies a framework is proposed in this paper wherein a set of energy functionals is applied on the approximation and the detailed coefficients of the image. The approximation coefficients of RGB components are modified for adjusting the average intensity value of the image followed by the color correction of these coefficients at finer scales. Subsequently, the processing of detailed coefficients are done for improving local contrast of the image. The performance of the proposed method is evaluated qualitatively and quantitatively on three underwater datasets at varying depths. Qualitative analysis is carried out by comparing the hue histogram of input and output images, whereas quantitative analysis comprises of PSNR, Entropy and SSIM quality metrics. The results of the proposed method are compared with state-of-the-art methods. From the obtained outcomes, it is observed that the proposed method significantly removes the color cast by improving the contrast of underwater images in addition to preserving its detailed structural features. [ABSTRACT FROM AUTHOR]

This paper presents a Bayesian learning approach for embedded feature selection. This approach employs a fully Bayesian framework to achieve a model which is sparse in both sample and feature domains. We introduce a novel multi-step algorithm based on Variational Approximation to efficiently compute all model parameters in order to optimize the maximum a posteriori probability (MAP) measure. Experiments on both synthetic and real datasets verify that the proposed method is successful in feature selection while achieving high accuracy in both regression and classification tasks. Compared to the existing methods, especially its non-fully Bayesian counterpart, the proposed algorithm results in much higher accuracies when the size of learning data is small. Moreover, the proposed method is more reliable (evident by less variance in accuracy) than other competing algorithms. [ABSTRACT FROM AUTHOR]

We address, in this paper, the problem of diagnosing intermittent sensor faults. In order to do so, we employ a model of intermittent loss of observations recently proposed in the literature, and use this model, together with an appropriately modified label automaton, to change the problem of detecting intermittent sensor faults into a problem of diagnosing the language generated by an automaton in the presence of intermittent faults, where the fault event is the unobservable event that models the non-observation of the event whose occurrence is recorded by the sensor subject to intermittent fault. We present necessary and sufficient conditions for diagnosability of intermittent sensor faults and propose two tests to verify intermittent sensor fault diagnosability: the first one based on diagnosers, which can also be used for online diagnosis, and a second one, based on verifiers, which has the advantage of having polynomial time complexity. [ABSTRACT FROM AUTHOR]

Numerous studies on marital issues have frequently resorted to statistical analysis or mathematical modeling on a well-mixed homogeneous population. However, such mathematical models have largely ignored the effects of heterogeneous contact pattern among individuals of the population. In this paper, we propose a pair model to describe the evolution of a marriage network, where an unmarried male and an unmarried female become friends with a certain probability through the introduction of their common friends. For convenience this probability is termed as the introduction probability. A threshold is obtained to determine whether there is a married couple or not. We verify the model by good agreement between the numerical solution of the model, computational simulations and the real marriage data in Beijing. The results show that the positive equilibrium of the model is steady and increases with the threshold. Moreover, the introduction probability contributes to increase both the threshold and the married population size. Furthermore, it is found that increasing the number of same sex friends, and balancing the sex ratio can also enlarge the married population size. All these results can provide some insights into the evolution and the structure of the marriage network. [ABSTRACT FROM AUTHOR]

As a rule, mathematical modeling of dynamic processes in nuclear reactors is conducted using an approach that treats a neutron flux in the multigroup diffusion approximation. In this approach, the basic model involves a multidimensional system of coupled parabolic-type equations. Similarly to common thermal phenomena, it is possible here to separate a regular mode of nuclear reactor operation that is associated with a selfsimilar development of a neutron field at large times. In this case, the main feature of dynamic processes is a minimal eigenvalue of the corresponding spectral problem. In the present paper, calculations of various eigenvalues are performed via the two-group model and discussed for the VVER-1000 reactor without a reflector and HWR reactor. [ABSTRACT FROM AUTHOR]

Tunneling times in complex bianisotropic materials have been examined in detail, with absorption and dispersion taken into account. Tunneling is characterized by the dwell and the phase tunneling time. In this paper, we have developed a theoretical model and derived the appropriate expressions for each of these quantities, as well as a relationship between them and the corresponding expression for the energy density. The model has been verified through numerical calculations based on experimental data. We have distinguished cases in which the phases of transmitted and incident wave match each other, and showed that for small angles of incidence, the time that the wave spends inside the barrier can be approximated as a linear function of the barrier width. The Hartman effect has been detected, although for very thick layers of metamaterial. [ABSTRACT FROM AUTHOR]

Model predictive control for max-plus linear discrete-event systems usually leads to a nonsmooth nonconvex optimization problem with real valued variables, which may be hard to solve efficiently. An alternative approach is to transform the given problem into a mixed integer linear programming problem. However, the computational complexity of current mixed integer linear programming algorithms increases in the worst case exponentially as a function of the prediction horizon. The focus of this paper is on making optimistic optimization suited to solve the given problem. Optimistic optimization is a class of algorithms that can find an approximation of the global optimum for general nonlinear optimization. A key advantage of optimistic optimization is that one can specify the computational budget in advance and guarantee bounds on the suboptimality with respect to the global optimum. We prove that optimistic optimization can be applied for the given problem by developing a dedicated semi-metric and by proving it satisfies the necessary requirements for optimistic optimization. Moreover, we show that the complexity of optimistic optimization is exponential in the control horizon instead of the prediction horizon. Hence, using optimistic optimization is more efficient when the control horizon is small and the prediction horizon is large. [ABSTRACT FROM AUTHOR]

We consider the k-Splittable Capacitated Network Design Problem (kSCND) in a graph G = ( V , E ) with edge weight w ( e ) ≥ 0 , e ∈ E . We are given a vertex t ∈ V designated as a sink, a cable capacity λ > 0 , and a source set S ⊆ V with demand d ( v ) ≥ 0 , v ∈ S . For any edge e ∈ E , we are allowed to install an integer number x ( e ) of copies of e . The kSCND asks to simultaneously send demand d ( v ) from each source v ∈ S along at most k paths to the sink t . A set of such paths can pass through an edge in G as long as the total demand along the paths does not exceed the capacity x ( e ) λ . The objective is to find a set P of paths of G that minimize the installing cost ∑ e ∈ E x ( e ) w ( e ) . In this paper, we propose a ( ( k + 1 ) / k + ρ ST ) -approximation algorithm to the kSCND, where ρ ST is any approximation ratio achievable for the Steiner tree problem . [ABSTRACT FROM AUTHOR]

Engineering and applied sciences use models of increasing complexity to simulate the behavior of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may become intractable in cases when a single simulation is time demanding. Particularly challenging is the reliability analysis of systems represented by computationally costly models, because of the large number of model evaluations that are typically required to estimate small probabilities of failure. In this paper, we demonstrate the potential of a newly emerged meta-modeling technique known as low-rank tensor approximations to address this limitation. This technique is especially promising for high-dimensional problems because: (i) the number of unknowns in the generic functional form of the meta-model grows only linearly with the input dimension and (ii) such approximations can be constructed by relying on a series of minimization problems of small size independent of the input dimension. In example applications involving finite-element models pertinent to structural mechanics and heat conduction, low-rank tensor approximations built with polynomial bases are found to outperform the popular sparse polynomial chaos expansions in the estimation of tail probabilities when small experimental designs are used. It should be emphasized that contrary to methods particularly targeted to reliability analysis, the meta-modeling approach also provides a full probabilistic description of the model response, which can be used to estimate any statistical measure of interest. [ABSTRACT FROM AUTHOR]

It is shown that the optical reciprocity theorem imposes certain constraints on the radiation field structure of a unidirectional point source (beam spread function (BSF)) in a turbid medium with spatially uniform optical properties. To satisfy the reciprocal relation, the BSF should have an additional symmetry property along with axial symmetry. This paper mathematically formulates the BSF symmetry condition that follows from the reciprocity theorem and discusses test results of some approximate analytical BSF models for their compliance with the symmetry requirement. A universal method for eliminating symmetry errors of approximate BSF models is proposed. [ABSTRACT FROM AUTHOR]

Taylor series approximation like q ( t + τ ) ≈ q + τ ∂ q ∂ t are often used to derive, extend or interpret typical heat conduction models. Researchers may take it for granted that the single-phase-lagging (SPL) model can be considered as an extension of the Cattaneo–Vernotte (CV) model because there is such approximation relationship between them. We point out in this paper that this Taylor series approximation itself has some defects based on analyses in mathematics, physics and some examples first. Then, we show essential differences in both mathematics and physics between the CV and SPL models. It is found that their mathematical characteristics and accordance with the laws of thermodynamics are significantly different, which indicates that using this approximation to connect the two models may be defective in some cases. What’s more, higher order approximation can’t solve these problems and defects. [ABSTRACT FROM AUTHOR]

Costas loop is a classical phase-locked loop (PLL) based circuit for carrier recovery and signal demodulation. The PLL is an automatic control system that adjusts the phase of a local signal to match the phase of the input reference signal. This tutorial is devoted to the dynamic analysis of the Costas loop. In particular the acquisition process is analyzed. Acquisition is most conveniently described by a number of frequency and time parameters such as lock-in range, lock-in time, pull-in range, pull-in time, and hold-in range. While for the classical PLL equations all these parameters have been derived (many of them are approximations, some even crude approximations), this has not yet been carried out for the Costas loop. It is the aim of this analysis to close this gap. The paper starts with an overview on mathematical and physical models (exact and simplified) of the different variants of the Costas loop. Then equations for the above mentioned key parameters are derived. Finally, the lock-in range of the Costas loop for the case where a lead-lag filter is used for the loop filter is analyzed. [ABSTRACT FROM AUTHOR]

Bayesian methods are widely accepted as the methodology for the analysis of reliability data. In practical applications such data are often expressed in an imprecise way. In such a case fuzzy sets are frequently used for modeling imprecision. In the paper we present some recent results on the application of the fuzzy Bayes methodology for the analysis of imprecise reliability data. We also present some useful approximations obtained using the concept of shadowed sets. [ABSTRACT FROM AUTHOR]

In this paper, we examine Bayes factor consistency in the context of Bayesian variable selection for normal linear regression models. We take a hierarchical Bayesian approach using a hyper- g prior (Liang et al. (2008) JASA). There are two regimes for computing Bayes factors, which differ in the choice of the base model. For both these regimes, we study conditions under which Bayes factors are consistent when the number of all the potential regressors grows with sample size n . This situation is not fully understood in the current literature, but has gained increasing importance recently. In the present case, Bayes factors are not analytically tractable and are calculated via Laplace approximation. A rigorous justification for these high-dimensional Laplace approximations is also provided. [ABSTRACT FROM AUTHOR]

We analyze the classical problem of the interaction between two charged surfaces separated by a solution containing neutralizing counter-ions. The focus is on obtaining a description where the solvent is treated explicitly rather than through a dielectric approximation as is conventionally done. We summarize the results of three papers where we have used a Stockmayer fluid model in Monte Carlo simulations. It is shown that the attractive ion–ion correlation mechanism is also operating when the solvent is described explicitly. There appears an oscillatory component to the force, but when this is accounted for, there is a semi-quantitative agreement between the continuum model and the model with explicit solvent. The properties of the continuum model can be reached in a molecular system by making the solvent molecules much smaller than the ions. It is demonstrated that having an explicit solvent model makes the analysis of force mechanisms more delicate due to the interplay between several different microscopic contributions to the force. Finally, it is argued that the agreement between the forces calculated using the continuum and the explicit solvent models, respectively, has as its basis the circumstance that the force between the surfaces is mainly caused by long-range ion–ion interactions, for which the dielectric approximation is most adequate. This argument applies equally well to an aqueous system as to the Stockmayer fluid. [ABSTRACT FROM AUTHOR]

The performance of a non-tonal speech recognition system degrades when confronted with the task of recognizing tonal words. Several speech recognition applications require tonal word recognition. Therefore, this paper considers how to create a suitable tone model for a tonal syllable recognition system serving application devices based on a one-stream scheme. The fundamental frequency contour (F0 contour) approximation model is proposed here to estimate F0 continuity contours for all of a tonal word. The processes of approximation include voice detection, F0 smoothing, F0 forecasting, and F0 normalization. To model the F0 contours of unvoiced regions belonging to F0 forecasting, a linear regression function is used to create an approximate F0 contour. Experimental results indicate that the proposed model improves the accuracy of tonal word recognition by 8.6% and 12.2%, respectively, compared with conventional random and exponential approaches. [ABSTRACT FROM AUTHOR]

In this paper, we develop a robust numerical method in pricing options, when the underlying asset follows a jump diffusion model. We demonstrate that, with the quadratic spline collocation method, the integral approximation in the pricing PIDE is intuitively simple, and comes down to the evaluation of the probabilistic moments of the jump density. When combined with a Picard iteration scheme, the pricing problem can be solved efficiently. We present the method and the numerical results from pricing European and American options with Merton’s and Kou’s models. [ABSTRACT FROM AUTHOR]

Full Stokes ice sheet models provide the most accurate description of ice sheet flow, and can therefore be used to reduce existing uncertainties in predicting the contribution of ice sheets to future sea level rise on centennial time-scales. The level of accuracy at which millennial time-scale palaeo-ice sheet simulations resolve ice sheet flow lags the standards set by Full Stokes models, especially, when Shallow Ice Approximation (SIA) models are used. Most models used in paleo-ice sheet modeling were developed at a time when computer power was very limited, and rely on several assumptions. At the time there was no means of verifying the assumptions by other than mathematical arguments. However, with the computer power and refined Full Stokes models available today, it is possible to test these assumptions numerically. In this paper, we review (Ahlkrona et al., 2013a) where such tests were performed and inaccuracies in commonly used arguments were found. We also summarize (Ahlkrona et al., 2013b) where the implications of the inaccurate assumptions are analyzed for two paleo-models – the SIA and the SOSIA. We review these works without resorting to mathematical detail, in order to make them accessible to a wider audience with a general interest in palaeo-ice sheet modelling. Specifically, we discuss two implications of relevance for palaeo-ice sheet modelling. First, classical SIA models are less accurate than assumed in their original derivation. Secondly, and contrary to previous recommendations, the SOSIA model is ruled out as a practicable tool for palaeo-ice sheet simulations. We conclude with an outlook concerning the new Ice Sheet Coupled Approximation Level (ISCAL) method presented in Ahlkrona et al. (2016), that has the potential to match the accuracy standards of full Stokes model on palaeo-timescales of tens of thousands of years, and to become an alternative to hybrid models currently used in palaeo-ice sheet modelling. The method is applied to an ice sheet covering Svalbard. [ABSTRACT FROM AUTHOR]

A precise theoretical description of W- and Z-boson production in the resonance region is essential for the correct interpretation of high-precision measurements of the W-boson mass and the effective weak mixing angle. Currently, the largest unknown fixed-order contribution is given by the mixed QCD-electroweak corrections of O ( α s α ) . We argue, using the framework of the pole expansion for the NNLO QCD-electroweak corrections established in a previous paper, that the numerically dominant corrections arise from the combination of large QCD corrections to the production with the large electroweak corrections to the decay of the W / Z boson. We calculate these so-called factorizable corrections of “initial–final” type and estimate the impact on the W-boson mass extraction. We compare our results to simpler approximate combinations of electroweak and QCD corrections in terms of naive products of NLO QCD and electroweak correction factors and using leading-logarithmic approximations for QED final-state radiation as provided by the structure-function approach or QED parton-shower programs. We also compute corrections of “final–final” type, which are given by finite counterterms to the leptonic vector-boson decays and are found to be numerically negligible. [ABSTRACT FROM AUTHOR]

Soft error analysis is very significant for a good tradeoff between processor design cost (e.g. area and power) and reliability. In this paper, we propose an approximate model driven framework for efficient soft error analysis in processors. The proposed framework includes: 1) an approximate Probabilistic Graphical Model (PGM) for the Single Bit Upset (SBU) estimation, uses average-and-max policy to handle the mapped PGM structure, node parameter and inference fast; 2) an approximate boundary model for the more complex Multi-Cell Upsets (MCU) case, adopts relax-and-strict way to reuse the approximate PGM model and characterize MCU patterns completely. The comprehensive results confirm that, compared with the state-of-the-art, the proposed two-level methodology based on approximate models achieves fast estimation up to more 15.37× speedup while only 8.14% accuracy loss on average. Furthermore, the complex MCU impacts are also estimated by the proposed method at the same order of magnitude as the runtime of the simple SBU case. [ABSTRACT FROM AUTHOR]