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The aim of this paper is the development of a mathematical model to compute the optimal inventory mix to face stochastic demand at minimum cost in a two-level supply chain. The paper addresses a multi-product dynamic lot-sizing problem under stochastic demand subject to capacity and service level constraints. This model is executed to compare a Make To Order (MTO) strategy to a Vendor Managed Inventory (VMI) partnership between the supplier and their customers. Both strategies provide the demand order to be produced. A schedule of production orders is determined over the planning horizon in order to minimize the inventory holding costs of the supply chain, taking into consideration that the supplier is also responsible of initiating the replenishment orders and deliveries of their customers according to the VMI partnership. The simulation model is illustrated empirically using a real case study: a paper manufacturing company that pursues to improve customer service level and supply chain inventory costs through a proper production planning of their paper machines and a suitable VMI order replenishment schedule. [ABSTRACT FROM AUTHOR]

Recently, Mao (2015) developed a new explicit method, called the truncated Euler–Maruyama (EM) method, for the nonlinear SDE and established the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition. In his another follow-up paper (Mao, 2016), he discussed the rates of L q -convergence of the truncated EM method for q ≥ 2 and showed that the order of L q -convergence can be arbitrarily close to q ∕ 2 under some additional conditions. However, there are some restrictions on the truncation functions and these restrictions sometimes might force the step size to be so small that the truncated EM method would be inapplicable. The key aim of this paper is to establish the convergence rate without these restrictions. The other aim is to study the stability of the truncated EM method. The advantages of our new results will be highlighted by the comparisons with the results in Mao (2015, 2016) as well as others on the tamed EM and implicit methods. [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]

Abstract In this paper, a new shock model called Marshall–Olkin run shock model is defined and studied. According to the model, two components are subject to shocks that may arrive from three different sources, and component i fails when it is subject to k consecutive critical shocks from source i or k consecutive critical shocks from source 3, i = 1 , 2. Reliability and mean residual life functions of such components are studied when the times between shocks follow phase-type distribution. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with the one-way classification analysis on the basis of conditional proportional reversed hazard rate models when treatment effects are random. Characteristics of the response variable including reversed hazard function, mean, variance and intraclass correlation are derived in explicit expressions. Estimations of the proposed model parameters are also obtained. Best predictions for score effects are given. The proposed model is an alternative approach for one-way classifications in which generalized linear models are applied for analysing continuous responses. For illustrative purposes, a real data set is analysed using the obtained results. [ABSTRACT FROM AUTHOR]

Abstract Semiparametric model is a kind of important mathematical modeling method of high dimensional biological Big Data in human health and disease. In this paper, we develop a M-type variable selection method based on Laplace Error Penalty (LEP) function for a class of high dimensional semiparametric models using a shrinkage idea. The proposed procedure can simultaneously select significant covariates with functional coefficients and local significant variables with parametric coefficients. The Laplace Error Penalty (LEP) function is constructed as an exponential function with two tuning parameters and is infinitely differentiable everywhere except at the origin. So the LEP oracle estimator can be easily obtained. We also proposed the computational algorithm in order to adapt to our method. Moreover, due to the robustness of the M-type loss function to outliers in the finite samples, our proposed variable selection method is more robust than the ones based on the least squares criterion. Finally, the method is illustrated with numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract The nonlinear grey Bernoulli model, which is often called the NGBM(1, 1), appeals considerable interest of research due to its effectiveness in time series forecasting. The success of the NGBM(1, 1) model proves that the nonlinear Bernoulli equation can be efficient to build grey prediction models. This paper is mainly aiming at building a more general nonlinear grey prediction model based on the Bernoulli equation and the modelling procedures of the GMC(1, n), which is called the nonlinear grey Bernoulli multivariate model, abbreviated as the NGBMC(1, n). The NGBMC(1, n) can be converted to the NGBM(1, 1) and the GMC(1, n) with different power parameters, thus it can be regarded as an extension of these models. Two case studies of forecasting the domestic income and foreign currency earning have been carried out to validate the effectiveness of the NGBMC(1, n) model, comparing to the novel linear multivariate grey models, including the GMC(1, n), DGM(1, n) and RDGM(1, n), and the classical ARIMA model. The advantages of the NGBMC(1, n) model in nonlinear time series forecasting over the existing linear models have been shown in the numerical results. Highlights • A novel nonlinear Bernoulli grey model NGBMC(1, n) is proposed. • The NGBMC(1, n) model is more general than the existing NGBM(1, 1) and GMC(1, n). • The NGBMC(1, n) model is quite easy-to-use and more efficient than the existing linear models. • The NGBMC(1, n) is successfully applied in tourist industry of China. • A new methodology of nonlinear grey models is provided. [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 Plants are essential to life. They are a source of food, medicine, clothing, and are important to a healthy environment. Unfortunately, plants can become infected with a disease. A viral infection is one way that a plant may become diseased. Often times, plants die from this infection. These viruses hurt the agriculture industry as billions of dollars are lost due to crop loss every year. An insect vector is typically the cause for the virus propagation. The vectors exhibit seasonal behavior as they are active in the warm months, but not as much so in the cooler months. To defend against the vectors, pesticides have been used. While the pesticides might be effective in controlling the vectors, they can have harmful side effects on the environment. An alternative solution is to introduce a predator, or just increase the number of a naturally present one, to prey on the insects. In this paper, we use a mathematical model of ordinary differential equation to model the dynamics of this biological process. We first present an autonomous system, then two nonautonomous systems, accounting for the periodic nature of the insects. To analyze the models, the basic reproductive number is used. We demonstrate a couple of approaches for determining this number: a time average approach and a linear operator approach. Afterwards, numerical simulations are used to demonstrate the results. Finally, comparisons are made between the models and the approaches. [ABSTRACT FROM AUTHOR]

Abstract The solution of linear systems with multiple shifts and multiple right-hand sides given simultaneously is required in many large-scale scientific and engineering applications. In this paper we introduce new flexible and deflated variants of the shifted block GMRES method for this problem class. The proposed methods solve the whole sequence of linear systems simultaneously, detecting effectively the linear systems convergence and allowing the use of variable preconditioning which may be particularly useful in some applications. Numerical experiments are illustrated to show the overall significant robustness of the iterative method for solving general sparse multi-shifted and multiple right-hand-side systems, and in realistic PageRank calculations. To the best of our knowledge, this is the first Krylov subspace method that combines deflation techniques and variable preconditioning for solving sequences of multi-shifted linear systems with multiple right-hand sides simultaneously. [ABSTRACT FROM AUTHOR]

Inspired by the iterative nature of many discretization methods for continuous dynamical systems, connections between iterative numerical methods in numerical linear algebra and continuous dynamical systems have been studied since 1970s. For stationary iterative methods solving linear systems, Chu (1988, 2008) discussed a connection to continuous dynamical systems by using the explicit Euler method, however, further understanding of stationary iterative methods might be limited due to the use of the explicit Euler method. This paper presents a new connection, based on the so-called discrete gradient methods, between SOR-type methods and gradient systems. There, the key of the discussion is the equivalence between SOR-type methods and the discrete gradient methods applied to gradient systems. The discussion leads to new interpretations for SOR-type methods. For example, a new derivation of SOR-type methods is found, these methods monotonically decrease a certain quadratic function, and a new interpretation of the relaxation parameter is obtained. Besides, while studying the new connection, a new discrete gradient is also obtained. [ABSTRACT FROM AUTHOR]

The stress–strength model has been widely used in reliability design of system. In the traditional stress–strength reliability theory, the system and each component are assumed to be only in one of two possible states being either working or failed, and the notion of stress–strength reliability is the probability that the strength is larger than the stress. In this paper, we study the stress–strength reliability of multi-state system based on generalized survival signature. It is supposed that the state of multi-state system is defined by using the ratio between strength and stress random variables. The definitions of generalized survival signature for a certain class of multi state systems with multi-state components in both discrete and continuous cases are given. In addition, the expressions of stress–strength reliability in both discrete and continuous situations are derived. In the case of continuous multi-state system, it is assumed that the random strength and stress are both from the Weibull distributions with different scale parameters, and the two different continuous kernel functions are Pareto and generalized half logistic distribution functions, respectively. Based on the assumptions, the stress–strength reliability is estimated by using both classical and Bayesian statistical theories. The uniformly minimum variance unbiased estimator and maximum likelihood estimator for the stress–strength reliability of the continuous multi-state system are derived. Under the squared error loss function, the exact expression of Bayes estimator for the stress–strength reliability of the continuous multi-state system is developed by using Gauss hypergeometric function. Finally, the Monte Carlo simulations are performed to compare the performances of the proposed stress–strength reliability estimators, and a real data set is also analyzed for an illustration of the findings. [ABSTRACT FROM AUTHOR]

In this paper, we further analyze the generalized Newton method for the generalized absolute value equations. Some new convergent conditions for the generalized Newton method are obtained, which are superior to those appeared in previously published works. Numerical experiments are given to demonstrate the effectiveness of the generalized Newton method. [ABSTRACT FROM AUTHOR]

The paper is mainly concerned with the oscillations of numerical solutions by the linear θ − methods for a kind of linear delay differential equations with positive and negative coefficients. Some conditions under which the numerical solutions are oscillatory are obtained and it is proved that oscillations of the analytical solutions are preserved by the numerical solutions under mild conditions. Numerical experiments are given to demonstrate our results. [ABSTRACT FROM AUTHOR]

In this paper, a new pressure stabilized finite element method is analyzed for solving the Stokes equations. The key feature of the method is using the curl integral instead of the standard Dirichlet integral and using the pressure stabilization instead of the inf–sup condition. Thus, the method is very flexibly applicable to two problems of Stokes equations in terms of velocity and pressure with either pressure-Dirichlet boundary condition or velocity-Dirichlet boundary condition. For both Stokes problems, the finite element scheme and the finite element space of velocity are the same and one, where only the finite element spaces of pressure have small differences. A general analysis of stability and error estimates is developed and applications to both Stokes problems are further analyzed. The method covers the low regularity solution of very weak non H 1 space solution of Stokes problem of pressure-Dirichlet boundary condition as well as higher regularity solutions of Stokes problems of either pressure-Dirichlet boundary condition or velocity-Dirichlet boundary condition. Numerical results are presented to illustrate the performance of the method and to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

CMRH method (Changing minimal residual with Hessenberg process) is an iterative method for solving nonsymmetric linear systems. This method is similar to QMR method but based on the Hessenberg process instead of the Lanczos process. On dense matrices, the CMRH method is less expensive and requires less storage than other Krylov methods. This paper presents a block version of the CMRH algorithm for solving linear systems with multiple right-hand sides. The new algorithm is based on the block Hessenberg process and the iterates are characterized by a block version of the quasi-minimization property. We analyze its main properties and show that under the condition of full rank of block residual the block CMRH method cannot break down. Finally, some numerical examples are presented to show the efficiency of the new method in comparison with the traditional CMRH method and a comparison with the block GMRES method is also provided. [ABSTRACT FROM AUTHOR]

This paper introduces a hybrid algorithm of Nelder–Mead and scatter search algorithms called SSNM. Numerical results for some known test problems with varying dimensions from 2 to 100 variables prove its great performance for a bounded or constrained problem. This paper also has a considerable contribution to the joint economic lot sizing (JELS) problem literature. This problem is considered for a two-stage supply chain with price-sensitive demand for geometric, geometric-then-equal size and optimal shipment policies. Solution procedures are also developed which use the SSNM algorithm in their steps. These models and solution procedures are novel in the JELS literature. [ABSTRACT FROM AUTHOR]

This paper can be regarded as the continuation of the work contained in papers Milošević (2011, 2013). At the same time, it represents the extension of the paper Wu et al. (2010). In this paper, the one-sided Lipschitz condition is employed in the context of the backward Euler method, for a class of neutral stochastic differential equations with constant delay. Sufficient conditions for this method to be well defined are revealed. Under certain nonlinear growth conditions, the convergence in probability is established for the continuous forward–backward Euler method, as well as for the discrete backward Euler method. Additionally, it is proved that the discrete backward Euler equilibrium solution is globally a.s. asymptotically exponentially stable, without requiring for the drift coefficient to satisfy the linear growth condition. [ABSTRACT FROM AUTHOR]

Lid-driven cavity flows have been widely investigated and accurate results have been achieved as benchmarks for testing the accuracy of computational methods. This paper verifies the accuracy of an adaptive mesh refinement method numerically using 2-D steady incompressible lid-driven cavity flows and coarser meshes. The accuracy is shown by verifying that the centres of vortices given in the benchmarks are located in the refined grids of refined meshes for Reynolds numbers 100, 1000 and 2500 using coarser meshes. The adaptive mesh refinement method performs mesh refinement based on the numerical solutions of Navier–Stokes equations solved by a finite volume method with a well known SIMPLE algorithm for pressure–velocity coupling. The accuracy of the refined meshes is shown by comparing the profiles of horizontal and vertical components of velocity fields with the corresponding components of the benchmarks together and drawing closed streamlines. The adaptive mesh refinement method verified in this paper can be applied to find the accurate numerical solutions of any mathematical models containing continuity equations for incompressible fluid, steady state fluid flows or mass and heat transfer. [ABSTRACT FROM AUTHOR]

We construct and analyze robust strong stability preserving IMplicit-EXplicit Runge-Kutta (IMEX RK) methods for models of flow with diffusion as they appear in astrophysics, and in many other fields where equations with similar structure arise. It turns out that besides the optimization of the region of absolute monotonicity, some other properties of the methods are crucial for the success of such simulations. In particular, the models in our focus dictate to also take into account the step size limits associated with dissipativity, positivity of the stiff parabolic terms which represent transport by diffusion, the uniform convergence with respect to different stiffness properties of those same terms, etc. Furthermore, in the literature, some other properties, like the inclusion of a part of the imaginary axis in the stability region, have been argued to be relevant. In this paper, we construct several new IMEX RK methods which differ from each other by taking various or even all of these constraints simultaneously into account. It is demonstrated for some simple examples as well as for the problem of double-diffusive convection, that the newly constructed schemes provide a significant computational advantage over other methods from the literature. Due to their accumulation of different stability properties, the optimized IMEX RK methods obtained in this paper are robust schemes that may also be useful for general models which involve the solution of advection-diffusion equations, or other transport equations with similar stability requirements. [ABSTRACT FROM AUTHOR]

Misspecifications (i.e. errors on the parameters) of state space models lead to incorrect inference of the hidden states. This paper studies weakly nonlinear state space models with additive Gaussian noises and proposes a method for detecting and correcting misspecifications. The latter induce a biased estimator of the hidden state but also happen to induce correlation on innovations and other residues. This property is used to find a well-defined objective function for which an optimization routine is applied to recover the true parameters of the model. It is argued that this method can consistently estimate the bias on the parameter. We demonstrate the algorithm on various models of increasing complexity. [ABSTRACT FROM AUTHOR]

Plants are a food source for man and many species. They also are sources of medicines, fibers for clothes and are essential for a healthy environment. But plants are subject to diseases. Many of these are caused by viruses. In plants most of the virus propagation is done by a vector, usually insects that bite infected plants and the susceptible plants. Chemical insecticides are commonly used to control the insects, but unfortunately these chemicals have toxic effects on humans, animals and the environment in general. An alternative is to introduce a new species, or just increase the number of a naturally present one, to prey on the insects and thus control their number. The different steps in the virus propagation process take time. In this paper we add a predator to a plant-virus propagation model with delays. The model is based on delay differential equations. There are five populations: susceptible and infected plants, susceptible and infected vectors, and predators. The infected vectors have no ill effects from the virus so they do not fight the virus and therefore they do not recover. The predators do not get sick from the virus. The total number of plants is assumed to be constant since for crops the framers will replace the death plants and one of the plant populations can be determined using the total constant plant population. Therefore we have a system of five delay ordinary differential equations in five unknowns. We assume that predators are introduced at the initial time and after their growth rate has a Holling 2 type dependence on the number of vectors. We consider two delays: the time it takes from the moment a plant is bitten by an infected vector to the moment the plant is infected; and a second smaller delay for the time from the moment a vector bites an infected plant to the moment the vector becomes infected. We determine the non-negative steady state solutions of the system of delay differential equations. We analyze their stability by calculating the eigenvalues of the linearized system about each equilibrium point. We do numerical simulations for certain values of the parameters. Finally we search for bifurcation points numerically using the software package biftool. Conditions are presented for which the disease is controlled or even eliminated. From the practical side, the model can be used to determine the amount of introduced predators necessary to eliminate the epidemic under different conditions. [ABSTRACT FROM AUTHOR]

Centrality measures play a central role in Complex Networks Theory as much as they provide a tool to rank nodes by their relevance in the processes occurring in a network. In this paper we propose a model for the eigenvector-like centralities of temporal networks that evolve on a continuous time scale. We analytically prove that these centralities can be approximated by the centralities of temporal networks on discrete time scale. [ABSTRACT FROM AUTHOR]

This paper presents a stochastic dynamic mathematical model to study the evolution of the unemployment rate and other relevant related variables in a country. This model is composed by three basic interrelated subsystems: demographic, economic and well-being ones. A key aspect of this model is that it considers three UN well-being variables simultaneously: Human Development Index, Gender Empowerment Index and Gender Differentiation Index. These variables involve key concepts for human development, as Health, Education, Economy and Female Labor. With this model, the most outstanding variables found in the literature in relation with unemployment control can be used to design strategies and scenarios to reduce the unemployment rate in the future. The model has been fitted for the case of Spain in the 2002–2014 period, the largest one with information about all the variables involved in the model. Finally, several tentative scenarios and strategies have been tested to reduce the unemployment rate in Spain in the horizon of year 2025, and the corresponding forecast evolution of the Gender Differentiation Index, National income per capita, Public debt and the ratio between Public debt and Gross domestic product are shown. [ABSTRACT FROM AUTHOR]

Realistic woven fabric appearance is very important for computer graphics applications. The appearance of a particular woven fabric is determined by multi-scale geometric structure and light directional reflectance. Accurately modeling structural detail of the fabric can produce realistic rendering effects of fabric appearance. But modeling these complex geometric details of woven fabrics is challenging. In this paper, a novel geometric method of modeling structural detail of woven fabric is presented based on the image. According to a single micro image, we propose efficient image processing techniques to capture the fine-scale detail geometric characters of fabric structure, which results in the highly efficient modeling advantage of our method over existing methods. Then considering the composite structure characters of fiber and yarn, the Frenet Frame is used to model the yarn geometric structure and the Spiral Equation is used to present the helix twisting structure of fiber on the yarn. Based on this geometric model, the woven fabric’s detail structure can be visualized realistically. Compared with the original fabric image, our method can model the fabric’s 3D geometric structure, and obtain high-quality rendering effects. [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 main purpose of this paper is to present a new corrected decoupled scheme combined with a spatial finite volume method for chemotaxis models. First, we derive the scheme for a parabolic–elliptic chemotaxis model arising in embryology. We then establish the existence and uniqueness of the numerical solution, and we prove that it converges to a corresponding weak solution for the studied model. In the last section, several numerical tests are presented by applying our approach to a number of chemotaxis systems. The obtained numerical results demonstrate the efficiency of the proposed scheme and its effectiveness to capture different forms of spatial patterns. [ABSTRACT FROM AUTHOR]

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

Using the Euler scheme to simulate the stochastic differential equations (SDEs) models in finance often gives rise to the problem that the exact solution is positive while the numerical solution is not. Recently, we find that this problem existed in the jump–diffusion models as well. Hence, this paper aims to construct a numerical method preserving positivity for jump–diffusion option pricing models. We generalize the balanced implicit method (BIM) to the jump–diffusion models, which already turned out to be efficient for preserving positivity in SDE models. Then the positivity of BIM for jump–diffusion models is proved under some conditions. Finally, a numerical example is simulated to verify the positivity and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Optimal control of water flooding reservoir is performed to calculate the optimal set of well controls to maximize economic profitability. However, calculating the optimal well controls requires major computational resources, which restricts its implementation in actual reservoir production. In this paper a reduced-order optimal control methodology mainly based on POD (Proper Orthogonal Decomposition) is proposed to optimize the operation of wells in water flooding reservoir. The methodology is decomposed into the ‘offline’ and ‘online’ calculations. The offline calculation consists in determining a reduced set of POD basis from several ‘snapshots’ obtained using reservoir simulator over a pre-determined set of time instants and well control parameters. In the online calculation, knowing the current economic parameters, the optimal well controls are determined only using a nonlinear programming method and POD reconstruction. The methodology is approved on a small scale, two-dimensional, water flooding reservoir model. The results show that the NPV obtained by the reduced-order optimal control methodology is approached to within 99% of the NPV obtained by the adjoint-gradient based methodology, besides, it is quite fast, where the achieved increase in calculation speed is several dozens of times, and its advantage of calculation speed significantly increases as the number of grid blocks increases. [ABSTRACT FROM AUTHOR]

A closed form of the L -localized solution set of an interval linear system with max-plus algebra is a finite union of interval vectors. This paper analyzes and proves some properties to reduce number of the union sets to be a smaller number of the union of interval vectors that are not subsets of each other. This result helps simplify the feasible set of an optimization problem with max-plus linear equation constraints. [ABSTRACT FROM AUTHOR]

The aircraft scheduling problem (ASP) is a salient problem in airport runway scheduling system. This paper originally proposes an Ant Colony (AC) algorithm based on the wake-vortex modeling (WVM) method for ASP. Numerical results validate that this new method has better performance than CPLEX, general AC algorithm, and approximation algorithm in Ma et al. (2014). It is a promising method to improve the efficiency of the aircraft scheduling system from a theoretical standpoint. [ABSTRACT FROM AUTHOR]

In the over-the-counter (OTC) markets, the holders of many contracts are vulnerable to counterparty credit risk. Because of this issue, vulnerable options must be considered. In addition, in a financial environment, the pricing of path-dependent options yields many interesting mathematical challenges. In this paper, we study the pricing of vulnerable path-dependent options using double Mellin transforms to investigate an explicit (closed) form pricing formula or semi-analytic formula in each path-dependent option. [ABSTRACT FROM AUTHOR]

As part of the new regulatory framework of Solvency II, introduced by the European Union, insurance companies are required to monitor their solvency by computing a key risk metric called the Solvency Capital Requirement (SCR). The official description of the SCR is not rigorous and has lead researchers to develop their own mathematical frameworks for calculation of the SCR. These frameworks are complex and are difficult to implement. Recently, Bauer et al. suggested a nested Monte Carlo (MC) simulation framework to calculate the SCR. But the proposed MC framework is computationally expensive even for a simple insurance product. In this paper, we propose incorporating a neural network approach into the nested simulation framework to significantly reduce the computational complexity in the calculation. We study the performance of our neural network approach in estimating the SCR for a large portfolio of an important class of insurance products called Variable Annuities (VAs). Our experiments show that the proposed neural network approach is both efficient and accurate. [ABSTRACT FROM AUTHOR]

Plants play a vital role in the everyday life of all organisms on earth. Sometimes, however, plants become infected with a virus. This can have a devastating effect on the ecosystem that depends on it. An insect–vector can cause the transmission of the virus from plant to plant. In this paper, a system of ordinary differential equations was first used to model the interaction between the insects and the plants. We found the equilibria of the model, and we analyzed the stability using the Reproductive number, derived by the next generation matrix. Afterwards, we introduced a delay to the model and a system of delay differential equations (DDE) was obtained. Analysis of the DDEs dynamics was performed including equilibria, stability, and bifurcations. Then, numerical solutions of the ODE and the DDE were compared and conclusions are given. [ABSTRACT FROM AUTHOR]

Precision in computations is a considerable challenge to adequately addressing many current scientific or engineering problems. The way in which the numbers are represented constitutes the first step to compute them and determines the validity of the results. The aim of this research is to provide a formal framework and a set of computational primitives to address high precision problems of mathematical calculation in engineering and numerical simulation. The main contribution of this research is a mathematical model to build an exact arithmetical unit able to represent without error rational numbers in positional notation system. The functions under consideration are addition and multiplication because they form an algebraic commutative ring which contains a multiplicative inverse for every non-zero element. This paper reviews other specialized arithmetic units based on existing formats to show ways to make high precision computing. It is proposed a formal framework of the whole arithmetic architecture in which the operators are based. Then, the design of the addition operation is detailed and its hardware implementation is described. Finally, extensive evaluation of this operator is performed to prove its ability for exact processing. [ABSTRACT FROM AUTHOR]

In this paper, we use a discrete time Markov additive process to model the surplus process for an insurance company. Assume that the interclaim times and the claim sizes are both regulated by an underlying Markov chain. We present a recursive formula for the Gerber–Shiu function by two methods. Some numerical examples are also given to show the solution procedure. [ABSTRACT FROM AUTHOR]

In this paper, we survey three different forms of Householder based transformations for quaternion matrices in the literature, and propose a new form of quaternion Householder based transformation. We propose real structure-preserving algorithms of these Householder based transformations, which make the procedure computationally more flexible and efficient. We compare the computation counts and assignment numbers of these algorithms. We also compare the effectiveness of these real structure-preserving algorithms applying to the quaternion QRD and the quaternion SVD. All these four real structure-preserving algorithms are more efficient, comparing to the algorithms which apply Quaternion Toolbox using quaternion arithmetics, or algorithms which directly performs real Householder transformations on the real representation of a quaternion matrix. Among these four real structure-preserving algorithms, the most efficient ones are based on quaternion Householder reflection, and new proposed Householder based transformation. [ABSTRACT FROM AUTHOR]

In this paper, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) finite element method for the elliptic problems with rapidly oscillating or high contrast coefficients. This general WG-GMS method features in high order accuracy on general meshes and can work with multiscale basis derived by different numerical schemes. A special case is studied under this WG-GMS framework in which the multiscale basis functions are obtained by solving local problem with the weak Galerkin finite element method. Convergence analysis and numerical experiments are obtained for the special case. [ABSTRACT FROM AUTHOR]

The advection–diffusion–reaction (ADR) systems are often used to describe the chemotaxis models arising in biology. In general, the stiffness from the reaction and diffusion terms often requires very restricted time step size, and the advection term depending on the concentration gradients of another component (the chemoattractant) may lead to sharp peaks in localized spatial regions. It is challenging to design numerical methods that can efficiently handle both difficulties. In this paper, we apply the operator splitting approach to solve the advection–diffusion–reaction systems. In particular, for advection term, we use the positivity-preserving DG method with strong stability preserving (SSP) high order time discretizations. For reaction–diffusion term, direct discontinuous Galerkin (DDG) method is used in spatial discretization and Krylov IIF method is applied in time discretization. Numerical examples are shown to demonstrate the accuracy, efficiency and robustness of the method. [ABSTRACT FROM AUTHOR]

Linear systems with multiple right-hand sides arise in many applications. To solve such systems efficiently, a new deflated block GCROT( m , k ) method is explored in this paper by exploiting a modified block Arnoldi deflation. Incorporating this modified block Arnoldi deflation, the new algorithm can address the possible linear dependence at each iteration during the block Arnoldi procedure and reduces expensive computational operations. Moreover, as a block version of GCROT( m , k ), the new method inherits the property of easy operability. Finally, some numerical examples also illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The shallow water equations are widely used to model flows in rivers and coastal areas. In this paper, we consider the shallow water flows in open channels with irregular geometry and a non-flat bottom topography, and design high order finite volume weighted essentially non-oscillatory (WENO) methods. A special source term approximation is introduced so that the proposed methods can preserve the still water steady state exactly. We also employ a simple positivity-preserving limiter to provide efficient and robust simulations near the wetting and drying front. The proposed methods are well-balanced for the still water steady state solutions, preserve the non-negativity of the wet cross section, and are genuinely high order accurate in smooth regions for general solutions and essentially non-oscillatory for general solutions with discontinuities. Numerical examples are performed at the end to verify these properties. [ABSTRACT FROM AUTHOR]

We consider coherent systems subjected to Marshall–Olkin type shocks coming at random times and destroying components of the system. The paper combines two important models, coherent systems and Marshall–Olkin type shocks and studies the mean residual life (MRL) and the mean inactivity time (MIT) functions of coherent systems that is subjected to random shocks. The considered models and theoretical results are supported with examples and graphical representations. [ABSTRACT FROM AUTHOR]

We consider model order reduction of mechanical systems with moving loads. Such systems have a time-varying input matrix that makes the direct application of standard model reduction methods difficult. In this paper, we present a two-step model reduction approach for systems with moving loads which is based on a low-rank approximation of the input matrix and applying Krylov subspace methods to the resulting linear time-invariant system with a modified input. Numerical results demonstrate the properties of the proposed model reduction method. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel approach to the problem of merging of Bézier curves with respect to the L 2 -norm. We give illustrative examples to show that the solution of the conventional merging problem may not be suitable for further modification and applications. As in the case of the degree reduction problem, we apply the so-called restricted area approach–proposed recently in Gospodarczyk (2015)–to avoid certain defects and make the resulting curve more useful. A method of solving the new problem is based on box-constrained quadratic programming approach. [ABSTRACT FROM AUTHOR]

This paper formulates the PageRank problem A x = x into a consistent singular linear system ( I − A ) x = 0 , and applies the full orthogonalization method (FOM) to solve it. This singular system is characterized by index one, namely i n d e x ( I − A ) = 1 . We analyze the breakdown performance of FOM on a general singular linear system, and conclude that FOM can determine a solution if it converges, without any unfortunate breakdowns for our target problem. Then we propose to use a vector extrapolation method to speed up the convergence performance of FOM. This extrapolation procedure is based on Ritz values, which directly stems from the Arnoldi-Extrapolation algorithm (Wu and Wei, 2010). Eventually numerical experiments are presented to illustrate the effectiveness of our approaches. [ABSTRACT FROM AUTHOR]

The mathematical models applied to real-life engineering structures result into large-scale dynamical systems. The efficient computation of their dynamical characteristics requires the usage of advanced numerical methods with parallel algorithms. The shooting method, in combination with a continuation method, presents a powerful tool for analyzing and investigating the dynamical characteristics of such systems. The efficiency and scalability of the shooting method are analyzed in the current paper for linear and nonlinear equations. Its applicability to large-scale systems is demonstrated by structural component of bridge discretized by three-dimensional finite elements. [ABSTRACT FROM AUTHOR]

Most of the models of epidemic propagations do not take into account the spatial distribution of the individuals. They give only the temporal change of the number of the infected, susceptible and recovered patients. In this paper we give some spatial discrete one-step iteration models for disease propagation and give conditions that guarantee some basic qualitative properties of the original process to the discrete models. Since the discrete models can be considered as the finite difference discretizations of continuous models of disease propagation given in the form of systems of partial differential equations, we can deduce conditions for the mesh size and the time step. Some of the results are demonstrated on numerical tests. [ABSTRACT FROM AUTHOR]

In this paper, we mainly focus on the derivation of a flexible condition number for weighted linear least squares problem and its estimation. With Fréchet derivative and Kronecker product, the explicit expression of the condition number is obtained. When the coefficient matrices are large and dense, considering the difficulties of explicitly forming the expression of condition number in computer, we also present its simplified form through a simple and easy to operate method. Two different condition estimation methods are introduced, and the numerical experiments are also performed to show the efficiency of the condition estimators. [ABSTRACT FROM AUTHOR]

General linear methods in the Nordsieck form have been introduced for the numerical solution of Volterra integral equations. In this paper, we introduce general linear methods of order p and stage order q = p for the numerical solution of Volterra integral equations in general form, rather than Nordsieck form. A - and V 0 ( α ) -stable methods are constructed and applied on stiff problems to show their efficiency. [ABSTRACT FROM AUTHOR]