Stochastic evolution of a nonlinear model of diffusion of information*

A theoretical method based on the concept of “system‐sized expansion” is applied to a generalization of Bartholomew's model of diffusion of information in a population of size N. The model considers a combination of mass‐mediated and interactively mediated messages, with the provision that the spreaders of information may not remain active for an indefinite period of time; it also takes into account the possibility that the parameters governing the process be time‐dependent. Explicit expressions for the time evolution of the diffusion process (including the probability distribution of the relevant variable, its mean value and variance) are derived in the asymptotic regime N ? 1. The nonlinear character of the model enables us to exploit our asymptotic expressions for studying finite‐size effects as well; the resulting expressions turn out to be reliable for N as low as 10.     

A Simple Approach for Multi‐fidelity Experimentation Applied to Financial Engineering

In practical applications, information about the accuracy or ‘fidelity’ of alternative surrogate systems may be ambiguous and difficult to determine. To address this problem, we propose to treat surrogate system fidelity level as a categorical factor in optimal response surface design. To design the associated experiments, we apply the Expected Integrated Mean Squared Error optimal design criterion, which takes into account both variance and bias errors. The performance of the proposed design was compared using three test cases to four types of alternatives using the Empirical Integrated Squared Error. Because of its ability to foster relatively accurate predictions, the proposed design is recommended in fidelity experimental design, particularly when the experimenters lack sufficient information about the fidelity levels of surrogate systems. The method was applied to the case of intraday trading optimization in which data were collected from the Taiwan Futures Exchange. We also calculated the implied volatility from the Merton's Jump‐diffusion model via the fast Fourier transform algorithm with three different models of varying fidelity levels. Copyright © 2014 John Wiley & Sons, Ltd.     

On entropy stable schemes for degenerate parabolic multispecies kinematic flow models

Entropy stable schemes for the numerical solution of initial value problems of nonlinear, possibly strongly degenerate systems of convection–diffusion equations were recently proposed in Jerez and Parés's study. These schemes extend the theoretical framework of Tadmor's study to convection–diffusion systems. They arise from entropy conservative schemes by adding a small amount of viscosity to avoid spurious oscillations. The main condition for feasibility of entropy conservative or stable schemes for a given model is that the corresponding first‐order system of conservation laws possesses a convex entropy function and corresponding entropy flux, and that the diffusion matrix multiplied by the inverse of the Hessian of the entropy is positive semidefinite. As a new contribution, it is demonstrated in the present work, first, that these schemes can naturally be extended to initial‐boundary value problems with zero‐flux boundary conditions in one space dimension, including an explicit bound on the growth of the total entropy. Second, it is shown that these assumptions are satisfied by certain diffusively corrected multiclass kinematic flow models of arbitrary size that describe traffic flow or the settling of dispersions and emulsions, where the latter application gives rise to zero‐flux boundary conditions. Numerical examples illustrate the behavior and accuracy of entropy stable schemes for these applications.     

A two-parameter friction model

The new friction model proposed in this paper takes all types of friction into account: sliding, pivoting and rolling friction. The model depends on two parameters. With a zero value of one parameter it is converted into the Contensou–Zhuravlev model, and with a zero value of the other parameter it is converted into the Coulomb model.The interaction of a body with the bearing surface during translational motion of the body is described fairly adequately by the classical model of dry friction (Coulomb's law). In the case of plane-parallel translational motion of the body, the Contensou–Zhuravlev model must be used;1, 2 this model takes both sliding friction and pivoting friction into account. The friction model proposed below is suitable for describing arbitrary translational motion of the body.     

On the stability and nonexistence of turing patterns for the generalized Lengyel‐Epstein model

This paper studies the dynamics of the generalized Lengyel‐Epstein reaction‐diffusion model proposed in a recent study by Abdelmalek and Bendoukha. Two main results are shown in this paper. The first of which is sufficient conditions that guarantee the nonexistence of Turing patterns, ie, nonconstant solutions. Second, more relaxed conditions are derived for the stability of the system's unique steady‐state solution.     

Nonfickian effect in time and space for diffusion processes

Diffusion processes are usually simulated using the classical diffusion equation. In certain scenarios, such equation induces anomalous behavior and consequently several improvements were introduced in the literature to overcome them. One of the most popular was the replacement of the diffusion equation by an integro‐differential equation. Such equation can be established considering a modification of Fick's mass flux where a delay in time is introduced. In this article, we consider mathematical models for diffusion processes that take into account a memory effect in time and space. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1589–1602, 2015     

A two-stage stochastic programming model for scheduling replacements in sow farms

This paper presents a formulation and resolution of a two-stage stochastic linear programming model with recourse for sow farms producing piglets. The proposed model considers a medium-term planning horizon and specifically allows optimal replacement and schedule of purchases to be obtained for the first stage. This model takes into account sow herd dynamics, housing facilities, reproduction management, herd size with initial and final inventory of sows and uncertain parameters such as litter size, mortality and fertility rates. These last parameters are explicitly incorporated via a finite set of scenarios. The proposed model is solved by using the algebraic modelling software OPL Studio from ILOG, in combination with the solver CPLEX to solve the linear models resulting from different instances considered. The article also presents results obtained with previous deterministic models assessing the suitability of the stochastic approach. Finally, the conclusions drawn from the study including an outlook are presented.      

Modelling of frictional forces in the dynamics of a sphere on a plane

A friction model is proposed that takes account of all forms of friction (sliding, spinning and rolling) and the permanent condition for the contact motion of the body on the plane. The model depends on three parameters and, in different special cases, transforms into the Contensou–Zhuravlev model and the author's model.     

Towards a numerical simulation of a high temperature flow

Two mathematical models of unsteady plasma flows based on 3D finite volume methods for Navier‐Stokes equations are presented. In the first, cold jet model, the nondimensional NS equations are solved by the artificial compressibility method, and the results include time‐varying velocity fields for different Reynolds numbers. The second formulation is a compressible Stegger‐Warming flux vector splitting scheme that takes into account the non‐perfect character of the plasma fluid. Temperature and composition dependent gas properties are to be evaluated from real data.     

融合Bass模型和三阶段过程模型的续集电影需求扩散研究

续集电影与母电影之间存在品牌溢出效应但不存在替代效应。现有多代扩散模型主要考虑替代效应,难以适用于续集电影。构建了一个融合Bass模型和三阶段过程模型的续集电影需求扩散模型,以预测续集电影的市场潜量和上映期间每日需求量。以2011年至2016年国内上映的续集电影相关数据对模型进行了验证,并与Marshall模型和SBM进行了比较。结果表明1)母电影品牌溢出效应、两代电影特征差距和市场扩张显著影响续集电影的市场潜量;2)电影需求过程存在显著的季节性波动;3)所建模型在拟合优度和预测精度方面均优于两个对比模型。所建模型一方面更适用于预测续集电影的需求扩散,另一方面研究对象拓展至不存在替代效应的多代短生命周期体验品,考虑了多代产品品牌溢出效应,是对已有多代扩散模型的补充。     

Concentrated portfolio selection models based on historical data

A new risk measure fully based on historical data is proposed, from which we can naturally derive concentrated optimal portfolios rather than imposing cardinality constraints. The new risk measure can be expressed as a quadratics of the introduced greedy matrix, which takes investors' joint behavior into account. We construct distribution‐free portfolio selection models in simple case and realistic case, respectively. The latest techniques for describing transaction cost constraints and solving nonconvex quadratic programs are utilized to obtain the optimal portfolio efficiently. In order to show the practicality, efficiency, and robustness of our new risk measure and corresponding portfolio selection models, a series of empirical studies are carried out with trading data from advanced stock markets and emerging stock markets. Different performance indicators are adopted to comprehensively compare results obtained under our new models with those obtained under the mean‐variance, mean‐semivariance, and mean‐conditional value‐at‐risk models. Out‐of‐sample results sufficiently show that our models outperform the others and provide a simple and practical approach for choosing concentrated, efficient, and robust portfolios. Copyright © 2014 John Wiley & Sons, Ltd.     

Global properties of a class of HIV infection models with Beddington–DeAngelis functional response

In this paper, the global properties of a class of human immunodeficiency virus (HIV) models with Beddington–DeAngelis functional response are investigated. Lyapunov functions are constructed to establish the global asymptotic stability of the uninfected and infected steady states of three HIV infection models. The first model considers the interaction process of the HIV and the CD4 ⁺ T cells and takes into account the latently and actively infected cells. The second model describes two co‐circulation populations of target cells, representing CD4 ⁺ T cells and macrophages. The third model is a two‐target‐cell model taking into account the latently and actively infected cells. We have proven that if the basic reproduction number R₀ is less than unity, then the uninfected steady state is globally asymptotically stable, and if R₀ > 1, then the infected steady state is globally asymptotically stable. Copyright © 2012 John Wiley & Sons, Ltd.     

Information initiatives of mobile retailers: a regression analysis of zero‐truncated count data with underdispersion

Our paper presents an empirical analysis of the association between firm attributes in electronic retailing and the adoption of information initiatives in mobile retailing. In our attempt to analyze the collected data, we find that the count of information initiatives exhibits underdispersion. Also, zero‐truncation arises from our study design. To tackle the two issues, we test four zero‐truncated (ZT) count data models—binomial, Poisson, Conway–Maxwell–Poisson, and Consul's generalized Poisson. We observe that the ZT Poisson model has a much inferior fit when compared with the other three models. Interestingly, even though the ZT binomial distribution is the only model that explicitly takes into account the finite range of our count variable, it is still outperformed by the other two Poisson mixtures that turn out to be good approximations. Further, despite the rising popularity of the Conway–Maxwell–Poisson distribution in recent literature, the ZT Consul's generalized Poisson distribution shows the best fit among all candidate models and suggests support for one hypothesis. Because underdispersion is rarely addressed in IT and electronic commerce research, our study aims to encourage empirical researchers to adopt a flexible regression model in order to make a robust assessment on the impact of explanatory variables. Copyright © 2014 John Wiley & Sons, Ltd.     

A novel multivariate grey model for forecasting the sequence of ternary interval numbers

A novel multivariate grey model suitable for the sequence of ternary interval numbers is presented in the paper. New model takes into account the influencing factors on the system behavior characteristic. New parameter setting makes the model directly applicable to the sequence of ternary interval number without the need to convert the sequence into real sequence. A compensation coefficient taken as a ternary interval number is added to the model equation. The accumulation method based on the new information priority is proposed to estimate coefficients. A connotative prediction formula is derived to replace the white response equation of the classical multivariate grey model. The single variable grey model, which takes into account the development trend of system behavior itself, is combined with the novel multivariate grey model based on the degree of grey incidence. Interval forecasts for China's electricity generation and consumer price index show that the new model has good performance.     

A mathematical model of anorexia and bulimia

In this paper, we propose a mathematical model to study the dynamics of anorexic and bulimic populations. The model proposed takes into account, among other things, the effects of peers' influence, media influence, and education. We prove the existence of three possible equilibria that without media influences are disease‐free, bulimic‐endemic, and endemic. Neglecting media and education effects, we investigate the stability of such equilibria, and we prove that under the influence of media, only one of such equilibria persists and becomes a global attractor. Which of the three equilibria becomes global attractor depends on the other parameters. Copyright © 2014 John Wiley & Sons, Ltd.     

The stresses in single lap joints with a functionally graded adhesive bondline: an efficient modelling approach

In this work, an efficient analytical model for the stress analysis of single lap joints with a functionally graded adhesive bondline is proposed which considers peel as well as shear stresses in the adhesive. The model takes into account the nonlinear geometric characteristics of a single lap joint under tensile loading and allows for the analysis of various adhesive Young's modulus variations. The obtained stress distributions are compared to results of detailed Finite Element analyses and show a good agreement for several single lap joint configurations. In addition, different adhesive Young's modulus distributions and their effect on the peel and shear stresses are studied and discussed in detail. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A dynamic binomial expansion technique for credit risk measurement: a Bayesian filtering approach

Credit risk measurement and management are important and current issues in the modern finance world from both the theoretical and practical perspectives. There are two major schools of thought for credit risk analysis, namely the structural models based on the asset value model originally proposed by Merton and the intensity‐based reduced form models. One of the popular credit risk models used in practice is the Binomial Expansion Technique (BET) introduced by Moody's. However, its one‐period static nature and the independence assumption for credit entities' defaults are two shortcomings for the use of BET in practical situations. Davis and Lo provided elegant ways to ease the two shortcomings of BET with their default infection and dynamic continuous‐time intensity‐based approaches. This paper first proposes a discrete‐time dynamic extension to the BET in order to incorporate the time‐dependent and time‐varying behaviour of default probabilities for measuring the risk of a credit risky portfolio. In reality, the ‘true’ default probabilities are unobservable to credit analysts and traders. Here, the uncertainties of ‘true’ default probabilities are incorporated in the context of a dynamic Bayesian paradigm. Numerical studies of the proposed model are provided.     

Vibrations of spatially suspended flexible pipe-beam with moving fluid

The nonlinear dynamic model of flexible pipe–beam suspended by spatial system of cables is proposed for vibration analysis of pipeline suspension bridges. The model, based on substructure technique, is considered as an assemblage of the following substructures: cables, hangers and pipe–beam. Equation of motion of pipe–beam is derived by Galerkin's FEM with the original finite element formulated in order to include moving mass of transported fluid. To describe cable vibrations, general continuum approach proposed in Ref.[1] is adopted with application into 3D model. Cable model takes into account initial sag, pre–tension force, large displacements and hangers' point reactions. Equation governing the motion of pipe–beam with cables and hangers is obtained regarding equilibrium conditions of interaction forces and compatibility of displacements at connection points between substructures. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dimension estimate of the exponential attractor for the chemotaxis‐growth system

We consider a chemotaxis‐growth model which takes into account diffusion, chemotaxis, production of chemical substance, and growth. We present estimates from above and below of the fractal dimension dim?? of the exponential attractor ?? in terms of the coefficients of the system. Comparisons are made between the sizes of the global and exponential attractors. Numerical simulations are presented which confirm the analytical results obtained. Copyright © 2006 John Wiley & Sons, Ltd.