Opinion strength influences the spatial dynamics of opinion formation

Opinions are rarely binary; they can be held with different degrees of conviction, and this expanded attitude spectrum can affect the influence one opinion has on others. Our goal is to understand how different aspects of influence lead to recognizable spatio-temporal patterns of opinions and their strengths. To do this, we introduce a stochastic spatial agent-based model of opinion dynamics that includes a spectrum of opinion strengths and various possible rules for how the opinion strength of one individual affects the influence that this individual has on others. Through simulations, we find that even a small amount of amplification of opinion strength through interaction with like-minded neighbors can tip the scales in favor of polarization and deadlock.     

长程选举模型的平均场极限

本文研究长程选举模型的平均场极限，利用对偶关系和特征函数方法证得长程选举模型的平均场极限满足下列微分方程：     

Short communication on the discrete deffuant and alternative models in one dimension

The discrete Deffuant model and its alternatives is a family of stochastic spatial models for the dynamics of binary opinions on f issues. Another parameter is also incorporated that prevents interaction between two agents whenever their opinion profiles are at a Hamming distance greater than the confidence threshold θ. By numerical simulations, it was conjectured in (Adamopoulos and Scarlatos, Complexity 2012, 17, 43) that one‐dimensional models exhibit a phase transition at a critical value . We report on recent mathematical results on this problem that originates from the community of complex systems. © 2016 Wiley Periodicals, Inc. Complexity 21: 437–439, 2016     

一维紧邻的接触过程与选举模型的混合过程的光滑性与单调性

证明了一维紧邻的接触过程与选举模型的混合过程,其极点平稳分布除在临界点λc 处外总是光滑的,且该混合过程具有单调性.     

Social influence and opinions

In this paper we describe an approach to the relationship between a network of interpersonal influences and the content of individuals’ opinions. Our work starts with the specification of social process rather than social equilibrium. Several models of social influence that have appeared in the literature are derived as special cases of the approach. Some implications for theories on social conflict and conformity also are developed in this paper.     

单纯形分布非线性模型的局部影响分析及其应用

讨论了单纯形分布非线性模型的局部影响分析问题.应用Cook(1986)的影响曲率方法研究了该模型关于微小扰动的局部影响,得到了局部影响分析的曲率度量.同时也应用PoonW Y和Poon Y S(1997)的保形法曲率方法研究了该模型的局部影响.对常见的扰动模型,分别进行了局部影响分析,得到了计算影响矩阵的简洁公式.最后还研究了两个实例,说明文中方法的应用价值.     

Modeling the effects of variable external influences and demographic processes on innovation diffusion

In this paper, a nonlinear mathematical model for innovation diffusion is proposed and analyzed by considering the effects of variable external influences (cumulative marketing efforts) and human population (variable marketing potential) in a society. The change in the population density is caused by various demographic processes such as immigration, emigration, intrinsic growth rate, death rate, etc.Thus, the problem of innovation diffusion is governed by three dynamic variables, namely, non adopters’ density, adopters’ density and the cumulative density of external influences. The model is analyzed by using the stability theory of differential equations and computer simulation.The model analysis shows that the main effect of the increase in cumulative density of external influences is to make the adopter population density reach its equilibrium at a much faster rate. It further shows that the density of adopters’ population increases as the parameters related to increase in non adopters’ population density increase. The effects of various parameters in the model on the nature of existing single equilibrium have also been discussed by using numerical simulation. It is shown that parameters related to the growth of non adopters’ population density have stabilizing effects on the system.     

Numerical approximations of chromatographic models

A numerical scheme based on modified method of characteristics with adjusted advection (MMOCAA) is proposed to approximate the solution of the system liquid chromatography with multi components case. For the case of one component, the method preserves the mass. Various examples and computational tests numerically verify the accuracy and efficiency of the approach.     

Nonexistence of Brownian models for certain multiclass queueing networks

We present two multiclass queueing networks where the Brownian models proposed by Harrison and Nguyen [3,4] do not exist. If self-feedback is allowed, we can construct such an example with a two-station network. For a three-station network, we can construct such an example without self-feedback.Research supported in part by Texas Instruments Corporation Grant 90456-034.     

Optimal control and numerical methods for hybrid stochastic SIS models

This work focuses on optimal controls of a class of stochastic SIS epidemic models under regime switching. By assuming that a decision maker can influence the infectivity period, our aim is to minimize the expected discounted cost due to illness, medical treatment, and the adverse effect on the society. In addition, a model with the incorporation of vaccination is proposed. Numerical schemes are developed by approximating the continuous-time dynamics using Markov chain approximation methods. It is demonstrated that the approximation schemes converge to the optimal strategy as the mesh size goes to zero. Numerical examples are provided to illustrate our results.     

A generalized real option pricing method of R&D investments: jump diffusion and external competition

ABSTRACT

Numerous studies have assessed Research and Development (R&D) investment using the real option pricing approach. This paper proposes a more general real option pricing method that both considers the specificity of R&D investment (such as uncertainty) and the R&D investment opportunity of a business in a market environment with external competitors. Specifically, we adopt a jump diffusion model to evaluate R&D investments that incorporate the uncertainties of these activities. The model values a pioneer's R&D investment opportunity allowing the chance that competitors may enter the market and the project value may vary with time. By construction and analysis of the model, we then analyse the optimal timing to realize profit on an investment. Overall, this model should facilitate a more comprehensive evaluation for R&D investments.     

Local influence analysis for semiparametric reproductive dispersion nonlinear models

The present paper proposes a semiparametric reproductive dispersion nonlinear model (SRDNM) which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models. Maximum penalized likelihood estimates (MPLEs) of unknown parameters and nonparametric functions in SRDNM are presented. Assessment of local influence for various perturbation schemes are investigated. Some local influence diagnostics are given. A simulation study and a real example are used to illustrate the proposed methodologies.     

Survival and coexistence in stochastic spatial Lotka–Volterra models

A spatially explicit, stochastic Lotka–Volterra model was introduced by Neuhauser and Pacala in Neuhauser and Pacala (Ann. Appl. Probab. 9, 1226–1259, 1999). A low density limit theorem for this process was proved by the authors in Cox and Perkins (Ann. Probab. 33, 904–947, 2005), showing that certain generalized rescaled Lotka–Volterra models converge to super-Brownian motion with drift. Here we use this convergence result to extend what is known about the parameter regions for the Lotka–Volterra process where (i) survival of one type holds, and (ii) coexistence holds. Supported in part by an NSERC Research grant.     

Stability and bifurcation in epidemic models describing the transmission of toxoplasmosis in human and cat populations

A five‐dimensional ordinary differential equation model describing the transmission of Toxoplamosis gondii disease between human and cat populations is studied in this paper. Self‐diffusion modeling the spatial dynamics of the T. gondii disease is incorporated in the ordinary differential equation model. The normalized version of both models where the unknown functions are the proportions of the susceptible, infected, and controlled individuals in the total population are analyzed. The main results presented herein are that the ODE model undergoes a trans‐critical bifurcation, the system has no periodic orbits inside the positive octant, and the endemic equilibrium is globally asymptotically stable when we restrict the model to inside of the first octant. Furthermore, a local linear stability analysis for the spatially homogeneous equilibrium points of the reaction diffusion model is carried out, and the global stability of both the disease‐free and endemic equilibria are established for the reaction–diffusion system when restricted to inside of the first octant. Finally, numerical simulations are provided to support our theoretical results and to predict some scenarios about the spread of the disease. Copyright © 2017 John Wiley & Sons, Ltd.     

Some exact solutions to multidimensional Landau-Lifshitz equation with uprush external field and anisotropy field

In this paper we give a method that can construct some exact solutions to a multidimensional Landau-Lifshitz equation with uprush external field and anisotropy field.     

Fractal and smoothness properties of space-time Gaussian models

Spatio-temporal models are widely used for inference in statistics and many applied areas. In such contexts, interests are often in the fractal nature of the sample surfaces and in the rate of change of the spatial surface at a given location in a given direction. In this paper, we apply the theory of Yaglom (1957) to construct a large class of space-time Gaussian models with stationary increments, establish bounds on the prediction errors, and determine the smoothness properties and fractal properties of this class of Gaussian models. Our results can be applied directly to analyze the stationary spacetime models introduced by Cressie and Huang (1999), Gneiting (2002), and Stein (2005), respectively.     

Emulation and complementarity in one‐dimensional alternatives of the axelrod model with binary features

We investigate the one‐dimensional dynamics of alternatives of the Axelrod model (ξ_t) with k binary features and confidence parameter ε = 0, 1,…, k. Simultaneously, the simple Axelrod model is also critically examined. Specifically, for small and large ε, simulations suggest that the convergent model (ξ_t) is emulated by a corresponding attractive model (η_t) with the same parameters (conditional on bounded confidence). (η_t) is more mathematically tractable than (ξ_t), and the very definitions of the two qualitative behaviors of cyclic particle systems (fluctuation and fixation) are applicable in special cases. Moreover, we observe a complementarity: for not too small k and $\varepsilon \approx {k \over 2}$ , (η_t) fixates (each site has a final type independent of the possibly infinite size of the lattice), whereas (ξ_t) fluctuates (each site changes type at arbitrarily larger times t as the size of the lattice increases). © 2011 Wiley Periodicals, Inc. Complexity, 2011     

On the approximation of continuous time threshold ARMA processes

Threshold autoregressive (AR) and autoregressive moving average (ARMA) processes with continuous time parameter have been discussed in several recent papers by Brockwellet al. (1991,Statist. Sinica,1, 401–410), Tong and Yeung (1991,Statist. Sinica,1, 411–430), Brockwell and Hyndman (1992,International Journal Forecasting,8, 157–173) and Brockwell (1994,J. Statist. Plann. Inference,39, 291–304). A threshold ARMA process with boundary width 2>0 is easy to define in terms of the unique strong solution of a stochastic differential equation whose coefficients are piecewise linear and Lipschitz. The positive boundary-width is a convenient mathematical device to smooth out the coefficient changes at the boundary and hence to ensure the existence and uniqueness of the strong solution of the stochastic differential equation from which the process is derived. In this paper we give a direct definition of a threshold ARMA processes with =0 in the important case when only the autoregressive coefficients change with the level of the process. (This of course includes all threshold AR processes with constant scale parameter.) The idea is to express the distributions of the process in terms of the weak solution of a certain stochastic differential equation. It is shown that the joint distributions of this solution with =0 are the weak limits as 0 of the distributions of the solution with >0. The sense in which the approximating sequence of processes used by Brockwell and Hyndman (1992,International Journal Forecasting,8, 157–173) converges to this weak solution is also investigated. Some numerical examples illustrate the value of the latter approximation in comparison with the more direct representation of the process obtained from the Cameron-Martin-Girsanov formula. It is used in particular to fit continuous-time threshold models to the sunspot and Canadian lynx series.Research partially supported by National Science Foundation Research Grants DMS 9105745 and 9243648.     

On the derivation of fractional diffusion equation with an absorbent term and a linear external force

Recently, the generalized fractional reaction–diffusion equation subject to an external linear force field has been proposed to describe the transport processes in disordered systems. The solution of this generalized model can be formally expressed in closed form through the Fox function. For the sack of completeness, we dedicate this work to construct a neatly derivation of the generalized fractional reaction–diffusion equation. Remarkably, such derivation could in general offer some novel and inspiring inspection to the phenomena of anomalous transport. For instance, there is a strong evidence that the fractional calculus offers some physical insight into the origin of fractional dynamics for a systems which exhibit multiple trapping.     

On analytical and numerical approaches to division and label structured population models

Even among cells in the same population, the concentration of a protein or cellular constituent can vary considerably. This heterogeneity can arise from several sources, including differences in kinetic rates between cells and distribution of cellular constituents through cell division. Compartmental models have been used to describe the distribution of the number of divisions undergone by cells in a population. More recently, such models have been coupled with the dynamics of intracellular labels and analytical solutions to the division and label structured population equations have been found. However, such approaches have thus far focused on simple models of intracellular dynamics such as the decay of an intracellular label. In this work, we demonstrate that analytical solutions are possible for more general forms of intracellular dynamics offering the promise to lend mathematical insight into population dynamics in more realistic biological settings.