Consensus formation of two-level opinion dynamics

Opinion dynamics have received significant attention in recent years. This paper proposes a bounded confidence opinion model for a group of agents with two different confidence levels. Each agent in the population is endowed with a confidence interval around her opinion with radius αd or (1-α)d, where α ∈ (0,1/2] represents the differentiation of confidence levels. We analytically derived the critical confidence bound d_c = 1/(4α) for the two-level opinion dynamics on ?. A single opinion cluster is formed with probability 1 above this critical value regardless of the ratio p of agents with high/low confidence. Extensive numerical simulations are performed to illustrate our theoretical results. Noticed is a clear impact of p on the collective behavior: more agents with high confidence lead to harder agreement. It is also experimentally revealed that the sharpness of the threshold d_c increases with α but does not depend on p.     

Deffuant model with general opinion distributions: First impression and critical confidence bound

In the Deffuant model for social influence, pairs of adjacent agents interact at a constant rate and mix up their opinions (represented by continuous variables) only if the distance between opinions is short according to a threshold. We derive a critical threshold for the Deffuant model on , above which the opinions converge toward the average value of the initial opinion distribution with probability one, provided the initial distribution has a finite second order moment. We demonstrate our theoretical results by performing extensive numerical simulations on some continuous probability distributions including uniform, Beta, power‐law and normal distributions. Noticed is a clear differentiation of convergence rate that unimodal opinions (regardless of being biased or not) achieve consensus much faster than even or polarized opinions. Hereby, the emergence of a single mainstream view is a prominent feature giving rise to fast consensus in public opinion formation and social contagious behavior. Finally, we discuss the Deffuant model on an infinite Cayley tree, through which general network architectures might be factored in. © 2013 Wiley Periodicals, Inc. Complexity 19: 38–49, 2013     

DIFFICULTY FOR CONSENSUS IN SIMULTANEOUS OPINION FORMATION OF SZNAJD MODEL

In the Sznajd model of 2000, a pair of neighboring agents on a square lattice convinces its six neighbors of the pair opinion if and only if the two agents of the pair share the same opinion. Now we replace the usual random sequential updating rule (corresponding to informal encounters) by simultaneous updating (like in formal votes during meetings) and find that this change makes a complete consensus much more difficult. The reason is that for simultaneous updating some agents simultaneously receive conflicting messages from different neighbor pairs (called frustration) and thus refuse to change their opinion.     

Poisson分布下基于鞍点逼近的慢性病风险差的置信区间构造

风险差是流行病学中重要的指标之一,常用来比较两种治疗或两种诊断的有效性.因此,风险差区间的精确估计对流行病病情的诊断以及治疗方案的选择有很重要的意义.结合Poisson抽样的优点以及慢性病发病周期长和发病率低的特点,利用鞍点逼近方法来构造了Poisson分布下风险差的置信区间.同时,通过实例和Monte Carlo模拟对传统的四种区间构造方法进行评价.模拟结果表明:在小样本情况下,鞍点逼近方法得到的置信区间大多数能保证覆盖率近似于期望的置信水平并且使得区间长度最短,是一种很好的置信区间构造方法.     

Meet,discuss, and segregate!

We present a model of opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions toward an average opinion, whereas low thresholds result in several opinion clusters. The model is further generalized to network interactions, threshold heterogeneity, adaptive thresholds, and binary strings of opinions. © 2002 Wiley Periodicals, Inc.     

平滑转换向量误差修正模型的非线性协整SupLM检验

本文考虑平滑转换向量误差修正模型的非线性协整检验问题,相对于传统的两步检验法,给出已知协整向量下的直接检验非线性协整的SupLM检验方法,通过定义平滑转换协整模型,给出SupLM检验统计量,在原假设下得到检验统计量的渐近分布和相关的bootstrap算法,模拟结果和实例计算表明了该方法的有效性。     

Asymptotics of an Efficient Monte Carlo Estimation for the Transition Density of Diffusion Processes

Discretized simulation is widely used to approximate the transition density of discretely observed diffusions. A recently proposed importance sampler, namely modified Brownian bridge, has gained much attention for its high efficiency relative to other samplers. It is unclear for this sampler, however, how to balance the trade-off between the number of imputed values and the number of Monte Carlo simulations under a given computing resource. This paper provides an asymptotically efficient allocation of computing resource to the importance sampling approach with a modified Brownian bridge as importance sampler. The optimal trade-off is established by investigating two types of errors: Euler discretization error and Monte Carlo error. The main results are illustrated with two simulated examples.      

Optimization algorithm with probabilistic estimation

In this paper, we present a stochastic optimization algorithm based on the idea of the gradient method which incorporates a new adaptive-precision technique. Because of this new technique, unlike recent methods, the proposed algorithm adaptively selects the precision without any need for prior knowledge on the speed of convergence of the generated sequence. With this new technique, the algorithm can avoid increasing the estimation precision unnecessarily, yet it retains its favorable convergence properties. In fact, it tries to maintain a nice balance between the requirements for computational accuracy and those for computational expediency. Furthermore, we present two types of convergence results delineating under what assumptions what kinds of convergence can be obtained for the proposed algorithm.The work reported here was supported in part by NSF Grant No. ECS-85-06249 and USAF Grant No. AFOSR-89-0518. The authors wish to thank the anonymous reviewers whose careful reading and criticism have helped them improve the paper considerably.     

慢性病发病率置信区间的构造

在流行病研究中,发病率是一个重要指标,该指标反映的是特定人群中某种疾病的发病程度.因此,对它的置信区间的构造在判别疾病发病程度上具有重要的医学意义.对于一些慢性疾(如癌症或心血管等),由于其发病周期长,发病率低,Poisson抽样下要比二项抽样,逆项抽样更符合事实.利用四种方法研究了泊松分布下慢性病发病率的置信区间构造,并通过Monte Ca·lo模拟对四种方法的表现性能进行比较.模拟结果表明:当发病率较高时,枢轴量方法无论在区间长度还是覆盖率上都袁现最佳:当发病率相对较低时,枢轴量方法在区间长度上略次于Wald统计量方法和得分方法,但是在覆盖率上袁现最佳.因此,枢轴量方法整体上表现的很好.     

二项抽样下基于鞍点逼近方法的流行病相对风险置信区间构造

相对风险是流行病学研究中的重要指标之一,它是度量一种暴露因素是否与某病的致病有联系的统计指标.以该指标的数值大小来表明这一暴露因素对某病的发生具有何种影响及影响的大小,体现了暴露与疾病的关联程度.精确地得到相对风险指标的区间估计,对病因推断具有重要意义.但是由于相对风险指标的估计量是两个概率值的估计量的比值,要得到其精确分布一般而言是很困难的,因此已有研究成果大都采用渐近方法估计相对风险的置信区间,这在小样本情况下表现不佳.在二项抽样条件下,对相对风险的点估计、置信区间估计一直被人们所关注.在二项采样下利用鞍点逼近的方法构造相对风险的置信区间,并通过实例与蒙特卡洛模拟,与传统的置信区间构造方法对比,模拟结果显示其优点,尤其是在小样本量条件下估计效果比较好.     

The information-based complexity of approximation problem by adaptive Monte Carlo methods

In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MWpr,α(Td), 1 < p < ∞, in the norm of Lq(Td), 1 < q < ∞, by adaptive Monte Carlo methods. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of this problem.     

有类间距离因素聚类结果的比较分析

本文对于有类间距离因素聚类结果的比较，提出了类结构的空间描述方法和比较相似度的度量指标──夹角余弦，并推导出它的一些性质．最后，用蒙特卡洛模拟的结果阐明用夹角余弦作为聚类结果的相似性度量指标是合理的．     

非仿射随机波动率的欧式障碍期权定价

研究非仿射随机波动率模型的欧式障碍期权定价问题时,首先介绍了非仿射随机波动率模型,其次利用投资组合和It^o引理,得到了该模型下扩展的Black-Schole偏微分方程.由于这个方程没有显示解,因此采用对偶蒙特卡罗模拟法计算欧式障碍期权的价格.最后,通过数值实例验证了算法的可行性和准确性.     

Improved Bounds and Simulation Procedures on the Value of the Multivariate Normal Probability Distribution Function

Improved bounds and simulation procedures on the value of the multivariate normal probability distribution function value are given in the paper. The author's variance reduction technique was based on the Bonferroni bounds involving the first two binomial moments only. The new variance reduction technique is adapted to the most refined new bounds developed in the last decade for the estimation the probability of union respectively intersection of events. Numerical test results prove the efficiency of the simulation procedures described in the paper.     

VORTEX DYNAMICS OF THE ANISOTROPIC GINZBURG-LANDAU EQUATION

In this article, using coordinate transformation and Gronwall inequality, we study the vortex motion law of the anisotropic Ginzburg-Landau equation in a smooth bounded domain Ω  R2, that is, ■tuε = 2Σ/j,k=1 (ajkj■xjkuε)xj + b(x)(1-ε|ε|2)uε/2u, x ∈Ω, and conclude that each vortex bj(t) (j=1, 2,···, N) satisfies dbdjt(t)= -(a1k(bj(t)b)■(xk))a(a (bj(t)), a2k(bj (t))/xk a(bj (t)) a(bj (t)) , where a(x) =(a11a22-a122(1/2)). We prove that all the vortices are pinned together to the critical points of a(x). Furthermore, we prove that these critical points can not be the maximum points.     

基于分子动力学模拟的金属构件的弹-塑性分解方法

针对金属多晶材料构件的分子动力学（MD）模拟,本文提出了一种新的弹-塑性分解方法.文章将MD运动轨迹分解为结构变形和热振动,给出了计算结构变形的方法和近似公式;针对金属多晶材料构件的当前构型,给出了基于FCC|BCC晶胞和四原子占位的四面体单元相组合的连续变形函数及计算变形梯度的算法;利用原子-连续关联模型,发展了计算当前构型应力场和弹性张量的算法.分析了当构件承受过大载荷后在材料内部所产生的微观缺陷,并将其分类标定为位错、层错、挛晶界、晶界和空位等;对于层错和挛晶界讨论了在弹性卸载过程中应满足的刚体运动约束方程;利用极小势能原理构造了基于当前构型的弹性卸载算法,进而给出了完整的基于MD模拟的计算弹-塑性应变的算法.最后,针对单晶铜纳米线拉伸的MD模拟,计算了弹-塑性应变场,验证了本文方法的合理性.
本文提出的基于MD模拟的弹-塑性分解方法,为从微观到宏观的多尺度和多模型耦合计算提供了算法支撑.     

Fast mixing for independent sets,colorings, and other models on trees

We study the mixing time of the Glauber dynamics for general spin systems on the regular tree, including the Ising model, the hard‐core model (independent sets), and the antiferromagnetic Potts model at zero temperature (colorings). We generalize a framework, developed in our recent paper (Martinelli, Sinclair, and Weitz, Tech. Report UCB//CSD‐03‐1256, Dept. of EECS, UC Berkeley, July 2003) in the context of the Ising model, for establishing mixing time O(nlog n), which ties this property closely to phase transitions in the underlying model. We use this framework to obtain rapid mixing results for several models over a significantly wider range of parameter values than previously known, including situations in which the mixing time is strongly dependent on the boundary condition. We also discuss applications of our framework to reconstruction problems on trees. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

DYNAMICS OF RELATIVISTIC FLUID FOR COMPRESSIBLE GAS

In this paper the relativistic fluid dynamics for compressible gas is studied.We show that the strict convexity of the negative thermodynamical entropy preserves invariant under the Lorentz transformation if and only if the local speed of sound in this gas is strictly less than that of light in the vacuum.A symmetric form for the equations of relativistic hydrodynamics is presented,and thus the local classical solutions to these equations can be deduced.At last,the non-relativistic limits of these local cla...