Opinion Dynamics
观点讨论的英语作文
观点讨论的英语作文Title: The Art of Engaging in Opinion Discussions。
Opinion discussions serve as a cornerstone of intellectual exchange, fostering critical thinking, broadening perspectives, and nurturing empathy. However, navigating such discussions requires finesse, respect, and an open mind. In this essay, I will explore the dynamics of opinion discussions, their importance, and strategies for effective engagement.To begin with, opinion discussions provide a platform for individuals to articulate their perspectives, beliefs, and values. These exchanges enable participants to express their thoughts, challenge prevailing notions, andcontribute to collective knowledge. Moreover, they encourage individuals to confront differing viewpoints, promoting intellectual growth and understanding.One crucial aspect of opinion discussions is respectfuldialogue. Respect forms the foundation of productive discourse, fostering an environment where individuals feel valued and heard. This involves active listening, acknowledging the validity of opposing viewpoints, and refraining from personal attacks or derogatory language. By fostering mutual respect, opinion discussions can transcend mere arguments and evolve into meaningful exchanges of ideas.Furthermore, effective communication skills are essential for navigating opinion discussions. This includes clarity in expression, logical reasoning, and evidence-based arguments. Articulating one's perspective cogently not only strengthens their argument but also facilitates comprehension and engagement from others. Additionally, active participation, asking probing questions, and seeking clarification demonstrate a genuine interest in understanding alternative viewpoints.Another key aspect of opinion discussions is empathy. Empathy entails putting oneself in another's shoes, recognizing their experiences, and understanding thecontext shaping their beliefs. By empathizing with others, individuals can bridge ideological divides, cultivate compassion, and foster mutual understanding. Empathy facilitates constructive dialogue by fostering a sense of shared humanity and common ground.Moreover, embracing diversity enriches opinion discussions by incorporating a wide array of perspectives and experiences. Diversity encompasses not only differences in opinion but also cultural backgrounds, identities, and life experiences. Embracing diversity fosters inclusivity, challenges biases, and broadens horizons. It encourages individuals to confront their own biases, assumptions, and preconceptions, fostering a more nuanced understanding of complex issues.In addition, critical thinking plays a pivotal role in opinion discussions. Critical thinking involves evaluating information objectively, discerning fact from opinion, and analyzing arguments rigorously. By honing critical thinking skills, individuals can discern logical fallacies, identify underlying assumptions, and construct well-reasonedarguments. Critical thinking fosters intellectual autonomy and equips individuals to navigate the complexities of opinion discussions effectively.Furthermore, cultivating a growth mindset is essential for productive opinion discussions. A growth mindsetentails embracing challenges, viewing feedback as an opportunity for growth, and persisting in the face of obstacles. It encourages individuals to approach opinion discussions with humility, recognizing that they have muchto learn from others. By fostering a growth mindset, individuals can overcome confirmation bias, embrace intellectual curiosity, and engage in continuous learning.In conclusion, opinion discussions are invaluable for fostering intellectual exchange, broadening perspectives, and nurturing empathy. By cultivating respect, effective communication skills, empathy, diversity, critical thinking, and a growth mindset, individuals can engage in productive and meaningful dialogue. Ultimately, opinion discussions serve as a catalyst for personal growth, social progress, and the advancement of knowledge.。
观点动力学综述
观点动力学综述
观点动力学是指人们在社会交往中持续形成、调整和改变自己的态度和行为，它是社会心理学的一个重要分支。
观点动力学的研究对象包括个体如何形成、维持和变化其观点，以及其对他人观点的影响力。
观点动力学的研究方法主要包括实验研究和观察研究。
在观点动力学的研究中，人们通常会遵循认知一致性理论、社会比较理论、社会认知理论和社会影响理论等基本原则。
这些原则通常涉及到个体的态度、信念、动机、情感和行为等方面。
观点动力学的研究主要有以下几个方面：
1. 观点变化的原因：研究个体为何会改变他们的观点，包括认知不一致、社会压力、信息来源、知识、情感等因素。
2. 观点变化的过程：研究个体在改变观点的过程中经历了哪些心理过程，包括认知冲突、认知调节、认知重组和认知选择等。
3. 观点变化的影响：研究观点变化对个体及其身边环境的影响，包括对个体的态度、信念、情感和行为等方面的影响，以及对他人的影响。
4. 观点变化的策略：研究有哪些策略可以帮助个体改变他们的观点，包括说服、影响等策略。
总之，观点动力学的研究有助于人们更好地理解人类社会交往
中的各种动态过程，以及如何管理自己的观点和影响他人的观点。
具有类万有引力的有界置信观点动力学分析与应用
具有类万有引力的有界置信观点动力学分析与应用刘青松 1习晓苗 1柴 利1摘 要 在社会网络中, Hegselmann-Krause 模型描述了置信阈值内不同邻居对个体的观点影响权重都相同且邻居对个体的吸引力与它们的观点差值成正比, 这是不切实际的. 为了克服经典Hegselmann-Krause 模型的不足, 提出具有类万有引力的有界置信观点动力学模型, 描述个体观点的更新依赖于观点之间的差值和邻居的权威性, 且不同邻居对个体的观点影响权重不同. 根据置信矩阵的性质证明观点的收敛性, 并分析具有衰减置信阈值的观点动力学行为, 给出观点收敛速率的显式解. 最后, 利用提出的观点动力学模型, 研究社会心理学中的“权威效应”和“非零和效应”. 仿真结果表明, 邻居的权威性有利于观点达成一致.关键词 观点动力学, 类万有引力, 有界置信, 社会网络, 收敛性引用格式 刘青松, 习晓苗, 柴利. 具有类万有引力的有界置信观点动力学分析与应用. 自动化学报, 2023, 49(9): 1967−1975DOI 10.16383/j.aas.c211134Analysis and Application of Bounded Confidence Opinion DynamicsWith Universal Gravitation-likeLIU Qing-Song 1 XI Xiao-Miao 1 CHAI Li 1Abstract In the social networks, the Hegselmann-Krause model describes that the different neighbors within the confidence threshold have the same influence weight on the individual ＇s opinion, and the attractiveness of neigh-bors to the individual is proportional to the opinion distance, which is unrealistic. In order to overcome the short-coming of the classical Hegselmann-Krause model, we propose a bounded confidence opinion dynamics model with universal gravitation-like in this paper, which captures the update of the individual opinion depending on both the opinion distance and the authority of neighbors, and it is shown that different neighbors have different influence weights on individual opinions. The convergence of opinions is proved in terms of the property of confidence matrix,and moreover, the dynamic behavior of the opinion with decaying confidence threshold is analyzed and the explicit solution of the opinion convergence rate is given. Finally, by employing our proposed opinion dynamics model, we study the authority effect and the non-zero-sum effect in social psychology. Simulation analyses reveal that the au-thority of the neighbor is beneficial to opinion achieving consensus.Key words Opinion dynamics, universal gravitation-like, bounded confidence, social networks, convergenceCitation Liu Qing-Song, Xi Xiao-Miao, Chai Li. Analysis and application of bounded confidence opinion dynamics with universal gravitation-like. Acta Automatica Sinica , 2023, 49(9): 1967−1975在过去的几十年中, 随着多智能体系统的兴起[1−3],社会网络引起了学者们的广泛关注, 涌现了许多研究成果[4]. 例如, Ghaderi 等[5]研究了具有固执个体的社会网络观点的收敛性, 给出了观点收敛时间的上界和下界. Xia 等[6]分析了具有偏见同化的非线性观点动力学模型的稳定性. Liu 等[7]提出一种观点扩散模型, 描述了双层连通网络的观点扩散过程,探讨了在所有持有相同观点的耦合主体下, 两种观点在三种类型的两层互连网络中的传播. 针对强连通的社会网络, Ye 等[8]研究了表达观点和私人观点之间的差异, 且给出了网络上保证意见指数快速收敛到极限的一般条件. 针对拟强连通社会网络, 刘青松等[9]研究了多维观点动力学行为, 给出了表达和私人观点收敛的充分条件. Hou 等[10]分析了具有有界置信的表达观点和私人观点动力学行为, 给出了最终聚类数主要由封闭个体率决定的结论.近年来, 学者们针对多自主体系统进行研究[11−14],提出了一些经典观点动力学模型, 促进了社会网络中观点动力学的深入研究. 20世纪50年代, 社会心收稿日期 2021-11-30 录用日期 2022-04-28Manuscript received November 30, 2021; accepted April 28,2022国家自然科学基金(61903282, 62173259), 中国博士后科学基金(2020T130488)资助Supported by National Natural Science Foundation of China (61903282, 62173259) and China Postdoctoral Science Founda-tion (2020T130488)本文责任编委 莫红Recommended by Associate Editor MO Hong 1. 武汉科技大学信息科学与工程学院 武汉 4300811. School of Information Science and Engineering, Wuhan Uni-versity of Science and Technology, Wuhan 430081第 49 卷 第 9 期自 动 化 学 报Vol. 49, No. 92023 年 9 月ACTA AUTOMATICA SINICASeptember, 2023理学家French[15]提出基于个体的观点形成模型. 1974年, DeGroot[16]提出基于个体加权平均的观点动力学模型, 即后来的DeGroot模型. 通过针对每个个体引入偏差, 将DeGroot模型推广到非线性观点动力学模型[6]. 另一方面, 通过引入个体对自身初始观点的固执, 文献[17]提出Friedkin-Johnsen 模型. 之后, Parsegov等[18]将Friedkin-Johnsen模型推广到了多维观点动力学模型. Tian等[19]研究了问题序列上的Friedkin-Johnsen观点动力学模型,给出了问题序列上观点达到一致的充要条件. 在考虑每次观点更新过程中, 随机选取一对个体进行观点交流, Deffuant等[20]提出Deffuant-Weisbuch模型. 随后, 通过两种不同的方法推广了Deffuant-Weisbuch模型[21], 验证了观点几乎必然达到一致.最近, Dong等[22]研究了基于领导概念的观点动态共识构建过程, Mei等[23]提出基于评价网络的学习过程模型.上述观点动力学模型是线性模型, 经典的Heg-selmann-Krause模型[24]是非线性模型, 描述了每个个体只与其置信阈值内的邻居进行观点交互. 与Def-fuant-Weisbuch模型[20]相比, Hegselmann-Krause 模型每次进行观点交流的个体的数量更多, 因而交流效率更高, 观点能够更快地收敛或者达成一致.在实际应用方面, Hegselmann-Krause观点动力学模型可应用于机器人平面、空间交会问题[25]和社会心理学中“权威效应”[26]等方面的研究. 故研究Heg-selmann-Krause或有界置信观点动力学模型, 具有重要应用价值和意义.近年来, 国内外学者针对有界置信模型进行了较为深入的研究[27], 例如Canuto等[28]通过欧拉方法, 研究了基于有界置信模型的动态系统的一致性问题. 通过考虑噪声环境, Su等[29]提出了具有噪声的有界置信模型, 展示了随机噪声如何显著地影响同步的观点, 给出了观点达成拟一致的充分条件.基于改进的有界置信模型, 针对初始观点分布, Yang 等[30]给出了观点收敛到一个聚类的充分条件. 通过正规化交流权重的凸性和Gronwall-Halanay型不等式, Haskovec[31]研究了具有时滞的有界置信模型的渐近一致性问题. 基于离散异构的有界置信模型, Vasca等[32]提出了一种基于非影响相似度区间的个体置信阈值自适应策略, 分析了有限时间的观点动力学行为.鉴于上述对有界置信观点动力学模型国内外研究现状的分析, 目前主要存在以下三个问题: 1)在改进的观点动力学模型中, 邻居对个体的影响力与其观点差异值成正比, 与实际情景存在一定的差距[28];2) 现有文献主要是采用仿真方法研究改进的有界置信模型, 缺乏较为完整的理论研究框架[27]; 3)现有的有界置信模型研究中, 较少研究观点动力学模型的应用[32], 例如考虑建立的观点动力学模型在社会心理学中的应用. 此外, 根据社会心理学中的认知理论可知[33], 由于不同个体社会背景和认知能力不一样, 不同邻居对个体产生的影响就会不一样[33];个体与邻居的观点差异值越大, 邻居对其影响应该越小[34].为了克服上述问题, 本文提出具有类万有引力的有界置信模型, 并分析了观点的演化问题. 本文的主要贡献如下:1)提出了新的具有类万有引力的有界置信观点动力学模型. 解决了Canuto等[28]模型中个体的影响力与其观点差异值成正比这一不符合实际情景的社会现象, 并考虑了个体的权威性;2)在理论上给出了观点收敛的充分条件且分析了基于衰减置信阈值的观点动力学模型, 完善了Chen等[27]的理论研究内容;3)应用本文提出的具有类万有引力的有界置信观点动力学模型, 研究了社会心理学中的“权威效应”和“非零和效应”[35], 填补了Vasca等[32]缺乏的应用研究;4)得到了邻居的权威性和正态分布的初始观点都有利于观点达成一致, 这一重要结论.1 问题描述首先, 回顾经典的有界置信观点动力学模型[24]:i∈V={1,2,···,n}x i(k)iN i=N(i,x(k))={j∈V||xj(k)−xi(k)|≤ε} i|N i|iε式中, , 表示个体的观点值.表示个体所有邻居的集合, 表示个体的邻居数目, 其中为置信度阈值.i1/|N i|ixj(k)−xi(k)j i|xj(k)−xi(k)|通过模型(1)可知, 个体的邻居对其影响权重全部相同即其权重都为. 事实上, 不同个体具有不同的认知水平和不一样的教育背景, 个体受影响程度或被其他个体影响的程度是不同的. 另一方面, 个体的观点值更新依赖于, 即邻居对个体的吸引力与观点差异值成正比. 实际上, 个体与邻居的观点差异值越大, 其对个体的影响越小. 为此, 本文提出一个具有类万有引力的有界置信观点动力学模型:1968自 动 化 学 报49 卷∑w ij (k )式中, 社会影响权重 为:w ij (k )由于社会影响权重 中:是受万有引力表达式的启发[27], 故称观点动力学模型(2)为具有类万有引力的有界置信观点动力学模型.tanh (·)众所周知, 万有引力的大小与物体的质量以及两个物体之间的距离有关. 物体的质量越大, 它们之间的万有引力就越大; 物体之间的距离越远, 它们之间的万有引力越小. 根据社会心理学中的认知理论可知[33], 个体权威性或者社会话语权越大, 其影响力(权重)越大; 个体与邻居的观点差异值越大, 邻居对其影响应该越小[34]. 根据上述关系, 将万有引力与影响力对应, 物体的质量与个体权威性对应, 物体之间的距离与观点差异值对应. 另一方面,类似于经典的Hegselmann-Krause 模型, 保证权重在[0, 1]之间, 故引入 函数给予保证. 综上所述, 便可得到权重式(4). 此外, 在本文的第4节中, 应用所提出的观点动力学模型研究社会心理学中的“权威效应”和“非零和效应”. 从应用结果可进一步地说明权重式(4)的合理性.d ij j i |N j |i j d ij =1d ij (k )j N (j,x (k ))i j x j (k )−x i (k )j i i 事实上, 描述了个体 与个体 观点值越接近, 彼此间的影响也就越大. 此外, 描述了个体 的邻居 的权威性或者社会话语权[27]. 从而本文提出的模型也很好地描述了, 在一个社会中, 拥有大量人脉资源的人享有更多的话语权, 对他人的社会影响也就更大. 注意到, 如果 , 则具有类万有引力的有界置信观点动力学模型(2)退化成经典Hegselmann-Krause 模型(1). 事实上, 是一个关于个体 邻居的个数 和个体 与个体 观点值之差 的函数. 易知个体 的邻居数越多, 与个体 的观点值相差越小, 则其对个体 的差异影响权重越大, 其函数关系见图1.j i w ij (k )(x j (k )−x i (k ))根据本文提出的具有类万有引力的有界置信观点动力学模型(2)可知, 个体 对个体 的影响由 所决定, 其函数关系见图2.x j (k )−x i (k )j N (j,x (k ))i j N (j,x (k ))j i x j (k )−x i (k )i j 由图2可知, 当 一定时, 个体 的邻居数 越多, 其对个体 的影响越大. 当个体 的邻居数 一定时, 个体 与个体 的观点值之差 越大, 个体 的观点值受到个体 的影响先增大后减小. 因此, 要想某个体能对指定个体施加更大的影响, 需要折中进行考虑.0.20−0.2002040601−1w i j (k )(x j (k ) − x i (k ))|N j |x j (k) − x i (k )j i 图 2 个体 对个体 观点的影响j iFig. 2 The influence of individual on theopinion of individual本文主要研究具有类万有引力的有界置信模型(2)的观点演化问题, 给出了观点收敛的充分条件,并将所提出的观点动力学模型应用到社会心理学中的“权威效应”和“非零和效应”.2 收敛性分析本节将分析具有类万有引力的有界置信观点动力学模型(2)的收敛性.i ∈V x i (0)x ∗i ∈R 定义 1. 在观点动力学模型(2)中, 对任意个体 的初始观点值 , 如果存在 , 使得:α∈R 则称模型(2)收敛. 特别地, 如果存在定常数 ,使得:1.00.5001−1d i j (k )|N j |x j (k) − x i (k )204060d ij (k )|N j |x j (k )−x i (k )图 1 关于 和 的函数图d ij (k )|N j |x j (k )−x i (k )Fig. 1 The trajectories of with respect to and 9 期刘青松等: 具有类万有引力的有界置信观点动力学分析与应用1969则称观点达成一致.x i (0)∈[0,1],i ∈V 定理 1. 对于任意观点初值 ,观点动力学模型(2)收敛.证明. 模型(2)可重写为:模型(5)可进一步写为:A (k,x (k ))a ij (k )式中, 置信矩阵 的元素为:A (k,x (k ))θ≥00≤tanh (θ)≤1∑j ∈N i \{i }w ij (k)∈(0,1)易知社会影响矩阵 是行随机矩阵.注意到, 对任意的 , 易得 . 则由式(3)可知, . 故:A (k,x (k ))即 的对角线元素大于0.j i j /∈N i w ij (k )=0i /∈N j w ji (k )=0a ij (k )=0a ji (k )=0,∀i,j ∈V A (k,x (k ))δ>0A (k,x (k ))δ另一方面, 当个体 与个体 的观点值之差大于置信阈值时即 , 则 . 类似地, ,则 . 因此, 当且仅当 . 此外, 易知 中一直存在正元素,即存在 , 使得 的最小正元素大于 .A (k,x (k ))综上所述, 矩阵 满足文献[36]给出模型收敛的充分条件, 从而模型(6)收敛. 故观点动力学模型(2)收敛. □根据定理1, 可得下列推论.x i (0)∈[0,1],i ∈V k τA (k,x (k ))=(1/n )1n 1T n ,k ≥k τ1n =[1,1,···,1]T 推论 1. 对于任意观点初值 ,如果观点动力学模型(6)在经过 次演化后观点达成一致, 则置信矩阵 ,其中 .k τ|x i (k )−x j (k )|→0,∀i,j ∈V,k ≥k τN i =N j =n,证明. 如果观点经过次演化后达成一致, 即 且 则:由式(3)可得:()a ij =1/n,k ≥k τ进一步地, 根据式(7)可知, . □为了得到进一步的结果, 令:x i (0)∈[0,1],i ∈V ε=1推论 2. 考虑观点动力学模型(2), 对于任意观点初值 . 如果置信阈值 且:则ε=1|N i |=n 证明. 由于置信阈值 , 则所有个体均可交流, 即 . 由观点动力学模型(2)可知:j i w ij (k )(x j (k )−x i (k ))i j w ji (k )(x i (k )−x j (k ))w ij (k )=w ji (k )注意到, 邻居 对个体的影响为 ,类似地, 邻居 对个体 的影响为 , 然而, . 易得:则式(9)可退化为:即x (k )=x (0)故 . □第2节主要考虑的是置信阈值不变的情况. 事实上, 观点动力学模型可看作一个谈判的过程模型.一方面, 个体期望它的邻居在每一轮谈判中显著地向它的观点靠拢, 以便继续谈判, 衰减置信阈值可描述这一情景[37]; 另一方面, 具有衰减置信阈值的观点动力学模型可应用于研究图中的社区检测[37]和社会心理学中的“非零和效应”. 故第3节将分析基于衰减置信阈值的观点动力学模型. 此外, 本文将利用建立的具有衰减置信阈值的Hegselmann-Krause 观点动力学模型研究社会心理学中的“非零1970自 动 化 学 报49 卷和效应” (见第4.2节).3 衰减的置信阈值为了描述个体在谈判的过程中, 个体期望它的邻居在每一轮谈判中显著地向它的观点靠拢, 以便继续谈判. 本节考虑下列具有衰减置信阈值的观点动力学模型:式中:和R >00<ρ≤1式中, 和 .x i (0)∈[0,1],i ∈V x i (k ),i ∈Vx i ∗i k ∈V 定理 2. 考虑观点动力学模型(10), 对于任意观点初值 , 观点 是收敛的. 进一步地, 令 表示个体 的最终观点值,对于所有的 , 则:证明. 根据式(10), 有:由式(12), 可得:w ij (k )∈(0,1/|N ρi |]j ∈N ρw ij (k )≤1注意到, , 则, 故:∀k,τ=0,1,···令 , 则由式(14)可知:因此:ρ∈(0,1)x i (k )k =0,1,···τ→∞式中, . 易知序列 , 是一个Cauchy 序列, 故其收敛. 通过令式(15)中的, 则可得式(13). □ε=1类似于观点动力学模型(2), 如果置信度阈值 且式(11)退化为式(8). 则观点动力学模型(10)具有和推论2一样的结论.4 观点动力学模型的应用4.1 权威效应本节将利用本文提出的具有类万有引力的有界置信观点动力学模型(2), 研究普遍存在的社会心理学现象: 权威效应. 所谓权威效应是指一个人要是地位高、有威信、受人敬重, 那他所说的话及所做的事就容易引起别人重视, 并让他们相信其正确性.权威效应的普遍存在, 一方面是由于人们总认为权威人物往往是正确的楷模, 服从他们会使自己具备安全感, 增加不会出错的保险系数; 另一方面, 由于人们总认为权威人物的要求往往和社会规范相一致, 按照权威人物的要求去做, 会得到各方面的赞许和奖励. 在现实生活中, 有很多利用权威效应的例子, 比如做广告时请权威人物赞誉某种产品, 在辩论说理时引用权威人物的话作为论据等. 在人际交往中, 利用权威效应, 能够引导或改变对方的观点和行为.考虑由10个个体组成的社会网络, 设初始观点值为:ε=0.2|N 4|=8置信阈值 . 根据初始观点值和置信阈值可得初始时刻个体之间的网络结构, 如图3所示(图中自环未画出). 易知个体4具有8个邻居即, 具有最大的权威性或者话语权.w ij 0.510.21w ij 0.460.24当观点动力学模型(2)中 为式(8)时, 即不考虑邻居的权威性, 其观点演化曲线如图4(a)所示, 其中形成两簇的最终观点值分别为 和 .当观点动力学模型(2)中 为式(3)时, 即考虑邻居的权威性, 其观点演化曲线如图4(b)所示, 其中形成两簇的最终观点值分别为 和 . 出现这一现象是由于受到了权威者个体4的影响 (图4中虚线为个体4的观点曲线), 两簇观点都向个体4的观点值靠近.为了说明初始条件的客观性, 可随机选取一个9 期刘青松等: 具有类万有引力的有界置信观点动力学分析与应用1971x (0)=[0.25,0.25,0.32,0.45,0.5,0.7,0.7,0.7,0.7,0.8]T ,|N 5|=7个体为权威个体, 不失一般性地, 选取个体5为权威个体, 个体初始观点值可设为 其网络拓扑图如图5所示. 易知, 个体5具有7个邻居即 .类似地, 其观点演化曲线如图6所示, 可以看出, 由于受到权威个体5的影响 (图6中虚线为个体5的观点曲线), 两簇观点都向个体5的观点值靠近.4.2 非零和效应本节将利用本文建立的具有衰减置信阈值的观点动力学模型(10), 研究社会心理学中“非零和效应”.“非零和效应”是一种合作下的博弈, 博弈中做一定的让步, 双方的收益或损失的总和不是零, 观点达成一致, 谈判便可成功[35]. 另一方面, 衰减置信阈值可描述个体期望它的邻居在每一轮谈判中显著地向它的观点靠拢, 以便继续谈判.R =0.8ρ=0.7x i (0)∈[0,1],i ∈V x (0)∈[0,1]n 为了利用本文提出的模型(10)研究社会心理学中“非零和效应”, 令 , , 当个体观点初值 均匀分布时, 观点动力学模型(10)的仿真结果如图7(a)所示, 观点达到了一致, 说明谈判取得成功, 实现了“非零和效应”.当个体观点初值 正态分布时, 其结果如图7(b)所示, 观点达到一致性的速度比个体观点初值均匀分布情况快, 说明谈判过程中, 当持中立观点的人较多时, 谈判取得成功的时间更少.1020102000.51.000.51.0xk /s k /s x(a)(b)图 7 非零和效应Fig. 7 Sum non-zero effect5 仿真分析5.1 基于固定置信阈值的模型仿真分析n =50ε=0.3x i (0)∈[0,1],i ∈V 本节将通过仿真分析本文所得到的理论结果.设群体总个体数 , 置信度阈值 , 观点初值 均匀分布. 将改进的Heg-12345678910图 3 网络拓扑结构 (个体4为权威个体)Fig. 3 Network structure (individual 4 is theauthoritative individual)0.20.40.60.8xk /s (a)(b)k /s 00.20.40.60.8图 4 权威效应 (个体4为权威个体)Fig. 4 Authority effect (individual 4 is theauthoritative individual)12345678910图 5 网络拓扑结构 (个体5为权威个体)Fig. 5 Network structure (individual 5 is theauthoritative individual)0.20.40.60.8x k /s k /s x0.20.40.60.8(a)(b)图 6 权威效应 (个体5为权威个体)Fig. 6 Authority effect (individual 5 is theauthoritative individual)1972自 动 化 学 报49 卷selmann-Krause 观点动力学模型[32]与本文提出的观点动力学模型(2)进行对比, 其观点演化曲线分别如图8(a)和图8(b)所示, 可以看出, 在改进的Hegselmann-Krause 模型[32]中, 观点形成拟一致.有趣的是在具有类万有引力的有界置信模型(2)中, 观点则出现两极分化. 这是因为在文献[32]改进的Hegselmann-Krause 模型中, 观点相似的个体不再进行交互, 而本文提出的具有类万有引力的有界置信模型(2)中, 考虑了影响权重的互异性.02040600.51.000.51.0xk /s020改进的模型模型 (2)|N j | = 14060204060204060k /s x00.51.00246xk /s k /s h (k)(a)(b)(d)(c)图 8 初值为均匀分布时的观点演化Fig. 8 Opinion evolution when the initial value isuniformly distributed|N j |=1当在具有类万有引力的有界置信模型(2)中不考虑个体权威性时即 , 其观点演化曲线如图8(c)所示, 观点仍然达到两极分化, 但其观点形成两极分化的速度比图8(b)的慢, 说明权威个体有利观点的演化速度.为了描述观点演化过程中所有观点的相对变化, 定义变量:η(k )=0其曲线如图8(d)所示. 可以看出, 在文献[32]改进的Hegselmann-Krause 模型中, 观点相对变化较大,而在具有类万有引力的有界置信模型(2)中, 观点相对变化较小; 另一方面, 在不考虑权威个体的模型(2)中, 观点相对变化最小, 但观点收敛速度最慢. 特别地, 如果 , 则群体观点收敛.在现实生活中, 针对一些(如不感兴趣的)话题, 大多数人的观点比较趋于中立, 而只有少部分x i (0)∈[0,1],i ∈V 人的观点比较极端. 为此, 设个体观点初值 为正态分布. 将改进的Hegselmann-Krause 模型与本文建立的有界置信模型(2)进行比较, 其观点曲线如图9(a)和图9(b)所示. 可以看出, 基于有界置信模型(2)的观点达到一致, 而基于改进的Hegselmann-Krause 模型的观点不收敛, 这是因为改进的Hegselmann-Krause 模型中, 观点相似的个体不再进行交互.20406000.51.000.51.020改进的模型模型 (2)|N j | = 140602040602040600.51.0024(a)(b)(d)(c)xxxh (k )k /s k /s k /s k /s图 9 初值为正态分布时的观点演化Fig. 9 Opinion evolution when the initial value isnormally distributed|N j |=1η(k )当具有类万有引力的有界置信模型(2)不考虑个体权威性时即 , 其观点曲线如图9(c)所示, 可以看出, 基于观点动力学模型(2)的观点达到一致速度较慢. 根据 的定义和图9(d)可知, 基于改进的Hegselmann-Krause 模型的观点相对变化最大.5.2 基于衰减置信阈值的模型仿真分析R =0.3ρ=0.7n =50x i (0)∈[0,1],i ∈V x (0)∈[0,1]n 本节将对具有衰减置信阈值的观点动力学模型(10)进行仿真分析. 设 , 和 ,当观点初值 均匀分布时, 观点动力学模型(10)形成了3个均匀的观点簇, 仿真结果如图10(a)所示. 当观点初值 正态分布时, 其结果如图10(b)所示, 形成了4个观点簇. 总之, 基于衰减置信阈值的模型(10)的观点都是收敛的.N c N m n x (0)R ρ设 表示群体最终观点簇数, 表示群体最大观点簇中的个体数量. 在个体数 和观点初值 以及阈值参数 都固定的情况下, 随着 的增9 期刘青松等: 具有类万有引力的有界置信观点动力学分析与应用1973N c N m ρN c =1大, 群体最终观点簇数量 减少, 如图10(c)所示.由图10(d)可知, 群体最大观点簇中个体数量 随着 的增大而增大. 特别地, 当 时, 则群体观点达到一致性.6 结束语本文提出具有类万有引力的有界置信观点动力学模型, 描述了不同邻居对个体的观点影响权重不一样, 且个体观点的更新与观点之间的差值和邻居的权威性有关. 根据置信矩阵的性质证明了观点的收敛性, 在不考虑邻居权威性的条件下, 给出了最终观点平均值的显式表达式. 在衰减置信阈值的条件下, 得到了观点收敛速率的显式解. 利用本文提出的观点动力学模型, 研究了社会心理学中的“权威效应”和“非零和效应”. 仿真分析表明, 邻居的权威性和正态分布的初始观点都有利于观点达成一致.ReferencesZhou B, Lin Z. 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Dynamic feedback mean square consensus con-trol based on linear transformation for leader-follower multi-agent systems. Acta Automatica Sinica , 2022, 48(10): 2474−2485(郑维, 张志明, 刘和鑫, 张明泉, 孙富春. 基于线性变换的领导－跟随多智能体系统动态反馈均方一致性控制. 自动化学报, 2022,48(10): 2474−2485)11Yi J W, Chai L, Zhang J. Average consensus by graph filtering:New approach, explicit convergence rate, and optimal design.IEEE Transactions on Automatic Control , 2020, 65(1): 191−20612Liu Q, Zhou B. Consensus of discrete-time multi-agent systems with state, input, and communication delays. IEEE Transac-tions on Systems, Man, and Cybernetics: Systems , 2020, 50(11):4425−443713Liu Q. Pseudo-predictor feedback control for multi-agent sys-tems with both state and input delays. IEEE/CAA Journal of Automatica Sinica , 2021, 8(11): 1827−183614French Jr J R. A formal theory of social power. Psychological Review , 1956, 63(3): 181−19415DeGroot M H. Reaching a consensus. Journal of the American Statistical Association , 1974, 69(345): 118−12116Friedkin N, Johnsen E. Social influence networks and opinion change. Advances Group Processes , 1999, 16: 1−2917Parsegov S E, Proskurnikov A V, Tempo R, Friedkin N E. Nov-el multidimensional models of opinion dynamics in social net-works. IEEE Transactions on Automatic Control , 2017, 62(5):2270−228518Tian Y, Wang L. Opinion dynamics in social networks with stubborn agents: An issue-based perspective. Automatica , 2018,96: 213−22319Deffuant G, Neau D, Amblard F, Weisbuch G. Mixing beliefs among interacting agents. Advances in Complex Systems , 2000,3: 87−9820Zhang J, Hong Y. Opinion evolution analysis for short-range and long-range Deffuant-Weisbuch models. Physica A: Statistic-al Mechanics and Its Applications , 2013, 392(21): 5289−52972102040600.51.00.51.0xk /s 0204060k /s xN cr r m(b)(a)(c)(d)图 10 模型(10)观点演化Fig. 10 Opinion evolution of model (10)1974自 动 化 学 报49 卷Dong Y, Ding Z, Martínez L, Herrera F. Managing consensusbased on leadership in opinion dynamics. Information Sciences ,2017, 397: 187−20522Mei W, Friedkin N E, Lewis K, Bullo F. Dynamic models of ap-praisal networks explaining collective learning. IEEE Transac-tions on Automatic Control , 2018, 63(9): 2898−291223Hegselmann R, Krause U. Opinion dynamics and bounded con-fidence models, analysis, and simulation. Journal of Artificial So-cieties and Social Simulation , 2002, 5(3): 1−3324Bullo F, Cortes J, Martinez S. Distributed Control of Robotic Networks. Princeton: Princeton University Press, 2009.25Cody W F. Authoritative effect of FDA regulations. The Busi-ness Lawyer , 1969, 24: 479−49126Chen Z, Lan H. Dynamics of public opinion: Diverse media and audiences ＇ choices. Journal of Artificial Societies and Social Sim-ulation , 2021, 24(2): 1−2127Canuto C, Fagnani F, Tilli P. An Eulerian approach to the ana-lysis of Krause ＇s consensus models. SIAM Journal on Control and Optimization , 2012, 50(1): 243−26528Su W, Chen G, Hong Y. Noise leads to quasi-consensus of Heg-selmann-Krause opinion dynamics. Automatica , 2017, 85:448−45429Yang Y, Dimarogonas D V, Hu X. Opinion consensus of modi-fied Hegselmann-Krause models. Automatica , 2014, 50(2):622−62730Haskovec J. A simple proof of asymptotic consensus in the Heg-selmann-Krause and Cucker-Smale models with normalization and delay. SIAM Journal on Applied Dynamical Systems , 2021,20(1): 130−14831Vasca F, Bernardo C, Iervolino R. Practical consensus in bounded confidence opinion dynamics. Automatica , 2021, 129:Article No. 10968332Gerrig R J. Psychology and Life (20th Edition). New York:Pearson, 2013.33Mei W, Bullo F, Chen G, Hendrickx J, Dörfler F. Rethinking the micro-foundation of opinion dynamics: Rich consequences of the weighted-median mechanism [Online], available: https:////abs/1909.06474, January 26, 202234Swingle P G, Santi A. Communication in non-zero-sum games.Journal of Personality and Social Psychology , 1972, 23(1): 54−6335Lorenz J. A stabilization theorem for dynamics of continuous opinions. Physica A: Statistical Mechanics and Its Applications ,2005, 355(1): 217−22336Morarescu I C, Girard A. Opinion dynamics with decaying con-fidence: Application to community detection in graphs. IEEE Transactions on Automatic Control , 2011, 56(8): 1862−187337刘青松 武汉科技大学信息科学与工程学院副教授. 2019年获得哈尔滨工业大学博士学位. 主要研究方向为社会网络, 观点动力学分析, 时滞系统和多智能体系统.E-mail: ********************.cn (LIU Qing-Song Associate profess-or at the School of Information Science and Engineer-ing, Wuhan University of Science and Technology. He received his Ph.D. degree from Harbin Institute of Technology in 2019. His research interest covers social networks, opinion dynamics analysis, time-delay sys-tems, and multi-agent systems .)习晓苗 武汉科技大学信息科学与工程学院硕士研究生. 2020年获得湖南科技大学学士学位. 主要研究方向为社会网络, 观点动力学分析.E-mail: *********************(XI Xiao-Miao Master student at the School of Information Scienceand Engineering, Wuhan University of Science and Technology. She received her bachelor degree from Hunan University of Science and Technology in 2020.Her research interest covers social networks and opin-ion dynamics analysis .)柴 利 武汉科技大学信息科学与工程学院教授. 2002年获得香港科技大学博士学位. 主要研究方向为分布式优化, 滤波器组框架, 图信号处理和网络化控制系统. 本文通信作者.E-mail: ***************.cn(CHAI Li Professor at the Schoolof Information Science and Engineering, Wuhan Uni-versity of Science and Technology. He received his Ph.D. degree from Hong Kong University of Science and Technology in 2002. His research interest covers distributed optimization, filter bank frames, graph sig-nal processing, and networked control systems. Corres-ponding author of this paper .)9 期刘青松等: 具有类万有引力的有界置信观点动力学分析与应用1975。
扩散模型入门知识点总结
扩散模型入门知识点总结一、概述扩散模型是一种描述社会现象或自然现象中信息，病毒，思想，意见等在群体中传播或扩散的数学模型。
通过建立适当的数学模型和算法，可以模拟和预测信息在不同条件下的传播过程，为科学研究和实际应用提供了重要的工具。
二、扩散模型的分类1. 信息传播模型：研究信息在网络中的传播规律，包括SIR模型，SIS模型等。
2. 社交网络模型：研究社交网络中信息，思想等的传播，包括小世界网络模型，随机网络模型等。
3. 群体行为模型：研究群体中信息，行为，意见等的扩散，包括Opinion Dynamics模型，社会学模型等。
4. 传染病模型：研究传染病在人群中的传播规律，包括SIR模型，SEIR模型等。
三、扩散模型中的基本概念1. 传播速度：描述信息或病毒在群体中传播的快慢程度。
2. 传播范围：描述信息或病毒在群体中传播的覆盖范围。
3. 传播路径：描述信息或病毒在群体中传播的路径和方式。
4. 传播规律：描述信息或病毒在群体中传播的规律性。
四、扩散模型的常用算法1. 广度优先搜索(BFS)算法：用于分析网络中信息的传播路径和范围。
2. 深度优先搜索(DFS)算法：用于分析网络中信息的传播路径和范围。
3. 病毒传播模型算法：描述病毒在人群中的传播规律。
4. Opinion Dynamics模型算法：描述群体中意见的扩散和变化规律。
五、扩散模型的应用1. 疾病传播预测：通过建立传染病模型，可以对疾病传播的趋势和范围进行预测。
2. 社交网络分析：通过分析社交网络中信息的传播路径和规律，可以优化信息传播策略。
3. 营销策略优化：通过分析消费者的行为和意见扩散规律，可以优化营销策略。
4. 政治舆论研究：通过分析社会舆论的扩散规律，可以预测政治事件的发展趋势。
六、扩散模型的发展趋势1. 多因素模型：将社会，心理，环境等因素纳入考虑，建立更加综合的扩散模型。
2. 非线性模型：研究更为复杂的扩散现象，建立非线性的扩散模型。
2003年考研英语完形填空真题解析范文
1.2003年考研英语完形填空真题解析Teachers need to be aware of the emotional, intellectual, and physical changes2.that young adults experience.3.And they also need to4.give serious 21 thought to5.how they can be best 22 accommodate such changes.6.Growing bodies need movement and 23exercise ,7.but not just in ways that emphasize competition. 但是不能只注重比赛8.24 Because they are adjusting to their new bodies9.and a whole host of new intellectual and emotional challenges, 一大堆10.teenagers are especially self-conscious11.and need the 25 confidence12.that comes from achieving success13.and knowing that their accomplishments14.are 26 admired by others.15.However, the typical teenage lifestyle is already filled with so much competition16.that it would be 27 to plan activities17.in which there are more winners than losers, 因此安排一些赢者多，输者少的活动是很明智的18.28 for example ,19.publishing newsletters 出版时事通讯刊印业务通讯20.with many student-written book reviews,21.29 displaying student artwork, and22.sponsoring book discussion clubs. 赞助23.A variety of small clubs24.can provide 30 multiple opportunities for leadership, 为培养领导才能提供多种机会25.multiple 多种的，倍数，26.leadership 领导能力，领导层27.as well as for practice in successful 31 group dynamics. 为成功的群体动力提供练习28.dynamics 力学，动力学29.Making friends is extremely important to teenagers,30.and many shy students31.need the 32 security of some kind of organization 需要加入某个组织以获得安全感32.with a supportive adult 33 barely visible in the backgrounda)需要有一位成人在只有后台看到见的地方提供支持In these activities,33.it is important to remember that the young teens34.have 34 short attention spans. 注意力持续时间很短35.A variety of activities should be organized36.35 so that participants can remain active as long as they want 这样参加活动的人就能想活动多久就活动多久37.and then go on to 36something else 然后就可以做一些其它的事情38.without feeling guilty39.and without letting the other participants 37 down . 也不会让其它参与者失望40.This does not mean that 这并不是说41.adults must accept irresponsibility. 大人必须接受不负责任的做法42.38 On the contrary43.they can help students acquire a sense of commitment 获得一种责任感44.by 39planning for roles45.that are within their 40 capability 他们力所能及46.and their attention spans 又在他们注意力时间范围47.and by having clearly stated rules.通过制定清楚的活动规则Teachers need to be aware of the emotional, intellectual, and physical changes that young adults experience. And they also need to give serious 21 to how they can be best 22 such changes. Growing bodies need movement and 23 , but not just in ways that emphasize competition. 24 they are adjusting to their new bodies and a whole host of new intellectual and emotional challenges, teenagers are especially self-conscious and need the 25 that comes from achieving success and knowing that their accomplishments are 26 by others. However, the typical teenage lifestyle is already filled with so much competition that it would be 27 to plan activities in which there are more winners than losers, 28 , publishing newsletters with many student-written book reviews, 29 student artwork, and sponsoring book discussion clubs. A variety of small clubs can provide 30 opportunities for leadership, as well as for practice in successful 31 dynamics. Making friends is extremely important to teenagers, and many shy students need the 32 of some kind of organization with a supportive adult 33 visible in the background.In these activities, it is important to remember that the young teens have 34 attention spans.A variety of activities should be organized 35 participants can remain active as long as they wantand then go on to 36 else without feeling guilty and without letting the other participants 37 . This does not mean that adults must accept irresponsibility. 38 they can help students acquire a sense of commitment by 39 for roles that are within their 40 and their attention spans and by having clearly stated rules.21.[A] thought[B]idea[C] opinion[D] advice22.[A] strengthen[B] accommodate[C] stimulate[D] enhance23.[A] care[B] nutrition[C] exercise[D] leisure24.[A] If[B] Although[C] Whereas[D] Because25.[A] assistance[B] guidance[C] confidence[D] tolerance26.[A] claimed[B] admired[C] ignored[D] surpassed27.[A] improper[B] risky[C] fair[D] wise28.[A] in effect[B] as a result[C] for example[D] in a sense29.[A] displaying[B] describing[C] creating[D] exchanging30.[A] durable[B] excessive[C] surplus[D] multiple31.[A] group[B] individual[C] personnel[D] corporation32.[A] consent[B] insurance[C] admission[D] security33.[A] particularly[B] barely[C] definitely[D] rarely34.[A] similar[B] long[C] different[D] short35.[A] if only[B] now that[C] so that[D] even if36.[A] everything[B] anything[C] nothing[D] something37.[A] off[B] down[C] out[D] alone38.[A] On the contrary[C] On the whole[B] On the average[D] On the other hand39.[A] making[B] standing[C] planning[D] taking40.[A] capability[B] responsibility[C] proficiency[D] efficiency文章背景这是一篇讲述关于如何帮助青少年适应变化的社科类议论文。
舆论对公关的影响英文作文
舆论对公关的影响英文作文Title: The Impact of Public Opinion on Public Relations。
Public relations, as a discipline, is intricately intertwined with the ebb and flow of public opinion. It serves as the bridge between organizations and the public, aiming to manage and shape perceptions. However, the dynamic nature of public opinion poses both challenges and opportunities for effective public relations strategies.First and foremost, public opinion acts as a barometer, constantly gauging the sentiments and attitudes of the masses towards various entities, be it corporations, governments, or individuals. Positive public opinion can serve as a valuable asset, enhancing trust, credibility,and goodwill towards an organization. Conversely, negative public sentiment can undermine reputation, erode trust, and lead to detrimental consequences such as boycotts, protests, or even legal actions.In the realm of public relations, the influence of public opinion manifests in several key ways. One such avenue is crisis management. In times of crisis, whether it be a product recall, a scandal, or a natural disaster, public opinion can either exacerbate or mitigate the situation. Effective crisis communication entails not only addressing the root cause of the crisis but also managing public perceptions and restoring trust. Failure to do so can result in lasting damage to reputation and brand image.Moreover, public opinion shapes the agenda andpriorities of public relations campaigns. By understanding the prevailing attitudes, values, and concerns of thetarget audience, PR professionals can tailor their messaging and strategies accordingly. For instance, in an era dominated by environmental consciousness, companiesthat demonstrate a commitment to sustainability and corporate social responsibility are more likely to garner favorable public opinion.The advent of social media has amplified the influence of public opinion on public relations. Platforms likeTwitter, Facebook, and Instagram serve as virtual town squares where individuals can express their views and opinions on a global scale. Consequently, issues and controversies can escalate rapidly, making real-time monitoring and response essential for PR practitioners. Social media also democratizes communication, allowing organizations to engage directly with their stakeholders and solicit feedback in ways previously unimaginable.Furthermore, public opinion can shape policy decisions and regulatory frameworks, thereby influencing the operating environment for organizations. Governments often respond to public pressure by enacting laws and regulations that reflect societal values and preferences. For example, public outcry over data privacy concerns has led to the implementation of stringent regulations such as the European Union's General Data Protection Regulation (GDPR), which has profound implications for businesses operating in the digital sphere.In conclusion, public opinion wields considerable influence over the practice of public relations. It servesas a reflection of societal values, attitudes, and expectations, shaping the reputations and fortunes of organizations. To navigate this complex landscape effectively, PR professionals must remain vigilant, adaptive, and responsive to the ever-evolving dynamics of public sentiment. By understanding and leveraging the power of public opinion, organizations can forge stronger connections with their stakeholders and cultivate apositive reputation in the eyes of the public.。
积极向前不回头的英语作文
Moving forward with optimism and determination is a key aspect of personal growth and success.Embracing this mindset can lead to a more fulfilling life,both personally and professionally.Here are some points to consider when writing an essay on the importance of moving forward without looking back:1.Introduction to the Concept:Begin by defining what it means to move forward without looking back.This could include a discussion of the importance of setting goals, embracing change,and letting go of past mistakes or failures.2.Overcoming Setbacks:Discuss how the ability to move forward is crucial in overcoming setbacks.Provide examples of individuals who have faced adversity and used it as a stepping stone to success.3.Learning from the Past:While its important not to dwell on the past,its also essential to learn from it.Explain how reflecting on past experiences can provide valuable lessons without becoming a hindrance to progress.4.The Power of Resilience:Resilience is the ability to bounce back from challenges. Describe how resilience can be developed and how it aids in moving forward.5.Setting and Achieving Goals:Elaborate on the process of setting realistic and achievable goals.Discuss the role of goalsetting in providing direction and motivation to move forward.6.Adapting to Change:Change is inevitable,and the ability to adapt is crucial.Discuss how embracing change can open up new opportunities and prevent stagnation.7.The Role of Perseverance:Perseverance is the continuous effort to achieve a goal despite obstacles.Highlight the importance of perseverance in the face of challenges.8.Maintaining a Positive Attitude:A positive attitude can significantly impact ones ability to move forward.Discuss the benefits of maintaining optimism and how it can influence outcomes.9.The Importance of SelfReflection:Regular selfreflection can help individuals understand their strengths and weaknesses,allowing them to make necessary adjustments to keep moving forward.10.Conclusion:Summarize the key points made in the essay and reiterate the importance of moving forward without looking back.Encourage readers to adopt this mindset in theirown lives.Remember to use clear and concise language,provide relevant examples,and structure your essay in a logical manner.By doing so,you will effectively convey the message that moving forward with a positive and determined attitude is essential for personal and professional development.。
自然与社会中的离散动力学
自然与社会中的离散动力学英文回答：Discrete dynamics is a branch of mathematics and physics that deals with systems that change in a step-by-step manner. It is concerned with understanding how these systems evolve over time and how they are influenced by various factors. In the context of natural and social sciences, discrete dynamics can be used to model and analyze a wide range of phenomena.In natural sciences, discrete dynamics can be applied to study the behavior of ecosystems, population dynamics, and the spread of diseases. For example, in ecology, discrete dynamics can be used to model the interactions between different species in an ecosystem. By studying how changes in one species affect the entire ecosystem, scientists can gain insights into the stability and resilience of natural systems.In social sciences, discrete dynamics can be used to study various social phenomena such as opinion dynamics, social network dynamics, and the spread of information. For instance, discrete dynamics can be used to model how opinions spread in a social network. By analyzing the dynamics of opinion formation and change, researchers can understand how ideas and beliefs propagate within a society.One example of discrete dynamics in action is the study of infectious diseases. By modeling the spread of a disease using discrete dynamics, scientists can simulate different scenarios and evaluate the effectiveness of various intervention strategies. This information can then be usedto inform public health policies and interventions.Another example is the study of financial markets. Discrete dynamics can be used to model the behavior ofstock prices and analyze patterns and trends. By understanding the dynamics of financial markets, investors can make more informed decisions and manage theirportfolios more effectively.中文回答：离散动力学是数学和物理学的一个分支，研究以逐步方式变化的系统。
关于互联网舆论英语作文
关于互联网舆论英语作文Title: The Impact of Internet Public Opinion。
The internet has become an integral part of our daily lives, revolutionizing the way we communicate, gather information, and express our opinions. One of the most significant phenomena facilitated by the internet is the emergence of internet public opinion, which plays a crucial role in shaping social discourse, influencing policies, and even impacting the economy. In this essay, we will delve into the dynamics, significance, and consequences of internet public opinion.Firstly, it's essential to understand the nature of internet public opinion. Unlike traditional forms of public opinion, which were primarily shaped by mainstream media, internet public opinion is decentralized and participatory. Social media platforms, forums, blogs, and online communities provide individuals with the means to voice their opinions, engage in discussions, and mobilize othersaround various issues. This democratization of public discourse has empowered ordinary citizens and marginalized voices that were previously overshadowed by powerful interest groups.Furthermore, internet public opinion has a profound impact on decision-making processes at both the individual and societal levels. Politicians, policymakers, and businesses closely monitor online discussions to gauge public sentiment and adjust their strategies accordingly. For instance, social media trends can influence election outcomes by shaping voters' perceptions of candidates and their policies. Similarly, companies rely on social listening tools to monitor consumer feedback and adapttheir marketing strategies to meet evolving demands.However, the influence of internet public opinion is not always benign. The anonymity and echo chamber effect of online communities can exacerbate polarization and spread misinformation. False narratives and conspiracy theories can quickly gain traction, leading to real-world consequences such as social unrest or public panic.Moreover, the viral nature of social media amplifies outrage culture, where minor incidents are blown out of proportion, leading to online mobs and unjustified backlash against individuals or organizations.Despite these challenges, internet public opinion also serves as a vital mechanism for accountability and transparency. Social media enables whistleblowers to expose wrongdoing and hold powerful institutions accountable for their actions. The #MeToo movement, for example, gained momentum on social media platforms, sparking a global conversation about sexual harassment and abuse. Similarly, citizen journalists use the internet to document human rights abuses and circumvent censorship in authoritarian regimes.In conclusion, internet public opinion is a double-edged sword with far-reaching implications for society. While it empowers individuals, fosters civic engagement, and drives positive social change, it also poses risks such as polarization, misinformation, and online harassment. To harness the potential of internet public opinion for thegreater good, it is crucial to promote digital literacy, foster constructive dialogue, and develop effective mechanisms for fact-checking and moderation. Only then can we ensure that the internet remains a democratic space where diverse voices are heard, and meaningful change can occur.。
找到关于消息的作文英语
找到关于消息的作文英语Title: The Power of Information: Exploring the Dynamics of News。
In today's rapidly evolving world, information holds a paramount significance. News, in particular, serves as the lifeblood of societies, shaping opinions, guiding decisions, and fostering connections across the globe. In this discourse, we delve into the multifaceted nature of news,its impact on individuals and communities, and its role in shaping the contemporary landscape.First and foremost, news serves as a catalyst for awareness and understanding. Through various media channels such as newspapers, television, radio, and digital platforms, individuals are informed about events, developments, and trends both locally and globally. Thisflow of information not only keeps the public abreast of current affairs but also empowers them to engage meaningfully with the world around them. Whether it'spolitical upheavals, socio-economic shifts, scientific breakthroughs, or cultural phenomena, news provides the essential context and analysis necessary for informed discourse.Moreover, news plays a pivotal role in shaping public opinion and influencing decision-making processes. Media outlets act as intermediaries between events and the public, framing narratives, and interpreting their significance.The editorial decisions, biases, and agendas inherent in news production can sway public perceptions, shaping attitudes towards individuals, institutions, and issues. Consequently, the dissemination of accurate, unbiased information is crucial for fostering a well-informed citizenry capable of making reasoned judgments and holding power to account.Furthermore, the advent of digital technology has revolutionized the news landscape, ushering in an era of unprecedented accessibility and immediacy. Social media platforms, in particular, have emerged as powerful conduits for news dissemination, enabling real-time updates andfostering citizen journalism. While this democratization of information has democratized the news ecosystem, it hasalso raised concerns about misinformation, echo chambers, and the erosion of journalistic standards. Theproliferation of fake news and viral rumors underscores the need for media literacy and critical thinking skills to navigate the complexities of the digital age.In addition to its informational and societal functions, news serves as a driver of social change and collective action. By shedding light on injustices, inequalities, and human rights violations, journalists and mediaorganizations play a crucial role in holding power to account and advocating for positive change. Whether it's exposing corruption, amplifying marginalized voices, or galvanizing public opinion around pressing issues, news has the power to mobilize communities, spark dialogue, and catalyze meaningful reform.Furthermore, news serves as a bridge between cultures, fostering cross-cultural understanding, and empathy. In an increasingly interconnected world, the exchange of news andinformation facilitates dialogue and exchange between individuals and communities from diverse backgrounds. By highlighting shared experiences, common challenges, and universal aspirations, news can transcend linguistic, cultural, and geographical barriers, forging connections and fostering a sense of global solidarity.In conclusion, news occupies a central place in the fabric of modern society, serving as a vital conduit of information, a catalyst for change, and a bridge between individuals and communities. Its impact extends far beyond the realm of journalism, influencing public opinion, shaping policy decisions, and fostering social cohesion. However, the proliferation of digital technology and the rise of misinformation pose significant challenges to the integrity and credibility of news media. Thus, it is incumbent upon individuals, institutions, and governments to uphold the principles of accuracy, transparency, and accountability in the pursuit of a well-informed and democratic society.。
opinion的名词解释
opinion的名词解释Opinion: A Reflection of Perspectives and SubjectivityIntroductionOpinion, a term that permeates our daily lives, plays a crucial role in shaping how we perceive the world and interact with others. It is a powerful reflection of our perspectives and subjectivity. In this article, we will delve into the multifaceted nature of opinion, examining its origins and influences on decision-making processes, societal dynamics, and personal growth.The Subjectivity of OpinionOpinions, by their very nature, are subjective. They are influenced by a myriad of factors, such as personal experiences, cultural background, education, and social environment. Each individual possesses a unique set of opinions that forms the lens through which they interpret and understand the world.The Formation of OpinionOpinions develop through a complex process, often a culmination of conscious and subconscious factors. They can be formed through exposure to various sources of information, including media, social interactions, and personal research. However, the emotional and psychological aspects also play a crucial role in shaping our opinions. Emotions like empathy, fear, anger, or joy can greatly influence our perspectives.The Role of Bias in OpinionBiases are inherent in human nature and can heavily impact the formation and expression of opinions. Confirmation bias, for example, refers to the tendency to seek out information that supports our existing beliefs, while disregarding evidence to the contrary. This can limit our ability to consider alternative viewpoints and hinder critical thinking.Societal Implications of OpinionOpinions have far-reaching implications for society, as they shape our interactions and influence decision-making processes. They define public discourse, fuel debates, and drive social change. In democratic societies, the aggregation of diverse opinions forms the foundation for governance, encouraging a balanced representation of public interests.The Influence of Opinion in Decision-MakingIn both personal and professional contexts, opinions play a crucial role in decision-making processes. Whether it is selecting a product to purchase or forming policies at the highest level of government, opinions guide our choices. But it is important to recognize that decisions should not solely rely on opinions; a healthy balance of evidence-based research, expert advice, and critical analysis is equally vital.Challenges of Opinion DiversityWhile opinion diversity can enrich our perspectives and enhance collective decision-making, it can also lead to conflicts and polarization. When opinions clash, and individuals fail to engage in respectful dialogue and empathy, it can result in societal divisions. Learning to navigate and appreciate diverse opinions is crucial for fostering a harmonious and inclusive society.The Evolving Nature of OpinionOpinions are not static; they evolve over time as individuals gain new experiences and encounter different perspectives. It is essential to remain open-minded and receptive to change. By actively seeking out new information and engaging in constructive dialogue, we can broaden our horizons and challenge our existing opinions.Personal Growth through OpinionOur opinions are integral to our personal growth and development. By critically examining our beliefs and seeking to understand opposing viewpoints, we expand our understanding of the world. Embracing diverse opinions fosters intellectual humility and encourages empathy, promoting personal growth and enhancing our ability to engage meaningfully with others.ConclusionOpinion, a reflection of perspectives and subjectivity, is a complex and powerful force that influences our lives and society. Understanding the multifaceted nature of opinion can help us appreciate the diversity of perspectives, engage in respectful dialogue, and foster personal as well as societal growth. As we navigate the intricacies of opinion, let us strive for open-mindedness, critical thinking, and empathy in our interactions and decision-making processes.。
两种观点英语作文
When approaching the task of writing an English essay that presents two viewpoints, it is essential to structure your essay in a clear and logical manner.Here is a stepbystep guide to help you craft a wellorganized essay that effectively presents two contrasting perspectives on a given topic.1.Introduction:Begin your essay with an introduction that provides a brief overview of the topic and introduces the two viewpoints you will be discussing.The introduction should also include a thesis statement that outlines the purpose of your essay.Example:In the debate over the use of social media,some argue that it has a positive impact on society,while others believe it has detrimental effects.This essay will explore both sides of the argument and aim to provide a balanced view on the role of social media in modern society.2.First Viewpoint:Dedicate the first body paragraph to the first viewpoint.Start with a topic sentence that clearly states the perspective you are about to discuss.Follow this with supporting evidence,examples,or arguments that back up this viewpoint.Example:Proponents of social media argue that it has revolutionized communication,allowing people to connect with others across the globe instantly.It has also provided a platform for individuals to share their ideas and creativity,fostering a sense of community and collaboration.3.Second Viewpoint:In the second body paragraph,present the opposing viewpoint.Again,start with a topic sentence that introduces the perspective.Provide evidence,examples,or arguments that support this viewpoint,ensuring that they are distinct from those used in the first paragraph.Example:On the other hand,critics of social media contend that it can lead to social isolation and a decrease in facetoface interactions.They argue that the constant need for online validation can negatively affect selfesteem and contribute to mental health issues such as anxiety and depression.4.Counterarguments:Optionally,you may include a section where you address potential counterarguments to each viewpoint.This can strengthen your essay by showing that you have considered multiple angles and are not presenting a onesided argument.Example:While it is true that social media can facilitate global communication,some may counter that the superficial nature of online interactions can never replace the depth of inperson relationships.Similarly,while social media can be a source of support for some,others may argue that the pressure to maintain an online presence can exacerbate feelings of inadequacy.5.Conclusion:Conclude your essay by summarizing the main points of both viewpoints and reiterating your thesis statement.You may also provide a personal opinion or a recommendation based on the discussion,but ensure that it is justified and wellreasoned. Example:In conclusion,while social media offers numerous benefits such as global connectivity and a platform for selfexpression,it also poses risks such as social isolation and mental health concerns.A balanced approach to using social media,recognizing its potential while being mindful of its pitfalls,is perhaps the most prudent course of action.Remember to use transitional phrases to guide your reader through the different sections of your essay,and ensure that your arguments are wellsupported and logically presented.。
乐观的重要性英语作文
Optimism is a vital trait that can significantly influence ones life in various ways.It is the ability to maintain a positive outlook on life,even in the face of adversity.Here are some reasons why optimism is so important:1.Mental Health:Optimistic individuals tend to have better mental health.They are less likely to suffer from depression and anxiety,as they focus on the positive aspects of life and believe in their ability to overcome challenges.2.Physical Health:Studies have shown that optimism can contribute to better physical health.People who are optimistic have stronger immune systems and are more likely to engage in healthy behaviors,such as regular exercise and a balanced diet.3.Stress Management:Optimism helps in managing stress effectively.When faced with difficult situations,optimistic people are more likely to find solutions rather than dwelling on the problems.4.Relationships:Being optimistic can make you more attractive to others.People are naturally drawn to those who are positive and uplifting.This can lead to stronger and more fulfilling relationships.5.Career Success:Optimistic individuals are more likely to succeed in their careers. They are more confident,take more risks,and are better at handling setbacks,which are all crucial for professional growth.6.Longevity:There is evidence to suggest that optimism can contribute to a longer life. People who maintain a positive attitude are more likely to live longer,healthier lives.7.Problem Solving:Optimists are better at problemsolving.They approach challenges with a cando attitude,which allows them to think creatively and find effective solutions.8.Motivation:Optimism is a powerful motivator.It drives people to set goals and work towards achieving them.The belief that good things will happen can propel individuals to take action.9.Resilience:Optimistic people are more resilient.They bounce back from setbacks more quickly and are less likely to be discouraged by failure.10.Happiness:Ultimately,optimism leads to greater happiness.By focusing on the positive,individuals can experience more joy and contentment in their daily lives.In conclusion,optimism is a powerful force that can enhance ones overall wellbeing.It is a mindset that can be cultivated and developed,leading to a more fulfilling and successful life.By choosing to see the good in every situation,we can improve our mental and physical health,strengthen our relationships,and achieve greater success in all areas of life.。
网络舆情应对处置流程
网络舆情应对处置流程1.网络舆情应对是指对网络上产生的有关某一方面舆情进行调查分析和应对处理的活动。
The response to online public opinion refers to the activity of investigating, analyzing and responding to the public opinion about a certain aspect on the Internet.2.处置流程是指对网络舆情进行处理时应遵循的一系列操作步骤和方法。
The disposal process refers to a series of operational steps and methods that should be followed when dealing with online public opinion.3.对于负面舆情，首先需要进行调查和分析，了解具体情况和舆情产生的原因。
For negative public opinion, it is necessary to conductan investigation and analysis first, to understand thespecific situation and the reasons for the public opinion.4.然后制定应对策略，根据分析结果合理地制定应对方案。
Then formulate a response strategy, and develop aresponse plan based on the analysis results.5.应对策略可以包括舆情引导、信息发布、舆情回应等多种手段。
Response strategies can include public opinion guidance, information release, and public opinion response, among other methods.6.在制定和实施应对方案时，需要考虑舆情的性质、影响范围和处理时效等因素。
具有遗忘个体的社会网络多维观点动力学分析与应用
具有遗忘个体的社会网络多维观点动力学分析与应用刘青松 1李明鹏 1柴 利2, 3摘 要 在个体观点演化过程中, 由于通讯技术和实际环境的限制, 个体之间往往不能进行充分的交流. 另一方面, 由于社会群体的从众压力影响, 个体会改变已形成的观点. 为此, 研究了具有遗忘个体和从众压力的拟强连通社会网络中表达/私人观点演化问题. 为刻画不同话题之间表达/私人观点的相互影响, 提出一个新的多维观点动力学模型. 根据逻辑矩阵和网络影响子矩阵的正则性, 给出表达观点和私人观点收敛的充分条件. 应用本文所提出的观点动力学模型, 复现了“多元无知”的社会现象. 仿真分析表明, 从众压力的恢复力越小, 表达观点与私人观点的差异越大.关键词 多维观点动力学, 遗忘个体, 逻辑矩阵, 表达观点, 私人观点引用格式 刘青松, 李明鹏, 柴利. 具有遗忘个体的社会网络多维观点动力学分析与应用. 自动化学报, 2023, 49(10):2201−2210DOI 10.16383/j.aas.c210091Analysis and Application of Multidimensional Opinion Dynamics onSocial Networks With Oblivion IndividualsLIU Qing-Song 1 LI Ming-Peng 1 CHAI Li 2, 3Abstract Due to the restriction of communication technology and real environment, individuals often do not com-municate enough with each other in the evolution process of opinions. On the other hand, individuals may alter their formed opinions under the pressures of conforming in a social community. In this paper, we analyse the evolu-tion problem of the expressed and private opinions for the quasi-strongly connected social networks with oblivion in-dividuals and the pressures to conform. To describe the interaction influences of expressed/private opinions on dif-ferent topics, a new multidimensional opinion dynamics model is proposed. Sufficient conditions guaranteeing the convergence of the expressed and private opinions are obtained in terms of the regularity of the logic matrix and in-fluence submatrix. By applying our proposed opinion dynamics model to reproduce the social phenomenons of plur-alistic ignorance. Simulation analyses show that the smaller the resilience of the pressures is, the larger the differ-ence is between expressed and private opinions.Key words Multidimensional opinion dynamics, oblivion individuals, logic matrices, expressed opinions, private opinionsCitation Liu Qing-Song, Li Ming-Peng, Chai Li. Analysis and application of multidimensional opinion dynamics on social networks with oblivion individuals. Acta Automatica Sinica , 2023, 49(10): 2201−2210近年来, 社会网络分析成为网络科学研究的热点之一, 吸引了来自控制科学、社会心理学和经济学等多个领域研究者的广泛关注[1−3]. 随着对多智能体系统[4−6]和复杂网络[7−10]研究的深入, 观点动力学中观点的形成和演化引起了学者们极大的关注, 产生了许多重要的结果, 促进了观点动力学相关方向的发展[11−12]. 观点动力学的研究, 不仅仅关注观点的一致现象[1], 而且还关注观点的极化现象[13] 和观点的分簇现象[14]. 例如, 采用仿真分析方法, Zhang 等[15]研究了连续时间有界置信模型的观点演化问题; 通过引入个人决策树和社会网络, Friedkin 等[12]分析了耦合矩阵对信念系统动力学的影响; Parsegov 等[16]在静态社会网络中, 提出了一个新的观点动力学模型, 并分析了观点的稳定性和收敛性. 此外, Li 等[17]提出了一种新的快速、准确检测集群结构的动态方法, 并且研究了电子商务系统中的动态聚类问题.一直以来, 学者们希望提出的观点动力学模型收稿日期 2021-01-29 录用日期 2021-04-29Manuscript received January 29, 2021; accepted April 29, 2021国家自然科学基金(61903282, 61625305), 中国博士后科学基金(2020T130488)资助Supported by National Natural Science Foundation of China (61903282, 61625305) and China Postdoctoral Science Founda-tion (2020T130488)本文责任编委 杨涛Recommended by Associate Editor YANG Tao1. 武汉科技大学信息科学与工程学院 武汉 4300812. 浙江大学工业控制技术全国重点实验室 杭州 3100273. 浙江大学控制科学与工程学院 杭州 3100271. School of Information Science and Engineering, Wuhan Uni-versity of Science and Technology, Wuhan 4300812. State Key Laboratory of Industrial Control Technology, Zhejiang Uni-versity, Hangzhou 3100273. College of Control Science and Engineering, Zhejiang University, Hangzhou 310027第 49 卷 第 10 期自 动 化 学 报Vol. 49, No. 102023 年 10 月ACTA AUTOMATICA SINICAOctober, 2023既简单又便于严格的数学分析, 与此同时, 又可以捕捉到丰富的社会性质. 故研究者从建立优异的数学模型模拟现实世界中个体的观点演变这一根本问题出发, 提出了许多经典的观点动力学模型. 例如, 1974年DeGroot[1]提出了基于智能体的观点演化模型(DeGroot模型). 在DeGroot模型中, 个体通过吸收上一时刻邻居的观点形成当前时刻的观点,使得社会群体观点达成一致. 然而, DeGroot模型无法解释在良好的通讯条件下, 个体观点极化的现象. 为此, Friedkin等[2]通过引入持续的外部输入(外部环境因素), 提出了Friedkin-Johnsen模型. 考虑个体间相互信任的情况, Hegselmann和Krause 提出一个新的具有有界置信区间的观点动力学模型(Hegselmann-Krause (H-K)模型)[14], 仿真结果表明在不同的置信区间内, 观点产生一致、极化和分簇的现象[14]. 后来, 学者们对DeGroot模型和H-K模型等进行改进并做了较为深入的研究[18−19].从社会心理学的角度完善观点动力学模型, 以增强模型的泛化能力和应用范围, 是一个值得研究的问题. 1951年Asch[20]做了一个关于因从众压力而产生观点扭曲的著名实验. 基于Asch的实验, 许多学者建立了相关的观点动力学模型, 并给出了严格的数学分析. 例如, Javarone[21]在全连通的网络条件下, 分析了从众压力对观点演化的影响, Cheng 等[22] 考虑了同时具有有界置信和个体压力的观点动力学模型. 最近, Shang[23]研究了表达观点和私人观点的一致性问题; Ye等[24]在社交网络是强连通的条件下, 提出了具有表达观点和私人观点的社会网络模型, 并分析了其收敛性. 基于合作与竞争的社交网络, Lin等[25]分析了观点的传播现象. Su等[26]研究了噪声导致H-K观点动力学模型拟一致性问题.受Ye等[24]研究强连通社会网络中观点演化问题的启发, 本文研究具有遗忘个体的拟强连通社会网络中观点演化问题, 并分析了观点动力学的收敛性和表达观点与私人观点之间的差异. 本文主要贡献如下:1) 提出了新的具有遗忘个体的多维观点动力学模型, 刻画出了不同话题之间表达/私人观点的相互影响 (详见第3节);2) 不同于Ye等[24]所研究的社会网络是强连通的和非周期的, 且不含有遗忘个体, 本文研究的社会网络是拟强连通的且含有遗忘个体;3) 应用本文提出的多维观点动力学模型, 复现了“多元无知”这一经典的社会现象;4) 给出了从众压力的恢复力越小, 表达观点与私人观点的差异越大这一重要结论, 并且分析了逻辑矩阵对表达观点和私人观点演化的影响.1 问题描述G=(V,ε,W)V={1,2,···,n}ε⊆V×VW=[w ij]∈R n×nj i w ij>0.iiG(W)G(W)N ii∑nj=1w ij=1(∑nj=1w ij≤1), W本节首先介绍图论中的一些基本概念[27]. 设是一个具有加权邻接矩阵的有向图,其中, 和分别表示节点的集合和边的集合, 非负矩阵为加权邻接矩阵. 如果存在从节点到节点的边,则 如果节点能够到达任意剩下的节点,则节点称为根节点. 如果所有节点都是根节点, 则图是强连通的. 如果至少存在一个根节点,则图是拟强连通的. 表示所有能够影响个体的个体集合. 如果则称矩阵是行随机的(行次随机的).λi<1i定义 1[16]. 如果, 则称个体是固执的. 如果个体既不是固执的也不受任何固执个体的影响,则称为遗忘个体.A∈R n×n,A∗= lim k→∞A k A A∗= 1n v T,v∈R n,A定义 2[16]. 对于矩阵 如果极限存在, 则称矩阵是正则的. 如果 则正则行随机矩阵称为完全正则的. G(W)本文将研究具有遗忘个体的拟强连通社会网络上观点演化问题, 具体的观点动力学模型描述如下:y i(k)∈R y i(k)∈R i ki∈I[1,n]={1,2,···, n}G(W)其中, 和 分别表示个体 在 时刻的私人观点和表达观点,. 注意到, 在Ye等[24]的工作中, 社会网络是强连通的和非周期的, 且不含有遗忘个体. 与Friedkin-Johnsen模型[16]的本质区别是在观点动力学模型(1)中, 每个个体都包含私人观点和表达观点.λi∈[0,1]iϕi∈[0,1] iϕii iw ij≥0ij∑j∈N iw ij=1∀i w ii≥0 iλi∈[0,1]i在观点动力学模型(1)中, 表示个体的私人观点受人际关系影响的敏感程度,表示个体对于从众压力的恢复程度. 的值越大,则个体所承受到的从众压力就越小, 意味着个体的表达观点和私人观点之间的差异越小. 实际上,私人观点是个体的主观观点, 个体根据上一时刻私人观点和上一时刻邻居的表达观点来更新当前时刻的私人观点. 然而, 表达观点会进行修正以符合邻居表达观点的加权平均. 表示个体分配给个体 的表达观点权重且, ,表示个体 对自身私人观点的自信程度. 设表示个体对人际交互影响(邻居的表达观点)的敏2202自 动 化 学 报49 卷1−λi y i (0)λi =1−w ii i φij ≥0∑j ∈N i φij =1.Ψ=[φij ]∈R n ×n G (Ψ)感程度, 则反映对于本身初始观点 的固执程度. 类似于Friedkin-Johnsen 模型的“耦合关系”, 令 . 模型(1)第2个子式的右侧表示个体 对于“本地舆论”的从众压力. 假设 ,且 矩阵 是行随机的, “本地舆论”对于个体的影响可以通过图 的连通性来描述.从众压力的形成过程并非恒定不变的, 根据通讯方式的不同, 个体承受从众压力的情况就会不同.例如, 在较小的会议室中, 无论是否存在私下交流,个体都可了解其余所有个体的表达观点. 在这种情况下, 所有个体的表达观点所分配的影响权重是相同的, 即i 然而, 如果个体很多, 通讯条件实际上会影响个体 对“本地舆论”的认知. 例如, 个体在大规模的网络空间里通过网络交流时, 由于距离和通讯方式的限制, 个体实际上也许无法获知部分个体的表达观点. 在这种情况下, 个体只能通过给定的通讯方式获取外部信息. 换言之, 个体通过人际影响网络认知“本地舆论”,即注意到模型(1)的第1个子式可写成根据式(1)和式(2),可得其中,Λ=diag {λ1,λ2,···,λn }Φ=diag {ϕ1,ϕ2,···,ϕn }W = W+ W W=diag {w 11,w 22,···,w nn }, W =[w ij ]∈R n ×n ,i =j w ii =0,∀i ∈I [1,n ] y (0)=y (0)y (1)=(ΛW +I n −Λ)y (0)其中, 矩阵 和 分别表示个体的固执程度和对从众压力的弹性恢复能力, 人际网络影响矩阵 , , ,为初始的表达观点和私人观点, .本文将研究具有遗忘个体的拟强连通社会网络G (W ) 中表达观点和私人观点的收敛问题 (详见第2节). 另一方面, 为了描述多个相互依赖话题上表达观点和私人观点演化问题, 建立了多维的观点动力学模型(详见第3节). 本文主要的研究框架如图1所示.图 1 本文研究框架Fig. 1 The research framework of this paper2 收敛性分析G (W )1n 1(n 1≤n )n 1+1n (λi =1,∀i ∈I [n 1+1,n ]) W W ,Ψ,Λ,Φ,y, y 本节将分析拟强连通社会网络 中观点动力学模型(1)的收敛性. 为了便于分析, 将固执个体和受固执个体影响的个体编号为 到 ,遗忘个体的编号则为 到 . 根据定义1, 易知所有遗忘个体只受邻居观点的影响 . 故 , 可分解为m =n −n 1y (1)(k )∈R n 1其中, 为遗忘个体量, 和10 期刘青松等: 具有遗忘个体的社会网络多维观点动力学分析与应用2203y (1)(k )∈R n1y (2)(k )∈R m y (2)(k )∈R m 分别表示固执个体的私人观点和表达观点, 和 分别表示遗忘个体的私人观点和表达观点.不同于Ye 等[24]所提出的观点动力学模型, 本文推广的观点动力学模型包含遗忘个体. 显然, 式(3)可改写为ξ(k +1)=y (1)(k +1),y (2)(k +1), y (1)(k ),y (2)(k )]T,Ω0=I n 1−Λ11,其中,其中n 1=n Ψ=W 显然, 如果 , 则式(5)退化成Ye 等[24]所建立的观点动力学模型. 此外, 如果 , 则基于遗忘个体私人观点的观点动力学模型类似于De-Groot 动力学模型[1].ΨW G (W 11)假设 1. 矩阵和 是行随机的, 网络 ϕi ∈(0,1),∀i ∈I [1,n ]λi ∈(0,1),∀i ∈I [1,n 1]是强连通且非周期的. 此外, 和 .A ∈R n ×n A ρ(A )<1.引理 1[24]. 对于矩阵 , 如果 是行次随机且不可约的, 则谱半径 G (W )n 1=n 引理 2. 在假设1满足的条件下, 如果社会网络中不含有遗忘个体(即 ), 则观点动力学模型(1)是收敛的.G (W )y i (k ) y i (k )证明. 根据Ye 等[24]的证明易知, 如果社会网络 中不含有遗忘个体, 则易得私人观点 和表达观点 都是收敛的.□W 22G (W )定理 1. 在假设1满足的条件下, 如果矩阵 是正则的, 则具有遗忘个体的社会网络 中表达观点和私人观点是收敛的.Ψ=W 证明. 首先证明具有遗忘个体且 的观点动力学模型(1)的收敛性.ζ(k +1)=[y (1)(k +1), y (1)(k ),y (2)(k +1), y (2)(k )]T设 ,并且其中,易知式(5)可写成注意到遗忘个体的观点演化不受初始的表达观点和私人观点的影响, 其演化过程类似于DeGroot 模型, 即注意到式(8)可写成根据式(9)和式(10), 可得2204自 动 化 学 报49 卷Ψ=W, W 22=0Ψ22=W 22= W22.另一方面, 由 可得, 进一步地, 由式(11)可得将式(12)代入式(8)中, 可得y (2)(k +1)= W 22 y (2)(k ). W 22同理可得, 由于 是正则的, 可得y (2)(k ) y(2)(k )W ∗22y (2)(0)故遗忘个体的私人观点 和表达观点 都收敛到 . 注意到其中,ρ(B )<1由式(14)和式(15)可知, 如果 , 则式(16)是收敛的.ρ(B )<11n 1V 1V 2G (W 11)G (B 11)G (B 22)B 21B 12V 1V 2G (B )下面只需证明 . 设标记从 到 的节点属于集合 , 剩下的节点都属于集合 . 根据网络 的连通性可知, 网络 和 都是强连通的. 进一步地, 由于矩阵 和 都存在大于0的元素, 故在节点集合 和节点集合 中, 节点之间存在双向路径. 因此, 网络 是强连通的.Λ11, W 11,Φ11,(In 1−Φ11),Ψ11B ≥0W 11Ψ11根据矩阵 都是非负矩阵, 可得 . 由于 和 都是行次随机矩阵, 故1n =[1,1,···,1]T 是行次随机矩阵, .ρ(B )<1根据引理1可知, . 因此,[]D ∗=lim k →∞D k E =Λ22W 2200I m F =[Ω0000].其中, , , Ψ=(1T n 1n )/n 最后, 证明具有遗忘个体且的社会网络中观点的收敛性, 即个体内所有个体可接收到彼此之间的表达观点.Ψ=(1T n 1n )/n 1n =[1,1,···,1]TG (D )G (B )G (P )根据 , , 可得网络 是强连通的. 利用类似于证明 的方法, 易证 是强连通的. 由引理1可知,由Ravazzi 等[28]的命题1可得Ω1=(I 2n −P )−1Ψ=(1T n 1n )/n 其中, . 故具有遗忘个体且 的社会网络中观点是收敛的.□G (W )将定理1与Ye 等[24]的结论比较, 本文研究的社会网络 是拟强连通的且含有遗忘个体, 意味着观点动力学模型(1)更加符合现实情况且不需严格的通讯方式.3 多维观点动力学分析为了描述具有遗忘个体的社会网络中不同话题之间表达观点和私人观点的相互影响, 建立如下多维观点动力学模型:y i (k )∈R d y i (k )∈R d i ∈I [1,n ]C ∈R d y ip (k )>0.5i 其中, , , , 逻辑矩阵 用于描述不同话题之间表达观点和私人观点的相互关系. 表示个体 的私人观点10 期刘青松等: 具有遗忘个体的社会网络多维观点动力学分析与应用2205p y ip (k )<0.5i p y ip (k )=0.5i y ip (k )>0.5i p yip (k )<0.5i p y ip (k )=0.5i 是支持话题 , 表示个体 的私人观点是反对话题 , 表示个体 的私人观点是中立的, 表示个体 的表达观点是支持话题 , 表示个体 的表达观点是反对话题 , 表示个体 的表达观点是中立的.注意到将观点动力学模型(17)的第2个子式代入其第1个子式可得类似于单维情形下的式(3), 由式(18)和式(17)的第2个子式可得P其中, 由式(6)给定.C G (W )定理 2. 在假设1满足的条件下, 如果逻辑矩阵 是行随机的, 则不含有遗忘个体的社会网络 上观点动力学模型(17)是收敛的, 且收敛值为Ω2=(I 2dn − P⊗C )−1.其中, 证明. 注意到⊗C ρ(C )=1ρ( P)<1y ∗=lim k →∞y (k ) y ∗=lim k →∞ y (k ).其中, 表示Kronecker积. 由 是行随机矩阵可得, . 根据定理1易知, 当 时, 不含遗忘个体的观点动力学模型(17)是收敛的. 设 且 由式(19)易知由上式可得观点的收敛值.□G (W )当拟强连通社会网络 含有遗忘个体时,在单维观点情形时, 式(5)可写成式(7). 类似地,在多维观点情形下有W 22C G (W )定理 3. 在假设1满足的条件下, 如果矩阵 和 都是正则的, 则具有遗忘个体的社会网络 上观点动力学模型(17)是收敛的.Ψ证明. 类似于定理1的证明, 根据矩阵 的结构将证明过程分为两个部分.Ψ=W 1) 当 时. 注意到意味着遗忘个体的私人观点和表达观点不受其余固执个体的影响. 因此, 由式(20)可得W 22C 由于矩阵 和 都是正则的, 可得遗忘个体的观点是收敛的, 即y (1)(k )y (1)(k )类似于定理1的证明, 由Ravazzi 等[28]的命题1可知, 和 是收敛的, 故观点动力学模型(17)是收敛的.Ψ=1n 1Tn1n 2) 当 时. 由定理1的证明可得易知,根据Ravazzi 等[28]的命题1可知, 观点动力学模型(17)是收敛的, 即由式(20)可知Ω3=(I 2dn −P ⊗C )−1其中, .G (W )综上所述, 具有遗忘个体的社会网络 观点动力学模型(17)是收敛的. □本节在拟强连通社会网络中, 提出新的具有遗忘个体的多维(表达和私人)观点动力学模型, 刻画出不同话题之间表达/私人观点的相互影响; 另一方面, 本文仅需社会网络是拟强连通, 意味着个体之间无需严格的通讯方式, 更加符合现实社会的情景, 故应用范畴取得突破.2206自 动 化 学 报49 卷的条件相吻合. 考虑由7个个体组成的社会群体,其中, 含有3个遗忘个体(蓝色). 网络结构如图2所示(未画出自环), 其所对应的网络影响矩阵为Λ=I n−diag{w ii}以及敏感度矩阵为. 设个体的初个体恢复力参数矩阵为易知, 个体2, 4和6是不受外界因素影响的遗忘个体, 且持反对观点. 根据图3可得, 个体1, 3, 5和7的表达观点从开始持支持态度演化到持反对态度,其私人观念和表达观念产生显著的差异. 这是因为从众压力的影响, 个体1, 3, 5和7不断修改已形成的表达观点来适应持反对态度的“本地舆论”. 图3中, 不同颜色的线型表示不同个体的表达/私人观点.2467531图 2 具有遗忘个体的社会网络Fig. 2 Social networks with oblivion individuals4.2 仿真分析Cϕi本节将分析逻辑矩阵和恢复力参数对个体私人观点与表达观点之间(差异)的影响. 考虑G(W)由7个个体组成的一个网络, 其中, 含有3个遗忘个体(蓝色). 人际影响网络结构如图4所示(未画出自环), 所对应的网络影响矩阵为Λ=I n−diag{w ii}Ψ=(1T717)/7y(0)= y(0)以及敏感度矩阵为. 根据个体数量, 设定“本地舆论”包含所有个体的表达观点, 即,. 令, 且4627351图 4 具有遗忘个体的社会网络Fig. 4 Social networks with oblivion individualsϕi=0.1C设, 分别设逻辑矩阵为C=C1G(W)由图5 ~ 11可知, 当不同话题的观点互不影响()时, 社会网络中所有个体的私图 3 多元无知Fig. 3 Pluralistic ignorance10 期刘青松等: 具有遗忘个体的社会网络多维观点动力学分析与应用2207C =C 2人观点和表达观点都是支持话题1, 反对话题2. 当时, 所有个体的私人观点和表达观点都还支持话题1, 但支持的态度有所减弱. 所有个体的表达观点却由之前都是反对话题2变成了支持话题2,个体1 ~ 4的私人观点仍然反对话题2, 但反对的态度有所减弱, 遗忘个体5 ~ 7的私人观点由之前都是反对话题2演化成了支持话题2.C =C 1C =C 2进一步地, 由图9 ~ 11可知, 当 时, 遗忘个体5 ~ 7分别对于话题1和话题2的私人观点与表达观点非常相近, 相对于话题1和话题2, 产生观点两极分化的现象. 当 时, 针对话题1和话题2, 遗忘个体5 ~ 7的私人观点与表达观点都21图 5 个体1的观点Fig. 5 Opinions of individual 121图 6 个体2的观点Fig. 6 Opinions of individual 221图 7 个体3的观点Fig. 7 Opinions of individual 3k /s k /s (b) C = C 2(a) C = C 1图 8 个体4的观点Fig. 8 Opinions of individual 421图 9 个体5的观点Fig. 9 Opinions of individual 521图 10 个体6的观点Fig. 10 Opinions of individual 621图 11 个体7的观点Fig. 11 Opinions of individual 72208自 动 化 学 报49 卷非常相近, 产生观点一致的现象.ϕi =0.1ϕi =0.3ϕi =0.6ϕi =0.9C =C 1ϕi 为了分析从众压力对于个体表达观点和私人观点差异的影响, 设 , , , 和 . 由图12可知, 恢复力参数 越大,个体的私人观点与表达观点越接近. 换言之, 从众压力越大, 个体私人观点与表达观点的差异越大.这与现实世界的经验一致, 即个体会因外部环境的影响而适当地改变自己的主观观点. 图12中, 不同颜色的线型表示不同个体的表达/私人观点.C =C 1图 12 观点动力学模型(17): C =C 1Fig. 12 Opinion dynamics model (17) with5 结束语本文提出了一个新的具有遗忘个体的多维观点动力学模型, 刻画出了不同话题之间表达/私人观点的互相影响. 在社会网络是拟强连通的条件下,根据逻辑矩阵和网络影响子矩阵的正则性, 给出了表达观点和私人观点收敛的充分条件. 应用本文所提出的观点动力学模型, 复现了“多元无知”的社会现象. 仿真分析表明从众压力的恢复力越小, 表达观点与私人观点的差异越大. 另外, 进一步讨论了逻辑矩阵对表达观点和私人观点演化的影响.在现实社会中, 个体的表达观点在传播和演变过程中, 观点传播的速度可能受个体自由意志或者社交媒体的影响. 因此, 针对观点传播速度的研究是一个值得考虑的问题. 这是本文的不足之处. 在未来的工作中, 一方面, 在考虑时间复杂度的基础上, 建立连续型的观点动力学社会模型, 深入研究观点传播或者演化的速度; 另一方面, 借鉴探究Bass模型在新领域扩展应用的思想[30]和利用DEA 模型评价优势的思想[31], 从一个全新的角度拓展社会网络的应用及说明观点动力学模型具有的优势.ReferencesDeGroot M H. 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Annual Reviews in Control , 2017, 43: 65−7927Ravazzi C, Frasca P, Tempo R, Ishii H. Ergodic randomized al-gorithms and dynamics over networks. IEEE Transactions on Control of Network Systems , 2015, 2(1): 78−8728Prentice D A, Miller D T. Pluralistic ignorance and alcohol use on campus: Some consequences of misperceiving the social norm.Journal of Personality and Social Psychology , 1993, 64(2):243−25629Yang Zhuo-Xuan, Ma Yuan-Pei, Li Hui-Jia. The relationship between efficiency and services types of water industry enter-prises in China based on DEA model. Journal of Liaocheng Uni-versity (Natural Science Edition), 2020, 33(6): 12−26(杨卓璇, 马源培, 李慧嘉. 基于DEA 模型的中国水行业上市企业的效率和业务类型关系研究. 聊城大学学报(自然科学版), 2020,33(6): 12−26)30Ma Yuan-Pei, Yang Zhuo-Xuan, Li Hui-Jia. Innovative product diffusion forecasting combined Bass model and LTV. Journal of Liaocheng University (Natural Science Edition), 2020, 33(4):26−32(马源培, 杨卓璇, 李慧嘉. 结合Bass 模型和LTV 的创新产品扩散预测. 聊城大学学报(自然科学版), 2020, 33(4): 26−32)31刘青松 武汉科技大学信息科学与工程学院副教授. 2019年获哈尔滨工业大学控制科学与工程系博士学位. 主要研究方向为社会网络, 观点动力学分析, 时滞系统和多智能体系统.E-mail: ********************.cn (LIU Qing-Song Associate profess-or at the School of Information Science and Engineer-ing, Wuhan University of Science and Technology. He received his Ph.D. degree from the Department of Con-trol Science and Engineering, Harbin Institute of Tech-nology in 2019. His research interest covers social net-works, opinion dynamics analysis, time-delay systems,and multiagent systems .)李明鹏 武汉科技大学信息科学与工程学院硕士研究生. 2019年获武汉科技大学信息科学与工程学院学士学位. 主要研究方向为社会网络, 观点动力学分析.E-mail: **********************(LI Ming-Peng Master student atthe School of Information Science and Engineering,Wuhan University of Science and Technology. He re-ceived his bachelor degree from the School of Informa-tion Science and Engineering, Wuhan University of Science and Technology in 2019. His research interest covers social networks and opinion dynamics analysis .)柴 利 浙江大学控制科学与工程学院教授. 2002年获香港科技大学电子工程系博士学位. 主要研究方向为分布式优化, 滤波器组框架, 图信号处理, 网络化控制系统. 本文通信作者.E-mail: ***************.cn(CHAI Li Professor at the Collegeof Control Science and Engineering, Zhejiang Uni-versity. He received his Ph.D. degree in electrical en-gineering from Hong Kong University of Science and Technology, China in 2002. His research interest cov-ers distributed optimization, filter bank frames, graph signal processing, and networked control systems. Cor-responding author of this paper .)2210自 动 化 学 报49 卷。
The emergence of design in pedestrian dynamics
Available online at Physics of Life Reviews10(2013)168–190/locate/plrevReviewThe emergence of design in pedestrian dynamics:Locomotion, self-organization,walking paths and constructal lawAntonio F.Miguel a,b,∗a Department of Physics,Evora University,Rua Romão Ramalho59,7000-671Evora,Portugalb Geophysics Center of Evora(CGE),PO Box84,7002-554Evora,PortugalReceived25February2013;accepted7March2013Available online26March2013Communicated by J.FontanariAbstractGait is inherent to human life and hence its importance is often overlooked.But walking remains the most basic form of transportation and almost all journeys begin and end with a walk,regardless of the modes used in-between.Gaining a good under-standing of pedestrian’s dynamics is thus a crucial step in meeting the mobility and accessibility needs of people by providing safe and quick walkingflows.This paper presents a critical and integrative review of research on pedestrian’s dynamics and associated topics.The review focuses on comprehensive theories and models,with an emphasis on the advances made possible by the application of the con-structal law.Constructal law points out that the emergence and evolution of design in pedestrian dynamics is analogous to that of animateflow systems.Most importantly,it also highlights that the basic features of pedestrian dynamics and supportive walking infrastructures can be optimally envisaged with the help of a few fundamental physics laws.©2013Elsevier B.V.All rights reserved.Keywords:Human gait;Walk–run transition speed;Fundamental pedestrian diagram;Self-organization;Walking paths;Constructal law1.IntroductionAlthough there are over250species of primates,only one moves primarily on two legs.Bipedalism developed approximately4–5million years ago and it was thefirst major adaptation that separated hominids from other primates [1–4].Human anatomy is built on a body planned for bipedal locomotion.The two distinct gait modes of humans are walking and running,which make use of strikingly different mechanics and energetics.Currently,the fastest human being on Earth,Usain Bolt,is able to run at a speed greater than10.44m/s.Regular pedestrians,however,tend to walk rather than run,and do this mainly at a comfort walking speed of around1.3m/s[5,6].The different speeds at which humans walk or run translate themselves into varying energy costs.Keeping energy spending low is highly desirable and leads to greater mobility,given that humans must carry their energy supply with them[7,8].*Correspondence to:Department of Physics,Evora University,Rua Romão Ramalho59,7000-671Evora,Portugal.Tel.:+351266745372;fax: +351266745394.E-mail address:afm@uevora.pt.1571-0645/$–see front matter©2013Elsevier B.V.All rights reserved./10.1016/j.plrev.2013.03.007A.F.Miguel/Physics of Life Reviews10(2013)168–190169Since the middle of last century,the study of the pedestrian dynamics has become an active subject of research in science[5–8].Pedestrian dynamics has theoretical importance and a multitude of practical applications.Primary questions such as why and how human walks,or how crowd dynamics occurs based on individual interactions,along with some more practical aspects like the design of pedestrian optimized facilities,have puzzled many researchers.In-situ observational studies and time-lapsefilms,together with the modeling have revealed important quantitative details and have led to a unique understanding of pedestrian dynamics with important practical implications[5,6].Despite the considerable progress in understanding various aspects of pedestrian dynamics,there has been no systematic attempt to integrate what remain disconnected,because of the wide scope of the subject.Fitting the“pieces”together will contributes decisively to a unified view of the topic.This paper starts with a brief description of basic mechanics of human locomotion and its energetic cost.Factor such as gender,age and environment are important in the walking speed choice.Pedestrians react to other pedestrians and obstacles,and can only move freely when there is enough free space in front of them.Then,the relation between spatial headway(distance to the predecessor)and speed of pedestrians is analyzed.Empirical data(i.e.,the fundamental diagram)available in the literature is presented and models of pedestrian interactions are introduced.The calibration and the validation of the models using empirical data are also discussed.Finally,I turn the attention to the Constructal law which constitutes the thermodynamics law of nonequilibrium (flow)systems with configuration.For these systems,this law provides new physical insights,and a unified view on domains apparently foreign to each other.The Constructal law is introduced and,then,the Constructal view of pedestrian dynamics is presented and discussed.Furthermore,the design of improved pedestrian facilities,using the Constructal law,is also addressed.The objective of this Constructal section is to forge a more structured and unified view that engage a set of issues which are addressed under different frameworks and disciplinary spaces.2.Modern human anatomy and locomotion:mechanics,energetics and gait speedBipedal locomotion is the sole form of locomotion in all healthy modern humans and it sets them apart from all other living primates[1–4].A large number of anatomical features are functionally related to this type of locomotion. The human pelvis is pronouncedly bowl-shaped,with an adapted musculature which allows the thighs to be angled in, the lower limbs are lengthened and have an enlarged joint surface area to properly support body weight,the vertebral column is shortened and S-shaped,for rigidity and balance,lining up head and trunk vertically above the feet,the hole through which the column cord enters the skull is situated near the center of the cranium which allows the head to balance easily atop the column,the feet have an arched shape with the enlarged great toe brought in line with the other toes,to absorb shock and a more efficient walk,are among other important evolutionary features[9,10].From an evolutionary perspective,the global impression of the human anatomy is that of a bio-cylinder shape[7,10].Although bipedalism is not the most stable and fast way of locomotion,it must clearly represent an evolutionary advantage to humans,because we still walk on two legs.Some of the advantages associated to bipedalism include the ability to carry things over longer distances,the freeing of arms and hands for other tasks(foraging and protection,for instance),the acquisition of improved long-distance perception and the improvement of body thermoregulation[1,9, 11–13].It is not uncommon to see apes such as chimpanzees walking on two legs in order to carry things.Octopuses have been also documented walking bipedally in order to camouflage themselves from predators[14].Placing six limbs close to their head,the octopus assumes the shape of a drifting plant,and then uses its two remaining limbs to walk away from predators.Another possible explanation for bipedalism is its lower energetic cost compared to other forms of locomotion. In a study by Taylor and Rowntree[15],chimpanzees(Pan troglodytes)and capuchin monkeys(Cebus capucinus) were trained to run on a treadmill on either two or four legs.Results showed that the energy spent by the animals on this exercise was fairly independent of the mode of locomotion they adopted.Fedak and Seeherman[16]also reported negligible differences of the scaling of energy requirements for locomotion between bipedal and quadrupedal behavior. On the other hand,Alexander[7]stated that gait of humans is distinct from the occasional bipedalism of apes because the patterns of force exerted on the ground are different,due to biomechanical differences in anatomy mentioned above.Therefore,the trajectory of the center of mass is completely different for gaits in humans and other animals [7,17].Sockol et al.[18]reported that the energy expended in human walking is approximately75%less than that expend in both quadrupedal and bipedal walking in chimpanzees.The study of Carrier et al.[8]also supported the170 A.F.Miguel/Physics of Life Reviews10(2013)168–190idea that humans are more economical when they walk.Besides,Alexander[7]stated that while the walk spends less energy than the gait pattern of quadrupedal mammals of the same body mass,running actually spends more.2.1.Forms of human gait:walking and runningPeople move across the Earth’s surface(are not be attached to one site),and this capability is called locomotion. Walking and running are the two most common forms of human gait.The increase of speed intuitively triggers the switch from a walk to a run.Walking gait is characterized by two distinct phases[19]:the stance phase,when the leg is on the ground,and the swing phase,when it is off the ground.The stance phase begins with heel-strike,as the foot strikes the ground.Most of the time just one foot is on the ground,with brief periods where both feet come in contact with the walking surface.The body vaults up and over each stiff leg in an arc.This gait pattern can be well approximated by a linear“inverted pendulum”[7,17,19,20].An ideal inverted pendulum system exhibits an optimal conversion of gravitational potential energy to kinetic energy.The energy converted by such an“inverted pendulum”mechanism can reduce the mechanical work required from the muscular system by up to70%[17].Running,in contrast,involves longer aerial phases,in which neither foot is in contact with the ground.In this case,the pendulum mechanism that characterizes gait switches to a spring-mass system,where bent legs bounce up between aerial phases [20].As feet hit the ground in a run,the leg springs compress,as a result of jointflexion,and the mass moves downwards.At the middle of the stance phase,the leg is maximally compressed,and the mass reaches its lowest point.The plantigrade foot posture of a runner is also very distinct of that of a walker[21],with its center of mass reaching the lowest point at the middle of the stance phase.In contrast,the center of mass of walkers is at its highest point precisely at the middle of the stance phase.Moreover,the stance limb sweeps through a larger angle during walking(∼30◦)than during running(∼19◦)[17].Finally,running involves a decrease of approximately35%in time of foot–ground contact and an increase of the peak ground reaction force by about50%,when compared to walking[17].Humans prefer changing their gait from walking to running and from running to walking at increasing and decreas-ing speeds.This switch occurs at a Froude number of0.5[22,23].For adults,it corresponds to a walking speed of about2m/s[24].Both walking and running are related to several demands that must be processed simultaneously:the propulsion of the body in the horizontal plane,the maintenance of a stable equilibrium(coordination between posture and move-ment),and a continuous and instantaneous adaptation to environmental requirements[25,26].This demands the use of the central and peripheral nervous system,the regulation of the skeletal segments and the contraction of mus-cles[27].Gait speed is therefore tightly linked to neurological development/degeneration,balance control,changes in limb length,and maturation.Studies performed by several authors[28,29]suggest that the gait speed is a quick, inexpensive,reliable measure of functional capacity.Recent studies also reported a significant association between walking speed and life span in seniors[30,31].Others[32],finally,presented evidence that successive step durations during walking actually present a typical structure over time,one that is characterized by a long-range dependence (i.e.,a scaling relationship).It is suggested that this dependence plays an important role in the adaptability and the flexibility of locomotion,since it disappears in individuals with neurodegenerative pathologies.2.2.Least energy-consuming gaitHumans carry their energy supply with them,and they are limited by the rate of production of metabolic energy in their bodies,that depends of the capacity of the cardiovascular system to absorb and distribute oxygen throughout the body.The slower energy is consumed,the less energy must be carried and greater mobility is achieved.A number of experimental studies have shown that the average metabolic energy consumption per unit distance traveled,E x,may be expressed by[33]E x=0.533M bu+0.3M b u(1)Here M b is the body mass and u is the gait speed.This equation has a minimum at a speed of∼1.33m/s,which is within the walking speed range(i.e.,below the average transition speed of∼2m/s between walking and run-ning[24]).This average speed is recurrently mentioned in the literature as the comfortable walking speed or desired walking speed[5,6,34].A.F.Miguel/Physics of Life Reviews10(2013)168–190171Fig.1.The comfortable walking speed versus decade of age:!female,"male(experimental data obtained from Bohannon[35]).Fig.2.The comfortable walking speed versus the body mass:!female,"male(experimental data obtained from[6]and[35]).Several studies[6,35]report the effect of gender and age on the comfortable walking speed of healthy humans (Fig.1).Speed is also expected to increase with the body mass due to fundamental structural reasons[36,37].The effect of the body mass on the comfortable walking speed is illustrated in Fig.2.From thisfigure,one can conclude that the comfortable walking speed scales sublinearly with body mass.Indeed,the power exponents depicted for females and males are0.182and0.156,respectively.3.Pedestrian’s guided locomotionPedestrians are attentive to details of the walking environment,especially those that are very close to them[38]. They feel uncomfortable if they get too close to other pedestrians(territorial effect or private“sphere”),as well as to physical obstacles.The vision(the eye)provides information about the environment,which is then cognitively interpreted and helps shape the way pedestrians evolve in space[39,40].This enables the selection of safer and straighter paths,and the circumvention of other pedestrians and obstacles.This guided behavior constitutes a primary and an essential feature in the perfecting of locomotion.To avoid other pedestrians or obstacles,pedestrians may adjust their comfortable speed to a lower self-selected speed.A number of researchers have studied the influence of pedestrian density(or interpersonal distances1)on1The concept“interpersonal distance”was introduced by Thompson and Marchant[41].The average interpersonal distance is obtained from the inverse of square root of pedestrians’density.172 A.F.Miguel/Physics of Life Reviews10(2013)168–190Fig.3.Experimental fundamental diagram of pedestrian movement:walking speed vs.pedestrian density(or interpersonal distance).Fig.4.Pedestrian density domains in the fundamental diagram of pedestrian movement.pedestrian speed[41–44].Several experimental studies have shown that pedestrians are able to walk at their com-fortable walking speed at densities up to0.2–0.8persons/m2.Beyond such values,an increase of pedestrian density leads to a pronounced reduction of walking speed.The walking speed–pedestrian density diagram depicted in Fig.3is known as the fundamental diagram of pedestrian movement[45–48].Seyfried et al.[45]suggested that this diagram can be divided into5density-domains.In alternative,Miguel[46]proposed that the array of points in this diagram may be divided into two major density-domains,as indicated in Fig.4:(i)Density-domain I:The interpersonal distance between the pedestrians is large enough(or the density of pedes-trians is small enough)and pedestrians are able to walk at their comfortable walking speed(0 δ δfs,whereδfs is the smaller interpersonal distance between the pedestrians that corresponds to the free walking speed).(ii)Density-domain II:Due to the reduction of the free available space,pedestrians adjust their speed,due to a natural desire of avoiding or reducing contact with other pedestrians.In this domain two sub-domains are identified which exhibit curves with different slopes:(a)the interpersonal distance between the pedestrians is not enough to walk at their comfortable walking speed,but is large enough to avoid contacts between them by a small reduction of walking speed;and(b)a more pronounced reduction in walking speed is required,since the space around each pedestrian is very small,and contacts with other pedestrians may hardly be avoided.A.F .Miguel /Physics of Life Reviews 10(2013)168–190173These pedestrian interactions can be cast into mathematical equations.Accordingly,pedestrians dynamics can be well approached within the framework of a Langevin-like equation of motion [49,50].The Langevin formulation is used to describe the Brownian particle’s motion as an Ornstein–Uhlenbeck process [51],and its position as the time integral of its velocity.Illustrative examples of this formulation for pedestrians are the social force and centrifugal force models.In the social force model [52,53],pedestrians’movement toward a destination results of the acceleration towards the desired walking speed,and the repulsive/attractive interactions with other pedestrians and obstacles.This model includes the concept of territorial effect (the private sphere)that leads to repulsive forces between pedestrians,as first suggested by Gipps and Marksjös [54].In the centrifugal force model [55,56],pedestrian movement results from the driving and repulsive forces acting on each pedestrian,with the repulsive forces being described similarly to centrifugal forces.Both models are able to capture and describe important features of pedestrian movement,such the formation of lanes in counter-flow,clogging at exit doors,oscillations at bottlenecks,among others [56].ngevin-like model for the pedestrian dynamicsA simple Langevin-like model can be derived from the above-present concept of density-domain II [46].At den-sity sub-domain IIa,pedestrians’interpersonal distances are still large enough,hence the deviation from the desired walking speed results from the necessary deceleration to adjust own speed to the speed of neighboring pedestrians.Therefore,M b d 2r dt=M b τ dr dt −dr ∗dt ,δrp δ δfs (2)and after integration of this equation,the walking speed within this domain,u IIa ,can be expressed asu IIa =u 0+1τ(δ−δfs ),δrp δ δfs (3)Here r is the position of the pedestrian,τis a relaxation time,(dr/dt −dr ∗/dt )is the mean relative speed to the pedestrians situated around,u 0is the free walking speed,δrt is the interpersonal distance that corresponds to the start of sub-domain IIb,and δfs is the smaller interpersonal distance between the pedestrians for whom free walking speed is still available.Pedestrians get too close to others at sub-domain IIb.The decrease of pedestrians’interpersonal distances leads to the presence of repulsive forces between them.These forces depend not only on the relative velocity of pedestrians,but also on the distance between them.Within this domain,M b d 2r dt=M b γ(r −r ∗) dr dt −dr ∗dt ,δmin <δ δrp (4)Integration of this equation yields the following walking speed,u IIb ,u IIb =u rp +γln δδrp ,δmin <δ δrp (5)where γis a coefficient,r −r ∗(=δ)is the mean interpersonal distance between the pedestrians,u rp is the walking speed corresponding to the minimum interpersonal distance where “repulsive forces”start to occur,and δmin is the smallest interpersonal distance possible between pedestrians in the domain.The average interpersonal distance and the pedestrians’density are related through the equation [41]δ=1√ρ(6)Substituting Eq.(6)into Eqs.(3)and (5)gives [46]u IIa =u 0−1τ √ρ−√ρfs √ρfs ρ ,ρfs ρ ρrp (7)u IIb =u rp +γ2ln ρrp ρ ,ρrp <ρ<ρmax (8)174 A.F.Miguel/Physics of Life Reviews10(2013)168–190Empirical data available in the literature can befitted with Eqs.(7)and(8),and the corresponding empirical coeffi-cients obtained.Pedestrian traffic may be unidirectional or multidirectional by nature.An examination of the results presented in prior studies indicates that both unidirectional and multidirectional streams are consistent with these two sub-domains, but that the interpersonal distance that corresponds to the start of“repulsive”forces is different[57].Therefore, a separate analysis must be performed,which yields the following coefficients[46,57]:–For unidirectional streams:τ=3.77s,u0=1.36m/s(0.3 ρ 1.4persons/m2);andγ=1.17m/s and u rp=0.995m/s(1.5 ρ 4.1persons/m2).–For multidirectional streams:τ=5.56s,u0=1.35m/s(0.14 ρ 0.88persons/m2);γ=1.10m/s and u rp=1.03m/s(0.89 ρ 5.2persons/m2).Although these results clearly support the existence of similar velocity–density domains for unidirectional and mul-tidirectional streams,the density range corresponding to each domain is actually different.Notice that neitherγnor u rp are significantly different between both streams,because these are quantities measured in the domain with less space available to pedestrians.On the other hand,the relaxation time is higher for the multidirectional streams.As the interpersonal distances between pedestrians in this domain are still large,the existence of multidirectional stream requires that pedestrians are more attentive,and more time to adjust their motion is needed.3.2.Diffusion coefficient model for the pedestrian dynamicsEinstein’s perspective of the Langevin’s approach of motion(i.e.a Wiener process)describes the penetrants mo-bility through a diffusion coefficient[58,59]and may be approached by a single coefficient.By analogy with kinetic theory,the pedestrian diffusion coefficient is related to mean walking speed and mean free interpersonal distance via the Einstein–Smoluchowski equation.The experimental data available in the literature is bestfitted by taking[57] (a)For unidirectional streams:D=1.512δ−0.588,0.47<δ 4.47m(9) (b)For multidirectional streams:D=1.498δ−0.593,0.43<δ 4.47m(10)These results also provide direct evidence supporting the differences between uni-and multidirectionalflows of pedestrians.Additionally,these coefficients are valid for the entire range of domain II.In summary,the models based on Langevin’s and Einstein’s pioneering studies in1905and1908[49,58],respec-tively,are able tofit well experimental data that relates walking speed to pedestrian density.The analysis of pedestrian dynamics as an Ornstein–Uhlenbeck type process,however,produces more insight into the“forces”that drive pedes-trian motion,and delivers different approaches according to pedestrian density sub-ranges(Eqs.(7)and(8)).On the other hand,a Wiener-type process,which is based on a single coefficient(Eqs.(9)and(10)),provides a more compact and simples approach of pedestrian motion.Despite their different mathematical formulation,all of these approaches are physically equivalent.Gillespie[60]presents a review of the arguments that lead to the conclusion that any diffusion coefficient may be linked with quantities such asτandγ.4.Constructal theory of pedestrian dynamics4.1.A new thermodynamics insight into dissipativeflow systemsSince Anaximenes of Miletus(585–528B.C.),laws are considered operative throughout Nature[61].This consti-tutes a magnificent triumph of reason and observation:laws tell us how things operate and can guide us in the quest for news knowledge.The invariance provides a structure and coherence to the laws just as the laws provide a structure and coherence to the set of natural events.A.F .Miguel /Physics of Life Reviews 10(2013)168–190175Thermodynamics is one of the bedrocks of modern science,and is firmly grounded into laws.Different laws provide us a view of natural phenomena.The zeroth law defines a useful property “temperature”(and proposes the equality of temperature as necessary and sufficient condition for thermal equilibrium).The first law defines useful extensive property “energy”(and asserts that energy is conserved).Since it is possible to take the same amount of internal energy “forward”and “backward”,the first law expresses symmetry.Although all processes must take place in accordance to the first law,the principle of conservation of energy is,by itself,insufficient to describe preferred directions of action in time.Both the reverse flow (hot to cold and cold to hot)and the immutability of configuration are not in violation of the first law [61].The second law of thermodynamics asserts the existence of extensive property entropy and states that this property in an adiabatically isolated system never decreases in time.The entropy is a Lyapunov function of the dynamical system and the “backward”process is not allowed [61].There is a “time asymmetry“or a “direction of time”or an “arrow of time”of the state of the system.The third law defines a state known as “absolute zero”(and relates the entropy of a system to its absolute temperature).Most real systems are however not isolated and may exhibit distinct characteristics.If two mixable liquids are let to mix in a vase,diffusion takes place spontaneously and a progressive decrease of initial individual concentrations will occur with a corresponding increase of entropy.But living organisms are able to maintain the differences of liq-uid concentrations in time (by chemical reactions and active transport).Prigogine named these systems ‘dissipative structures’because they cannot exist independently of their environment [62,63].These “structures”make an effort to avoid a transition into thermodynamic equilibrium by a continuous exchange of materials and energy with the en-vironment.Therefore,they are also able to self-organize through instabilities that lead to irreversible bifurcations and new stable system states [62,63].Another of Prigogine’s contributions was the minimum entropy production principle (or Prigogine theorem),which applies to open linear nonequilibrium systems in the stationary (or approaching the stationary)state.At every instant,currents of fluid,heat,mass,or information are flowing through animate and inanimate,dissipative open systems.This involves a state of organizational structure intimately coupled with nodes and channels of supply and distribution.The ubiquitous generation of configuration (design,organization)in these nonequilibrium systems is covered by the constructal law of Adrian Bejan,which states that “For a finite-size flow system to persist in time (to live )it must evolve such that it provides greater and greater access to the currents that flow through it ”[64–70].This new law asserts that for any flow system there is a property “configuration”and relates the generation of configuration to its greater access to flow.2This is possible because systems have the freedom to morph (i.e.,freedom to change the configuration in time)to achieve their purpose of higher global performance under constraints.Flows occur against resistances (imperfections)that constantly cause energy dissipation and try to slow them down.Therefore,the emergence of configuration (organization)with a purpose,defined by the constructal law,also requires that entropy changes.For the sake of simplicity,let us consider a linear pressure–flow relation (or potential–current relation).In this case,the resistance,R ,is related with the time rate of entropy generation,d ˙S g ,by R =1T V 2d ˙Sg and R =T d ˙S g 2,where V is the potential (or pressure difference),I is the current (or flow),and T is the absolute temperature.Minimization of resistance in morphing configurations under constant I and constant V (constraints)corresponds not only to a minimization of the entropy generation rate but to a maximization of the entropy generation,respectively.In summary,configuration emerges in systems that have a purpose and are far from equilibrium,and the emergence of this organization requires that entropy changes.The constructal law is not only connected to the entropy generation rate,but it also provides the reasons for why and how design occurs in nonequilibrium systems.4.2.Constructal view of human gaitEngines (man-made,animal,geophysical)use energy to produce the work required for driving movement.In order to induce movement,they should be able to overcome internal and external resistances (i.e.,energy input is matched by energy loss).Such thermodynamic “imperfections”cannot be avoided,and the constructal improvement of functions implies the generation of a design that distributes imperfections optimally to fill the flow space.Therefore,the constructal law is about both the necessity and the evolution of design to occur.2“Maximum flow access”corresponds to minimum travel time or minimum transfer time [67].Therefore,“for a finite-size flow system to persist in time it must evolve such that it provides a minimum travel time to currents that flow through it”.。
173-社会科学问题的模拟研究
引论 一、引论
• 舆论问题
•
谣言传播问题
•
……..
意见传播模型 二、Sznajd模型
1、一维Sznajd模型 • 规则
意见传播模型 二、Sznajd模型
1、一维Sznajd模型 • 结果
意见传播模型 二、Sznajd模型
1、一维Sznajd模型•源自参考文献：KATARZYNA SZNAJD-WERON, JOZEF SZNAJD.OPINION EVOLUTION IN CLOSED COMMUNITY. International Journal of Modern Physics C, Vol. 11, No. 6 (2000) 1157-1165.
展望 三、展望
介绍若干进一步的结果： – 团队模型 – 多意见的意见传播模型 – 网络上的意见传播模型 小世界网络 无尺度网络 – 其他
参考文献 四、推荐阅读
Claudio Castellanc, Santo Fortunatc and Vittorio Loreto, Statistical physics of social dynamics, Reviews of Modern Physics 81 (2) (2009), pp. 591–646. Fei Ding , Yun Liu, Bo Shen, Xia-Meng Si, An evolutionary game theory model of binary opinion formation. Physica A 389 (2010) 1745-1752. Lorenz J , Continuous opinion dynamics under bounded confidence: A survey. INTERNATIONAL JOURNAL OF MODERN PHYSICS C . , Vol. 18, No. 12 (2007) 1819-1838.
Opinion Dynamics
Opinion Dynamics林颖婷 2011.12.23•内容提纲• （一）意见动力学 概要 • （二）几个经典模型 • （三）其他模型和扩展Statistical physics of social dynamics, C. Castellano, S. Fortunato, V. Loreto, Rev. Mod. Phys. 81 (2009) 591. Adaptive coevolutionary networks: a review, Thilo Gross and Bernd Blasius, Journal of the Royal Society 5(2008)259. S. Boccaletti et al, Complex networks: Structure and dynamics , Physics Reports 424(2006)175（一) Opinion Dynamics• 研究意义： 舆情研究是社会学中很早就开始关注的问题。
每个人 都有自己的倾向。
人类也具有社会性，很多情况下都必须 通过达成共识，发挥集体力量，才能得到更好的发展。
• 研究手段：相互作用的个体=》agent-based modeling，interaction network 通过从个体的微观动力学入手，来寻找影响宏观现象形成 的关键因素 • 选取的动力学机制和相互作用网络会对结果产生极大的影 响 • 统计物理和非线性动力学一些概念• Opinion：倾向、种类；离散、连续；二元、多 元 • 状态的描述： comsensus:一致 Ploarization : 两种意见对抗 Fragmentation、diversity：多种意见共存 相变:Phase Transition一般关注的焦点形成一致、极化、共存的条件 达到一致的收敛时间 共存相的斑图：随机分布，形成团簇 集团的大小分布 个体意见改变的一些人类行为动力学特征，如时间间隔分 布 • 标度律 • • • • •(二)Ising Model• A binary variable modelH =− 1 σ iσ j ∑ 2 <i , j >p = exp(−ΔE / k BT )m=1 N∑σii• Potts model – nonbinary variable model复杂网络上的Ising相变和临界现象A. D. Sánchez, J. M. López, and M. A. Rodríguez, Nonequilibrium Phase Transitions in Directed Small-World Networks, Phys. Rev. Lett. 88, 048701 (2002) A. Barrat and M. Weigt, On the properties of small-world network models ,Eur. Phys. J. B 13, 547 (2000) C. P. Herrero, Ising model in small-world networks, Phys. Rev. E 65, 066110 (2002) B. Bianconi ，Mean field solution of the Ising model on a Barabasi-Albert network，Phys. Lett. A 303, 166(2002) S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Critical phenomena in complex networks, Rev. Mod. Phys. 80, 1275–1335 (2008)（三） 几个基本模型• Voter Model • Majority rule model • Sznajd model • Social impact theory • Bounded confidence models (Continuous opinions)3.1 Voter Modelat each time step one site is selected at random and made equal to one of its nearest neighbors.Incomplete ordering of the voter model on small-world networks, C. Castellano, D. Vilone, A. Vespignani, Euprophysics Letters 63(2003)1533.2 Majority ModelThe agent will adopt the local/global majority state certainly or priority.P. L. Krapivsky and S. Redner, Dynamics of Majority Rule in TwoState Interacting Spin Systems ,Phys. Rev. Lett. 90, 238701 (2003) M. Mobilia and S. Redner, Majority versus minority dynamics: Phase transition in an interacting two-state spin system, Phys. Rev. E 68, 046106 (2003) P Chen and S Redner，Consensus formation in multi-state majority and plurality models, J. Phys. A 38 (2005) 72393.3 Sznajd modelin the Sznajd model one has an outward flow of influence.On a chain, this set is a bond with two people at its ends.K. Sznajd-Weron, J. Sznajd, Opinion evolution in closed community , IJMPC 11, 1157(2000) Election results and the Sznajd model on Barabasi network, A.T. Bernardes, D. Stauffer and J. Kertész, EPJB 25,123(2002)K. Sznajd-Weron, J. Sznajd, Opinion evolution in closed community , IJMPC 11, 1157(2000The case of 2D3.4 Social impact theory• pi : persuasiveness • dij: distancesi : supportiveness α: parameterA. Nowak et al, Simulating the coordination of individual economic decisions, Physica A 287, 613(2000)3.5 Bounded confidence models• Deffuant modelμis convergence parameter [0,-1/2]G. Deffuant, D. Neau, F. Amblard, G. Weisbuch, Adv. Complex Syst. 3 (2000) 87;• Hegselmann-Krause model (HK model)Agent takes the average opinion of his neighbours.(四) 其他模型举例以及扩展• （1）人际关系网 (a)不同关系网络 SW、BA、有向网、 层次网、社团结构 (b)随着动力学演化的网络拓扑 • （2）接受机制 从众、权威效应、记忆效应、固执等 • （3）人类行为4.1 the coevolution of networks and opinions <1>On each step we pick a vertex i at random. If ki isn’t zero, then (1) With probabilityφ, choose random one of his edges, move the other end to a vertex chosen randomly from the set of all vertices having the same opinion with him; (2) With probability 1-φ , we set his opinion equal to random one’s of his neighbours.Community sizes, Time to reach consensusthe coevolution of networks and opinions <2> At each time step,i) the spins are updated random sequentially based on a simple majority rule: their state will be changed to the majority in the next time step; in the case of a tie, the spin remains unchanged. ii) the links are updated as follows: two nodes carrying equal (unequal) spins are connected with probability p (q). In this letter, we focus on the special case q =1−pI. J. Benczik, Lack of consensus in social systems, EPL 82, 48006(2008) F. Schweitzer and L. Behera，Nonlinear voter models: the transition from invasion to coexistence，EPJB 67, 301(2009) M.Mobilia, Fixation and polarization in a three-species opinion dynamics model, EPL 95 , (2011)4.2 接受机制（1）Effects of social diversityYang, H.-X. et al, Effects of social diversity on the emergence of global consensus in opinion dynamics, Phys. Rev. E 80, 046108(2009) Yang, H.-X. et al, Effects of social diversity on the evolutionary game and opinion dynamics, Physics Procedia 3, 1859(2010)• At each step: (1)At first, randomly select an agent i, and one of his neighbors j. The probability i changes his value to that of j is nj/N (2)Then, With probabilityα another random agent k is assigned a new random integer which does not appear anywhere else in the system.谢谢大家！。
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Opinion Dynamics林颖婷 2011.12.23•内容提纲• （一）意见动力学 概要 • （二）几个经典模型 • （三）其他模型和扩展Statistical physics of social dynamics, C. Castellano, S. Fortunato, V. Loreto, Rev. Mod. Phys. 81 (2009) 591. Adaptive coevolutionary networks: a review, Thilo Gross and Bernd Blasius, Journal of the Royal Society 5(2008)259. S. Boccaletti et al, Complex networks: Structure and dynamics , Physics Reports 424(2006)175（一) Opinion Dynamics• 研究意义： 舆情研究是社会学中很早就开始关注的问题。
每个人 都有自己的倾向。
人类也具有社会性，很多情况下都必须 通过达成共识，发挥集体力量，才能得到更好的发展。
• 研究手段：相互作用的个体=》agent-based modeling，interaction network 通过从个体的微观动力学入手，来寻找影响宏观现象形成 的关键因素 • 选取的动力学机制和相互作用网络会对结果产生极大的影 响 • 统计物理和非线性动力学一些概念• Opinion：倾向、种类；离散、连续；二元、多 元 • 状态的描述： comsensus:一致 Ploarization : 两种意见对抗 Fragmentation、diversity：多种意见共存 相变:Phase Transition一般关注的焦点形成一致、极化、共存的条件 达到一致的收敛时间 共存相的斑图：随机分布，形成团簇 集团的大小分布 个体意见改变的一些人类行为动力学特征，如时间间隔分 布 • 标度律 • • • • •(二)Ising Model• A binary variable modelH =− 1 σ iσ j ∑ 2 <i , j >p = exp(−ΔE / k BT )m=1 N∑σii• Potts model – nonbinary variable model复杂网络上的Ising相变和临界现象A. D. Sánchez, J. M. López, and M. A. Rodríguez, Nonequilibrium Phase Transitions in Directed Small-World Networks, Phys. Rev. Lett. 88, 048701 (2002) A. Barrat and M. Weigt, On the properties of small-world network models ,Eur. Phys. J. B 13, 547 (2000) C. P. Herrero, Ising model in small-world networks, Phys. Rev. E 65, 066110 (2002) B. Bianconi ，Mean field solution of the Ising model on a Barabasi-Albert network，Phys. Lett. A 303, 166(2002) S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Critical phenomena in complex networks, Rev. Mod. Phys. 80, 1275–1335 (2008)（三） 几个基本模型• Voter Model • Majority rule model • Sznajd model • Social impact theory • Bounded confidence models (Continuous opinions)3.1 Voter Modelat each time step one site is selected at random and made equal to one of its nearest neighbors.Incomplete ordering of the voter model on small-world networks, C. Castellano, D. Vilone, A. Vespignani, Euprophysics Letters 63(2003)1533.2 Majority ModelThe agent will adopt the local/global majority state certainly or priority.P. L. Krapivsky and S. Redner, Dynamics of Majority Rule in TwoState Interacting Spin Systems ,Phys. Rev. Lett. 90, 238701 (2003) M. Mobilia and S. Redner, Majority versus minority dynamics: Phase transition in an interacting two-state spin system, Phys. Rev. E 68, 046106 (2003) P Chen and S Redner，Consensus formation in multi-state majority and plurality models, J. Phys. A 38 (2005) 72393.3 Sznajd modelin the Sznajd model one has an outward flow of influence.On a chain, this set is a bond with two people at its ends.K. Sznajd-Weron, J. Sznajd, Opinion evolution in closed community , IJMPC 11, 1157(2000) Election results and the Sznajd model on Barabasi network, A.T. Bernardes, D. Stauffer and J. Kertész, EPJB 25,123(2002)K. Sznajd-Weron, J. Sznajd, Opinion evolution in closed community , IJMPC 11, 1157(2000The case of 2D3.4 Social impact theory• pi : persuasiveness • dij: distancesi : supportiveness α: parameterA. Nowak et al, Simulating the coordination of individual economic decisions, Physica A 287, 613(2000)3.5 Bounded confidence models• Deffuant modelμis convergence parameter [0,-1/2]G. Deffuant, D. Neau, F. Amblard, G. Weisbuch, Adv. Complex Syst. 3 (2000) 87;• Hegselmann-Krause model (HK model)Agent takes the average opinion of his neighbours.(四) 其他模型举例以及扩展• （1）人际关系网 (a)不同关系网络 SW、BA、有向网、 层次网、社团结构 (b)随着动力学演化的网络拓扑 • （2）接受机制 从众、权威效应、记忆效应、固执等 • （3）人类行为4.1 the coevolution of networks and opinions <1>On each step we pick a vertex i at random. If ki isn’t zero, then (1) With probabilityφ, choose random one of his edges, move the other end to a vertex chosen randomly from the set of all vertices having the same opinion with him; (2) With probability 1-φ , we set his opinion equal to random one’s of his neighbours.Community sizes, Time to reach consensusthe coevolution of networks and opinions <2> At each time step,i) the spins are updated random sequentially based on a simple majority rule: their state will be changed to the majority in the next time step; in the case of a tie, the spin remains unchanged. ii) the links are updated as follows: two nodes carrying equal (unequal) spins are connected with probability p (q). In this letter, we focus on the special case q =1−pI. J. Benczik, Lack of consensus in social systems, EPL 82, 48006(2008) F. Schweitzer and L. Behera，Nonlinear voter models: the transition from invasion to coexistence，EPJB 67, 301(2009) M.Mobilia, Fixation and polarization in a three-species opinion dynamics model, EPL 95 , (2011)4.2 接受机制（1）Effects of social diversityYang, H.-X. et al, Effects of social diversity on the emergence of global consensus in opinion dynamics, Phys. Rev. E 80, 046108(2009) Yang, H.-X. et al, Effects of social diversity on the evolutionary game and opinion dynamics, Physics Procedia 3, 1859(2010)• At each step: (1)At first, randomly select an agent i, and one of his neighbors j. The probability i changes his value to that of j is nj/N (2)Then, With probabilityα another random agent k is assigned a new random integer which does not appear anywhere else in the system.谢谢大家！。