美赛校内论文.docx

1、美赛校内论文Spread of Internet RumoursQiangPu ChenYu Zhang LiYe Pan Chongqing University SummerIntroductionCurrent estimates reveal that roughly two billion people are using every day the Internet and its numerous services, like E-mail, the World Wide Web, and social networks. Especially networks provide

2、new and easily accessible ways for interaction and communication among individuals, thus making the Internet an ideal environment for the spread of all kinds of information. The dynamics of such information spreading processes constitute an important topic in many disciplines. But sometimes rumors o

3、n the internet are awful. Rumors are an important form of social communications, and their spreading plays a significant role in a variety of human affairs. The spread of rumors can shape the public opinion in a country, greatly impact financial markets and cause panic in a society during wars and e

4、pidemics outbreaks. Analytic formulation With the development of Internet communication technology, spread of rumours is not only from one person to another but rely on Internet. So both the scope and speed of rumours spread has been expanded and raised. In recent years, increasing numbers of Intern

5、et rumours has become a big reason which affects social stability. The analysis focused on the following issues about Internet rumors spread. Model the spread of Internet rumours. Analyze how to control the negative impact of rumors based on first issue. Verify the model above. Suggestion for preven

6、tion and control of Internet rumours.AssumptionsSymbol Definitions Table1. Symbol and DefinitionsSymbolDefinitions为不知道谣言的人遇到传播者而被感染的概率，为传播者遇到不传谣的人而变为不传谣者的概率Model developmentPart1 The network rumors spread model1.1 BackgroundRumors spread around political activities and military struggle and it is ge

7、nerally unfounded or serious deviation from the actual. 4With the development of Internet communication technology, spread of rumors is not only from one person to another but rely on Internet. The network rumor unlike general model of the spread of the virus and also different from the general form

8、 of word of mouth communication. It has two important features:(1) Internet rumors spread is a two-way communication process, It is not only the process of information diffusion but also the sender and receivers confrontation in the information field and cognitive domains. Here is a simple spread sc

9、hematic diagram.(2)In the complex networks rumors spread, most people do not know each other.So for the two questions above, We firstly establish a small-world network model to to ensure that the spread of rumors is a two-way process. At the same time, we set the clustering coefficient to exclude re

10、lationship between each other.1.2 Model overviewIn 1998, Watts and Strogatz proposed the concept of small-world networks and established the WS model. Experimental results show that the most real networks have small-world characteristics (smaller shortest path) and clustering features (large cluster

11、ing coefficient). WS small-world network model have small-world characteristics and clustering features at the same time, its good to represent real network.1.3 1.3.1 The construction process of Small-world model a) Start from the rules figure: Consider a nearest neighbor coupling network that conta

12、ining N points and the points surrounded by a ring. Wherein each node adjacent to the left and right with it each of K / 2 nodes connected, K is an even number.b) Randomized reconnection: re-connection of each side of the network With probability p randomly. In order to maintain a simple graph natur

13、e in the process of randomized reconnection, we stipulate that can have at most one edge between any two different predetermined node. And every node can not have a side connected with itself.In the WS model, p = 0 corresponds to completely rule network and P = 1 corresponds to the completely random

14、 network.we can control the transition from the completely rule network to completely random network by adjusting the. We will get the following graphic by adjusting the different p-value. we have established a two-way network if we get similar graphics by Matlab. Figure1. The network diagram change

15、 of adjusting the p-value We take the P values are,。we provide two graphics by calculating and drawing.We find the output results are consistent in Figure 1. That means we ensure a rumor spread on the network is bi-directional.下面我们通过设置集聚系数进一度排除在复杂网络中人之间的熟悉关系。集聚系数是用来描述图或网络中的顶点（节点）之间结集成团的程度的系数。具体来说，是一

16、个点的邻接点之间相互连接的程度，因为在现实中的复杂网络是稀疏的，所以我们设置集聚系数为的，通过Matlab,得到以下图形： 说明对话框后 1.3.2 基于小世界网络的谣言传播我们把人群分成没有听过谣言的人、谣言传播者和听到谣言但并不传播谣言的人3 种类型，用i(t)，s(t)，r(t)分别代表着3 种类型在人群中的比例，在小世界模型等指数型均匀网络上建立平均场方程为：通过matlab编程，我们得到了如下图形：结果分析：事实上，整个谣言传播的过程可以简单的概括如下：首先系统里只有少量的传播者，其它都为无知者，免疫者的数量为0。随着传播者开始散播谣言，无知者的数量很快减少，传播者的数量急剧增加。随

17、着谣言的进一步扩散，免疫者的数量开始增加，而传播者的数量达到一个峰值以后开始下降。最后，传播者的数量变为了0，而网络里就只剩下免疫者和少量的无知者，恰恰是这部分人从来没有受到过谣言的骚扰Part 2 how to control negative rumor spread现实生活中，每当有危及国计民生的谣言的时候，政府往往会出来辟谣，我们这里把政府辟谣的言论与谣言假定为两个相互竞争的种群，借助种群竞争模型来分析“以言辟谣”这种情况。Step1: summarizeIn real life, Government tends to use its positive influence to st

18、op the rumors spreading whenever rumors to undermine social stability. Assume that the government speech and rumors for two competing populations. We establish a population competition model to analyze this case.Step2: Assumptionschange in value obey Logistic law when two kinds remarks exist indepen

19、dently.The speech-oriented of Government are positive.Stp3: the control model经分析我们建立以下两个模型 By further analysis, We know that the small-world network model is uniform network or index network, its degree distribution of the network connection can be approximated by a Poisson distribution. Its distrib

20、ution has a peak in the degree of average value (k) Then exponentially fast decay. However, in recent years, the the complex network study shows that many complicated network connection function has the form of a power-law. Its node degree has not obvious characteristic length, So we have further ad

21、opted the BA scale-free network correction to revise.Part 3 model validation3.1 The Analysis of the Problem前两问中，我们分别建立了网络谣言的传播模型以及对谣言的消极影响的控制模型，但是由于模型自身的一些局限性可能会影响最终的结果，所以下面我们分别对上述模型进行验证。We establish the network rumors spread model and the negative impact of rumors control model in the previous two

22、questions. However we should verify the model due to some limitations of the model itself. Here is our model validation.3.2 .1 Verify the network rumors spread model based on cellular automataIn order to verify the model about the network rumor spreadr, we introduced a structure of the cellular auto

23、maton to deal the problem.Cellular automata are discrete-time dynamical systems comprising finite-state units, called cells, whose states evolve in time as a result of the interactions with other cells. Since their introduction nearly five decades ago by von Neumann 1, cellular automata have acquire

24、d an ever more prominent status as a modeling tool in several research areas and have even come to be regarded by some as a central abstraction in the modeling of natures fundamental processes 4. 现假设参与事件的整个群体是一个LL规模的二维网格，其中每一个个体占据其中一个格子。格子中的个体即为一个元胞，每个元胞都具有自己的观点S，S可以为正观点(+1)负观点(-1) 和保留意见（0）其中的一种。每个个

25、体都具有8个相邻的邻居个体，这些邻居个体和当前个体之间的位置关系如图1所示。It is assumed that the entire group participating in the event is a L L scale two-dimensional grid，each individual to occupy one of the lattice. individual shall be a cell in the Lattice and each cell has its own point of view S. S can be a positive point of vie

26、w or a negative point or a qualified opinion. Each individual having eight adjacent and the positional relationship between neighbors individual and current individual have shown in Figure 1 by AutoCAD. Figure2. The cellular automata neighbors model上面是我们对元胞模型的基本陈述，在本题中，我们根据对影响网络谣言传播发展及变化趋势的分析，将元胞的情感

27、的变化作为主要因素，进而对谣言的发展趋势进行仿真。The above is a basic statement of our cellular model. In the title, we take cellular emotional changes as major factors based on the analysis of the impact of the development and changes of the network rumor spread trends. Then we make a trend of the development simulation o

28、f rumors.将元胞自动机二维网络中元胞抽象为用网络谣言传播系统中的个体。每个元胞存在3种可能状态：格子为0，表示该格子上的人对谣言的传播不做贡献；为1，表示该格子上的人对谣言持支持意见；为一1 ，表示该格子上的人持反对意见。首先在个体观点的初始分布采用均匀分布的情况下，随机生成了一个的网格，每个格子随机分配的值，并进行整值化，（蓝色表示该元胞持支持态度，红色表示反对态度，空白表示保留意见）。仿真中的初始分布情况如图2。Assume cellular which in two-dimensional network as the individual in the network rumo

29、r spread system. Each cell have three kinds of possible states: Plaid to 0, indicating that the people on the lattice have no contribution to the spread of rumors. To 1, indicating that the people have the supportive comments on rumors. To 1, indicating that the people have the opposite comments on

30、rumors.First in the case that individual viewpoints satisfy uniformly distributed, generating a grid randomly. Each grid is randomly assigned a value of and rounded.(Blue means the Cellular take supportive attitude , red take opposite attitude, Blank expressed take reservations ) Simulation of the i

31、nitial distribution is shown in Figure 2.Figure 3.The initial distribution diagram由于初始状态观点概率呈均匀分布，在对谣言的发展趋势无引导策略时呈现自然演进状态，所以可以看出图中分布杂乱无章。Since the initial state probability is uniformly distributed，the development trend of the rumors in a natural evolution of the state . we can see that the distribu

32、tion is scattered.进一步我们通过设置相关的系数值，仿真得到在谣言传播中期和末期的分布情况，如图： intermediate state Final stateFigure4.Network rumor system evolution of simulation结果分析：由上图可以看出，在观点均匀分布的初始状态下，随着邻居元胞和时间的影响，谣言的发展变化趋于几乎正观点和负观点相均衡的状态，一种观点很难最终占据整个群体的结果。另一方面由于从众现象的影响，系统中谣言的发展最终趋于群聚的现象，即一定区域内人员的观点趋于一致。由最终结果可以看出，随着谣言的传播，系统中谣言免疫者逐渐增加，并且最后越来越多。和ws小世界模型最后得到的结果吻合，即可验证其正确性。BA model is proposed to explain t