2016美国大学生数学建模特等奖论文集（ICM，含赛题）D49436.pdf资源-CSDN文库

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根据给定文件的信息，我们可以提炼出以下相关的IT与数学建模知识点： ### 一、美国大学生数学建模竞赛概述美国大学生数学建模竞赛（MCM/ICM）是一项国际性的学术竞赛活动，旨在通过解决实际问题来培养参赛者的数学建模能力、团队合作能力和论文写作能力。该竞赛每年举行一次，吸引了来自世界各地的众多大学生参加。 ### 二、论文题目解析：“Who Moved My Opinion?” #### 1. **研究背景** 随着社会网络的不断演化，信息成为了一种能够极大地影响公众意见的新类型财产。在这一背景下，研究信息如何流动、通信网络如何演变以及这些因素如何共同作用于公众意见变得尤为重要。 #### 2. **研究方法** - **通信网络的构建**：论文中定义了两种类型的通信方式——大众传播(Mass Communication)和个人间传播(Interpersonal Communication)。通过结合这两种传播方式，构建了一个单层通信网络模型，用以表示特定的通信技术。 - **多层信息网络的构建**：在此基础上，根据不同的传播技术将时间划分为六个阶段，并基于单层网络构建了多层信息网络。 - **信息属性的定义**：定义了信息的三个属性——极端性(extremeness)、娱乐性(entertainment)和新颖性(newness)，并通过无差异曲线的概念确定了信息的固有价值。 - **Pareto原则的应用**：通过Pareto原则来识别新闻。 #### 3. **动态信息流模型** - **模型构建**：结合多层信息网络和信息的固有价值，构建了动态信息流模型。该模型用于描述信息如何在社会网络中流动。 - **模型验证**：利用BBC Tech的一条新闻数据进行模拟实验，验证模型的有效性和可靠性。结果显示，真实接收节点数量为44个，而模型预测结果为43.85个，标准误差为4.63，表明模型具有良好的预测能力和可靠性。 ### 三、其他相关知识点 - **Life-Cycle Theory（生命周期理论）**：生命周期理论被引入到模型中，用于分析网络关系的变化以及信息在网络中的传播过程。 - **Indifference Curve（无差异曲线）**：无差异曲线是一种经济学概念，在这里被用来衡量信息的价值。具体来说，它是用来确定信息固有价值的一个关键工具。 - **Pareto Principle（帕累托原则）**：帕累托原则又称80/20法则，被用来筛选新闻中最具影响力的部分。这一原则认为在任何一组事物中，最重要的往往只占一小部分。通过上述分析，可以看出这篇论文深入探讨了信息在网络中的传播机制及其对公众意见的影响。通过对不同传播技术和网络结构的建模，不仅揭示了信息流动的基本规律，还提供了定量分析的方法。这对于理解当代社会中信息传播的特点以及如何有效管理和引导公众意见具有重要的理论和实践意义。

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Team # 49436 Page 1 of 22

For office use only

________________

Team Control Number

49436

Problem Chosen

For office use only

________________

2016

MCM/ICM

Summary Sheet

Who Moved My Opinion?

As society’s networks evolve, information becomes a new kind of property because of its

great power to change public opinion. In our paper, we study the flow of information, the

evolution of communication networks and the information’s influence on publics.

At the beginning, we describe the topologies of two types of communications which are

Mass Communication and Interpersonal Communication. By combining these two types of

communications, we construct the single-layer communication network which represents a

certain communication technique. Then we study the six periods classified by the techniques

and construct the multi-layer information networks based on the single-layer network.

Then we define the three attributes of information which are extremeness, entertainment

and newness. By using the concept of Indifference Curve, we determine the inherent value of

information based on its attributes. And we find the news according to the Pareto Principle.

Combining the multi-layer information networks and the inherent value of information,

we construct the dynamic information flow model. This model is used to describe how

information flows within our society’s networks.

In order to validate our models, we find data of a piece of news of BBC Tech and simulate

the information flow in today’s society. We find that the real amount of received nodes are 44

and our model’s result is 43.85. Also, the standard error of received nodes’ amount is 4.63. So,

the predict capacity and the reliability of our model is great.

We define the capacity as the user percentage, and the relations as the relative strength of

networks. By introducing the Life-Cycle Theory, we build a prediction model to predict the

relations and capacities of networks in 2050. We find that there will be 7 communication

techniques at that time and the strongest network is a rising network whose capacity is 0.9611.

Later, we modify our information flow model by appending the opinion of people. Then

we use this model to describe the mechanism of the change of public opinion based on

Threshold Effect. Then we analyze the influence of four main parameters in our model and get

three main conclusions: (1) Stubborn minorities. (2) Powerful media. (3) More homogeneous

more efficient.

Finally, we give the strengths and weaknesses of our models.

Team # 49436 Page 2 of 22

Contents

1. Introduction .................................................................................................. 3

1.1 Problem Background ............................................................................... 3

1.2 Previous Research .................................................................................... 3

1.3 Our Work .................................................................................................. 3

2. Assumptions and Justification ...................................................................... 4

3. Topology of Information Networks .............................................................. 4

3.1 Two Types of Communications ............................................................... 4

3.2 A Slice of Toast: Construct Single-Layer Network .................................. 6

3.3 Slices of Toast: Construct Multi-Layer Networks ................................... 7

4. Model of Inherent Value of Information ...................................................... 8

4.1 Attributes of Information ......................................................................... 9

4.2 The Inherent Value of Information ........................................................... 9

4.3 Pick News out of Information ................................................................ 10

5. The Dynamic Information Flow Model ..................................................... 10

5.1 The Forwarding Rules of Media Nodes ................................................. 11

5.2 The Forwarding Rules of Person Nodes ................................................ 11

6. How a BBC’s News Disseminated: Validate Our Model ........................... 12

6.1 Find Data for Simulation ....................................................................... 12

6.2 Simulation .............................................................................................. 12

6.3 Results .................................................................................................... 13

7. The Evolution of Information Networks .................................................... 13

7.1 Definitions of capacities and relationships of networks ........................ 14

7.2 Emergence of a New Network ............................................................... 14

7.3 The Peak of Different Networks ............................................................ 14

7.4 Networks’ Evolution Based on Life-Cycle Theory ................................ 14

7.5 Prediction of Society’s Information Networks in 2050 ......................... 16

8. Change People’s Minds: An Opinion-Changing Model ............................. 16

8.1 The Opinion of Publics .......................................................................... 17

8.2 The Opinion-Changing Mechanism ....................................................... 17

9. Sensitivity analyses .................................................................................... 18

9.1 More people agree at first, more people agree at last ............................ 18

9.2 Want a bigger influence, go to find a media .......................................... 19

9.3 More Homogeneous, More Efficient ..................................................... 19

9.4 Media Nodes vs. Person Nodes ............................................................. 20

10. Strengths and Weaknesses .......................................................................... 21

10.1 Strengths .............................................................................................. 21

10.2 Weaknesses .......................................................................................... 21

11. References .................................................................................................. 22

Team # 49436 Page 3 of 22

1. Introduction

1.1 Problem Background

Under a certain network situation, the flow and the speed of information are

influenced by two main factors: (1) The inherent value of information. (2) Whether the

information is forwarded by big media. However, the evolution of the society’s

information network never stops, which allows us to study the evolution of the society’s

functions and structure by taking a historical perspective of flow of information.

In the paper, we have been asked to answer the following questions:

 Establish models to describe the flow of information and find what makes

news.

 Test our models’ reliability and prediction capability.

 Predict the relationships and capacities of 2050’s society information network.

 Define people’s opinion and use our models to find how publics’ interest and

opinion can be changed by information.

 Test our model with the four aspects in the flow of information.

1.2 Previous Research

Scholars have been studying the society’s information networks for a long time.

At the beginning, they use the epidemic model to describe the flow of information. In

1998, D.J.Watts and S.H.Strogatz establish WS Small World Model to show the flow

of information and find that the speed of information is fastest in the Small World

Model[1]. In 2002, Staniford S, Paxson V and Weaver N use the Random Constant

Spread Model to study the information flow on the Internet [2]. D.J.Watts and

P.S.Dodds find that the flow of information is easily influenced by the people who are

easily influenced [3]. Also, there have been many experts studying the evolution of

society’s information networks. In these researches, Ellision.N.B’s and Castells M ‘s

work is impressive [4][5].

1.3 Our Work

We firstly build a single-layer information networks. Then we form a multi-layer

networks by combining single-layer networks with the same nodes. After that, we

define the information forward mechanism to allow information to flow in our networks.

Secondly, we use a real information flow’s example to validate our model. We find data

on the Facebook and use our model to simulate it. Thirdly, we explore the principle of

the information networks’ evolution. Then we make a prediction of capacities and

relationships in 2050.Fourthly, we model how people’s opinion be changed. According

to the threshold effect, we give a certain mechanism of people changing their mind.

Finally, we apply our models to analyze how information value, people’s initial opinion,

information source and topology influence spread range and public opinion.

Team # 49436 Page 4 of 22

2. Assumptions and Justification

 The information does not change when it flows within the social information

networks. In the flow of information, the content of information may change

randomly and it is nearly impossible to consider the random changes in the contents

of information.

 Information’s size is the same. In real world, the size of information will influence

the time. However, the size will only change the time and will not influence the

flow mode.

 The population does not change. The population changes the nodes. But it will

not change the way in which information flows in the networks.

 Information’s value satisfies the Pareto Principle. The Pareto principle states

the phenomenon that for many events, roughly 80% of the effects come from 20%

of the causes [8]. We assume that the value of information also accords with it.

 Communication between people is directed. Although the relations of people are

undirected, the information flow has a direction. Directed communication can

describe the information flow better.

 People will forward information that is valuable and consistent with their

opinion. In our daily life, people like the information of high inherent value and

consistent opinion with them. In addition, they are also willing to share it.

 Once a new technique emerged, the network based on the former technique

will begin to decay. Usually, the new technique is better than the old one. Thus

people are more willing to use the new technique. The old technique will not decay

right away in real world. But the time difference is usually small, so the assumption

makes sense.

3. Topology of Information Networks

In this section, we will study the topology of information networks and construct

multi-layer networks of information flow. First, we introduce two types of

communications in information networks. Then we define the nodes and the edges in

our models. Furthermore, we use these two types of communications to build a single-

layer network which represents the network of a certain kind of communication

technique. Finally, we obtain the multi-layer networks with the consideration of several

communication techniques being used at the same time.

3.1 Two Types of Communications

In the information networks, there are mainly two types of communications: Mass

Communication and Interpersonal Communication. Mass Communications are the

communications between media and the publics. And Interpersonal Communications

are the communications between people. [6] We will discuss the two types of

communications because they have significantly different topologies.

Team # 49436 Page 5 of 22

3.1.1 The Mass Communication

The Mass Communications developed quickly as technology improved. The first

medium come with the emergence of newspaper, which created a brand new way for

publics to gain information. With the inventions of the radio and television, media could

reach a wider range of publics. And as Internet went into more and more households,

media provided publics with varieties of information. One of the characters of Mass

Communications is that a medium can reach many people in a star topology, so this

kind of topology has a great ability of spreading information. Since media are connected,

the topology of the Mass Communication is as follow:

Figure 1. The topology of Mass Communication.

In this figure, dots represent publics and triangles represents media. Edges

represent the communications between publics and media. Nowadays, these media

include broadcasting companies such as ABC (American Broadcasting Corporation),

newspapers such as The Times and webs that have relatively great influence.

3.1.2 The Interpersonal Communication

The Interpersonal Communications always exist in our society. The very simple

example of Interpersonal Communications is speech. But as the techniques improved

quickly, the Interpersonal Communications became rich in forms from speech, mail,

telegraph, telephone to nowadays instant messages. Abundant techniques make

Interpersonal Communications much stronger and more complex. The topology of

Interpersonal Communications has random-like edges linking the person nodes. The

figure below shows a topology of Interpersonal Communications.

Figure 2. The topology of Interpersonal Communication.

3.1.3 Nodes

As we discussed above, we divide nodes into two types: one is media node, the

other is person node. Media nodes represent the media that are the centers of Mass

Communications. And person nodes represent publics. In our models, all of the nodes

have four attributes:

 The type. The type of a node shows that this node is whether a media node or

person node.

 The degree. The degree of a node is the number of nodes that connect to this

node.

 The state. A node can be in one of three states which are

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