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2016美国大学生数学建模特等奖论文集(ICM,含赛题)D47876.pdf
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For office use only
T1
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Team Control Number
47876
Problem Chosen
D
For office use only
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Abridge the Distance between Human Minds
—Research on Social Information Circulation
Summary
Information circulation network is as complicated as the human brain, while brain with wisdom
seeks to explore the mysteries of the information circulation network.
First, we establish a model of information circulation network (ICP). Then we establish five
network topology graphs and qualitatively analyze evolution of five periods. Based on classical
epidemic model, we introduce the super-spreader, which can effectively accelerate the circulation of
information as the central node. The differential equations and their results give us reasonable
circulation laws: the density of the spreader and the super-spreader rapidly increase at the beginning,
then they reach a peak and decline rapidly; the ignorant density shows a rapid downward trend while
the immune density generally increases.
We build the fuzzy comprehensive evaluation model (NF) to filter what qualifies as news. We
propose audience awareness index (AAI) to indicate the inherent value of information. Then we use
four given examples to test the model. Undoubtedly, the assassination of Abraham Lincoln was
qualified as news; and so does the important person’s assassination today. As for information of
Taylor’s style transition, it becomes news today, but it might not be news in 1860.
Then we use the neural network prediction model (ICNP) to predict the networks’ relationships
and capacities. We get the node number and the node degree via previous data from three states in
USA. And the results of ICNP model are: in the fifth period, node number of New York is 22535000,
and its relative error is 15.32%; in the fifth period, node degree is 13533000, and its relative error is
20.58%. So it validates the reliability of ICP model. In around 2050, node number of New York is
34885000 and node degree is 23766000.
Finally, we build our model (PIINI) considering the interest attenuation mechanism and social
strengthening mechanism. Taking the interaction of information circulation network and public
interests into account, we establish differential equations similarly. And it comes to interaction laws:
the density of the spreader and nodes in connection state rapidly increase at the beginning, they reach
a peak and then decline rapidly. The ignorant density shows a rapid downward trend while the
immune density generally increases.
As a part of ICM’s Information Analytics Division, we have accomplished the given assignments.
Keyword: Information Circulation Network Epidemic Model Differential Equation,
BP Neural Networks
![](https://csdnimg.cn/release/download_crawler_static/88982072/bg2.jpg)
Abridge the Distance between Human Minds
—Research on Social Information Circulation
Content
1. Restatement of the Problem .................................................................................... 1
2. Introduction ............................................................................................................. 1
3. Assumptions ............................................................................................................ 2
4. Justification of Our Approach ................................................................................. 2
5. Symbol Descriptions ............................................................................................... 3
6. The Model ............................................................................................................... 3
6.1 Information circulation network model (ICN) ..................................................... 3
6.1.1 Topological Properties .................................................................................. 4
6.1.2 The model construction ................................................................................. 4
6.1.3 To solve the model ........................................................................................ 7
6.2 News filter model (NF) ........................................................................................ 8
6.2.1 Influential factors of audience’s awareness index ........................................ 8
6.2.2 The model construction ................................................................................. 8
6.2.3 The process to test the model ........................................................................ 9
6.3 Information circulation network prediction model (ICNP) ............................... 10
6.3.1 Influential factors ........................................................................................ 10
6.3.2 The model construction ............................................................................... 10
6.3.3 To solve the model ...................................................................................... 12
6.4 Public interest and information network interaction model (PIINI) .................. 12
6.4.1 The model construction ............................................................................... 13
6.4.2 To solve the model ...................................................................................... 16
7. Sensitivity Analysis ............................................................................................... 17
8. Strengths and Weaknesses .................................................................................... 19
9. Conclusions ........................................................................................................... 19
References
Appendix (data and data source)
![](https://csdnimg.cn/release/download_crawler_static/88982072/bg3.jpg)
Team # 47876 Page 1 of 19
1. Restatement of the Problem
Information spread quickly in today’s tech-connected communications network;
sometimes it is due to the inherent value of the information itself, and other times it is
due to the information finding its way to influential or central network nodes that
accelerate its spread through social media.
Explore the flow of information and filter or find what qualifies as news.
Validate your model’s reliability.
Predict the communication networks’ relationships and capacities around the year
2050.
Explore how public interest and opinion can be changed through information
networks in today’s connected world.
Determine how information value, people’s initial opinion and bias, form of the
message or its source, and the topology or strength of the information network in a
region, country, or worldwide could be used to spread information and influence
public opinion.
Interpretation of these problems
We should build a model to indicate how information circulate in social network.
We should figure out an improved model to filter what qualifies as news based on
first model.
We should predict present network’s relationship and capacity to validate first
model by using our model’s prediction ability, and predict future network’s
relationship and capacity in around 2050.
We should build another model to explore the interaction of public interest and
information network.
2. Introduction
Social information circulation network is a very active research area. Building the
social information circulation network is the hot area of complex network research.
That research has very important value for understanding the dynamic behavior of the
network.
Previous work
In previous analysis, most of models are based on the classical epidemic model SI,
SIS and SIR, etc.
[1, 2]
The IC model
[3, 4]
proposed by Jacob Goldenberg and the LT
model
[5]
proposed by Mark Granovetter is most widely studied currently. And Jaewon
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Team # 47876 Page 2 of 19
Yang and other researchers proposed a linear influence model
[6]
by the analysis of
Twitter’s users’ behaviors.
From the aspect of social psychology, the mass information circulation process is
placed in a environment affected by a variety of social forces and psychological factors.
Massa described the analysis and prediction of perceived user behavior based on trust
framework
[7]
. Jamali and other researchers
[8]
use TrustWalker model to predict
behaviors’ of users. Josang A
[9]
build a user trust prediction system to describe the
development of trust between different users.
3. Assumptions
Table 1 assumptions
Assumptions
Overall
1) We do not take time delay during information circulation between
two nodes into account.
ICN model
2) We think the public interest is consistent.
3) We do not take social strengthening into account.
4) We do not consider the difference between different information.
5) We think the influence between two nodes will not affect our model.
NF model
6) We think the audience awareness is the only indicator of public
interest and opinion.
ICNP model
7) We do not consider secondary factors.
8) We think the network is universal around the world.
PIINI model
9) We do not consider secondary factors.
4. Justification of Our Approach
ICN model
Dynamics of epidemic disease can effectively portray on the circulation
characteristics of complex network, which is an important basis for the current network
circulation dynamics. Super-spreader plays an important role in the information
circulation network. On the basis of classical epidemic model we introduce of the super-
spreader and establish differential equations which can effectively portray information
circulation network’s characteristics.
NF model
News is objective report of what audiences are concerned about. The concept of
audience awareness is vague, but we can qualitatively analyze audience awareness
index has a positive influence on inherent value of information. The fuzzy
comprehensive evaluation model can characterize the transition state between news and
information. Therefore, it is appropriate to use NF model to filter what qualifies as news.
ICNP model
Information circulation network is a complex and random system, influenced by
many factors. Using the statistical forecasting model to predict might have defects
![](https://csdnimg.cn/release/download_crawler_static/88982072/bg5.jpg)
Team # 47876 Page 3 of 19
especially when the sample data are not enough and when historical data are volatile.
And we use BP neural network to build ICNP model, which can overcome this
shortcoming.
PIINI model
Strengthening social mechanism is an important distinction between the
information circulation and the spread of disease. Social interest attenuation mechanism
is also significant in information circulation network. Proposed PIINI model takes
social interest attenuation and social strengthening into account, so it can be effectively
and reasonably reveal laws in the information circulation network.
5. Symbol Descriptions
There are some major symbols appear in the model, as shown below:
Table 2 symbol descriptions
Index
Definition
Formula
Node
number(N)
The number of nodes include
connected and disconnected nodes.
--
Node degree(k
i
)
The degree of nodes is the number of
connected nodes. And give adjacent
matrix
ij
NN
Aa
.
11
NN
i i j ji
jj
k a a
Node degree
average (<k>)
The average of all node degrees of
the network.
11
1
NN
i ji
ii
k k a
N
Network
density(D)
Network density is a symptom of
network’s completeness.
2
1
L
D
NN
Clustering
coefficient(C
i
)
Clustering coefficient represent the
probability of any two nodes being
neighbors. E
i
is the edges between
node i and neighbors k
i
.
2
-1 2 -1
ii
i
i i i i
EE
C
k k k k
Notes: we will explain other symbols when we use them.
6. The Model
6.1 Information circulation network model (ICN)
Social network is a complex network, which is composed of social individuals as
well as the social relationships between individual members.
[10]
In the related social
network research, researchers used
, , G V E W( )
graph to build model. V is the set
of network nodes;
E V V
is the set of relationships between social individuals; W
is the weight of social individuals.
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