1. General Threshold and Cascade Models
Lecture 2-4
General Threshold and Cascade Models
Weili Wu Ding-Zhu Du
University of Texas at Dallas
First, I want to thank you for you presence. ********In this presentation I will try to introduce The social network which is a theoretical structure to study relationships between individuals, groups, organizations, or even entire societies. 
It is related to a wide range of disciplines. These disciplines include, but are not limited to information science, biology, economics, geography, communication studies, and so on..
The study of social networks begins with the late eighteenth century, two sociologists (Émile [ei'mi:l] Durkheim and Ferdinand ['fɝdənænd] Fer迪南de Tönnies) foreshadowed the idea of social networks in their theories and research of social groups.
Nowadays, we study social networks using network analysis to identify social communities, pick influential person, and design good software.

2. Outline General Threshold Model General Cascade Model σGT(A)=σGC(A)
Brief overview of social networks
How to build applications on top of the social network
–  Think about a social network being MS Windows, We can build applications on it.

3. General Threshold Model

4. General Threshold Model1 2 3

5. LT: Stop! w v Y Inactive Node 0.6 Active Node 0.2 Threshold 0.2 0.3
Active neighbors X
0.1
0.4 U
0.3
0.5
Stop!
0.2
0.5 w v

6. Outline General Threshold Model General Cascade Model σGT(A)=σGC(A)
Brief overview of social networks
How to build applications on top of the social network
–  Think about a social network being MS Windows, We can build applications on it.

7. General Cascade Model 1 2 3
Order-independentce Assumption

8. Explanation of 3
Theorem

9. IC: Y
0.6
Inactive Node
0.2
0.2
0.3
Active Node
Newly active
node X U
0.1
0.4
Successful
attempt
0.5
0.3
0.2
Unsuccessful
attempt
0.5 w v
Stop!

10. MC: Y
0.6
Inactive Node
0.2
0.2
0.3
Active Node
Newly active
node X U
0.1
0.4
Successful
attempt
0.5
0.3
0.2
Unsuccessful
attempt
0.5 w v
Stop!

11. Is the MC model a special case of General Cascade model?

12. Outline General Threshold Model General Cascade Model σGT(A)=σGC(A)
Brief overview of social networks
How to build applications on top of the social network
–  Think about a social network being MS Windows, We can build applications on it.

13. Equivalence
Theorem
Proof 1 2

14. Proof of 1
Is it well-defined?

16. General Threshold

17. General Cascade ？

19. Proof of 2

20. General Cascade

21. General Threshold

23. References

24. Welcome to Submit Papers
A New Springer Journal
Computational Social Networks
Editor-in-Chief:
Ding-Zhu Du
My T. Thai
Social network analysis [SNA] is the mapping and measuring of relationships and flows between people, groups, organizations, computers or other information/knowledge processing entities.
The nodes in the network are the people and groups while the links show relationships or flows between the nodes.
The advantage of social network analysis is that, unlike many other methods, it focuses on interaction (rather than on individual behavior).
Network analysis allows us to examine how the configuration of networks influences how individuals and groups, organizations, or systems function.
Welcome to Submit Papers

25. THANK YOU!