Social Media Mining: An Introduction

P1: qVa Trim: 6.125in×9.25in Top: 0.5in Gutter: 0.75in
CUUS2079-07 CUUS2079-Zafarani 978 1 107 01885 3 January 13, 2014 17:17

7.7 Exercises 213

Information Cascades

5. Briefly describe the independent cascade model (ICM).


6. What is the objective of cascade maximization? What are the usual
   constraints?


7. Follow the ICM procedure until it converges for the following graph.
   Assume that nodeiactivates nodejwheni−j≡1(mod3) and
   node 5 is activated at time 0.

4

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5

6 1

Epidemics

8. Discuss the mathematical relationship between the SIR and the SIS
   models.


9. Based on our assumptions in the SIR model, the probability that an
   individual remains infected follows a standard exponential distribu-
   tion. Describe why this happens.


10. In the SIR model, what is the most likely time to recover based on
    the value ofγ?


11. In the SIRS model, compute the length of time that an infected
    individual is likely to remain infected before he or she recovers.


12. After the model saturates, how many are infected in the SIS model?