COMS W 4995 - 1 : Intro to Social Networks Fall 2012 Handouts # 2 – Reinforcement process
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چکیده
Dynamics of a simple balls and bins reinforcement process The following dynamics have been introduced by G. Yule in 1925 to model evolution of species and their repartition within different classes, or “genus”. We model a species as a ball which is contained in a bin that model its associated class or genus. Once a specied appear it is never removed and it does not change genus (i.e., once a ball is created, it remains forever in the same bin). The main dynamics is the apparition of new species. We assume that the process is initialized at time t = 0 with an arbitrary number of genera containing each an arbitrary number of species. The time follows discrete time slots denoted t = 1, 2, . . ., and we introduce the following notation:
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