A general solution to the preferential selection model

08/06/2020

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by   Jake Ryland Williams, et al.

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We provide a general analytic solution to Herbert Simon's 1955 model for time-evolving novelty functions. This has far-reaching consequences: Simon's is a pre-cursor model for Barabasi's 1999 preferential attachment model for growing social networks, and our general abstraction of it more considers attachment to be a form of link selection. We show that any system which can be modeled as instances of types—i.e., occurrence data (frequencies)—can be generatively modeled (and simulated) from a distributional perspective with an exceptionally high-degree of accuracy.