Taylor's Law in Innovation Processes

Area of Science:

• Complex Systems Science
• Statistical Physics
• Information Science

Background:

• Taylor's law characterizes fluctuation scaling in open systems.
• Urn-based modeling effectively captures complex system dynamics.
• Understanding innovation scaling is crucial for various scientific fields.

Purpose of the Study:

• To analytically estimate Taylor's law exponents in urn models.
• To demonstrate the universality of Taylor's law exponents in human activity systems.
• To explore the relationship between Taylor's law, Poisson-Dirichlet processes, and innovation dynamics.

Main Methods:

• Analytical estimation of Taylor's law exponents using triangular urn models.
• Modeling innovation dynamics through Poisson-Dirichlet processes.
• Analysis of four diverse human activity datasets: written language, music listening (Last.fm), Twitter hashtags, and collaborative tagging (Del.icio.us).

Main Results:

• Analytical estimations of Taylor's law exponents were derived from triangular urn models.
• A non-trivial Taylor's law exponent was identified as a universal feature in systems related to human activities.
• Standard models accurately predicted Taylor's law for Twitter and Del.icio.us data, while written language and Last.fm data required a generalized model accounting for temporal correlations.

Conclusions:

• Taylor's law, particularly its generalized form, is essential for understanding innovation dynamics in human activity systems.
• The study highlights the connection between urn models, Poisson-Dirichlet processes, and the universal scaling laws observed in human-generated data.
• Taylor's law serves as a fundamental complement to Zipf's and Heaps' laws in characterizing complex system evolution.