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Taylor's Law in Innovation Processes.

Francesca Tria1, Irene Crimaldi2, Giacomo Aletti3

  • 1Physics Department, Sapienza University of Rome, P.le Aldo Moro 5, 00185 Rome, Italy.

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Summary
This summary is machine-generated.

Taylor's law, which describes innovation fluctuations in open systems, was analyzed using urn models. A generalized Taylor's law exponent is a universal feature in human activity systems, complementing Zipf's and Heaps' laws.

Keywords:
Poisson–Dirichlet processPólya’s urnTaylor’s lawadjacent possibleinnovation dynamicstriangular urn schemes

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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.