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Open AccessFeature PaperArticle

Taylor’s Law in Innovation Processes

Physics Department, Sapienza University of Rome, P.le Aldo Moro 5, 00185 Rome, Italy
IMT School for Advanced Studies Lucca, Piazza San Ponziano 6, 55100 Lucca, Italy
ADAMSS Center, Università Degli Studi di Milano, 20133 Milan, Italy
Complexity Science Hub Vienna, Josefstädter Strasse 39, A-1080 Vienna, Austria
Author to whom correspondence should be addressed.
Entropy 2020, 22(5), 573;
Received: 24 April 2020 / Revised: 11 May 2020 / Accepted: 13 May 2020 / Published: 19 May 2020
(This article belongs to the Special Issue Statistical Mechanics of Complex Systems)
Taylor’s law quantifies the scaling properties of the fluctuations of the number of innovations occurring in open systems. Urn-based modeling schemes have already proven to be effective in modeling this complex behaviour. Here, we present analytical estimations of Taylor’s law exponents in such models, by leveraging on their representation in terms of triangular urn models. We also highlight the correspondence of these models with Poisson–Dirichlet processes and demonstrate how a non-trivial Taylor’s law exponent is a kind of universal feature in systems related to human activities. We base this result on the analysis of four collections of data generated by human activity: (i) written language (from a Gutenberg corpus); (ii) an online music website (; (iii) Twitter hashtags; (iv) an online collaborative tagging system ( While Taylor’s law observed in the last two datasets agrees with the plain model predictions, we need to introduce a generalization to fully characterize the behaviour of the first two datasets, where temporal correlations are possibly more relevant. We suggest that Taylor’s law is a fundamental complement to Zipf’s and Heaps’ laws in unveiling the complex dynamical processes underlying the evolution of systems featuring innovation. View Full-Text
Keywords: innovation dynamics; Taylor’s law; adjacent possible; Poisson–Dirichlet process; Pólya’s urn; triangular urn schemes innovation dynamics; Taylor’s law; adjacent possible; Poisson–Dirichlet process; Pólya’s urn; triangular urn schemes
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Tria, F.; Crimaldi, I.; Aletti, G.; Servedio, V.D.P. Taylor’s Law in Innovation Processes. Entropy 2020, 22, 573.

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