{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T05:11:55Z","timestamp":1782882715252,"version":"3.54.5"},"reference-count":47,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,19]],"date-time":"2020-05-19T00:00:00Z","timestamp":1589846400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Taylor\u2019s 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\u2019s 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\u2013Dirichlet processes and demonstrate how a non-trivial Taylor\u2019s 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 (Last.fm); (iii) Twitter hashtags; (iv) an online collaborative tagging system (Del.icio.us). While Taylor\u2019s 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\u2019s law is a fundamental complement to Zipf\u2019s and Heaps\u2019 laws in unveiling the complex dynamical processes underlying the evolution of systems featuring innovation.<\/jats:p>","DOI":"10.3390\/e22050573","type":"journal-article","created":{"date-parts":[[2020,5,20]],"date-time":"2020-05-20T02:48:24Z","timestamp":1589942904000},"page":"573","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Taylor\u2019s Law in Innovation Processes"],"prefix":"10.3390","volume":"22","author":[{"given":"Francesca","family":"Tria","sequence":"first","affiliation":[{"name":"Physics Department, Sapienza University of Rome, P.le Aldo Moro 5, 00185 Rome, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0305-6459","authenticated-orcid":false,"given":"Irene","family":"Crimaldi","sequence":"additional","affiliation":[{"name":"IMT School for Advanced Studies Lucca, Piazza San Ponziano 6, 55100 Lucca, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7466-2969","authenticated-orcid":false,"given":"Giacomo","family":"Aletti","sequence":"additional","affiliation":[{"name":"ADAMSS Center, Universit\u00e0 Degli Studi di Milano, 20133 Milan, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3221-5973","authenticated-orcid":false,"given":"Vito D. P.","family":"Servedio","sequence":"additional","affiliation":[{"name":"Complexity Science Hub Vienna, Josefst\u00e4dter Strasse 39, A-1080 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/310585","article-title":"Relative Frequency as a Determinant of Phonetic Change","volume":"40","author":"Zipf","year":"1929","journal-title":"Harv. Stud. Class. Philol."},{"key":"ref_2","unstructured":"Zipf, G.K. (1935). The Psychobiology of Language, Houghton-Mifflin."},{"key":"ref_3","unstructured":"Zipf, G.K. (1949). Human Behavior and the Principle of Least Effort, Addison-Wesley."},{"key":"ref_4","unstructured":"Herdan, G. (1960). Type-Token Mathematics: A Textbook of Mathematical Linguistics, Mouton en Company."},{"key":"ref_5","unstructured":"Heaps, H.S. (1978). 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