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Dynamics of text generation with realistic Zipf distribution [article]

Damián H. Zanette, Marcelo A. Montemurro
2002 arXiv   pre-print
We investigate the origin of Zipf's law for words in written texts by means of a stochastic dynamical model for text generation.  ...  It is shown that the multiplicative dynamics of our model leads to rank-frequency distributions in quantitative agreement with empirical data.  ...  Simon [10] , simulates the dynamics of text generation as a multiplicative process that leads to Zipf's law for asymptotically long texts. The second model is due to B.  ... 
arXiv:cond-mat/0212496v1 fatcat:c63e5y4ervckhkgrk2oh73kpoi

Beyond Zipf's law: Modeling the structure of human language [article]

M. Angeles Serrano, Alessandro Flammini, Filippo Menczer
2009 arXiv   pre-print
As a result, we find a connection between the bursty nature of rare words and the topical organization of texts and identify dynamic word ranking and memory across documents as key mechanisms explaining  ...  the non trivial organization of written text.  ...  It is not the first time that a generative model for text has walked parallel paths with models of network growth.  ... 
arXiv:0902.0606v1 fatcat:pfayiez57rbsbkzs3injqlovqm

Citations and the Zipf-Mandelbrot's law [article]

Z. K. Silagadze
1999 arXiv   pre-print
The observed regularity indicates not so much the peculiar character of the underlying (complex) process, but more likely, than it is usually assumed, its more stochastic nature.  ...  A curious observation was made that the rank statistics of scientific citation numbers follows Zipf-Mandelbrot's law. The same pow-like behavior is exhibited by some simple random citation models.  ...  In fact such texts exhibit no Zipfian distribution at all, but log-normal distribution, the latter giving in some cases a very good approximation to the Zipf's law.  ... 
arXiv:physics/9901035v2 fatcat:zsopkbt3kvbdzecsnj64me3pbe

Modeling Statistical Properties of Written Text

M. Ángeles Serrano, Alessandro Flammini, Filippo Menczer, Enrico Scalas
2009 PLoS ONE  
Beyond Zipf's law for word frequencies, here we focus on burstiness, Heaps' law describing the sublinear growth of vocabulary size with the length of a document, and the topicality of document collections  ...  As a result, we find a connection between the bursty nature of rare words and the topical organization of texts and identify dynamic word ranking and memory across documents as key mechanisms explaining  ...  It is not the first time that a generative model for text has walked parallel paths with models of network growth.  ... 
doi:10.1371/journal.pone.0005372 pmid:19401762 pmcid:PMC2670513 fatcat:for67zr65bcbjhvrfaarxm32oy

Zipf's and Taylor's laws

Charlotte James, Sandro Azaele, Amos Maritan, Filippo Simini
2018 Physical review. E  
stationary distribution of the processes follows Zipf's law.  ...  Despite the numerous models proposed to explain the presence of Zipf's law, there is no consensus on how it originates from a microscopic process of individuals dynamics without fine tuning.  ...  This reveals a general connection between Zipf's law and Taylor's law in microscopic stochastic processes of population dynamics under realistic assumptions. FIG . 1. a) Zipf's law, data.  ... 
doi:10.1103/physreve.98.032408 fatcat:joam7e7zqvg5phgt6ykkkswyby

The dynamics of correlated novelties [article]

F. Tria, V. Loreto, V.D.P. Servedio, S.H. Strogatz
2013 arXiv   pre-print
The model, a generalization of Polya's urn, predicts statistical laws for the rate at which novelties happen (analogous to Heaps' law) and for the probability distribution on the space explored (analogous  ...  to Zipf's law), as well as signatures of the hypothesized process by which one novelty sets the stage for another.  ...  On the right panel we illustrate a generic adjacent possible step of the dynamics.  ... 
arXiv:1310.1953v1 fatcat:litxa2naxbcz7m4fftsdlw4ey4

Solvable null model for the distribution of word frequencies

J. F. Fontanari, L. I. Perlovsky
2004 Physical Review E  
Zipf's law asserts that in all natural languages the frequency of a word is inversely proportional to its rank. The significance, if any, of this result for language remains a mystery.  ...  Biol. 3, 87 (1972)], which we show to produce an exponential distribution of word frequencies.  ...  On the one hand, the finding that texts produced by the random emission of symbols and spaces, so that words of the same length are equiprobable, also generate word frequency distributions that follow  ... 
doi:10.1103/physreve.70.042901 pmid:15600443 fatcat:j4wjuvamn5ejfmiwmjgag7fdgm

Zipf's Law Arises Naturally When There Are Underlying, Unobserved Variables

Laurence Aitchison, Nicola Corradi, Peter E. Latham, Olaf Sporns
2016 PLoS Computational Biology  
Recently, methods from statistical physics were used to show that a fairly broad class of models does provide a general explanation of Zipf's law.  ...  Empirically, these advances allowed us extend this explanation to important classes of data, including word frequencies (the first domain in which Zipf's law was discovered), data with variable sequence  ...  However, it is important to understand the realistic case: how a finite range of frequencies with an uneven distribution might lead to something similar to, but not exactly, Zipf's law.  ... 
doi:10.1371/journal.pcbi.1005110 pmid:27997544 pmcid:PMC5172588 fatcat:uq3swipzwrh2rm2opf7mlsyagq

Zipf's Law and Avoidance of Excessive Synonymy

Dmitrii Manin
2008 Cognitive Science  
Zipf's law states that if words of language are ranked in the order of decreasing frequency in texts, the frequency of a word is inversely proportional to its rank.  ...  We suggest that Zipf's law may arise from the evolution of word semantics dominated by expansion of meanings and competition of synonyms.  ...  When run, both these models reliably generate interval sets with sizes distributed by Zipf's law with exponent B = 1.  ... 
doi:10.1080/03640210802020003 pmid:21585444 fatcat:qpacd65nv5gj5gvwu4egci2uxm

Zipf's law arises naturally in structured, high-dimensional data [article]

Laurence Aitchison, Nicola Corradi, Peter E. Latham
2016 arXiv   pre-print
Recently, methods from statistical physics were used to show that a fairly broad class of models does provide a general explanation of Zipf's law.  ...  Empirically, these advances allowed us extend this explanation to important classes of data, including word frequencies (the first domain in which Zipf's law was discovered), data with variable sequence  ...  However, it is important to understand the realistic case: how a finite range of frequencies with an uneven distribution might lead to something similar to, but not exactly, Zipf's law.  ... 
arXiv:1407.7135v4 fatcat:lnhesg7p7zgolieo4tgvgyzm2m

Universality of Zipf's law

Bernat Corominas-Murtra, Ricard V. Solé
2010 Physical Review E  
Here we show that Zipf's law is, in fact, an inevitable outcome of a very general class of stochastic systems.  ...  Zipf's law is the most common statistical distribution displaying scaling behavior. Cities, populations or firms are just examples of this seemingly universal law.  ...  Zipf, who observed that it accounts for the frequency of words within written texts ͓5,8͔.  ... 
doi:10.1103/physreve.82.011102 pmid:20866560 fatcat:tv3725k2wzfgla3jdclaarqvuy

Some new approaches to the study of the Earth's magnetic field reversals

G. Consolini, P. De Michelis
2003 Annals of Geophysics  
In detail, the occurrence of 1/f-noise in the Power Spectral Density (PSD), relative to geomagnetic fi eld reversals, the existence of a Zipf's law behaviour for the cumulative distribution of polarity  ...  Paleomagnetic studies clearly show that the polarity of the magnetic fi eld has been subject to reversals. It is generally assumed that polarity intervals are exponentially distributed.  ...  We remark that a gamma distribution generally occurs in out-of-equilibrium dynamical systems (Sornette, 2000) .  ... 
doi:10.4401/ag-4372 doaj:382ad863f5b64d32bec1788eca9fc9b6 fatcat:xzxnajzfubc6lmuxf4j5wzbyky

Extreme robustness of scaling in sample space reducing processes explains Zipf's law in diffusion on directed networks

Bernat Corominas-Murtra, Rudolf Hanel, Stefan Thurner
2016 New Journal of Physics  
The result that Zipf's law emerges as a generic feature of diffusion on networks, regardless of its details, and that the exponent of visiting times is related to the amount of cycles in a network could  ...  We demonstrate mathematically that in the absence of noise the scaling exponents converge to -1 (Zipf's law) for almost all prior distributions.  ...  To create much more realistic structures, we generate arbitrary random DAGs.  ... 
doi:10.1088/1367-2630/18/9/093010 fatcat:yutnhl7q3bdbpdyik32jhiylaa

Scaling laws in natural conversations among elderly people

Masato S Abe, Mihoko Otake-Matsuura
2021 PLoS ONE  
in terms of scaling laws, namely, Zipf's law and Heaps' law.  ...  Moreover, variations in Heaps' exponents were associated with the ratio of new words taken from the other participants' speech.  ...  Seiki Tokunaga, Megumi Kubota, and Kaai Yamaguchi for their assistance with data collection.  ... 
doi:10.1371/journal.pone.0246884 pmid:33606774 pmcid:PMC7894956 fatcat:ijtl4va6svcjfaafxrqn7gclvu

Semiotic Dynamics in Online Social Communities

C. Cattuto
2007 Towards New Milestones in Our Quest to Go Beyond the Standard Model  
On studying the frequency distribution of tags, we find a generalized Zipf's behavior and quantitatively describe the observed distributions in terms of a previously introduced Yule-Simon process with  ...  Communities of web users categorize resources by associating metadata with them, in the form of freely chosen text labels, or tags.  ...  The Commission is not responsible for any use that may be made of data appearing in this publication.  ... 
doi:10.1142/9789812779120_0020 fatcat:n3ifq34t65cblodb3f22fff4dm
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