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Dynamics of text generation with realistic Zipf distribution
[article]

2002
*
arXiv
*
pre-print

We investigate the origin

arXiv:cond-mat/0212496v1
fatcat:c63e5y4ervckhkgrk2oh73kpoi
*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. ...##
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Beyond Zipf's law: Modeling the structure of human language
[article]

2009
*
arXiv
*
pre-print

As a result, we find a connection between the bursty nature

arXiv:0902.0606v1
fatcat:pfayiez57rbsbkzs3injqlovqm
*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. ...##
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Citations and the Zipf-Mandelbrot's law
[article]

1999
*
arXiv
*
pre-print

The observed regularity indicates not so much the peculiar character

arXiv:physics/9901035v2
fatcat:zsopkbt3kvbdzecsnj64me3pbe
*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. ...##
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Modeling Statistical Properties of Written Text

2009
*
PLoS ONE
*

Beyond

doi:10.1371/journal.pone.0005372
pmid:19401762
pmcid:PMC2670513
fatcat:for67zr65bcbjhvrfaarxm32oy
*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. ...##
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Zipf's and Taylor's laws

2018
*
Physical review. E
*

stationary

doi:10.1103/physreve.98.032408
fatcat:joam7e7zqvg5phgt6ykkkswyby
*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. ...##
###
The dynamics of correlated novelties
[article]

2013
*
arXiv
*
pre-print

The model, a

arXiv:1310.1953v1
fatcat:litxa2naxbcz7m4fftsdlw4ey4
*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*. ...##
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Solvable null model for the distribution of word frequencies

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 ...

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

2016
*
PLoS Computational Biology
*

Recently, methods from statistical physics were used to show that a fairly broad class

doi:10.1371/journal.pcbi.1005110
pmid:27997544
pmcid:PMC5172588
fatcat:uq3swipzwrh2rm2opf7mlsyagq
*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. ...##
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Zipf's Law and Avoidance of Excessive Synonymy

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. ...

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

2016
*
arXiv
*
pre-print

Recently, methods from statistical physics were used to show that a fairly broad class

arXiv:1407.7135v4
fatcat:lnhesg7p7zgolieo4tgvgyzm2m
*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. ...##
###
Universality of Zipf's law

2010
*
Physical Review E
*

Here we show that

doi:10.1103/physreve.82.011102
pmid:20866560
fatcat:tv3725k2wzfgla3jdclaarqvuy
*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. ...##
###
Some new approaches to the study of the Earth's magnetic field reversals

2003
*
Annals of Geophysics
*

In detail, the occurrence

doi:10.4401/ag-4372
doaj:382ad863f5b64d32bec1788eca9fc9b6
fatcat:xzxnajzfubc6lmuxf4j5wzbyky
*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) . ...##
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Extreme robustness of scaling in sample space reducing processes explains Zipf's law in diffusion on directed networks

2016
*
New Journal of Physics
*

The result that

doi:10.1088/1367-2630/18/9/093010
fatcat:yutnhl7q3bdbpdyik32jhiylaa
*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. ...##
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Scaling laws in natural conversations among elderly people

2021
*
PLoS ONE
*

in terms

doi:10.1371/journal.pone.0246884
pmid:33606774
pmcid:PMC7894956
fatcat:ijtl4va6svcjfaafxrqn7gclvu
*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. ...##
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Semiotic Dynamics in Online Social Communities

2007
*
Towards New Milestones in Our Quest to Go Beyond the Standard Model
*

On studying the frequency

doi:10.1142/9789812779120_0020
fatcat:n3ifq34t65cblodb3f22fff4dm
*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. ...
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