Related papers: Zipf's law in Multifragmentation
Zipf's law predicts a power-law relationship between word rank and frequency in language communication systems, and is widely reported in texts yet remains enigmatic as to its origins. Computer simulations have shown that language…
We present a thermodynamic formulation for scale-invariant systems based on the principle of extreme information. We create an analogy between these systems and the well-known thermodynamics of gases and fluids, and study as a compelling…
A three parameter scaling relationship between isotopic distributions for elements with Z$\leq 8$ has been observed that allows a simple description of the dependence of such distributions on the overall isospin of the system. This scaling…
Isotope yields have been analyzed within the framework of a Modified Fisher Model to study the power law yield distribution of isotopes in the multifragmentation regime. Using the ratio of the mass dependent symmetry energy coefficient…
Most of various large-size complex systems in nature and society can be well described as complex networks (graphs) to better understand the evolutional mechanisms and dynamical functions behind themselves. Of some part follow scale-free…
Zipf's law appears in many application areas but does not have a closed form expression, which may make its use cumbersome. Since it coincides with the truncated version of the Zeta distribution, in this paper we propose three approximate…
Natural languages are full of rules and exceptions. One of the most famous quantitative rules is Zipf's law which states that the frequency of occurrence of a word is approximately inversely proportional to its rank. Though this `law' of…
Zipf's law is a hallmark of several complex systems with a modular structure, such as books composed by words or genomes composed by genes. In these component systems, Zipf's law describes the empirical power law distribution of component…
We inspect the deductive connection between the neural scaling law and Zipf's law -- two statements discussed in machine learning and quantitative linguistics. The neural scaling law describes how the cross entropy rate of a foundation…
Here we sketch a new derivation of Zipf's law for word frequencies based on optimal coding. The structure of the derivation is reminiscent of Mandelbrot's random typing model but it has multiple advantages over random typing: (1) it starts…
The statistical characterization of the distribution of visible matter in the universe is a central problem in modern cosmology. In this respect, a crucial question still lacking a definitive answer concerns how large are the greatest…
Zipf's law is just one out of many universal laws proposed to describe statistical regularities in language. Here we review and critically discuss how these laws can be statistically interpreted, fitted, and tested (falsified). The modern…
Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Based on the idea from general fractals and scaling,…
The Zipf power law and its connection with the inhomogeneity of the system is investigated. We describe the statistical distributions of the domain masses in the Potts model near the temperature-induced phase transition. We found that the…
We investigate the origin of Zipf's law for words in written texts by means of a stochastic dynamical model for text generation. The model incorporates both features related to the general structure of languages and memory effects inherent…
Languages across the world exhibit Zipf's law of abbreviation, namely more frequent words tend to be shorter. The generalized version of the law - an inverse relationship between the frequency of a unit and its magnitude - holds also for…
We address the role of multiplicative stochastic processes in modeling the occurrence of power-law city size distributions. As an explanation of the result of Zipf's rank analysis, Simon's model is presented in a mathematically elementary…
We study rank-size distribution of cities in Japan on the basis of data analysis. From the census data after World War II, we find that the rank-size distribution of cities is composed of two parts, each of which has independent power…
We have translated fractional Brownian motion (FBM) signals into a text based on two ''letters'', as if the signal fluctuations correspond to a constant stepsize random walk. We have applied the Zipf method to extract the $\zeta '$ exponent…
Certain fluctuations in particle number at fixed total energy lead exactly to a cut-power law distribution in the one-particle energy, via the induced fluctuations in the phase-space volume ratio. The temperature parameter is expressed…