Related papers: Zipf's law arises naturally in structured, high-di…

Zipf's law implies the statistical distributions of hyperbolic type, which can describe the properties of stability and entropy loss in linguistics. We present the information theory from which follows that if the system is described by…

Statistical laws describe regular patterns observed in diverse scientific domains, ranging from the magnitude of earthquakes (Gutenberg-Richter law) and metabolic rates in organisms (Kleiber's law), to the frequency distribution of words in…

For words, rank-frequency distributions have long been heralded for adherence to a potentially-universal phenomenon known as Zipf's law. The hypothetical form of this empirical phenomenon was refined by Ben\^{i}ot Mandelbrot to that which…

In this paper we describe a relation between the Zipf law and statistical distributions for the Fortuin-Kasteleyn clusters in the Ising model.It has been shown,that histograms for fixed domain masses present the right-skewed distributions.

Fractals, 1/f noise, Zipf's law, and the occurrence of large catastrophic events are typical ubiquitous general empirical observations across the individual sciences which cannot be understood within the set of references developed within…

Long-range correlations are found in symbolic sequences from human language, music and DNA. Determining the span of correlations in dolphin whistle sequences is crucial for shedding light on their communicative complexity. Dolphin whistles…

Zipf's law can be used to describe the rank-size distribution of cities in a region. It was seldom employed to research urban internal structure. In this paper, we demonstrate that the space-filling process within a city follows Zipf's law…

We report about universality of rank-integration distributions of open spaces in city space syntax similar to the famous rank-size distributions of cities (Zipf's law). We also demonstrate that the degree of choice an open space represents…

The inverse relationship between the length of a word and the frequency of its use, first identified by G.K. Zipf in 1935, is a classic empirical law that holds across a wide range of human languages. We demonstrate that length is one…

A major problem for evolutionary theory is understanding the so called {\em open-ended} nature of evolutionary change, from its definition to its origins. Open-ended evolution (OEE) refers to the unbounded increase in complexity that seems…

The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about…

Pareto distributions, and power laws in general, have demonstrated to be very useful models to describe very different phenomena, from physics to finance. In recent years, the econophysical literature has proposed a large amount of papers…

This paper presents an extensive survey of regular distributions in natural and social sciences. The survey includes studies from a wide scope of academic disciplines, in order to create an inventory of the different mathematical functions…

Some authors have recently argued that a finite-size scaling law for the text-length dependence of word-frequency distributions cannot be conceptually valid. Here we give solid quantitative evidence for the validity of such scaling law,…

We present empirical data on frequency and pattern of misprints in citations to twelve high-profile papers. We find that the distribution of misprints, ranked by frequency of their repetition, follows Zipf's law. We propose a stochastic…

This paper provides a new geospatial perspective on whether or not Zipf's law holds for all cities or for the largest cities in the United States using a massive dataset and its computing. A major problem around this issue is how to define…

The power law is ubiquitous in natural and social phenomena, and is considered as a universal relationship between the frequency and its rank for diverse social systems. However, a general model is still lacking to interpret why these…

The performance of deep learning in natural language processing has been spectacular, but the reasons for this success remain unclear because of the inherent complexity of deep learning. This paper provides empirical evidence of its…

We study a resource utilization scenario characterized by intrinsic fitness. To describe the growth and organization of different cities, we consider a model for resource utilization where many restaurants compete, as in a game, to attract…

The pioneering research of G. K. Zipf on the relationship between word frequency and other word features led to the formulation of various linguistic laws. The most popular is Zipf's law for word frequencies. Here we focus on two laws that…