相关论文: Log-log Convexity of Type-Token Growth in Zipf's S…

Power law distributions characterise several natural and social phenomena. The Zipf law for cities is one of those. The study views the question of whether that global regularity is independent of different spatial distributions of cities.…

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…

Zipf's law establishes a scaling behavior for word-frequencies in large text corpora. The appearance of Zipfian properties in human language has been previously explained as an optimization problem for the interests of speakers and hearers.…

We show that Zipf's Law for the largest clusters is not valid in an exact sense at the critical point of the fragmentation phase transition, contrary to previous claims. Instead, the extracted distributions of the largest clusters reflects…

Stochastic equations constitute a major ingredient in many branches of science, from physics to biology and engineering. Not surprisingly, they appear in many quantitative studies of complex systems. In particular, this type of equation is…

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…

We study the rank distribution, the cumulative probability, and the probability density of returns of stock prices of listed firms traded in four stock markets. We find that the rank distribution and the cumulative probability of stock…

The length of coding sequence series in microbial genomes were regarded as a fluctuating system and characterized by the methods of statistical physics. The distribution and the correlatin properties of 50 genomes including bacteria and…

In this paper we deal with the structural properties of weighted networks. Starting from an empirical analysis of a linguistic network, we analyse the differences between the statistical properties of a real and a shuffled network and we…

In this paper the Zipf-Mandelbrot law is revisited in the context of linguistics. Despite its widespread popularity the Zipf--Mandelbrot law can only describe the statistical behaviour of a rather restricted fraction of the total number of…

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…

Systems evolving according to the standard concept of biological or technological evolution are often described by catalytic evolution equations. We study the structure of these equations and find a deep relationship to classical…

We begin with the extraordinary observation that the length distribution of 80 million proteins in UniProt, the Universal Protein Resource, measured in amino acids, is qualitatively identical to the length distribution of large collections…

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…

We show that statistical criticality, i.e. the occurrence of power law frequency distributions, arises in samples that are maximally informative about the underlying generating process. In order to reach this conclusion, we first identify…

Physics seeks to uncover the laws of Nature and express them through mathematical equations. Despite the vast diversity of natural phenomena, physical equations exhibit structural regularities that set them apart from arbitrary mathematical…

We propose a dynamical mechanism for a scale dependent error growth rate, by the introduction of a class of hierarchical models. The coupling of time scales and length scales is motivated by atmospheric dynamics. This model class can be…

The task of finding a criterion allowing to distinguish a text from an arbitrary set of words is rather relevant in itself, for instance, in the aspect of development of means for internet-content indexing or separating signals and noise in…

We present a general approach to explain the Zipf's law of city distribution. If the simplest interaction (pairwise) is assumed, individuals tend to form cities in agreement with the well-known statistics

In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…