Related papers: MetaZipf. (Re)producing knowledge about city size …
The shape of urban settlements plays a fundamental role in their sustainable planning. Properly defining the boundaries of cities is challenging and remains an open problem in the Science of Cities. Here, we propose a worldwide model to…
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…
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. The observed regularity indicates not so…
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…
This work proves that ranks and shares are statistically dependent on one another, based on simple combinatorics. It presents a formula for rank-share distribution and illustrates that Zipfs law, is descended from expected values of various…
We study the distribution of neighborhoods across a set of 12 global cities and find that the distribution of neighborhood sizes follows exponential decay across all cities under consideration. We are able to analytically show that this…
Human development has far-reaching impacts on the surface of the globe. The transformation of natural land cover occurs in different forms and urban growth is one of the most eminent transformative processes. We analyze global land cover…
Scaling properties of language are a useful tool for understanding generative processes in texts. We investigate the scaling relations in citywise Twitter corpora coming from the Metropolitan and Micropolitan Statistical Areas of the United…
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…
In this article, the relationship between two well-accepted empirical propositions regarding the distribution of population in cities, namely, Gibrat's law and Zipf's law, are rigorously examined using the Chinese census data. Our findings…
Zipf's law states that the probability of a variable being larger than $s$ is roughly inversely proportional to $s$. In this paper, we evaluate Zipf's law for the distribution of firm size by the number of employees in Brazil. We use…
We describe the link between the Zipf law and statistical distributions for the Fortuin-Kasteleyn clusters in Ising as well as Potts models. From these results it is seen that Zipf's law can be a criterion of a phase transition, but it does…
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…
Zipf's law has been found in many human-related fields, including language, where the frequency of a word is persistently found as a power law function of its frequency rank, known as Zipf's law. However, there is much dispute whether it is…
Power-law distributions with various exponents are studied. We first introduce a simple and generic model that reproduces Zipf's law. We can regard this model both as the time evolution of the population of cities and that of the asset…
The spatial distribution of people exhibits clustering across a wide range of scales, from household ($\sim 10^{-2}$ km) to continental ($\sim 10^4$ km) scales. Empirical data indicates simple power-law scalings for the size distribution of…
In this paper we derive the maximum entropy characteristics of a particular rank order distribution, namely the discrete generalized beta distribution, which has recently been observed to be extremely useful in modelling many several…
We present an extensive analysis of long-term statistics of the queries to websites using logs collected on several web caches in Russian academic networks and on US IRCache caches. We check the sensitivity of the statistics to several…
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…
We analyse the statistical properties of public transport networks. These networks are defined by a set of public transport routes (bus lines) and the stations serviced by these. For larger networks these appear to possess a scale-free…