Related papers: MetaZipf. (Re)producing knowledge about city size …
The binary many-step Markov chain with the step-like memory function is considered as a model for the analysis of rank distributions of words in stochastic symbolic dynamical systems. We prove that the envelope curve for this distribution…
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…
Zipf's law in language lacks a definitive origin, debated across fields. This study explains Zipf-like behavior using geometric mechanisms without linguistic elements. The Full Combinatorial Word Model (FCWM) forms words from a finite…
We examine the relationship between two different types of ranked data, frequencies and magnitudes. We consider data that can be sorted out either way, through numbers of occurrences or size of the measures, as it is the case, say, of moon…
In this paper, a statistical analysis of the structure of one blog community, a kind of social networks, is presented. The quantities such as degree distribution, clustering coefficient, average shortest path length are calculated to…
Many large cities are found at locations with certain first nature advantages. Yet, those exogenous locational features may not be the most potent forces governing the spatial pattern of cities. In particular, population size, spacing and…
Background: Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings…
We discuss the meaning of Zipf's law in nuclear multifragmentation. We remark that Zipf's law is a consequence of a power law fragment size distribution with exponent $\tau \simeq 2$. We also recall why the presence of such distribution is…
Rudimentary mathematical analysis of simple network models suggests bandwidth-independent saturation of network growth dynamics and hints at linear decrease in information density of the data. However it strongly confirms Metcalfe's law as…
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…
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…
Scaling laws are powerful summaries of the variations of urban attributes with city size. However, the validity of their universal meaning for cities is hampered by the observation that different scaling regimes can be encountered for the…
We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a…
The scaling exponent of a hierarchy of cities used to be regarded as a fractal parameter. The Pareto exponent was treated as the fractal dimension of size distribution of cities, while the Zipf exponent was treated as the reciprocal of the…
Cities are often compared through scaling laws, usually expressed as power-law relations between population size and aggregate urban quantities related to infrastructure, socioeconomic activity, or environmental impacts. These laws are…
The interaction of all mobile species with their environment hinges on their movement patterns: the places they visit and how frequently they go there. In human society, where the prevalent form of cohabitation is in cities, the highly…
Understanding quantitative relationships between urban elements is crucial for a wide range of applications. The observation at the macroscopic level demonstrates that the aggregated urban quantities (e.g., gross domestic product) scale…
There is strong expectation that cities, across time, culture and level of development, share much in common in terms of their form and function. Recently, attempts to formalize mathematically these expectations have led to the hypothesis…
Degree distributions of graph representations for compact urban patterns are scale-dependent. Therefore, the degree statistics alone does not give us the enough information to reach a qualified conclusion on the structure of urban spatial…
This article investigates the evolution of the $h-$index in a complex network including two communities (in the sense of having different features) with the same number of authors whose yearly productions follow the Zipf's law. Models…