Related papers: Zipf's law arises naturally in structured, high-di…
It has been shown recently that a specific class of path-dependent stochastic processes, which reduce their sample space as they unfold, lead to exact scaling laws in frequency and rank distributions. Such Sample Space Reducing processes…
Urban scaling and Zipf's law are two fundamental paradigms for the science of cities. These laws have mostly been investigated independently and are often perceived as disassociated matters. Here we present a large scale investigation about…
Throughout history most young adults have chosen to live where their parents did while a smaller number moved away. This is sufficient, by proof and simulation, to account for the well-known power law distributions of city sizes. The model…
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…
n-tuple power law widely exists in language, computer program code, DNA and music. After a vast amount of Zipf analyses of n-tuple power law from empirical data, we propose a model to explain the n-tuple power law feature existed in these…
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…
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…
History-dependent processes are ubiquitous in natural and social systems. Many such stochastic processes, especially those that are associated with complex systems, become more constrained as they unfold, meaning that their sample-space, or…
The different between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law…
The problem of compression in standard information theory consists of assigning codes as short as possible to numbers. Here we consider the problem of optimal coding -- under an arbitrary coding scheme -- and show that it predicts Zipf's…
Human language, the most powerful communication system in history, is closely associated with cognition. Written text is one of the fundamental manifestations of language, and the study of its universal regularities can give clues about how…
An expression is proposed for determining the error caused on entropy estimates by finite sample effects. This expression is based on the Ansatz that the ranked distribution of probabilities tends to follow an empirical Zipf law.
The frequency distributions of DNA k-mers are shaped by fundamental biological processes and offer a window into genome structure and evolution. Inspired by analogies to natural language, prior studies have attempted to model genomic k-mer…
We propose hypotheses describing the empirical finding of an association between the exponents of urban GDP scaling and Zipf's law for cities. These hypotheses represent various combinations of directional or reciprocal causal links between…
Inverse power-law interaction forms, such as the inverse-square law, recur across a wide range of physical, social, and spatial systems. While traditionally derived from specific microscopic mechanisms, the ubiquity of these laws suggests a…
The article discusses the frequency of characters of Oracle,concluding that the frequency and the rank of a word or character is fit to Zipf-Mandelboit Law or Zipf's law with three parameters,and figuring out the parameters based on the…
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 importance of statistical patterns of language has been debated over decades. Although Zipf's law is perhaps the most popular case, recently, Menzerath's law has begun to be involved. Menzerath's law manifests in language, music and…
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…
The science of cities seeks to understand and explain regularities observed in the world's major urban systems. Modelling the population evolution of cities is at the core of this science and of all urban studies. Quantitatively, the most…