It is shown that the distribution of word frequencies for randomly generated texts is very similar to Zipf's law observed in natural languages such as the English. The facts that the frequency of occurrence of a word is almost an inverse power law function of its rank and the exponent of this inverse power law is very close to 1 are largely due to the transformation from the word's length to it...

Networks describe various complex natural systems including social systems. Recent studies have shown that these networks share some common properties. While studying complex systems, data collection phase is difficult for social networks compared to other networks such as the WWW, Internet, protein or linguistic networks. Many interesting social networks such as movie actors’ collaboration, sc...

Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportat...

This study provides an analysis of the dynamics of fixed-size directed Boolean networks governed by generalizations of elementary cellular automata rules 22 and 126, under a power-law distribution of parent nodes and a popularity parent assignment. The analysis shows the existence of a two-piece chaotic attractor for smaller values of the power-law parameter which evolves into a “cloud”-like at...

This article describes a methodology for fitting experimental data to the discrete power-law distribution and provides the results of a detailed simulation exercise used to calculate accurate cutoff values used to assess the fit to a power-law distribution when using the maximum likelihood estimation for the exponent of the distribution. Using massively parallel programming computing, we were a...

Several studies on real complex networks from different fields as biology, economy , or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like P (k) ≈ k −γ , where P (k) denotes the frequency of the nodes that are connected to k other nodes. Here we have carried out a study on scale-free networks, where a line grap...

It was recently pointed out that the distribution of times between solar flares (the flare waiting-time distribution) follows a power law for long waiting times. Based on 25 years of soft X-ray flares observed by Geostationary Operational Environmental Satellite instruments, it is shown that (1) the waiting-time distribution of flares is consistent with a time-dependent Poisson process and (2) ...

We discuss the distribution of the gravitational force created by a Poissonian distribution of field sources (stars, galaxies,...) in different dimensions of space d. In d = 3, when the particle number N → +∞, it is given by a Lévy law called the Holtsmark distribution. It presents an algebraic tail for large fluctuations due to the contribution of the nearest neighbor. In d = 2, for large but ...

The present study attempted deriving and solving the falling- cylinder governing equations for power law model non-Newtonian fluids. Based on this theoretical study, a novel falling- cylinder rheometer (FCR) was designed and constructed to measure the Theological properties of non-Newtonian fluids. Different falling cylinders with predesigned densities were used to determine the apparent viscos...

Recently, many research contributions focus on showing that specific real-life phenomena or measured quantities of our everyday life obey a power-law, a scale free distribution. Inspired by the numerous studies in power-laws, in this paper, we explore the existence of power-law relationships in musical data. We provide the context where such power-laws do exist, and we give experimental results...