Related papers: Big Data and Large Numbers. Interpreting Zipf's La…
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…
We study a resource utilization scenario characterized by intrinsic fitness. To describe the growth and organization of different cities, we consider a model for resource utilization where many restaurants compete, as in a game, to attract…
An important body of quantitative linguistics is constituted by a series of statistical laws about language usage. Despite the importance of these linguistic laws, some of them are poorly formulated, and, more importantly, there is no…
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…
Using data from gene expression databases on various organisms and tissues, including yeast, nematodes, human normal and cancer tissues, and embryonic stem cells, we found that the abundances of expressed genes exhibit a power-law…
Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes, or texts as sets of words. On one hand, the joint occurrence of…
In this article, I conduct a textual and contextual analysis of the empirical literature on Zipf's law for cities. Building on previous meta-analysis material openly available, I collect full texts and bibliographies of 66 scientific…
Time evolution of the cities and of the languages is considered in terms of multiplicative noise and fragmentation processes; where power law (Pareto-Zipf law) and slightly asymmetric log-normal (Gauss) distribution result for the size…
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 we combine statistical analysis of large text databases and simple stochastic models to explain the appearance of scaling laws in the statistics of word frequencies. Besides the sublinear scaling of the vocabulary size with…
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…
Zipf's law is shown to arise as the variational solution of a problem formulated in Fisher's terms. An appropriate minimization process involving Fisher information and scale-invariance yields this universal rank distribution. As an example…
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…
Statistical regularities in human language have fascinated researchers for decades, suggesting deep underlying principles governing its evolution and information structuring for efficient communication. While Zipf's Law describes the…
When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since the population size has no natural upper limit, this leads to systems in which there are…
The empirical studies of city-size distribution show that Zipf's law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their…
Some of the progress in determining the phase boundaries of the nuclear phase diagram, the location of the critical point of the nuclear fragmentation phase transition, and the values of the critical exponents of this transition is…
A new angle of view is proposed to find the simple rules dominating complex systems and regular patterns behind random phenomena such as cities. Hierarchy of cities reflects the ubiquitous structure frequently observed in the natural world…
In his pioneering research, G. K. Zipf observed that more frequent words tend to have more meanings, and showed that the number of meanings of a word grows as the square root of its frequency. He derived this relationship from two…
We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary…