Related papers: A Rank-Based Approach to Zipf's Law

We study a mean-field version of rank-based models of equity markets such as the Atlas model introduced by Fernholz in the framework of Stochastic Portfolio Theory. We obtain an asymptotic description of the market when the number of…

In structured system theory, a pattern matrix is a matrix with entries either fixed to zero or free to take arbitrary numbers. The (generic) rank of a pattern matrix is the rank of almost all its realizations. The resilience of various…

The rank-size distribution of cities follows Zipf's law, and the Zipf scaling exponent often tends to a constant 1. This seems to be a general rule. However, a recent numerical experiment shows that there exists a contradiction between the…

Close examination of wealth distributions reveal the existence of two distinct power law regimes. The Pareto exponents of the super-rich, identified for example in rich lists such as provided by Forbes are smaller than the Pareto exponents…

Societies experience politically stable and unstable phases along history, whereas political power is usually passed to new elite groups by these changes. Structural dynamics of the elites in a society have been proposed to be one of the…

This paper analyzes the equilibrium distribution of wealth in an economy where firms' productivities are subject to idiosyncratic shocks, returns on factors are determined in competitive markets, dynasties have linear consumption functions…

Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…

Stopwords are words that are not very informative to the content or the meaning of a language text. Most stopwords are function words but can also be common verbs, adjectives and adverbs. In contrast to the well known Zipf's law for…

The rankability of data is a recently proposed problem that considers the ability of a dataset, represented as a graph, to produce a meaningful ranking of the items it contains. To study this concept, a number of rankability measures have…

A model of distribution of the wealth in a society based on the properties of complex networks has been proposed. The wealth is interpreted as a consequence of communication possibilities and proportional to the number of connections…

Two power series models are proposed to represent self-similarity and they are compared to the Zipf and Benford distributions. Since evolution of a social network is associated with replicating self-similarity at many levels, the nature of…

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…

Kauffman net is a dynamical system of logical variables receiving two random inputs and each randomly assigned a boolean function. We show that the attractor and transient lengths exhibit scaleless behavior with power-law distributions over…

We show that the laws of Zipf and Benford, obeyed by scores of numerical data generated by many and diverse kinds of natural phenomena and human activity are related to the focal expression of a generalized thermodynamic structure. This…

Natural language data follows a power-law distribution, with most knowledge and skills appearing at very low frequency. While a common intuition suggests that reweighting or curating data towards a uniform distribution may help models…

The dependence with text length of the statistical properties of word occurrences has long been considered a severe limitation quantitative linguistics. We propose a simple scaling form for the distribution of absolute word frequencies…

We consider an ideal closed stock market, in which 100 traders have economic activities. The assets of the traders change through buying and selling stocks. We simulate the assets under conservation of both total currency and total number…

We propose an opinion model based on agents located at the vertices of a regular lattice. Each agent has an independent opinion (among an arbitrary, but fixed, number of choices) and its own degree of conviction. The latter changes every…

We show that size-rank distributions with power-law decay (often only over a limited extent) observed in a vast number of instances in a widespread family of systems obey Tsallis statistics. The theoretical framework for these distributions…