Related papers: Zipf's law and L. Levin's probability distribution…
We statistically investigate the distribution of share price and the distributions of three common financial indicators using data from approximately 8,000 companies publicly listed worldwide for the period 2004-2013. We find that the…
Given two events $A$ and $B$, Bayes' law is based on the argument that the probability of $A$ given $B$ is proportional to the probability of $B$ given $A$. When probabilities are interpreted in the Bayesian sense, Bayes' law constitutes a…
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…
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…
Most of various large-size complex systems in nature and society can be well described as complex networks (graphs) to better understand the evolutional mechanisms and dynamical functions behind themselves. Of some part follow scale-free…
As the most fundamental empirical law, Zipf's law has been studied from many aspects. But its meaning is still an open problem. Some models have been constructed to explain Zipf's law. In the letter, a new concept named nonsymmetric entropy…
Previously referred to as `miraculous' in the scientific literature because of its powerful properties and its wide application as optimal solution to the problem of induction/inference, (approximations to) Algorithmic Probability (AP) and…
We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two…
Data of proportional elections show a striking feature: If the parties are ranked according to the number of their voters, the number of votes grows exponentially with the rank of the party. This so-called Zipf's law has been reported…
We address the role of multiplicative stochastic processes in modeling the occurrence of power-law city size distributions. As an explanation of the result of Zipf's rank analysis, Simon's model is presented in a mathematically elementary…
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…
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…
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…
Let us consider a homogeneous Markov chain with discrete time and with a finite set of states $E_0,\ldots,E_n$ such that the state $E_0$ is absorbing, states $E_1,\ldots,E_n$ are nonrecurrent. The goal of this work is to study frequencies…
Power law distributions characterise several natural and social phenomena. The Zipf law for cities is one of those. The study views the question of whether that global regularity is independent of different spatial distributions of cities.…
Yuri Manin's approach to Zipf's law (Kolmogorov complexity as energy) is applied to investigation of biological evolution. Model of constructive statistical mechanics where complexity is a contribution to energy is proposed to model…
We present a general approach to explain the Zipf's law of city distribution. If the simplest interaction (pairwise) is assumed, individuals tend to form cities in agreement with the well-known statistics
Any positive word comprised of random sequence of tokens form a finite alphabet can be reduced (without change of length) using an appropriate size Braid group relationships. Surprisingly the Braid relations dramatically reduce the…
The time variation of the rank $k$ of words for six Indo-European languages is obtained using data from Google Books. For low ranks the distinct languages behave differently, maybe due to syntaxis rules, whereas for $k>50$ the law of large…
Zipf's law states that the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat's rule of proportional growth but require additional constraints. We show that Gibrat's rule, at all…