Related papers: A universal model for languages and cities, and th…
Here we present a new class of optimality for coding systems. Members of that class are displaced linearly from optimal coding and thus exhibit Zipf's law, namely a power-law distribution of frequency ranks. Within that class, Zipf's law,…
Usually, the study of city population distribution has been reduced to power laws. In such analysis, a common practice is to consider cities with more than one hundred thousand inhabitants. Here, we argue that the distribution of cities for…
Cities are typical dynamic complex systems that connect people and facilitate interactions. Revealing universal collective patterns behind spatio-temporal interactions between residents is crucial for various urban studies, of which we are…
The distribution of living languages is investigated and scaling relations are found for the diversity of languages as a function of the country area and population. These results are compared with data from Ecology and from computer…
Zipf's law in its basic incarnation is an empirical probability distribution governing the frequency of usage of words in a language. As Terence Tao recently remarked, it still lacks a convincing and satisfactory mathematical explanation.…
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…
Evidences are presented concerning tantalizing regularities in cities' population-flows in what regards to space and time correlations. The former exhibit a distance-behavior (for large distances) compatible with the inverse square law,…
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…
A mere hyperbolic law, like the Zipf's law power function, is often inadequate to describe rank-size relationships. An alternative theoretical distribution is proposed based on theoretical physics arguments starting from the Yule-Simon…
The pioneering research of G. K. Zipf on the relationship between word frequency and other word features led to the formulation of various linguistic laws. The most popular is Zipf's law for word frequencies. Here we focus on two laws that…
As early indicated by Charles Darwin, languages behave and change very much like living species. They display high diversity, differentiate in space and time, emerge and disappear. A large body of literature has explored the role of…
We use Monte Carlo simulations and assumptions from evolutionary game theory in order to study the evolution of words and the population dynamics of a system comprising two interacting species which initially speak two different languages.…
In this article, we investigate the properties of phoneme N-grams across half of the world's languages. We investigate if the sizes of three different N-gram distributions of the world's language families obey a power law. Further, the…
Inspired by language competition processes, we present a model of coupled evolution of node and link states. In particular, we focus on the interplay between the use of a language and the preference or attitude of the speakers towards it,…
Zipf's law is the most common statistical distribution displaying scaling behavior. Cities, populations or firms are just examples of this seemingly universal law. Although many different models have been proposed, no general theoretical…
It is traditionally assumed that Zipf's law implies the power-law growth of the number of different elements with the total number of elements in a system - the so-called Heaps' law. We show that a careful definition of Zipf's law leads to…
This paper revisits Menzerath's Law, also known as the Menzerath-Altmann Law, which models a relationship between the length of a linguistic construct and the average length of its constituents. Recent findings indicate that simple…
Zipf's law is found when the vocabulary of long written texts is ranked according to the frequency of word occurrences, establishing a power-law decay for the frequency vs rank relation. This law is a robust statistical property observed…
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
Many large cities are found at locations with certain first nature advantages. Yet, those exogenous locational features may not be the most potent forces governing the spatial pattern of cities. In particular, population size, spacing and…