Related papers: Taylor's law for Human Linguistic Sequences
Despite being a paradigm of quantitative linguistics, Zipf's law for words suffers from three main problems: its formulation is ambiguous, its validity has not been tested rigorously from a statistical point of view, and it has not been…
Several theoretical results concerning event-by-event fluctuations are discussed: (1) a role of the global conservation laws and concept of statistical ensembles; (2) strongly intensive measures are introduced; they give a possibility to…
It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. Several examples originate from areas, such as quantitative linguistics…
Of basic interest is the quantification of the long term growth of a language's lexicon as it develops to more completely cover both a culture's communication requirements and knowledge space. Here, we explore the usage dynamics of words in…
We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a…
Nonextensive statistics is a formalism of statistical mechanics that describes the ocurrence of power-law distributions in complex systems, particularly the so-called $q$ exponential family of distributions. In this work we present the use…
The physics of randomness and regularities for languages (mother tongues) and their lifetimes and family trees and for the second languages are studied in terms of two opposite processes; random multiplicative noise [1], and fragmentation…
Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized…
A family of information theoretic models of communication was introduced more than a decade ago to explain the origins of Zipf's law for word frequencies. The family is a based on a combination of two information theoretic principles:…
The recent availability of electronic datasets containing large volumes of communication data has made it possible to study human behavior on a larger scale than ever before. From this, it has been discovered that across a diverse range of…
Inferring the processes underlying the emergence of observed patterns is a key challenge in theoretical ecology. Much effort has been made in the past decades to collect extensive and detailed information about the spatial distribution of…
The application of thermodynamic reasoning in the study of learning systems has a long tradition. Recently, new tools relating perfect thermodynamic adaptation to the adaptation process have been developed. These results, known as…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. In their original definition, patterns only allow for…
For a fixed positive integer $\;k,\;$ limit laws of linearly normalized $\;k$-th upper order statistics are well known. In this article, a comprehensive study of tail behaviours of limit laws of normalized $k$-th upper order statistics…
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…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
An evolutionary model for emergence of diversity in language is developed. We investigated the effects of two real life observations, namely, people prefer people that they communicate with well, and people interact with people that are…
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
We present a study of morphological irregularity. Following recent work, we define an information-theoretic measure of irregularity based on the predictability of forms in a language. Using a neural transduction model, we estimate this…
Human history leaves fingerprints in human languages. Little is known over language evolution and its study is of great importance. Here, we construct a simple stochastic model and compare its results to statistical data of real languages.…