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The known three-component reaction-diffusion system modeling competition and co-existence of different language speakers is under study. A modification of this system is proposed, which is examined by Lie symmetry method; furthermore exact…
As the recent studies indicate, the structure imposed onto written texts by the presence of punctuation develops patterns which reveal certain characteristics of universality. In particular, based on a large collection of classic literary…
Kolmogorov complexity of a finite binary word reflects both algorithmic structure and the empirical distribution of symbols appearing in the word. Words with symbol frequencies far from one half have smaller combinatorial richness and…
As in statistical physics, the concept of universality plays an important, albeit qualitative, role in the field of comparative mythology. Here we apply statistical mechanical tools to analyse the networks underlying three iconic…
This paper introduces a statistical and other analysis of peer reviewers in order to approach their "quality" through some quantification measure, thereby leading to some quality metrics. Peer reviewer reports for the Journal of the Serbian…
In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its…
Several complex systems are characterized by presenting intricate characteristics taking place at several scales of time and space. These multiscale characterizations are used in various applications, including better understanding…
We define a new quantitative measure for an arbitrary factorial language: the entropy of a random walk in the prefix tree associated with the language; we call it Markov entropy. We relate Markov entropy to the growth rate of the language…
In this paper, we first describe the generalized notion of Cramer-Rao lower bound obtained by Naudts (2004) using two families of probability density functions, the original model and an escort model. We reinterpret the results in Naudts…
An analytical formula for the occurence probability of Markovian stochastic paths with repeatedly visited and/or equal departure rates is derived. This formula is essential for an efficient investigation of the trajectories belonging to…
A statistical physics study of punctuation effects on sentence lengths is presented for written texts: {\it Alice in wonderland} and {\it Through a looking glass}. The translation of the first text into esperanto is also considered as a…
Words are fundamental linguistic units that connect thoughts and things through meaning. However, words do not appear independently in a text sequence. The existence of syntactic rules induces correlations among neighboring words. Using an…
Statistical laws describe regular patterns observed in diverse scientific domains, ranging from the magnitude of earthquakes (Gutenberg-Richter law) and metabolic rates in organisms (Kleiber's law), to the frequency distribution of words in…
We consider weighted graphs satisfying sub-Gaussian estimate for the natural random walk. On such graphs, we study symmetric Markov chains with heavy tailed jumps. We establish a threshold behavior of such Markov chains when the index…
Texts exhibit considerable stylistic variation. This paper reports an experiment where a corpus of documents (N= 75 000) is analyzed using various simple stylistic metrics. A subset (n = 1000) of the corpus has been previously assessed to…
The search for linguistic patterns, stylometry and forensic linguistics have in the theory of complex networks, their structures and associated mathematical tools, allies with which to model and analyze texts. In this paper we present a new…
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…
The Kolmogorov-Smirnov statistic is usually introduced as a supremum, but its finite-sample behavior is governed by a more local question: where does the empirical process first cross a boundary? This letter gives a partial answer through a…
In the article the fact is verified that the list of words selected by formal statistical methods (frequency and functional genre unrestrictedness) is not a conglomerate of non-related words. It creates a system of interrelated items and it…
In English literature, the 19th century witnessed a significant transition in styles, themes, and genres. Consequently, the novels from this period display remarkable diversity. This paper explores these variations by examining the…