On the Variational Principle for Generalized Gibbs Measures

We present a novel approach to establishing the variational principle for Gibbs and generalized (weak and almost) Gibbs states. Limitations of a thermodynamical formalism for generalized Gibbs states will be discussed. A new class of intuitively weak Gibbs measures is introduced, and a typical example is studied. Finally, we present a new example of a non-Gibbsian measure arising from an industrial application.Comment: To appear in Markov Processes and Related Fields, Proceedings workshop Gibbs-nonGibb

A concentration inequality for interval maps with an indifferent fixed point

For a map of the unit interval with an indifferent fixed point, we prove an upper bound for the variance of all observables of $n$ variables $K:[0,1]^n\to\R$ which are componentwise Lipschitz. The proof is based on coupling and decay of correlation properties of the map. We then give various applications of this inequality to the almost-sure central limit theorem, the kernel density estimation, the empirical measure and the periodogram.Comment: 26 pages, submitte

Exponential distribution for the occurrence of rare patterns in Gibbsian random fields

We study the distribution of the occurrence of rare patterns in sufficiently mixing Gibbs random fields on the lattice $\mathbb{Z}^d$, $d\geq 2$. A typical example is the high temperature Ising model. This distribution is shown to converge to an exponential law as the size of the pattern diverges. Our analysis not only provides this convergence but also establishes a precise estimate of the distance between the exponential law and the distribution of the occurrence of finite patterns. A similar result holds for the repetition of a rare pattern. We apply these results to the fluctuation properties of occurrence and repetition of patterns: We prove a central limit theorem and a large deviation principle.Comment: To appear in Commun. Math. Phy

Linearly edge-reinforced random walks

We review results on linearly edge-reinforced random walks. On finite graphs, the process has the same distribution as a mixture of reversible Markov chains. This has applications in Bayesian statistics and it has been used in studying the random walk on infinite graphs. On trees, one has a representation as a random walk in an independent random environment. We review recent results for the random walk on ladders: recurrence, a representation as a random walk in a random environment, and estimates for the position of the random walker.Comment: Published at http://dx.doi.org/10.1214/074921706000000103 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Diazatriphenylenes and their thiophene analogues: Synthesis and applications

This review highlights the recent advances in the field of the synthesis of diazatriphenylenes and their structural analogues, such as phenanthrenes, fused with the thiophene ring, and naphthalenes, condensed with two thiophene rings. Also applications of these compounds are considered. © ARKAT USA, Inc.The research was financially supported by the Russian Science Foundation (Project No. 16-13-10435) and the Russian Foundation for Basic Research (research project №. 17-03-00011-А)

Linking markemes in Russian and British literary texts of the first half of the nineteenth century

The paper aims at visualizing and analyzing the markeme links in literary texts of Russian and British writers of the first half of nineteenth century. According to the target goal, the tasks of determining the preferred markeme links between the authors, substantial study of maximum force markeme links and comparing the linking markeme vocabulary in Russian and English literary texts have been solved. The topicality of this study is conditioned by the need to devise the ways of cognitive-graphical representations of analytic data and their semantic interpretation and by the scarcity of comparative quantitative studies of the language of Russian and English literary texts, which could present information for comparative and typological analysis of language and literary processes.The study of markeme links is one of the ways of formalized content analysis of the text. The scientists identified regularities to which the texts in natural languages are subject. This enables the use of the mathematical apparatus in linguistic studies. The use of both digital and traditional linguistic studies methods allows analyzing text corpora with mathematical and statistical methods and composing national text corpora, corpora of translations, interactive maps, creating social networks of writers, poets, philosophers, modeling script texts into picture line, analyzing text sentiment, running network analysis and so on. This article suggests analyzing markeme links of maximum force in pairs of authors when comparing “with each other”. The method of markeme analysis proposed by A.A. Kretov as one of the means to formalize the semantical analysis of the text is used to solve the set tasks. It provides a means of presenting a complete picture of literary works language markeme composition of any chronological interval or historical period. It also gives the possibility to analyze texts practically of any wordage. Besides the method of markeme analysis allows analyzing markeme composition of literary (especially - fiction) works of individual authors or groups of authors, markeme specifications and the influence of social and cultural processes on markeme dynamics, studying the evolution of markeme vocabulary through several chronological intervals and establishing literary and genetic links between authors who belong to the same or different chronological intervals an individual DH prospect developed by A.A. Kretov, his colleagues and scholars. Its potential is not limited with solving the given problems. As a qualitative and quantitative analysis, markemological studies employ markeme analysis as a method. This method allows formalizing semantic analysis of texts. Markeme analysis is a method of computer-based identification of keywords, or markemes, followed by visualization of obtained data in the form of bar graphs, charts, graphs, clusters that undergo semantic interpretation. A.A. Kretov developed sharply defined notions on how to identify markemes using a special formula to calculate author's weight or Index of Textual Markedness. The computational formula expresses functionality between a frequency weight and a length weight of a word. As the length weight of a word is constant because it depends on the length of the word in letters or sounds, it is the value of frequency weight that determines the value of InTeM. When a word distribution in the text exceeds a standard frequency distribution threshold for this word, the value of its InTeM becomes positive thereby expressing the level of significance for the word in the particular text. The texts are processed with word thematic analysis manipulation programs “TemAl” and “ProTemAl-Engl” developed in Voronezh State University. “TemAl” processes Russian texts and “ProTemAl-Engl” does the same with English texts. These programs calculate the value of InTeM for each word as well. To guarantee comparability of markeme weights of different authors the procedure of normalizing InTeM values is carried out. This is due to the fact that too often there is great difference both in number of works and their length in words written by different authors and their availability in digital form. InTeM normalizing eliminates their incorrect correlation. The analysis of linking markemes that establish markeme links between two or more authors allows determining the degree of markeme similarity between the authors of chronological interval. Mutual markemes are selected from each author markeme list. Index of Markeme Similarity (IMaS) is the measurable parameter that gives possibility to determine the degree of generality of markeme lexicon of two authors. The computation of IMaS in each pair of authors belonging to the chronological interval is based on the value of total normalized indices of textual markedness of their mutual markemes. The mutual markemes of those two writers that have the largest value of IMaS are their linking markemes. The value of IMaS determines the power of markeme link. When the value of IMaS is the largest for only one writer in the pair, a directional or oriented link of maximum power is formed. In case the value of IMaS is the largest for both writers in the pair, mutually oriented link is formed between them. The present study results in the analysis of linking markemes in the texts of Russian and British writers of the first half of the nineteenth century in reference to the distinguished centre of attraction. The method of visualizing the links between the authors who belong to the same chronological interval allows to distinguish the centre of attraction and intermediate centres of zero, first and second degree, to compute the power of centripetal links, to stratify and analyze linking markemes, to study markeme specificity of the centre of attraction and to distinguish markemes that provide an indirect link between the centre of attraction and intermediate centres. The use of the algorithm of visualizing markeme relations between the authors provides a means of revealing existing centrifugal and centripetal markeme links between the writers, distinguishing the centre of attraction, identifying its major figures and the authors who have direct or indirect markeme links of maximum force with each of them. Obtained data make it possible to compute the power of the center of attraction and the semantic study of maximum force markeme links leads to the specification of both the intermediate centres that are represented by key figures of the centre of attraction and the centre of attraction itself