A Language as a Self-Organized Critical System
A natural language (represented by texts generated by native speakers) is considered as a complex system, and the type thereof to which natural languages belong is ascertained. Namely, the authors hypothesize that a language is a self-organized critical system and that the texts of a language are “avalanches” flowing down its word cooccurrence graph. The respective statistical characteristics for distributions of the number of words in the texts of English and Russian languages are calculated; the samples were constructed on the basis of corpora of literary texts and of a set of social media messages (as a substitution to the oral speech). The analysis found that the number of words in the texts obeys power-law distribution.
In this paper, we propose a new way to develop a service for sharing knowledge in the university cluster by searching for appropriate experts. The method is based on a modern approach to the search for experts with the help of topic modeling. The service has been implemented in the form of a decision support system called EXPERTIZE.
The paper describes the structure and possible applications of the theory of K-representations (knowledge representations) in bioinformatics and in the development of a Semantic Web of a new generation. It is an original theory of designing semantic-syntactic analyzers of natural language (NL) texts with the broad use of formal means for representing input, intermediary, and output data. The current version of the theory is set forth in a monograph by V. Fomichov (Springer, 2010). The first part of the theory is a formal model describing a system consisting of ten operations on conceptual structures. This model defines a new class of formal languages – the class of SK-languages. The broad possibilities of constructing semantic representations of complex discourses pertaining to biology are shown. A new formal approach to developing multilingual algorithms of semantic-syntactic analysis of NL-texts is outlined. This approach is realized by means of a program in the language PYTHON.
The paper is written with the assumption that the purpose of a mathematical theory of citation is to explain bibliometric regularities at the level of mathematical formalism. A mathematical formalism is proposed for the appearance of power law distributions in social citation systems. The principal contributions of this paper are an axiomatic characterization of citation distributions in terms of the Ekeland variational principle and a mathematical exploration of the power law nature of citation distributions. Apart from its inherent value in providing a better understanding of the mathematical underpinnings of bibliometric models, such an approach can be used to derive a citation distribution from first principles.
Current approaches to testing hypotheses on degree distribution of the market graph and of identifying power law in data are discussed, main drawbacks of these approaches are identified and ways to overcome them are provided. Brief summary on methodology used is given and main aspects are highlighted. Discussed methodology is applied to testing hypotheses on degree distribution of multiple market graphs and results obtained are presented. It is shown that more stable market research techniques question presence of power law in degree distribution.
A new model of a stock market as a nonlinear random dynamical system with additive noise in three-dimensional phase space is offered. Implementations of this model in the adiabatic approximation possess all the key signs of fractal market, making the model a reasonable evolutionary model for a stock market. The use of adiabatic approximation allows us to model a stock market as a nonlinear random dynamical system with multiplicative noise with the power-law in one-dimensional phase space. This model shows fractality, long memory and 1/f noise in a stock market.
The paper shows an incompleteness of theoretical foundations of the Computational Semantics branches called Semantic Role Labeling and Frame-Semantic Parsing. This situation is a consequence of a seeming lack of a semantic formalism allowing to describe semantic structures of complex sentences and discourses pertaining to arbitrary application domains. It is concluded that the theory of K-representations (knowledge representations) provides a formalism of the kind, determining a new class of formal languages — the class of SK-languages (standard knowledge languages). Some new expressive mechanisms of SK-languages are illustrated. The central ideas of a method of semantic parsing of natural language (NL) texts proposed by the theory of K-representations are set forth. The method employs the class of SK-languages for constructing semantic representations of texts. The final part of the paper considers the application of the method to designing NL-interfaces for software management. A file manager with a NL-interface NLC-1 (Natural Language Commander — Version One) has been developed, the system is implemented with the help of the functional programming language Haskell.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.
I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables