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## Аппроксимация функций с помощью нейронных сетей и нечетких систем

This paper surveys some parts of approximation theory for functions of one and several real variables. Approximation of functions by algebraic polynomials is a classical theory. The paper contains some results from this theory. First results on approximation of functions by neural networks and fuzzy systems have appeared as responses on practical requirements. It was necessary to know is it possible to approximate an arbitrary continuous function by such aggregates. Later, these fields were developed like the theory of approximation of functions by algebraic polynomials. In this paper we consider some results on approximation of functions by neural networks and fuzzy systems.

The article discusses development of the segmented characters classifier of the Russian alphabet a nd of the Arabic numerals on the basis of block neural network structures including the plurality of blocks for each individual character recognition and for the synthesis block decision. Keywords: pattern recognition, neural network, training of neural n etworks, base of hand - written characters, recognition of hand - written characters

Intelligent Systems Conference (IntelliSys) 2018 is the fourth research conference in the series. This conference is a part of SAI conferences being held since 2013. The conference series has featured keynote talks, special sessions, poster presentation, tutorials, workshops, and contributed papers each year. The conference focus on areas of intelligent systems and artificial intelligence (AI) and how it applies to the real world. IntelliSys is one of the best respected Artificial Intelligence (AI) Conference.

The application of neural networks for prediction of long-term changes of observed parameter on the example of thermal treatment control of concrete products is considered. Experimental results are presented, and the algorithm of the work plan of an actuating mechanism is proposed.

Development of linguistic technologies and penetration of social media provide powerful possibilities to investigate users’ moods and psychological states of people. In this paper we discussed possibility to improve accuracy of stock market indicators predictions by using data about psychological states of Twitter users. For analysis of psychological states we used lexicon-based approach, which allow us to evaluate presence of eight basic emotions in more than 755 million tweets. The application of Support Vectors Machine and Neural Networks algorithms to predict DJIA and S&P500 indicators are discussed.

In work the developed model of adaptive management by the vertically integrated companies based on the system approach supporting the mechanism of an operational management in a uniform cycle of strategic planning, within the limits of faster time is presented. Thus for a finding of optimum values of operating parameters special algorithms of a class of genetic algorithms are used, neural networks the example of the developed system of adaptive management for the vertically-integrated oil company is etc. presented.

This book constitutes the refereed proceedings of the 6th IAPR TC3 International Workshop on Artificial Neural Networks in Pattern Recognition, ANNPR 2014, held in Montreal, QC, Canada, in October 2014. The 24 revised full papers presented were carefully reviewed and selected from 37 submissions for inclusion in this volume. They cover a large range of topics in the field of learning algorithms and architectures and discussing the latest research, results, and ideas in these areas.

The paper theorizes on the general architectonics of idealized cognitive models (ICMs) and their involvement in metonymy and metaphor. The article posits that an ICM's structure should reflect the architecture of the neural network/s engaged in processing of a given concept. The ICM nodes, or cogs, construct a complex, hierarchically organized neural connections, with the superior nodes being highly selective, invariant and prototypical. Signals travelling from one cog to another within one ICM are essentially metonymical, while a cog shared by two or more ICMs marks a metaphoric shift.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.