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## Проблемы теоретической кибернетики: XVIII международная конференция (Пенза, 19–23 июня 2017 г.)

The chapter studies a dynamic risk model defined on infinite time interval, where both insurance and per-claim reinsurance policies are chosen by the insurer in order to minimize a functional of the form of variation coefficient under constraints imposed with probability one on insured's and reinsurer's risks. We show that the optimum is achieved at constant policies, the optimal reinsurance is a partial stop loss reinsurance and the optimal insurance is a combination of stop loss and deductible policies. The results are illustrated by a numerical example involving uniformly distributed claim sizes.

Proceedings include extended abstracts of reports presented at the III International Conference on Optimization Methods and Applications “Optimization and application” (OPTIMA-2012) held in Costa da Caparica, Portugal, September 23—30, 2012.

Studied is a possibility of increasing the accuracy of diagnostics by examining a number of diagnostic rules as a set of expert assessments, which allows one to combine them («mix of expert opinions»). Proposed is to use of the principle of minimum-information-mismatch in Kullback - Leibler metric to highlight the rule most appropriate for classification of a particular object. Program and results of experimental study are presented in the problem of automatic recognition of gray-scale images. It is shown that the developed approach can significantly improve the quality of diagnostics.

A novel method for evaluating classification reliability is proposed based on the discernibility of a pattern’s class against other classes from the pattern’s location. Use of three measures of discernibility is experimentally compared with conventional techniques based on the classification scores for class labels. The classification accuracy can be drastically enhanced through discernibility measures by using the most reliable – “elite” – patterns. It can be further boosted by forming an amalgamation of the elites of different classifiers. Improved performance is achieved at the price of rejecting many patterns. There are situations where this price is worth paying – when the non-reliable accuracy rates lead to the need in manually testing of very complex technical devices or in diagnostics of human diseases. Contrary to conventional techniques for estimating reliability, the proposed measures are applicable on small datasets as well as on datasets with complex class structures where conventional classifiers show low accuracy rates.

This volume contains a selection of contributions from the "First International Conference in Network Analysis," held at the University of Florida, Gainesville, on December 14-16, 2011. The remarkable diversity of fields that take advantage of Network Analysis makes the endeavor of gathering up-to-date material in a single compilation a useful, yet very difficult, task. The purpose of this volume is to overcome this difficulty by collecting the major results found by the participants and combining them in one easily accessible compilation.

This book constitutes the refereed proceedings of the 9th International Conference on Cellular Automata for Research and Industry, ACRI 2010, held in Ascoli Piceno, Italy, in September 2010. The first part of the volume contains 39 revised papers that were carefully reviewed and selected from the main conference; they are organized according to six main topics: theoretical results on cellular automata, modeling and simulation with cellular automata, CA dynamics, control and synchronization, codes and cryptography with cellular automata, cellular automata and networks, as well as CA-based hardware. The second part of the volume comprises 35 revised papers dedicated to contributions presented during ACRI 2010 workshops on theoretical advances, specifically asynchronous cellular automata, and challenging application contexts for cellular automata: crowds and CA, traffic and CA, and the international workshop of natural computing.

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.