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## Impact of Interventions on discrete outcomes: Maximum-likelihood Estimation of the Binary Choice Models with Binary Endogenous Regressors

In this article, we describe the switch_probit command, which implements the maximum likelihood method to fit the model of the binary choice with binary endogenous regressors.

In aerospace industry one of the main issues is the problem of the qualified specialists education. During the learning process positive incentives improve the effectiveness of the education . One of such incentives is the rating system. In this work the construction and evaluation of the specialized rating system is regarded with examples on the distance learning system that is used for learning mathematical courses by students of aerospace disciplines.

The methodology, used in this research, allow to identify the structure of non-linear connections in the models of statistical interconnections. The empirical base of research is the reasons for revoking of licenses of Russian banks from 01.2013 to 12.2015 in two groups — due to economic reasons and laundering of money. Models of binary choice for the forecast of revoking licenses were built with the help of the fractional polynomial regression. Models were built for above-mentioned groups. Each model contains financial and social variables. The latter have been got with the help of networks theory from banks relationship analysis.

In the paper tourist trips of Russians abroad were studied and major trends were identified. The main indicators of international tourism in the world and Russia were analyzed. The impact of socio-demographic characteristics of the individuals on the likelihood of a tourist trip abroad was simulated on the basis of binary choice models.

This paper presents the approach to the design of angle of arrival estimator for narrow-band noise-like signal based on artificial neural network (ANN). The multilayer perceptron type ANNs are trained to minimize the sum of squared errors or maximize the likelihood function using the deterministic approach with the data samples generated by the single station model. The special type of output neuron processing unit is developed to perform sensible angle estimation by the signals obtained from previous network level. The results of numerical simulation show the significant increase in the estimation procedure speed for trained ANN in comparison with direct maximum likelihood estimator. The cost of the performance boost is accuracy deterioration which is no more than 10 percent at moderate SNR values.

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.