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## Nonlinear models of BPSK Costas loop

Rigorous nonlinear analysis of the physical model of Costas loop is very difficult task, so for analysis, simplified mathematical models and numerical simulation are widely used. In the work it is shown that the use of simplified mathematical models, and the application of non rigorous methods of analysis may lead to wrong conclusions concerning the operability of Costas loop.

Concurrent EEG and fMRI acquisitions in resting state showed a correlation between EEG power in various bands and spontaneous BOLD fluctuations. However, there is a lack of data on how changes in the complexity of brain dynamics derived fromEEG reflect variations in the BOLD signal. The purpose of our study was to correlate both spectral patterns, as linear features of EEG rhythms, and nonlinear EEG dynamic complexity with neuronal activity obtained by fMRI. We examined the relationships between EEG patterns and brain activation obtained by simultaneous EEG-fMRI during the resting state condition in 25 healthy right-handed adult volunteers. Using EEG-derived regressors, we demonstrated a substantial correlation of BOLD signal changes with linear and nonlinear features of EEG. We found the most significant positive correlation of fMRI signal with delta spectral power. Beta and alpha spectral features had no reliable effect on BOLD fluctuation. However, dynamic changes of alpha peak frequency exhibited a significant association with BOLD signal increase in right-hemisphere areas. Additionally, EEG dynamic complexity as measured by the HFD of the 2–20Hz EEG frequency range significantly correlated with the activation of cortical and subcortical limbic system areas. Our results indicate that both spectral features of EEG frequency bands and nonlinear dynamic properties of spontaneous EEG are strongly associated with fluctuations of the BOLD signal during the resting state condition.

In this volume we have collected papers based on the presentations given at the International Conference on Computer Simulations in Physics and beyond (CSP2015), held in Moscow, September 6-10, 2015. We hope that this volume will be helpful and scientifically interesting for readers.

The Conference was organized for the first time with the common efforts of the Moscow Institute for Electronics and Mathematics (MIEM) of the National Research University Higher School of Economics, the Landau Institute for Theoretical Physics, and the Science Center in Chernogolovka. The name of the Conference emphasizes the multidisciplinary nature of computational physics. Its methods are applied to the broad range of current research in science and society. The choice of venue was motivated by the multidisciplinary character of the MIEM. It is a former independent university, which has recently become the part of the National Research University Higher School of Economics.

Computer simulation, an active learning technique, is now one of the advanced pedagogical technologies. The use of simulation games in the educational process allows students to gain a firsthand understanding of the processes of real life. Public administration, public policy, and political science courses increasingly adopt simulation games in universities worldwide. Besides person-to-person simulation games, there are computer-based simulations in public administration education. Currently in Russia the use of computer-based simulation games in Master of Public Administration (MPA) curricula is quite limited. This paper focuses on computer-based simulation games for students of MPA programs. Our aim was to analyze outcomes of implementing such games in MPA curricula. We have done so by (1) developing three computer- based simulation games about allocating public finances, (2) testing the games in the learning process, and (3) conducting a posttest examination to evaluate the effect of simulation games on students’ knowledge of municipal finances. This study was conducted in the National Research University Higher School of Economics (HSE) and in the Russian Presidential Academy of National Economy and Public Administration (RANEPA) during the period September to December 2015, in Saint Petersburg, Russia. Two groups of students were randomly selected in each university and then randomly allocated either to the experimental or the control group. In control groups (n=12 in HSE, n=13 in RANEPA) students had traditional lectures. In experimental groups (n=12 in HSE, n=13 in RANEPA) students played three simulation games apart from traditional lectures. This exploratory research shows that the use of computer-based simulation games in MPA curricula can improve students’ outcomes by 38%. In general, the experimental groups had better performance on the posttest examination (figure 2). Students in the HSE experimental group had 27.5% better scores than students in the HSE control group. Students of the RANEPA experimental group had 38.0% better scores than students in the RANEPA control group. Research indicates that lecture-based courses are less effective than courses with more interactive approaches. Therefore, our study highlights the need to implement computer-based simulation games in MPA programs in Russian universities. Computer-based simulation games provide students with practical skills for their future careers.

Computer simulation of mechanical testing is used primarily for the correct interpretation of their results and is particularly relevant in cases, when the properties of the material during deformation are essentially nonlinear. For example: when we study mechanical properties of materials with high rate sensitivity. First of all it is superplastic titanium alloys. Superplastic materials exhibit the ability to severe plastic deformation without discontinuities if forming occurs in a narrow range of strain rates, specific to each alloy and temperature-dependent. In the study of superplastic materials, it’s necessary to maintain a constant rate of deformation of the sample. This is achieved by conducting an experiment with a special program loading, crosshead speed at which change during the experiment.

This issue contains works on nonlinear analysis represented on the 8th congress of the International Society for Analysis, its Applications, and Computation (ISAAC), Moscow, Russia, August 22--27, 2011.

The article discusses the utility of automated revenue management systems, designed for the needs of civil aviation. The analysis of revenue management systems in Russian airlines and Russian carrier position in the international air transportation market are provided. The need to use the automated revenue management system to increase profits of the operator is identified. A strategy of selling tickets, taking into account overbooking as revenue management strategy, allowing both to increase employment of passenger seats and reduce the loss of the carrier from possible no-show passengers to register, is considered. Creation of the simulator to assess the effectiveness of the commercial activities of the airline is proposed.

Computer simulations of electrostatic discharges (ESD) effect on high-power MOSFET-transistors with built-in protection have been carried out. It was found that the transistors with low gate-source capacitance are more sensitive to the ESD effect.The dependence between printed circuit board (PCB) capacity, causing breakdown of MOSFET-transistor gate dielectric, and ESD voltage was established. It is shown that for transistor haying low gate-source capacitance, the existence of the built-in protection does not prevent gate dielectric breakdown at electrostatic discharges. It is recommended to provide external ESD protection for high-power MOSFET-transistors with built-in protection having low gate-source capacitance, for example, having turned on the ESD protection diode in the electric circuit.

Conference covers both fundamental problems ofthe theory, and application to research of complex organizational and technical systems.

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.