Measure of Synchronism of Multidimensional Chaotic Sequences Based on Their Symbolic Representation in a T-Alphabet

A new approach to analysis of the synchronization of chaotic oscillations in two (or more) coupled oscillators is described that makes it possible to reveal changes in the structure of attractors and detect the appearance of intermittency. The proposed method is based on a symbolic analysis developed previously in the velocity-curvature space of multidimensional sequences and maps. The method is tested by application to a Lorentz system. The results confirm the informativity of the analyzer and reveal specific features of changes in the structure of an attractor of the three-component test system.Comment: 6 pages, 3 figures, 1 table, Preprint version of article published in: Technical Physics Letters, 2012, Vol. 38, No. 9, pp. 804-80

Estimation of the TQ-complexity of chaotic sequences

A new approach is proposed to the quantitative estimation of the complexity of multidimensional discrete sequences in terms of the shapes of their trajectories in the extended space of states. This approach is based on the study of the structural properties of sequences and is suitable for estimating the complexity of both chaotic and stochastic sequences. It is constructed on the method, proposed earlier by the author, of symbolic CTQ-analysis of multidimensional discrete sequences and mappings. The algorithm proposed manipulates not only the frequency of occurrence of symbols, but also takes into account their sequence order. An example (financial time series) is given that demonstrates the application of the tools developed.Comment: 11 pages, 6 figures, 1 table, Paper 99 in Proceedings of the 1st IFAC Conference MICNON 201

Generalized synchronization of multidimensional chaotic systems in terms of symbolic CTQ-analysis

A new approach is proposed to the analysis of generalized synchronization of multidimensional chaotic systems. The approach is based on the symbolic analysis of discrete sequences in the basis of a finite T-alphabet. In fact, the symbols of the T-alphabet encode the shape (the geometric structure) of a trajectory of a dynamical system. Investigation of symbolic sequences allows one to diagnose various regimes of chaos synchronization, including generalized synchronization. The characteristics introduced allow one to detect and study the restructuring and intermittency behavior of attractors in systems (the time structure of synchronization). The measure of T-synchronization proposed is generalized without restrictions to complex ensembles of strongly nonstationary and nonidentical large-dimensional oscillators with arbitrary configuration and network (lattice) topology. The main features of the method are illustrated by an example.Comment: 13 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1505.0431

Recursive Tangential-Angular Operator as Analyzer of Synchronized Chaos

A method for the quantitative analysis of the degree and parameters of synchronization of the chaotic oscillations in two coupled oscillators is proposed, which makes it possible to reveal a change in the structure of attractors. The proposed method is tested on a model system of two unidirectionally coupled logistic maps. It is shown that the method is robust with respect to both the presence of a low-intensity noise and a nonlinear distortion of the analyzed signal. Specific features of a rearranged structure of the attractor of a driven subsystem in the example under consideration have been studied.Comment: 7 pages, 5 figures, An expanded and corrected version of article published in: Technical Physics Letters, 2011, Vol. 37, No. 8, pp. 784-78

Wormholes in the Braneworld

We discuss brane wormhole solution when classical brane action contains 4d curvature. The equations of motion for the cases with R=0 and $R\ne 0$ are obtained. Their numerical solutions corresponding to wormhole are found for specific boundary conditions

Analysis of the Time Structure of Synchronization in Multidimensional Chaotic Systems

A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be considered as methodologically incomplete.Comment: 13 pages, 6 figures, Preprint version of article published in: J. Exp. Theor. Phys., 2015, Vol. 120, No. 5, pp. 912-92

Comment on "Shallow donor states near a semiconductor-insulator-metal interface"

In a recent paper Hao et al. [Phys. Rev. B 80, 035329 (2009)] reported variational calculations of energy spectrum for shallow hydrogenic donor in the structure of semiconductor/insulator/metal with a new type of trial wave function. They also performed calculations for semiconductor/insulator system and found that their method gives energy values lower than those obtained by MacMillen and Landman [Phys. Rev. B 29, 4524 (1984)]. As follows from these results MacMillen and Landman have got much larger errors in energy values than they expected. However we confirm that the theoretical approach suggested by MacMillen and Landman gives rather accurate energy values for the system of hydrogenic donor near the interface between semiconductor and insulator.Comment: 2 pages, 2 table

The class of second order quasilinear equations: models, solutions and background of classification

The paper is concerned with the unsteady solutions to the model of mutually penetrating continua and quasilinear hyperbolic modification of the Burgers equation (QHMB). The studies were focused on the peculiar solutions of models in question. On the base of these models and their solutions, the ideas of second order quasilinear models classification were developed.Comment: 11 pages, 6 figure

On a phenomenology of the accelerated expansion with a varying ghost dark energy

Subject of our study it is the accelerated expansion of the large scale universe, where a varying ghost dark energy can take the role of the dark energy. The model of the varying ghost dark energy considered in this work it is a phenomenological modification of the ghost dark energy. Recently, three other phenomenological models of the varying ghost dark energy have been suggested and the model considered in this work will complete the logical chain of considered modifications. The best fit of theoretical results to the luminosity distance, has been used to obtain preliminary constraints on the parameters of the models. This does help us to reduce amount of discussion. On the other hand, detailed comparison of theoretical results with observational data has been left as a subject of another discussion elsewhere. Moreover, a look to considered models via $Om$ and statefinder hierarchy analysis is presented and discussed for different forms of interaction between the varying ghost dark energy and cold dark matter

Implementation of deep learning algorithm for automatic detection of brain tumors using intraoperative IR-thermal mapping data

The efficiency of deep machine learning for automatic delineation of tumor areas has been demonstrated for intraoperative neuronavigation using active IR-mapping with the use of the cold test. The proposed approach employs a matrix IR-imager to remotely register the space-time distribution of surface temperature pattern, which is determined by the dynamics of local cerebral blood flow. The advantages of this technique are non-invasiveness, zero risks for the health of patients and medical staff, low implementation and operational costs, ease and speed of use. Traditional IR-diagnostic technique has a crucial limitation - it involves a diagnostician who determines the boundaries of tumor areas, which gives rise to considerable uncertainty, which can lead to diagnosis errors that are difficult to control. The current study demonstrates that implementing deep learning algorithms allows to eliminate the explained drawback.Comment: 7 pages, 5 figures, 2 table