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## Efficient algorithms for the recognition of topologically conjugate gradient-like diffeomorhisms

It is well known that the topological classification of structurally stable flows on surfaces as well as the topological classification of some multidimensional gradient-like systems can be reduced to a combinatorial problem of distinguishing graphs up to isomorphism. The isomorphism problem of general graphs obviously can be solved by a standard enumeration

algorithm. However, an efficient algorithm (i. e., polynomial in the number of vertices) has not yet been developed for it, and the problem has not been proved to be intractable (i. e., NP-complete). We give polynomial-time algorithms for recognition of the corresponding graphs for two gradient-like systems. Moreover, we present efficient algorithms for determining the

orientability and the genus of the ambient surface. This result, in particular, sheds light on the classification of configurations that arise from simple, point-source potential-field models in efforts to determine the nature of the quiet-Sun magnetic field.

The contribution of electron–phonon scattering to conductivity of a quantum cylinder in a lon-gitudinal magnetic field has been studied. It has been shown that the conductivity of the nanotube undergoes Aharonov–Bohm oscillations with variations in the magnetic flux through the nanotube cross section. The formulas describing the temperature dependence of the resistance of the nanostructure both in the case of an isotropic phonon spectrum and with allowance for the effects of phonon confinement have been obtained in the analytical form.

In quiet low-latitude Earth's ionosphere, a rather developed current system that is responsible for the S_{q} magnetic-field variations is formed in quiet sunny days under the action of tidal streams. The density of the corresponding currents is maximal at the equatorial latitudes in the midday hours, where the so-called equatorial current jet is formed. In this work, we discuss the nature of the equatorial current jet. The original part of this paper is dedicated to the study of the value of its response to external effects. First of all, it is related to estimating the possibility of using the equatorial current jet for generating the low-frequency electromagnetic signals during periodic heating of the ionosphere by the heating-facility radiation. The equatorial current jet can also produce electrodynamic response to the natural atmospheric processes, e.g., an acoustic-gravitational wave.

This book presents open optimization problems in graph theory and networks. Each chapter reflects developments in theory and applications based on Gregory Gutin’s fundamental contributions to advanced methods and techniques in combinatorial optimization.

Researchers, students, and engineers in computer science, big data, applied mathematics, operations research, algorithm design, artificial intelligence, software engineering, data analysis, industrial and systems engineering will benefit from the state-of-the-art results presented in modern graph theory and its applications to the design of efficient algorithms for optimization problems.

Topics covered in this work include:

· Algorithmic aspects of problems with disjoint cycles in graphs

· Graphs where maximal cliques and stable sets intersect

· The maximum independent set problem with special classes

· A general technique for heuristic algorithms for optimization problems

· The network design problem with cut constraints

· Algorithms for computing the frustration index of a signed graph

· A heuristic approach for studying the patrol problem on a graph

· Minimum possible sum and product of the proper connection number

· Structural and algorithmic results on branchings in digraphs

· Improved upper bounds for Korkel--Ghosh benchmark SPLP instances

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.

The review is devoted to the presentation of results, including recently obtained by the authors, on the topological classification of Morse-Smale systems and the topology of ambient manifolds.

A form for an unbiased estimate of the coefficient of determination of a linear regression model is obtained. It is calculated by using a sample from a multivariate normal distribution. This estimate is proposed as an alternative criterion for a choice of regression factors.