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## Finite plateau in spectral gap of polychromatic constrained random networks

We consider the canonical ensemble of multilayered constrained Erdos-Renyi networks (CERN) and regular random graphs (RRG), where each layer represents graph vertices painted in a specific color. We study the critical behavior in such networks under changing the fugacity, µ, which controls the number of monochromatic triads of nodes. The behavior of considered systems is investigated via the spectral properties of the adjacency and Laplacian matrices of corresponding networks. For some wide region of µ we find the formation of a finite plateau in the number of the intercolor links, which exactly matches the finite plateau for the algebraic connectivity of the network (the value of the first non-vanishing eigenvalue of the Laplacian matrix, λ2). We claim that at the plateau the restoring of the spontaneously broken Z2 symmetry by the mechanism of modes collectivization in clusters of different colors occurs. The phenomena of a finite plateau formation holds for the polychromatic (multilayer) networks with M > 2 colors.

The 11th International Conference on Security and its Applications (CNSA 2018) was held in Zurich, Switzerland, during January 02~03, 2018. The 5th International Conference on Data Mining and Database (DMDB 2018) and The 5th International Conference on Artificial Intelligence and Applications (AIAP 2018) was collocated with The 11th International Conference on Security and its Applications (CNSA 2018). The conferences attracted many local and international delegates, presenting a balanced mixture of intellect from the East and from the West. The goal of this conference series is to bring together researchers and practitioners from academia and industry to focus on understanding computer science and information technology and to establish new collaborations in these areas. Authors are invited to contribute to the conference by submitting articles that illustrate research results, projects, survey work and industrial experiences describing significant advances in all areas of computer science and information technology.

In this chapter we attempt to briefly describe a history of massive networks, their place in modern life, and discuss open problems related to them. We start with giving a historical overview indicating the most influential milestones in the development of networks. Then we consider how real-life massive datasets can be represented in terms of networks describing some examples and summarizing properties of such networks. We also discuss cases of modeling real-life massive networks. In addition, we give some examples of how to optimize in massive networks and in which areas we can apply these techniques. We conclude by discussing open problems of massive networks.

We study the planar matching problem, defined by a symmetric random matrix with independent identically distributed entries, taking values 0 and 1. We show that the existence of a perfect planar matching structure is possible only above a certain critical density of allowed contacts, $p_{c}$. This problem has an important application for the prediction of the optimal folding of RNA-type polymers. Using an alternative formulation of the problem in terms of Dyck paths and a matrix model of planar contact structures, we provide an analytical estimation for the value of the transition point, $p_{c}$, in the thermodynamic limit. This estimation is close to the critical value, $p_{c}\approx 0.38$, obtained in numerical simulations based on an exact dynamic-programming algorithm. We characterize the corresponding critical behavior of the model and discuss the relation of the perfect-imperfect matching transition to the known molten-glass transition in the context of random RNA secondary structure's formation. In particular, we provide strong evidence supporting the conjecture that the molten-glass transition at $T=0$ occurs at $p_{c}$

The paper investigates the process of evolutionary transformation of cooperation and integration modes of industrial and construction enterprises in St.-Petersburg. The period of research (1995-2015) covered three crises in the Russian economy: the crisis after the default of 1998-1999, the global financial crisis of 2008-2009, and the current crisis of 2014-2015. The results obtained enable us to analyze the evolution of the intellectual capital management system in networks, as well as the evolution of networks themselves during changes in the business environment. The network form of integration was chosen as the main objet of this research. The paper is aimed at identifying the path of knowledge management development in different types of networks. One of the peculiarities of the network form of integration is the high level of independence of the network participants that interact with each other. Key issues in this cooperation would be the following: How to organize an effective transfer of knowledge and technologies within a network? How to find a balance between open systems of innovation and the protection of the intellectual property of network participants? How to evaluate the intellectual capital of a network? Is it necessary to make an assessment for each participant separately? Should one take into account synergies that increase the value of the intellectual capital because of the network participants’ interaction and knowledge sharing? How to increase competitiveness of each company and of the whole network by the effective use of the intellectual capital? How to measure the impact of open innovations on the intellectual capital of the companies interacting within a network? Thus, it is important to reveal how knowledge management system is developing within a network of inter-related enterprises. On the base of interviews of top-managers of companies in industrial and construction companies there were identified five different types of networks and knowledge management systems within these types. It is demonstrated how the knowledge management model is growing and becoming mature from the amorphous type of network cooperation to the integrated type.

Abstract — this paper presents simulation system TriadNS. This simulation system is dedicated for computer networks design and analyses. Nowadays new types of computer network exist: SDN (software-defined networks) and SON (self-organizing networks). Authors discusses routing algorithm SBARC and consider the ability of simulation system TriadNS to simulate and to analyze characteristics of this algorithm, so one may conclude that TriadNS is applicable for a design of new types of computer networks.

The article considers some paradoxical properties of network structures which are studied in the modern networks science; and some conclusions for social cognition, effective construction of social and communication environments, management and forecasting are drawn. In this connection, such a phenomenon of communication and organization of social life as intersubjectivity is discussed. The concept of enactivism developed in the modern cognitive science and in the nonclassical epistemology is involved. It is shown that interactivity in social networks is a) dynamic process, b) interaction and coordination of two or more bodily organized cognitive subjects, c) the production of meanings in the mutual play of interacting subjects, the so-called partisipational production of meanings.

The collection of articles presents the materials of the 15th "Bosporan phenomenon", which is an international scientific conference devoted to the comparative analysis of the Bosporan Kingdom and its relations with other states of the ancient world and Greek cities-colonies of the Northern black sea region, to the identification of common and specific features in its state structure, historical environment, evolution, social and political life, material and spiritual culture. The publication is intended for professionals and a wide range of readers interested in the problems of ancient history.

In this work, we explore the properties of antiferromagnetic cycloid and the phase transitions between commensurate and incommensurate magnetic states in epitaxial BiFeO3 film. Additional magnetic anisotropy induced by strain effects in the films allocates cycloids with the definite directions of spin rotation. Peculiar feature of the cycloids propagating in the films whose symmetry is different from the single crystals is the orientation of spin rotational plane that does not contain electric polarization in contrast with the bulk materials. We construct a diagram of phase transitions induced by magnetic field applied along normal to the surface and show considerable decrease of the strength of magnetic field destroying cycloid in films compared with the bulk.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

By using superconducting quantum interference device (SQUID) magnetometry, we investigated anisotropic high-field (H less than or similar to 7T) low-temperature (10 K) magnetization response of inhomogeneous nanoisland FeNi films grown by rf sputtering deposition on Sitall (TiO2) glass substrates. In the grown FeNi films, the FeNi layer nominal thickness varied from 0.6 to 2.5 nm, across the percolation transition at the d(c) similar or equal to 1.8 nm. We discovered that, beyond conventional spin-magnetism of Fe21Ni79 permalloy, the extracted out-of-plane magnetization response of the nanoisland FeNi films is not saturated in the range of investigated magnetic fields and exhibits paramagnetic-like behavior. We found that the anomalous out-of-plane magnetization response exhibits an escalating slope with increase in the nominal film thickness from 0.6 to 1.1 nm, however, it decreases with further increase in the film thickness, and then practically vanishes on approaching the FeNi film percolation threshold. At the same time, the in-plane response demonstrates saturation behavior above 1.5-2T, competing with anomalously large diamagnetic-like response, which becomes pronounced at high magnetic fields. It is possible that the supported-metal interaction leads to the creation of a thin charge-transfer (CT) layer and a Schottky barrier at the FeNi film/Sitall (TiO2) interface. Then, in the system with nanoscale circular domains, the observed anomalous paramagnetic-like magnetization response can be associated with a large orbital moment of the localized electrons. In addition, the inhomogeneous nanoisland FeNi films can possess spontaneous ordering of toroidal moments, which can be either of orbital or spin origin. The system with toroidal inhomogeneity can lead to anomalously strong diamagnetic-like response. The observed magnetization response is determined by the interplay between the paramagnetic-and diamagnetic-like contributions.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

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.