Modeling and Analysis of Affiliation Networks with Subsumption

An affiliation (or two-mode) network is an abstraction commonly used for representing systems with group interactions. It consists of a set of nodes and a set of their groupings called affiliations. We introduce the notion of affiliation network with subsumption, in which no affiliation can be a subset of another. A network with this property can be modeled by an abstract simplicial complex whose facets are the affiliations of the network. We introduce a new model for generating affiliation networks with and without subsumption (represented as simplicial complexes and hypergraphs, respectively). In this model, at each iteration, a constant number of affiliations is sampled uniformly at random and then nodes are selected from these affiliations with a fixed probability. This results in an implicit preferential attachment growth and a power-law in the degree distribution (where degree is defined as the number of affiliations a node belongs to). We develop a theoretical model of this network generation procedure, prove that the degree distribution in the hypergraph case is governed by the Yule-Simon distribution, then find the exponent of its power-law tail. Similarly, we show that in the simplicial complex case, the degree distribution also has a power-law tail, and we develop a numerical technique for computing its exponent. We show that the affiliation size distributions can be concisely described via their generating functions. We develop two numerical techniques for solving the resulting functional equations, find the generating functions and compute their PMFs. Furthermore, we show that at the limit the affiliation size distribution can be approximated by a shifted Poisson or related distribution. We study the process of a giant component formation in the network, develop a theoretical estimate of the critical threshold for one of the model parameters and compare it with experiments. For a qualitative analysis of our network generation procedure, we study the average pairwise distance in the network, its assortativity, and clustering coefficient, and use Q-analysis methods to compare our networks with other synthetic networks and real-world networks

MEANING-OF-LIFE ORIENTATIONS AND REPRESENTATIONS OF MODERN YOUNG PEOPLE CONCERNING THEIR SELF-REALIZATION IN SOCIAL-CULTURAL SPACE OF PSKOV REGION

The article raised an important issue of opportunities modern young people in the framework of socio-cultural conditions of the region - the Pskov region. Presents a program of experimental research and its results. Examines the relationship between meaning-of-life and value orientations of graduates of various educational institutions: schools, colleges and the University and attitude toward the past, present and future of the Pskov region and opportunities. The comparative analysis of different groups of graduates in the studied characteristics was done.

Adaptive observer for a LTV system with partially unknown state matrix and delayed measurements

Problem of adaptive state observer synthesis for linear time-varying (LTV) system with unknown time-varying parameter and delayed output measurements is considered. State observation problem has attracted the attention of many researchers $[4]$. In this paper the results proposed in the $[2]$, $[9]$, $[10]$ are developed. It is supposed that the state matrix can be represented as sum of known and unknown parts. Output vector is measured with known constant delay. An adaptive identification algorithm which reconstructs unknown state and unknown time varying parameter is proposed.Comment: 6 pages, 10 figure

Generalized Parameter Estimation-based Observers: Application to Power Systems and Chemical-Biological Reactors

In this paper we propose a new state observer design technique for nonlinear systems. It consists of an extension of the recently introduced parameter estimation-based observer, which is applicable for systems verifying a particular algebraic constraint. In contrast to the previous observer, the new one avoids the need of implementing an open loop integration that may stymie its practical application. We give two versions of this observer, one that ensures asymptotic convergence and the second one that achieves convergence in finite time. In both cases, the required excitation conditions are strictly weaker than the classical persistent of excitation assumption. It is shown that the proposed technique is applicable to the practically important examples of multimachine power systems and chemical-biological reactors.Comment: 13 pages, 8 figure

РЕЦЕНЗИЯ НА СТАТЬЮ И.Л. ГУФЕЛЬДА, М.И. МАТВЕЕВОЙ И О.Н. НОВОСЕЛОВА «ПОЧЕМУ МЫ НЕ МОЖЕМ ОСУЩЕСТВИТЬ ПРОГНОЗ СИЛЬНЫХ КОРОВЫХ ЗЕМЛЕТРЯСЕНИЙ»

In the review, directions of future studies of the seismic process are considered. The priority shall be given to studies of the barrier effect of degassing and research of processes that take place in marginal structures. A scenario of preparation of the seismic process and associated events is described with regard to uncertainties in development of critical seismotectonic situations.В отзыве рассматриваются направления дальнейших исследований сейсмического процесса, в которых на первый план выдвигаются работы по изучению барьерного эффекта дегазации, а также процессов в граничных структурах. Представлен сценарий подготовки сейсмического процесса и сопутствующих явлений с учетом неопределенности развития критических сейсмотектонических ситуаций

О СТАТЬЕ И.Л. ГУФЕЛЬДА «ГЕОЛОГИЧЕСКИЕ СЛЕДСТВИЯ АМОРФИЗАЦИИ ЛИТОСФЕРЫ И ВЕРХНЕЙ МАНТИИ, ВЫЗВАННЫЕ ВОДОРОДНОЙ ДЕГАЗАЦИЕЙ»

The commentary discusses possible directions for further research on the complex of issues arising in the analysis of the interaction of ascending hydrogen flows with the solid phase of the lithosphere and upper mantle.В комментарии рассматриваются возможные направления дальнейших исследований по комплексу вопросов, возникающих при анализе процессов взаимодействия восходящих водородных потоков с твердой фазой литосферы и верхней мантии