A computable estimate of the readiness coefficient for a standard binary-state system is established in the case where both working and repair time distributions possess heavy tails.

The book is dedicated to mathematical models of mob control with threshold (conformity) collective decision-making of the agents. Based on the analysis results of the interconnection between the micro- and macromodels of active network structures, the static (deterministic, stochastic and game-theoretic) and dynamic (discrete- and continuous-time) models of mob control are considered. Much attention is given to models of informational confrontation. Many results are applicable not only to mob control problems, but also to control problems arising in social groups, online social networks, etc. The book is intended to the researchers and practitioners, as well as the undergraduate and postgraduate students, doctoral candidates specializing in the field of collective behavior modeling.

We consider a number of graph kernels and proximity measures including commute-time kernel, regularized Laplacian kernel, heat kernel, exponential diffusion kernel (also called “communicability”), etc., and the corresponding distances as applied to clustering nodes in random graphs and several well-known datasets. The model of generating random graphs involves edge probabilities for the pairs of nodes that belong to the same class or different predefined classes of nodes. It turns out that in most cases, logarithmic measures (i.e., measures resulting after taking logarithm of the proximities) perform better while distinguishing underlying classes than the “plain” measures. A comparison in terms of reject curves of interclass and intra-class distances confirms this conclusion. A similar conclusion can be made for several well-known datasets. A possible origin of this effect is that most kernels have a multiplicative nature, while the nature of distances used in cluster algorithms is an additive one (cf. the triangle inequality). The logarithmic transformation is a tool to transform the first nature to the second one. Moreover, some distances corresponding to the logarithmic measures possess ameaningful cutpoint additivity property. In our experiments, the leader is usually the logarithmic Communicability measure. However, we indicate some more complicated cases in which other measures, typically, Communicability and plain Walk, can be the winners.

We consider a distributed Radio Direction Finding System (RDFS) and the structure of its hardware. A classical diagnostic model of the distributed RDFS according to the binary criterion is presented, which includes diagnostic graphs and a set of tests. We propose a theoretical basis for diagnosing of the distributed RDFS according to the n-dimensional criterion. An example of implementation of the diagnostic approach to the distributed RDFS for states “failure”, “deterioration”, “normal” is presented.