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The nonparametric estimation of the probability density function (pdf) requires smoothing parameters like bandwidths of kernel estimates. We consider the so-called discrepancy method proposed in \cite{Markovich:book}, \cite{Vapnik} as a data-driven smoothing tool alternative to cross-validation. This is based on the using of the von Mises-Smirnov's (M-S) and the Kolmogorov-Smirnov's (K-S) nonparametric statistics as measures in the space of cumulative distribution functions (cdfs). The unknown smoothing parameter is found as a solution of the discrepancy equation. On its left-hand side stands the measure between the empirical cdf and the nonparametric estimate of the cdf. The latter is obtained as a corresponding integral of the pdf estimator. The right-hand side is equal to a quantile of the asymptotic distribution of the M-S or K-S statistic. The discrepancy method considered earlier for light-tailed pdfs is investigated now for heavy-tailed pdfs.

This paper designs an allotment mechanism for a limited amount of an infinitely divisible good (resource) among a finite number of agents under transferable utility. The mechanism is efficient in the sense of total agents’ utility maximization. As a solution, we introduce an adaptation of the Groves–Ledyard “quadratic government” that was initially suggested for the problem of public good.

The paper is concerned with a controllable multiple queuing system (QS) where control with a constant time step reduces to connecting spare service devices or to disconnection of main service devices. The maximal average profit from serving the demands in a multi-step planning period is taken to be the criterion of the QS operation optimality. Two models are considered. In first one the QS is assumed to have a simple demands arrival flow at a random rate that varies with homogeneous Markov chain. It is assumed that it takes one step for a stationary mode to set in QS. The second model does not assume a stationary mode but the simple input flow rate is assumed to vary with the specified time function. For both models algorithms are obtained that determine the optimal switching strategies.

Probabilistic aspects of caching are considered. The caching serves to keep popular contents inside a memory unit called 'cache' to be able to access them quickly. Using extreme value theory we propose a caching strategy called Cluster Caching Rule driven by content popularity that may change in time. A non-Poisson request arrival process is used when requests are statistically correlated. The idea of the new approach is to locate in cache only contents whose popularity exceeds a sufficiently large threshold. Due to dependence and possible heavy-tailed distribution of inter-requests and inter-arrival times of documents, the popularity process builds clusters of exceedances. The cluster and inter-cluster sizes are geometrically distributed as derived in Markovich (2014). We use it to calculate means of the cache utilization and occupancy. We escape assumptions like a constant size of content and a Poisson request process that are typical in the literature.

Статья содержит дополнения и улучшения к уже опубликованной статье автора "MODELING CLUSTERS OF EXTREME VALUES".

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This book demonstrates how to apply modern approaches to complex system control in practical applications involving knowledge-based systems. The dimensions of knowledge-based systems are extended by incorporating new perspectives from control theory, multimodal systems and simulation methods. The book is divided into three parts: theory, production system and information system applications. One of its main focuses is on an agent-based approach to complex system analysis. Moreover, specialised forms of knowledge-based systems (like e-learning, social network, and production systems) are introduced with a new formal approach to knowledge system modelling. The book, which offers a valuable resource for researchers engaged in complex system analysis, is the result of a unique cooperation between scientists from applied computer science (mainly from Poland) and leading system control theory researchers from the Russian Academy of Sciences’ Trapeznikov Institute of Control Sciences.

We explore the dependence structure in the sampled sequence of complex networks. We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like node degrees, number of followers or income of the nodes in Online Social Networks etc, which satisfy two mixing conditions. Several useful extremes of the sampled sequence like $k$th largest value, clusters of exceedances over a threshold, first hitting time of a large value etc are investigated. We abstract the dependence and the statistics of extremes into a single parameter that appears in Extreme Value Theory, called extremal index (EI). In this work, we derive this parameter analytically and also estimate it empirically. We propose the use of EI as a parameter to compare different sampling procedures. As a specific example, degree correlations between neighboring nodes are studied in detail with three prominent random walks as sampling techniques.

The term “pattern” refers to a combination of values of some features such that objects with these feature values significantly differ from other objects. This concept is a useful tool for the analysis of behavior of objects in both statics and dynamics. If the panel data describing the functioning of objects in time is available, we can analyze pattern changing behavior of the objects and identify either well adapted to the environment objects or objects with unusual and alarming behavior.In this paper we apply static and dynamic pattern analysis to the analysis of innovative development of the Russian regions in the long run and obtain a classification of regions by the similarity of the internal structure of these indicators and groups of regions carrying out similar strategies.

In many applications it is important to evaluate the impact of clusters of observations caused by the dependence and heaviness of tails in time series. We consider a stationary sequence of random variables $\{R_n\}_{n\ge 1}$ with marginal cumulative distribution function $F(x)$ and the extremal index $\theta\in[0,1]$. The clusters contain consecutive exceedances of the time series over a threshold $u$ separated by return intervals with consecutive non-exceedances. \\ We derive geometric forms of asymptotically equal distributions of the normalized cluster and inter-cluster sizes that depend on $\theta$. The inter-cluster size determines the number $T_1(u)$ of inter-arrival times between observations of the process $R_t$ arising between two consecutive clusters. The cluster size is equal to the number $T_2(u)$ of inter-arrival times within clusters. The inferences are valid when $u$ is taken as a sufficiently high quantile of the process $\{R_n\}$. The derived geometric models allow us to obtain the asymptotically equal means of $T_1(u)$ and $T_2(u)$ and other indices of clusters.