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A network evolution with predicted tail and extremal indices of PageRank and the Max-Linear Model used as node influence indices in random graphs is considered. The tail index shows a heaviness of the distribution tail. The extremal index is a measure of clustering (or local dependence) of the stochastic process. The cluster implies a set of consecutive exceedances of the process over a sufficiently high threshold. Our recent results concerning sums and maxima of non-stationary random length sequences of regularly varying random variables are extended to random graphs. Starting with a set of connected stationary seed communities as a hot spot and ranking them with regard to their tail indices, the tail and extremal indices of new nodes that are appended to the network may be determined. This procedure allows us to predict a temporal network evolution in terms of tail and extremal indices. The extremal index determines limiting distributions of a maximum of the PageRank and the Max-Linear Model of newly attached nodes. The exposition is provided by algorithms and examples. To validate our theoretical results, our simulation and real data study concerning a linear preferential attachment as a tool for network growth are provided.

The Concrete Damage Model that is implemented in the LS-Dyna code is capable of simulating the behavior of plain concrete under complex static and dynamic loading conditions. However, the values for the numerous parameters, which are required as an input, are left for the user to provide. In this study the Concrete Damage Model was calibrated for a wide range of strong concretes, using triaxial-compression-test data that were obtained from the literature. In contrast, the adjustment of the parameters of the present model is provided as a function of the unconfined compressive strength of the concrete. Although, not enough validation has been done either in higher pressures or in actual tests, it is evident that the presently calibrated model shows better agreement with published test results than the model currently available in LS-Dyna.

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, which satisfy two mixing conditions. Several useful extremes of the sampled sequence like the kth largest value, clusters of exceedances over a threshold, and first hitting time of a large value 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.

Nonparametric analysis of univariate heavy-tailed data , Nonparametric analysis of univariate heavy-tailed data , کتابخانه دیجیتال جندی شاپور اهواز