In analogy to the representation of the standard probabilistic average as an expected value of a random variable, a geometric approach to aggregation is proposed. Several properties of such aggregation operators are investigated, and the relationship with distinguished classes of aggregation operators is discussed.

Geometrical concepts, including distance functions between observations , geometric variabilities and proximity functions, are used to develop some new aspects of multivariate analysis. These include the innuence of principal components in comparing populations, the detection of atypical observations in discrimination with mixed variables, and the construction of orthogonal expansions for a con...

The aim of this paper, we use Stein’s method and the w-function associated with the Yule random variable to obtain a non-uniform bound for the point metric of the Yule and geometric distributions. Three numerical examples are provided to illustrate the obtained result. AMS Subject Classification: 62E17, 60F05

Many real-world networks were found to be highly clustered, and contain a large amount of small cliques. We here investigate the number cliques any size k contained in geometric inhomogeneous random graph: scale-free network model containing geometry. The interplay between scale-freeness geometry ensures that connections are likely form either high-degree vertices, or close by vertices. At same...

The localization game is a two player combinatorial played on graph G=(V,E). cops choose set of vertices S1⊆V with |S1|=k. robber then chooses vertex v∈V whose location hidden from the cops, but learn distance between current position and in S1. If this information sufficient to locate robber, win immediately; otherwise another S2⊆V |S2|=k, may move neighboring vertex. new distances are present...