In this paper, we deal with the fundamental concepts and properties of ergodicity coefficients in a hierarchical sense by making use of partition. Moreover, we establish a hierarchial Hajnal’s inequality improving some previous results.

By taking the governing measure of a Dirichlet process as essentially the realization of a Dirichlet process itself, a hierarchical Dirichlet process emerges. This distribution enables the Bayesian treatment of two level hierarchical random effects models, with results paralleling those of Ferguson (1973).

An overview of theoretical and computational methods in the rapidly advancing field of Nanomechanics and Micromechanics of materials is given. This overview emphasizes the Multiscale Modelling of Materials (MMM) approach, which relies on a reduction of the degrees of freedom at natural length scales. Two main challenges are identified in the MMM approach: (i) the computational complexity of ful...

For the past decade, the need of multimedia mining has increased tremendously, especially in image data due to inexpensive digital technologies and fast mounting of image data. In this paper, we, first, show an algorithm, SpIBag (Spatial Item Bag Mining), which discovers frequent spatial patterns in images. Due to the properties of image data, SpIBag considers a bag of items together with a spa...

A compressed quad tree based replacement for approximate voronoi diagrams with near linear complexity using hierarchial clustering and prioritized point location among balls and with applications for improved approximate nearest neighbour search using point location among equal balls, fat triangulations of proximity diagrams in two and higher dimensions and for fast approximate proximity search.