Identity has remained a popular concept for many decades, being widely used in scientific research. This reflects not only the importance of phenomena standing behind this notion, but also wide and deep changes accompanying transition societies from industrial to post-industrial, late modern, post-modern, network or information society. Regardless disputes about nature new era, researchers agre...

The aim of this paper is to study continuum models for surface diffusion taking into account free adatoms on the surface, which is of particular importance in the (self-assembled) growth of nanostructures. The extended model yields a coupled system of parabolic differential equations for the surface morphology and the adatom density, involving a cross-diffusion structure. We investigate two dif...

We show that it is possible, for every machine universal for Kolmogorov complexity, to enumerate the lexicographically least description of a length n string in O(n) attempts. In contrast to this positive result for strings, we find that, in any Kolmogorov numbering, no enumerator of nontrivial size can generate a list containing the minimal index of a given partial-computable function. One can...

In this paper new methodologies for clustering and dimensionality reduction of large data sets are illustrated using both a least-squares and maximum likelihood approach. The methodologies are described by both real applications and Monte Carlo simulations.