In this paper, we develop a family of data clustering algorithms that combine the strengths of existing spectral approaches to clustering with various desirable properties of fuzzy methods. In particular, we show that the developed method “Fuzzy-RW,” outperforms other frequently used...

Fitness landscapes are an important concept in molecular evolution since evolutionary adaptation as well as {\it in vitro} selection of biomolecules can be viewed as a hill-climbing-like process. Global features of landscapes can be described by statistical measures such as correlation functions...

According to the Darwinian theory of evolution, adaptation results from spontaneously generated genetic variation and natural selection. Mathematical models of this process can be seen as describing a dynamics on an algebraic structure which in turn is defined by the processes which generate...

In this paper we prove a Faber-Krahn-type inequality for regular trees and give a complete characterization of extremal trees. The main tools are rearrangements and perturbation of regular trees.

The current Special Issue brought out the newest trends in Econophysics that have made use of the most recent available tools, such as Big Data. The emphasis of the reprint is on deciphering the effects of current world events, such as the repercussions of the recent war conflicts, the oil and...

This paper revisits the methodology of Stein (1975, 1986) for estimating a covariance matrix in the setting where the number of variables can be of the same magnitude as the sample size. Stein proposed to keep the eigenvectors of the sample covariance matrix but to shrink the eigenvalues. By...