The combined effect of temperature and disorder on interlayer exchange coupling in magnetic multilayers

We study the combined effect of temperature and disorder in the spacer on the interlayer exchange coupling. The temperature dependence is treated on ab initio level. We employ the spin-polarized surface Green function technique within the tight-binding linear muffin-tin orbital method and the Lloyd formulation of the IEC. The integrals involving the Fermi-Dirac distribution are calculated using an efficient method based on representation of integrands by a sum of complex exponentials. Application is made to Co/Cu_{100-x}M_x/Co(001) trilayers (M=Zn, Au, and Ni) with varying thicknesses of the spacer.Comment: 5 pages, LaTeX, 1 figure. Submitted to Phil. Mag.

A statistical approach to persistent homology

Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying space. In this paper we take a statistical approach to this problem. We assume that the data is randomly sampled from an unknown probability distribution. We define two filtered complexes with which we can calculate the persistent homology of a probability distribution. Using statistical estimators for samples from certain families of distributions, we show that we can recover the persistent homology of the underlying distribution.Comment: 30 pages, 2 figures, minor changes, to appear in Homology, Homotopy and Application

Evaluation of the optical conductivity tensor in terms of contour integrations

For the case of finite life-time broadening the standard Kubo-formula for the optical conductivity tensor is rederived in terms of Green's functions by using contour integrations, whereby finite temperatures are accounted for by using the Fermi-Dirac distribution function. For zero life-time broadening, the present formalism is related to expressions well-known in the literature. Numerical aspects of how to calculate the corresponding contour integrals are also outlined.Comment: 8 pages, Latex + 2 figure (Encapsulated Postscript

Hamilton and the square root of minus one

Quaternions, objects consisting of a scalar and a vector, sound like a mysterious concept from the past. In the nineteenth century, the theory of quaternions was praised as one of the most brilliant achievements in mathematical physics. The originator of this theory, Hamilton, surely one of the greatest scientists in that area, spent about 18 years in discussing all kinds of algebraic and geometric properties of quaternions. His research was communicated to the Philosophical Magazine in three series of papers comprising a total of 29 contributions. In this commentary, these three series of papers are revisited concentrating primarily on the algebraic properties of quaternions

A systems biology approach to the evolution of plant–virus interactions

Omic approaches to the analysis of plant-virus interactions are becoming increasingly popular. These types of data, in combination with models of interaction networks, will aid in revealing not only host components that are important for the virus life cycle, but also general patterns about the way in which different viruses manipulate host regulation of gene expression for their own benefit and possible mechanisms by which viruses evade host defenses. Here, we review studies identifying host genes regulated by viruses and discuss how these genes integrate in host regulatory and interaction networks, with a particular focus on the physical properties of these networks.This work was supported by grants from the Spanish MICINN (BFU2009-06993) and Generalitat Valenciana (PROMETEO2010/019). GR is supported by a fellowship from Generalitat Valenciana (BFPI2007-160) and JC by a contract from MICINN (Grant TIN2006-12860).Peer reviewe

Real quadratic fields with class numbers divisible by n

In this note I prove that the class number of Q([radical sign][Delta](x)) is infinitely often divisible by n, where [Delta](x) = x2n + 4.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33975/1/0000247.pd