Derived Subgroups of Fixed Points in Profinite Groups

The main result of this paper is the following theorem. Let q be a prime, A an elementary abelian group of order q^3. Suppose that A acts as a coprime group of automorphisms on a profinite group G in such a manner that C_G(a)' is periodic for each nontrivial element a in A. Then G' is locally finite.Comment: To appear in Glasgow Mathematical Journal (2011). 11 page

The Anatomy of a Scientific Rumor

The announcement of the discovery of a Higgs boson-like particle at CERN will be remembered as one of the milestones of the scientific endeavor of the 21st century. In this paper we present a study of information spreading processes on Twitter before, during and after the announcement of the discovery of a new particle with the features of the elusive Higgs boson on 4th July 2012. We report evidence for non-trivial spatio-temporal patterns in user activities at individual and global level, such as tweeting, re-tweeting and replying to existing tweets. We provide a possible explanation for the observed time-varying dynamics of user activities during the spreading of this scientific "rumor". We model the information spreading in the corresponding network of individuals who posted a tweet related to the Higgs boson discovery. Finally, we show that we are able to reproduce the global behavior of about 500,000 individuals with remarkable accuracy.Comment: 11 pages, 8 figure

Modulated phases and devil's staircases in a layered mean-field version of the ANNNI model

We investigate the phase diagram of a spin-$1/2$ Ising model on a cubic lattice, with competing interactions between nearest and next-nearest neighbors along an axial direction, and fully connected spins on the sites of each perpendicular layer. The problem is formulated in terms of a set of noninteracting Ising chains in a position-dependent field. At low temperatures, as in the standard mean-feild version of the Axial-Next-Nearest-Neighbor Ising (ANNNI) model, there are many distinct spatially commensurate phases that spring from a multiphase point of infinitely degenerate ground states. As temperature increases, we confirm the existence of a branching mechanism associated with the onset of higher-order commensurate phases. We check that the ferromagnetic phase undergoes a first-order transition to the modulated phases. Depending on a parameter of competition, the wave number of the striped patterns locks in rational values, giving rise to a devil's staircase. We numerically calculate the Hausdorff dimension $D_{0}$ associated with these fractal structures, and show that $D_{0}$ increases with temperature but seems to reach a limiting value smaller than $D_{0}=1$.Comment: 17 pages, 6 figure

Partners and relatives. Articulating modernity and tradition in Portuguese large family firms

Large family enterprises are different from other kinds of large firms in Portugal. The formation of kinship relationships found in the social context of large family firms is also of a different nature than those found in other social groups. Both features are due to the overlapping of family and economic relations that characterises large family firms. Based on research developed among large Portuguese family firms, this article analyses changes in the succession for leadership positions in these organisations over the last 100 years. Although these wealth entrepreneurial families are strongly rooted on traditional social values (as they claim their aristocratic origin) they develop strong strategies to integrate modernity symbols and meritocratic criteria in the incorporation of relatives into the firm. I will argue that the articulation of family tradition with modern economic rationality is central to the survival of traditional large family firms in contemporary world economy.info:eu-repo/semantics/publishedVersio