A hypercyclic finite rank perturbation of a unitary operator

A unitary operator $V$ and a rank $2$ operator $R$ acting on a Hilbert space \H are constructed such that $V+R$ is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can be supercyclic.Comment: published in Mathematische Annale

Applicability of ecological evaluation tools in estuarine ecosystems: the case of the lower Mondego estuary (Portugal)

Abstract In accordance with the Water Framework Directive guidelines (WFD, 2000, European Communities Official Journal L327 2000/60/EC), classification schemes and ecological evaluation tools (based on benthic invertebrate fauna data sets from 1990 to 2002) were applied in the lower Mondego estuary. Two distinct scenarios could be tested due to the implementation of mitigation practices in 1999, following a long eutrophication process, which started by the early 1980s. Some discrepancies in the results were found by the application of the different indices. The AMBI index (accounting for taxonomic composition) and the ABC method (accounting for abundance and biomass k-dominance patterns) classifications often disagreed with those based on species diversity (Margalef and Shannon-Wiener). The ambiguous results made the classification a complex task to achieve, contrary to the Directive’s objective of maintaining it simple and clear. Our results suggest the necessity of adjusting some of the indices and their ranges to estuarine characteristics, namely to account the typical dominance and abundance of some particular species. These aspects are not taken into consideration by some of the indices proposed, which are more adapted to typical marine conditions. Based on our results, these widely applied indices might still improve their efficiency in estuarine systems allowing their use in the resembling types already established within the new Directive agenda

Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics

The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain requirements of the theory. The discussion of such limitations arising from the so-called superselection rules is the main purpose of this paper. Some of their principal consequences are also discussed. The univalence, mass and particle number superselection rules of non-relativistic quantum mechanics are also derived using rather simple methods.Comment: 22 pages, no figure

Dynamic Critical Behavior of the Chayes-Machta Algorithm for the Random-Cluster Model. I. Two Dimensions

We study, via Monte Carlo simulation, the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts ferromagnet to non-integer q \ge 1. We consider spatial dimension d=2 and 1.25 \le q \le 4 in steps of 0.25, on lattices up to 1024^2, and obtain estimates for the dynamic critical exponent z_{CM}. We present evidence that when 1 \le q \lesssim 1.95 the Ossola-Sokal conjecture z_{CM} \ge \beta/\nu is violated, though we also present plausible fits compatible with this conjecture. We show that the Li-Sokal bound z_{CM} \ge \alpha/\nu is close to being sharp over the entire range 1 \le q \le 4, but is probably non-sharp by a power. As a byproduct of our work, we also obtain evidence concerning the corrections to scaling in static observables.Comment: LaTeX2e, 75 pages including 26 Postscript figure

Inflation, Renormalization, and CMB Anisotropies

In single-field, slow-roll inflationary models, scalar and tensorial (Gaussian) perturbations are both characterized by a zero mean and a non-zero variance. In position space, the corresponding variance of those fields diverges in the ultraviolet. The requirement of a finite variance in position space forces its regularization via quantum field renormalization in an expanding universe. This has an important impact on the predicted scalar and tensorial power spectra for wavelengths that today are at observable scales. In particular, we find a non-trivial change in the consistency condition that relates the tensor-to-scalar ratio "r" to the spectral indices. For instance, an exact scale-invariant tensorial power spectrum, n_t=0, is now compatible with a non-zero ratio r= 0.12 +/- 0.06, which is forbidden by the standard prediction (r=-8n_t). Forthcoming observations of the influence of relic gravitational waves on the CMB will offer a non-trivial test of the new predictions.Comment: 4 pages, jpconf.cls, to appear in the Proceedings of Spanish Relativity Meeting 2009 (ERE 09), Bilbao (Spain

Dynamic and static properties of the invaded cluster algorithm

Simulations of the two-dimensional Ising and 3-state Potts models at their critical points are performed using the invaded cluster (IC) algorithm. It is argued that observables measured on a sub-lattice of size l should exhibit a crossover to Swendsen-Wang (SW) behavior for l sufficiently less than the lattice size L, and a scaling form is proposed to describe the crossover phenomenon. It is found that the energy autocorrelation time tau(l,L) for an l*l sub-lattice attains a maximum in the crossover region, and a dynamic exponent z for the IC algorithm is defined according to tau_max ~ L^z. Simulation results for the 3-state model yield z=.346(.002) which is smaller than values of the dynamic exponent found for the SW and Wolff algorithms and also less than the Li-Sokal bound. The results are less conclusive for the Ising model, but it appears that z<.21 and possibly that tau_max ~ log L so that z=0 -- similar to previous results for the SW and Wolff algorithms.Comment: 21 pages with 12 figure

Mitochondrial echoes of first settlement and genetic continuity in El Salvador

Background: From Paleo-Indian times to recent historical episodes, the Mesoamerican isthmus played an important role in the distribution and patterns of variability all around the double American continent. However, the amount of genetic information currently available on Central American continental populations is very scarce. In order to shed light on the role of Mesoamerica in the peopling of the New World, the present study focuses on the analysis of the mtDNA variation in a population sample from El Salvador. Methodology/Principal Findings: We have carried out DNA sequencing of the entire control region of the mitochondrial DNA (mtDNA) genome in 90 individuals from El Salvador. We have also compiled more than 3,985 control region profiles from the public domain and the literature in order to carry out inter-population comparisons. The results reveal a predominant Native American component in this region: by far, the most prevalent mtDNA haplogroup in this country (at ~90%) is A2, in contrast with other North, Meso- and South American populations. Haplogroup A2 shows a star-like phylogeny and is very diverse with a substantial proportion of mtDNAs (45%; sequence range 16090–16365) still unobserved in other American populations. Two different Bayesian approaches used to estimate admixture proportions in El Salvador shows that the majority of the mtDNAs observed come from North America. A preliminary founder analysis indicates that the settlement of El Salvador occurred about 13,400±5,200 Y.B.P.. The founder age of A2 in El Salvador is close to the overall age of A2 in America, which suggests that the colonization of this region occurred within a few thousand years of the initial expansion into the Americas. Conclusions/Significance: As a whole, the results are compatible with the hypothesis that today's A2 variability in El Salvador represents to a large extent the indigenous component of the region. Concordant with this hypothesis is also the observation of a very limited contribution from European and African women (~5%). This implies that the Atlantic slave trade had a very small demographic impact in El Salvador in contrast to its transformation of the gene pool in neighbouring populations from the Caribbean facade

Caracterización de genes implicados en la biosíntesis de estreptolidigina

La estreptolidigina es un antibiótico perteneciente a la familia de los ácidos tetrámicos (Schobert y Schlenk, 2008) producido por Streptomyces lydicus. Estudios biosintéticos usando precursores marcados han demostrado la incorporación de propionato, acetato, metionina y ácido glutámico (probablemente en forma de metil-aspártico) en la formación de la estructura principal del antibiótico (Chen y Harrison, 2004; Chen et al., 2006). Estos estudios apuntan a un sistema híbrido policétido sintasa-sintetasa de péptidos no ribosomales para la biosíntesis de estreptolidigina, lo cual se ha confirmado con el reciente aislamiento y caracterización del agrupamiento génico responsable de la biosíntesis del antibiótico (Ola- no et al., 2009). Dentro de la ruta se han identificado genes encargados de la regulación y secreción del antibiótico y otros genes que codifican proteínas involucradas en el aporte y modificación final del precursor aminoacídico. En esta comunicación se presentan los experimentos de inactivación y expresión de los genes slgZ y slgM, para demostrar o comprobar su participación en la biosíntesis del antibiótico estreptolidigina