Conditional probabilities with Dirac observables and the problem of time in quantum gravity

We combine the "evolving constants" approach to the construction of observables in canonical quantum gravity with the Page--Wootters formulation of quantum mechanics with a relational time for generally covariant systems. This overcomes the objections levied by Kucha\v{r} against the latter formalism. The construction is formulated entirely in terms of Dirac observables, avoiding in all cases the physical observation of quantities that do not belong in the physical Hilbert space. We work out explicitly the example of the parameterized particle, including the calculation of the propagator. The resulting theory also predicts a fundamental mechanism of decoherence.Comment: 4 pages, no figures, RevTe

Anti-de Sitter massless scalar field spacetimes in arbitrary dimensions

We consider $d$-dimensional static spacetimes in Einstein gravity with a cosmological constant in the presence of a minimally coupled massless scalar field. The spacetimes have a $(d-2)$-dimensional base manifold given by an Einstein space and the massless scalar field depends only on the radial coordinate. The field equations are decoupled in the general case, and can be solved exactly for the cases when either the cosmological constant vanishes or the base manifold is Ricci flat. We focus on the case of a negative cosmological constant and a Ricci-flat base manifold. The solution has a curvature singularity located at the origin, where also the scalar field diverges. Since there is no event horizon surrounding this singularity, the solution describes a naked singularity dressed with a nontrivial scalar field. This spacetime is an asymptotically locally anti-de Sitter one when the Ricci-flat base manifold is locally flat. The asymptotic solution for an arbitrary Einstein base manifold is found and the corresponding mass, calculated through the canonical generator of the time-translation invariance, is shown to be finite. The contribution to the mass from the scalar field at infinity is also discussed.Comment: 14 pages, 1 figure. Typos correcte

On Nichols algebras over PGL(2,q) and PSL(2,q)

We compute necessary conditions on Yetter-Drinfeld modules over the groups \mathbf{PGL}(2,q)=\mathbf{PGL}(2,\FF_q) and \mathbf{PSL}(2,q)=\mathbf{PSL}(2,\FF_q) to generate finite dimensional Nichols algebras. This is a first step towards a classification of pointed Hopf algebras with group of group-likes isomorphic to one of these groups. As a by-product of the techniques developed in this work, we prove that there is no non-trivial finite-dimensional pointed Hopf algebra over the Mathieu groups $M_{20}$ and $M_{21}=\mathbf{PSL}(3,4)$.Comment: Minor change

On Nichols algebras over SL(2,Fq) and GL(2,Fq)

We compute necessary conditions on Yetter-Drinfeld modules over the groups SL(2,Fq) and GL(2,Fq) to generate finite dimensional Nichols algebras. This is a first step towards a classification of pointed Hopf algebras with a group of group-likes isomorphic to one of these groups.Comment: Major exposition revision, including referees remarks. To appear in J. Math. Phys. 13 page

Prevalence of depression in patients with breast cancer

1.- INTRODUCCIÓN: La depresión es una sintomatología muy frecuente en los pacientes diagnosticados con cáncer de mama y su tratamiento. Se plantea una revisión de la literatura para analizar la prevalencia de la depresión en personas con cáncer de mama. 2.- METODOS: Revisión sistemática. Bases de datos: EMBASE (1999-2010) PUBMED (1981-2010). Se incluyeron los artículos que relacionaban prevalencia y depresión en cáncer de mama. 3.- RESULTADOS: Se localizaron 49 estudios; sólo 12 cumplieron los criterios de inclusión, se encontró 7 estudios descriptivos y 5 analíticos. La prevalencia de depresión encontrada en los estudios oscila entre el 6%-57%. 4.- CONCLUSIONES: La disparidad de datos obtenidos conlleva a la falta de una evidencia empírica de la prevalencia de la depresión en personas con cáncer de mama.1. – INTRODUCTION: Depressive disorder is a usual symptom in patients with breast cancer diagnoses and treatment. The purpose of this study is to systematically analize the prevalence of depression in breast cancer people. 2. – METHODS: Systematic review. Database: EMBASE (1999-2010), PUBMED (1981-2010). We included articles that related depression prevalence to breast cancer. 3. – RESULTS: 49 studios were located. Only 12 met inclusion criteria. We found 7 descriptive studios and 5 analytic studios. The prevalence of depression found in studies ranges from 6%- 57%. 4. – CONCLUSION: The disparity of the data obtained connotes a lack of empiric evidence of the prevalence of depression on people with breast cancer

Additive averages of multiplicative correlation sequences and applications

We study sets of recurrence, in both measurable and topological settings, for actions of $(\mathbb{N},\times)$ and $(\mathbb{Q}^{>0},\times)$. In particular, we show that autocorrelation sequences of positive functions arising from multiplicative systems have positive additive averages. We also give criteria for when sets of the form $\{(an+b)^{\ell}/(cn+d)^{\ell}: n \in \mathbb{N}\}$ are sets of multiplicative recurrence, and consequently we recover two recent results in number theory regarding completely multiplicative functions and the Omega function

Análisis interregional utilizando una matriz insumo-producto bi-regional de Argentina

This paper presents a regional case study using a Bi-Regional Input-Output (BRIO) matrix of Buenos Aires City (BAC) and the Rest of Argentina (ROA), constructed from the Argentinian Input-Output matrix. A hybrid approach was applied to obtain the BRIO matrix, which combines pure non-survey methods with matrix-balancing methods like RAS or Cross-Entropy. Once the BRIO matrix was obtained, our study has focused on analyzing the BAC regional structure and the interconnections between regions. We have also estimated the regional and national carbon footprint for the BAC and Argentina, respectively. Results show that service and industry sectors play an important role in the economy of BAC and some of them have strong interregional spillover effects over the rest of the country. In addition, the results also show that sectors on BAC with the highest regional multipliers are also the ones with highest emissions.Este artículo presenta un caso de estudio regional utilizando una matriz Bi-Regional Input-Output (BRIO) de la Ciudad de Buenos Aires (BAC) y el Resto de Argentina (ROA), construida a partir de la matriz Input-Output de Argentina. Se ha utilizado una metodología híbrida para obtener la matriz BRIO, la cual combina métodos indirectos puros y métodos de calibración de matrices como RAS y Entropía Cruzada. Una vez obtenida la matriz BRIO, nuestro estudio se ha centrado en analizar la estructura regional de la BAC y las interconexiones entre regiones. También hemos realizado la estimación de la huella de carbono nacional y regional para Argentina y en la BAC, respectivamente. Los resultados muestran que los sectores de servicios e industria juegan un papel importante en la economía de la BAC y algunos de ellos tienen fuertes efectos indirectos interregionales sobre el resto del país. Además, los resultados también muestran que los sectores de la BAC con los multiplicadores regionales más altos también son los que tienen las emisiones más altas

Averages of completely multiplicative functions over the Gaussian integers -- a dynamical approach

We prove a pointwise convergence result for additive ergodic averages associated with certain multiplicative actions of the Gaussian integers. We derive several applications in dynamics and number theory, including: (i) Wirsing's theorem for Gaussian integers: if $f\colon \mathbb{G} \to \mathbb{R}$ is a bounded completely multiplicative function, then the following limit exists: $$\lim_{N \to \infty} \frac{1}{N^2} \sum_{1 \leq m, n \leq N} f(m + {\rm i} n).$$ (ii) An answer to a special case of a question of Frantzikinakis and Host: for any completely multiplicative real-valued function $f: \mathbb{N} \to \mathbb{R}$, the following limit exists: $$\lim_{N \to \infty} \frac{1}{N^2} \sum_{1 \leq m, n \leq N} f(m^2 + n^2).$$ (iii) A variant of a theorem of Bergelson and Richter on ergodic averages along the $\Omega$ function: if $(X,T)$ is a uniquely ergodic system with unique invariant measure $\mu$, then for any $x\in X$ and $f\in C(X)$, $$\lim_{N\to\infty}\frac{1}{N^2}\sum_{1 \leq m, n \leq N} f(T^{\Omega(m^2 + n^2)}x)=\int_Xf \ d\mu.$$Comment: 32 page

Quantum vacuum fluctuations and the principle of virtual work in inhomogeneous backgrounds

We discuss several aspects of the stress-energy tensor for a quantum scalar field in an inhomogeneous background, the latter being modeled by a variable mass. Using a perturbative approach, dimensional regularization, and adiabatic subtraction, we present all-order formal expressions for the stress-energy tensor. Importantly, we provide an explicit proof of the principle of virtual work for Casimir forces, taking advantage of the conservation law for the renormalized stress-energy tensor. We discuss also discontinuity-induced divergences. For the particular case of planar inhomogeneities, we corroborate the perturbative results with a WKB-inspired expansion.Fil: Franchino Viñas, Sebastián Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Mantiñan, M. N.. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro | Universidad Nacional de Cuyo. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro; ArgentinaFil: Mazzitelli, Francisco Diego. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro | Universidad Nacional de Cuyo. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentin