Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes

The folk questions in Lorentzian Geometry, which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime $(M,g)$ admits a smooth time function $\tau$ whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting $M= \R \times {\cal S}$, $g= - \beta(\tau,x) d\tau^2 + \bar g_\tau$, (b) if a spacetime $M$ admits a (continuous) time function $t$ (i.e., it is stably causal) then it admits a smooth (time) function $\tau$ with timelike gradient $\nabla \tau$ on all $M$.Comment: 9 pages, Latex, to appear in Commun. Math. Phys. Some comments on time functions and stably causal spacetimes are incorporated, and referred to gr-qc/0411143 for further detail

Leibnizian, Galilean and Newtonian structures of spacetime

The following three geometrical structures on a manifold are studied in detail: (1) Leibnizian: a non-vanishing 1-form $\Omega$ plus a Riemannian metric \h on its annhilator vector bundle. In particular, the possible dimensions of the automorphism group of a Leibnizian G-structure are characterized. (2) Galilean: Leibnizian structure endowed with an affine connection $\nabla$ (gauge field) which parallelizes $\Omega$ and \h. Fixed any vector field of observers Z ($\Omega (Z) = 1$), an explicit Koszul--type formula which reconstruct bijectively all the possible $\nabla$'s from the gravitational ${\cal G} = \nabla_Z Z$ and vorticity $\omega = rot Z/2$ fields (plus eventually the torsion) is provided. (3) Newtonian: Galilean structure with \h flat and a field of observers Z which is inertial (its flow preserves the Leibnizian structure and $\omega = 0$). Classical concepts in Newtonian theory are revisited and discussed.Comment: Minor errata corrected, to appear in J. Math. Phys.; 22 pages including a table, Late

El Quijote en las escuelas

Estudio premiado por la Asociación provincial de maestros de escuelas públicas de Barcelona, en el Certamen literario conmemorativo del 3er. centenario de la publicación de "El Quijote

Phylogeography of SARS-CoV-2 pandemic in Spain: a story of multiple introductions, micro-geographic stratification, founder effects, and super-spreaders

Spain has been one of the main global pandemic epicenters for coronavirus disease 2019 (COVID-19). Here, we analyzed >41 000 genomes (including >26 000 high-quality (HQ) genomes) downloaded from the GISAID repository, including 1 245 (922 HQ) sampled in Spain. The aim of this study was to investigate genome variation of novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and reconstruct phylogeographic and transmission patterns in Spain. Phylogeographic analysis suggested at least 34 independent introductions of SARS-CoV-2 to Spain at the beginning of the outbreak. Six lineages spread very successfully in the country, probably favored by super-spreaders, namely, A2a4 (7.8%), A2a5 (38.4%), A2a10 (2.8%), B3a (30.1%), and B9 (8.7%), which accounted for 87.9% of all genomes in the Spanish database. One distinct feature of the Spanish SARS-CoV-2 genomes was the higher frequency of B lineages (39.3%, mainly B3a+B9) than found in any other European country. While B3a, B9, (and an important sub-lineage of A2a5, namely, A2a5c) most likely originated in Spain, the other three haplogroups were imported from other European locations. The B3a strain may have originated in the Basque Country from a B3 ancestor of uncertain geographic origin, whereas B9 likely emerged in Madrid. The time of the most recent common ancestor (TMRCA) of SARS-CoV-2 suggested that the first coronavirus entered the country around 11 February 2020, as estimated from the TMRCA of B3a, the first lineage detected in the country. Moreover, earlier claims that the D614G mutation is associated to higher transmissibility is not consistent with the very high prevalence of COVID-19 in Spain when compared to other countries with lower disease incidence but much higher frequency of this mutation (56.4% in Spain vs. 82.4% in rest of Europe). Instead, the data support a major role of genetic drift in modeling the micro-geographic stratification of virus strains across the country as well as the role of SARS-CoV-2 super-spreaders

Comentarios sobre frases de El Quijote que tienen relación con la educación é instrucción públicas tema que obtuvo el primer premio... en el Certamen Nacional celebrado por la Asociación provincial de Maestros públicos de Barcelona para solemnizar el III centenario de la obra inmortal de Cervantes

Sign. y antep.La h. de lám. es un retrato del aut

Quantum fields during black hole formation: how good an approximation is the Unruh state?

We study the quantum effects of a test Klein-Gordon field in a Vaidya space-time consisting of a collapsing null shell that forms a Schwazschild black hole, by explicitly obtaining, in a (1 + 1)-dimensional model, the Wightman function, the renormalised stress-energy tensor, and by analysing particle detector rates along stationary orbits in the exterior black hole region, and make a comparison with the folklore that the Unruh state is the state that emerges from black hole formation. In the causal future of the shell, we find a negative ingoing flux at the horizon that agrees precisely with the Unruh state calculation, and is the source of black hole radiation, while in the future null infinity we find that the radiation flux output in the Unruh state is an upper bound for the positive outgoing flux in the collapsing null shell spacetime. This indicates that back-reaction estimates based on Unruh state calculations over-estimate the energy output carried by so-called pre-Hawking radiation. The value of the output predicted by the Unruh state is however approached exponentially fast. Finally, we find that at late times, stationary observers in the exterior black hole region in the collapsing shell spacetime detect the local Hawking temperature, which is also well characterised by the Unruh state, coming from right-movers. Early-time discrepancies between the detector rates for the Unruh state and for the state in the collapsing shell spacetime are explored numerically

Defining the Behavior of IoT Devices through the MUD Standard : Review, Challenges, and Research Directions

With the strong development of the Internet of Things (IoT), the definition of IoT devices' intended behavior is key for an effective detection of potential cybersecurity attacks and threats in an increasingly connected environment. In 2019, the Manufacturer Usage Description (MUD) was standardized within the IETF as a data model and architecture for defining, obtaining and deploying MUD files, which describe the network behavioral profiles of IoT devices. While it has attracted a strong interest from academia, industry, and Standards Developing Organizations (SDOs), MUD is not yet widely deployed in real-world scenarios. In this work, we analyze the current research landscape around this standard, and describe some of the main challenges to be considered in the coming years to foster its adoption and deployment. Based on the literature analysis and our own experience in this area, we further describe potential research directions exploiting the MUD standard to encourage the development of secure IoT-enabled scenarios

Breakup and neutron-transfer effects on 6He+206Pb elastic scattering below the Coulomb barrier

The elastic scattering and inclusive α-particle yield for the 6He + 206Pb system at an incident energy of 18 MeV, just below the nominal Coulomb barrier, have been measured. The α-particle yield at forward angles is also reported. The data are analyzed by means of continuum-discretized coupled-channels, distorted wave Born approximation, and coupled reaction channels calculations. Couplings to the one-neutron- and two-neutron-transfer reactions are found to be able to account for most of the absorption in the entrance channel.This work was supported in part by Grant No. FPA2010-22131-C02-01 from the Spanish Ministry of Science