The Seven Sisters DANCe III: Projected spatial distribution

Methods. We compute Bayesian evidences and Bayes Factors for a set of variations of the classical radial models by King (1962), Elson et al. (1987) and Lauer et al. (1995). The variations incorporate different degrees of model freedom and complexity, amongst which we include biaxial (elliptical) symmetry, and luminosity segregation. As a by-product of the model comparison, we obtain posterior distributions and maximum a posteriori estimates for each set of model parameters. Results. We find that the model comparison results depend on the spatial extent of the region used for the analysis. For a circle of 11.5 parsecs around the cluster centre (the most homogeneous and complete region), we find no compelling reason to abandon Kings model, although the Generalised King model, introduced in this work, has slightly better fitting properties. Furthermore, we find strong evidence against radially symmetric models when compared to the elliptic extensions. Finally, we find that including mass segregation in the form of luminosity segregation in the J band, is strongly supported in all our models. Conclusions. We have put the question of the projected spatial distribution of the Pleiades cluster on a solid probabilistic framework, and inferred its properties using the most exhaustive and least contaminated list of Pleiades candidate members available to date. Our results suggest however that this sample may still lack about 20% of the expected number of cluster members. Therefore, this study should be revised when the completeness and homogeneity of the data can be extended beyond the 11.5 parsecs limit. Such study will allow a more precise determination of the Pleiades spatial distribution, its tidal radius, ellipticity, number of objects and total mass.Comment: 39 pages, 31 figure

Las matemáticas en el bachillerato a distancia: restricciones epistemológicas y pedagógicas

El mundo está experimentando una verdadera revolución en la difusión del conocimiento y en la mejora de la instrucción a través del avance de las tecnologías de la comunicación y la información. Esta es la tercera revolución en el aprendizaje, siendo la primera la invención del lenguaje escrito y la segunda el desarrollo de la imprenta y los libros. En la actualidad podemos encontrar enseñanza virtual en todos los niveles de enseñanza, es por ello que los sistemas educativos se enfrentan a grandes desafíos en la cada vez más demanda educación a distancia, con el propósito de proporcionar todo el espectro de servicios de educación para todos, en cualquier lugar y en cualquier momento con un enfoque centrado en un aprendizaje efectivo. A pesar de este gran desarrollo de la educación a distancia, no existen muchos estudios al respecto. La finalidad de este trabajo es estudiar las restricciones de orden epistemológico y pedagógico que puede presentar la enseñanza de las matemáticas en el bachillerato a distancia

Cloning of Gaussian states by linear optics

We analyze in details a scheme for cloning of Gaussian states based on linear optical components and homodyne detection recently demonstrated by U. L. Andersen et al. [PRL 94 240503 (2005)]. The input-output fidelity is evaluated for a generic (pure or mixed) Gaussian state taking into account the effect of non-unit quantum efficiency and unbalanced mode-mixing. In addition, since in most quantum information protocols the covariance matrix of the set of input states is not perfectly known, we evaluate the average cloning fidelity for classes of Gaussian states with the degree of squeezing and the number of thermal photons being only partially known.Comment: 8 pages, 7 figure

The Seven Sisters DANCe. I. Empirical isochrones, Luminosity and Mass Functions of the Pleiades cluster

The DANCe survey provides photometric and astrometric (position and proper motion) measurements for approximately 2 millions unique sources in a region encompassing $\approx$80deg$^{2}$ centered around the Pleiades cluster. We aim at deriving a complete census of the Pleiades, and measure the mass and luminosity function of the cluster. Using the probabilistic selection method described in Sarro+2014, we identify high probability members in the DANCe ($i\ge$14mag) and Tycho-2 ($V\lesssim$12mag) catalogues, and study the properties of the cluster over the corresponding luminosity range. We find a total of 2109 high probability members, of which 812 are new, making it the most extensive and complete census of the cluster to date. The luminosity and mass functions of the cluster are computed from the most massive members down to $\approx$0.025M$_{\odot}$. The size, sensitivity and quality of the sample result in the most precise luminosity and mass functions observed to date for a cluster. Our census supersedes previous studies of the Pleiades cluster populations, both in terms of sensitivity and accuracy.Comment: Language Edition Done. Final version to be published in A&A. Tables will be published at CDS. Meanwhile, they can be requested to H. Bouy (hbouy -at- cab . inta - csic . es