Lusternik-Schnirelmann category of simplicial complexes and finite spaces

In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This category has the property of being homotopy invariant under strong equivalences, and only depends on the simplicial structure rather than its geometric realization. In a similar way to the classical case, we also develop a notion of geometric category for simplicial complexes. We prove that the maximum value over the homotopy class of a given complex is attained in the core of the complex. Finally, by means of well known relations between simplicial complexes and posets, specific new results for the topological notion of category are obtained in the setting of finite topological spaces.Comment: 18 pages, 10 figures, this is a new version with some minor changes and a new exampl

MIMAC-He3 : A Micro-TPC Matrix of Chambers of He3 for direct detection of Wimps

The project of a micro-TPC matrix of chambers of \hetrois for direct detection of non-baryonic dark matter is presented. The privileged properties of He3 are highlighted. The double detection (ionization - projection of tracks) is explained and its rejection evaluated. The potentialities of MIMAC-He3 for supersymmetric dark matter search are discussed.Comment: to appear in Proc. of the 9th International Conference on Topics in Astroparticle and Underground Physics (TAUP 2005), Zaragoza, Sept. 200

A basic reference state suitable for anomaly-coupled ocean-atmosphere climate models

AbstractA large class of ocean-atmosphere models exists in which the ocean state is coupled to the model of the atmosphere only through the anomalies of the ocean state. The sea surface temperatures are defined with respect to a mean reference state, i.e., they are the difference between the ocean state and a reference state. Due to coupled model drift, the choice of reference state is important and it can have a large impact on the variability in the model. The reference state can be calculated as an average throughout the coupled simulation and various methods of doing this (moving average, exponentially weighted moving average and accumulated mean) are compared in this note. The accumulated mean method appears to be the sole method of the three which gives both unbiased anomalies and a convergent reference state. It is recommended for use in anomaly-coupled models for improving variability and predictability

Supersymmetric FRW model and the ground state of supergravity

In this work we construct the vacuum configuration of supergravity interacting with homogeneous complex scalar matter fields. The corresponding configuration is of the FRW model invariant under the $n=2$ local conformal time supersymmetry, which is a subgroup of the four dimensional space-time supersymmetry. We show, that the potential of the scalar matter fields is a function of the K\"ahler potential and of the arbitrary parameter $\alpha$. This parameter enumerates the vacuum states. The scalar matter potential induces the spontaneous breaking of supersymmetry in supergravity. On the quantum level our model is a specific supersymmetric quantum mechanics, which admits quantum states in supergravity, and the states with zero energy are described by the wave function of the FRW universe.Comment: 18 pages, Revtex, submitted to PR

The classroom of Physical Education and students with disabilities

Este estudio versa sobre el proceso de construcción y validación de un instrumento estandarizado cuyo objetivo ha sido analizar la realidad educativa de los docentes de Educación Física en la etapa de primaria ante alumnado con discapacidad motora y derivar del mismo los elementos clave que justifiquen la construcción de un plan de formación permanente del profesorado en este ámbito. El proceso llevado a cabo paso por llevar a cabo en primer lugar un juicio de expertos y expertas para posteriormente someter el borrador de aquí derivado a un pilotaje con un total de 57 docentes de Córdoba. El cuestionario definitivo goza de las suficientes garantías para ser aplicado, analizado e interpretado y ha permitido extraer como dimensiones formativas las siguientes: didáctica de la Educación Física, herramientas didáctico educativas, estrategias de trabajo en el aula, habilidades para el ejercicio de la docentes y recursos tecnológicos

Evidence of the missing baryons from the kinematic Sunyaev-Zeldovich effect in Planck data

Under the terms of the Creative Commons Attribution license.-- et al.We estimate the amount of the missing baryons detected by the Planck measurements of the cosmic microwave background in the direction of central galaxies (CGs) identified in the Sloan galaxy survey. The peculiar motion of the gas inside and around the CGs unveils values of the Thomson optical depth τT in the range 0.2-2×10-4, indicating that the regions probed around CGs contain roughly half of the total amount of baryons in the Universe at the epoch where the CGs are found. If baryons follow dark matter, the measured τT's are compatible with the detection of all of the baryons existing inside and around the CGs.C. H.-M. acknowledges the support of Ramón y Cajal Fellowship No. RyC-2011-08262, Marie Curie Career Integration Grant No. 294183, and Spanish Ministerio de Economía y Competitividad Project No. AYA2012-30789. Y.-Z. M thanks ERC for its support through Starting Grant No. 307209.Peer Reviewe