Intra-group diffuse light in compact groups of galaxies. HCG 79, HCG 88 and HCG 95

Deep $B$ and $R$ images of three Hickson Compact Groups, HCG 79, HCG 88 and HCG 95, were analyzed using a new wavelet technic to measure possible intra-group diffuse light present in these systems. The method used, OV\_WAV, is a wavelet technic particularly suitable to detect low-surface brightness extended structures, down to a $S/N = 0.1$ per pixel, which corresponds to a 5-$\sigma$-detection level in wavelet space. The three groups studied are in different evolutionary stages, as can be judged by their very different fractions of the total light contained in their intra-group halos: $46\pm11$% for HCG 79 and $11\pm26$% for HCG 95, in the $B$ band, and HCG 88 had no component detected down to a limiting surface brightness of $29.1 B mag arcsec^{-2}$. For HCG 95 the intra-group light is red, similar to the mean colors of the group galaxies themselves, suggesting that it is formed by an old population with no significant on-going star formation. For HCG 79, however, the intra-group material has significantly bluer color than the mean color of the group galaxies, suggesting that the diffuse light may, at least in part, come from stripping of dwarf galaxies which dissolved into the group potential well.Comment: Two suggested references added to the introductio

Gravity with extra dimensions and dark matter interpretation: A straightforward approach

Any connection between dark matter and extra dimensions can be cognizably evinced from the associated effective energy-momentum tensor. In order to investigate and test such relationship, a higher dimensional spacetime endowed with a factorizable general metric is regarded to derive a general expression for the stress tensor -- from the Einstein-Hilbert action -- and to elicit the effective gravitational potential. A particular construction for the case of six dimensions is provided, and it is forthwith revealed that the missing mass phenomenon may be explained, irrespective of the dark matter existence. Moreover, the existence of extra dimensions in the universe accrues the possibility of a straightforward mechanism for such explanation. A configuration which density profile coincides with the Newtonian potential for spiral galaxies is constructed, from a 4-dimensional isotropic metric plus extra-dimensional components. A Miyamoto-Nagai \emph{ansatz} is used to solve Einstein equations. The stable rotation curves associated to such system are computed, in full compliance to the observational data, without fitting techniques. The density profiles are reconstructed and compared to that ones obtained from the Newtonian potential.Comment: 13 pages, 6 figure

Stability of switched linear differential systems

We study the stability of switched systems where the dynamic modes are described by systems of higher-order linear differential equations not necessarily sharing the same state space. Concatenability of trajectories at the switching instants is specified by gluing conditions, i.e. algebraic conditions on the trajectories and their derivatives at the switching instant. We provide sufficient conditions for stability based on LMIs for systems with general gluing conditions. We also analyse the role of positive-realness in providing sufficient polynomial-algebraic conditions for stability of two-modes switched systems with special gluing conditions

A Generalized Approach to Complex Networks

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the network topology to new network growth models. First, the concepts of node degree and clustering coefficient are extended in order to characterize not only specific nodes, but any generic subnetwork. Second, the consideration of distance transform and rings are used to further extend those concepts in order to obtain a signature, instead of a single scalar measurement, ranging from the single node to whole graph scales. The enhanced discriminative potential of such extended measurements is illustrated with respect to the identification of correspondence between nodes in two complex networks, namely a protein-protein interaction network and a perturbed version of it. The use of other measurements derived from mathematical morphology are also suggested as a means to characterize complex networks connectivity in a more comprehensive fashion.Comment: 10 pages, 2 figur