Neutrino masses and mixings in a Minimal S_3-invariant Extension of the Standard Model

The mass matrices of the charged leptons and neutrinos, that had been derived in the framework of a Minimal S_3-invariant Extension of the Standard Model, are here reparametrized in terms of their eigenvalues. The neutrino mixing matrix, V_PMNS, is then computed and exact, explicit analytical expressions for the neutrino mixing angles as functions of the masses of the neutrinos and charged leptons are obtained. The reactor, theta_13, and the atmosferic, theta_23, mixing angles are found to be functions only of the masses of the charged leptons. The numerical values of theta_13{th} and theta_23{th} computed from our theoretical expressions are found to be in excellent agreement with the latest experimental determinations. The solar mixing angle, theta_12{th}, is found to be a function of both, the charged lepton and neutrino masses, as well as of a Majorana phase phi_nu. A comparison of our theoretical expression for the solar angle theta_12{th} with the latest experimental value theta_12{exp} ~ 34 deg allowed us to fix the scale and origin of the neutrino mass spectrum and obtain the mass values |m_nu1|=0.0507 eV, |m_nu2|=0.0499 eV and |m_nu3|=0.0193 eV, in very good agreement with the observations of neutrino oscillations, the bounds extracted from neutrinoless double beta decay and the precision cosmological measurements of the CMB.Comment: To appear in the Proceedings of the XXIX Symposium on Nuclear Physics, Cocoyoc, Mex., January 2006. Some typographical errors on formulae correcte

Ensembles based on the Rich-Club and how to use them to build soft-communities

16 pages, 5 figures16 pages, 5 figures16 pages, 5 figuresEnsembles of networks are used as null-models to discriminate network structures. We present an efficient algorithm, based on the maximal entropy method to generate network ensembles defined by the degree sequence and the rich-club coefficient. The method is applicable for unweighted, undirected networks. The ensembles are used to generate correlated and uncorrelated null--models of a real networks. These ensembles can be used to define the partition of a network into soft communities

Skew group algebras, invariants and Weyl Algebras

The aim of this paper is two fold: First to study finite groups $G$ of automorphisms of the homogenized Weyl algebra $B_{n}$, the skew group algebra $B_{n}\ast G$, the ring of invariants $B_{n}^{G}$, and the relations of these algebras with the Weyl algebra $A_{n}$, with the skew group algebra $A_{n}\ast G$, and with the ring of invariants $A_{n}^{G}$. Of particular interest is the case $n=1$. In the on the other hand, we consider the invariant ring \QTR{sl}{C}[X]^{G} of the polynomial ring $K[X]$ in $n$ generators, where $G$ is a finite subgroup of Gl(n,\QTR{sl}{C}) such that any element in $G$ different from the identity does not have one as an eigenvalue. We study the relations between the category of finitely generated modules over \QTR{sl}{C}[X]^{G} and the corresponding category over the skew group algebra \QTR{sl}{C}% [X]\ast G. We obtain a generalization of known results for $n=2$ and $G$ a finite subgroup of $Sl(2,C)$. In the last part of the paper we extend the results for the polynomial algebra $C[X]$ to the homogenized Weyl algebra $B_{n}$

On quark-lepton complementarity

Recent measurements of the neutrino solar mixing angle and the Cabibbo angle satisfy the empirical relation theta_{sol} + theta_{C} ~ 45^{o}. This relation suggests the existence of a correlation between the mixing matrices of leptons and quarks, the so called quark-lepton complementarity. Here, we examine the possibility that this correlation originates in the strong hierarchy in the mass spectra of quarks and charged leptons, and the seesaw mechanism that gives mass to the Majorana neutrinos. In a unified treatment of quarks and leptons in which the mass matrices of all fermions have a similar Fritzsch texture, we calculate the mixing matrices V_{CKM} and U_{MNSP} as functions of quark and lepton masses and only two free parameters, in very good agreement with the latest experimental values on masses and mixings. Three essential ingredients to explain the quark-lepton complementarity relation are identified: the strong hierarchy in the mass spectra of quarks and charged leptons, the normal seesaw mechanism and the assumption of maximal CP violation in the lepton sector.Comment: 6 pages, to appear in "Particles and fields: Xth Mexican Workshop on Particles and Fields" (Morelia, Mich. Mexico, November 6-12, 2005), Eds. A. Bashir and L. Villasenor, AIP Conference proceedings (2006