Lepton masses, mixings and FCNC in a minimal S_3-invariant extension of the Standard Model

The mass matrices of the charged leptons and neutrinos, previously derived in a minimal S_3-invariant extension of the Standard Model, were reparametrized in terms of their eigenvalues. We obtained explicit, analytical expressions for all entries in the neutrino mixing matrix, V_PMNS, the neutrino mixing angles and the Majorana phases as functions of the masses of charged leptons and neutrinos in excellent agreement with the latest experimental values. The resulting V_PMNS matrix is very close to the tri-bimaximal form of the neutrino mixing matrix. We also derived explicit analytical expressions for the matrices of the Yukawa couplings and computed the branching ratios of some selected flavour changing neutral current processes as functions of the masses of the charged leptons and the neutral Higgs bosons. We find that the S_3 x Z_2 flavour symmetry and the strong mass hierarchy of the charged leptons strongly suppress the FCNC processes in the leptonic sector well below the present experimental upper bounds by many orders of magnitude.Comment: One paragraph added with comparison to tri-bimaximal mixing, two lines changed in abstract, references added, typographical errors correcte

Berry Phase of a Resonant State

We derive closed analytical expressions for the complex Berry phase of an open quantum system in a state which is a superposition of resonant states and evolves irreversibly due to the spontaneous decay of the metastable states. The codimension of an accidental degeneracy of resonances and the geometry of the energy hypersurfaces close to a crossing of resonances differ significantly from those of bound states. We discuss some of the consequences of these differences for the geometric phase factors, such as: Instead of a diabolical point singularity there is a continuous closed line of singularities formally equivalent to a continuous distribution of `magnetic' charge on a diabolical circle; different classes of topologically inequivalent non-trivial closed paths in parameter space, the topological invariant associated to the sum of the geometric phases, dilations of the wave function due to the imaginary part of the Berry phase and others.Comment: 28 pages Latex, three uuencoded postcript figure

Covariant description of parametrized nonrelativistic Hamiltonian systems

The various phase spaces involved in the dynamics of parametrized nonrelativistic Hamiltonian systems are displayed by using Crnkovic and Witten's covariant canonical formalism. It is also pointed out that in Dirac's canonical formalism there exists a freedom in the choice of the symplectic structure on the extended phase space and in the choice of the equations that define the constraint surface with the only restriction that these two choices combine in such a way that any pair (of these two choices) generates the same gauge transformation. The consequence of this freedom on the algebra of observables is also discussed.Comment: 15 pages, latex file. corrected typos, minor changes done to match published versio

Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories

The most general action, quadratic in the B fields as well as in the curvature F, having SO(3,1) or SO(4) as the internal gauge group for a four-dimensional BF theory is presented and its symplectic geometry is displayed. It is shown that the space of solutions to the equations of motion for the BF theory can be endowed with symplectic structures alternative to the usual one. The analysis also includes topological terms and cosmological constant. The implications of this fact for gravity are briefly discussed.Comment: 13 pages, LaTeX file, no figure

Contribution of the Residual Body in the Spatial Organization of Toxoplasma gondii Tachyzoites within the Parasitophorous Vacuole

Toxoplasma gondii proliferates and organizes within a parasitophorous vacuole in rosettes around a residual body and is surrounded by a membranous nanotubular network whose function remains unclear. Here, we characterized structure and function of the residual body in intracellular tachyzoites of the RH strain. Our data showed the residual body as a body limited by a membrane formed during proliferation of tachyzoites probably through the secretion of components and a pinching event of the membrane at the posterior end. It contributes in the intravacuolar parasite organization by the membrane connection between the tachyzoites posterior end and the residual body membrane to give place to the rosette conformation. Radial distribution of parasites in rosettes favors an efficient exteriorization. Absence of the network and presence of atypical residual bodies in a ΔGRA2-HXGPRT knock-out mutant affected the intravacuolar organization of tachyzoites and their exteriorization

Random Networks with given Rich-club Coefficient

In complex networks it is common to model a network or generate a surrogate network based on the conservation of the network's degree distribution. We provide an alternative network model based on the conservation of connection density within a set of nodes. This density is measure by the rich-club coefficient. We present a method to generate surrogates networks with a given rich-club coefficient. We show that by choosing a suitable local linking term, the generated random networks can reproduce the degree distribution and the mixing pattern of real networks. The method is easy to implement and produces good models of real networks.Comment: revised version, new figure