Symmetry breaking in the genetic code: Finite groups

We investigate the possibility of interpreting the degeneracy of the genetic code, i.e., the feature that different codons (base triplets) of DNA are transcribed into the same amino acid, as the result of a symmetry breaking process, in the context of finite groups. In the first part of this paper, we give the complete list of all codon representations (64-dimensional irreducible representations) of simple finite groups and their satellites (central extensions and extensions by outer automorphisms). In the second part, we analyze the branching rules for the codon representations found in the first part by computational methods, using a software package for computational group theory. The final result is a complete classification of the possible schemes, based on finite simple groups, that reproduce the multiplet structure of the genetic code. (C) 2010 Elsevier Ltd. All rights reserved.

Crossed products by twisted partial actions and graded algebras

For a twisted partial action e of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A x(Theta) G is proved to be associative. Given a G-graded k-algebra B = circle plus(g is an element of G) B-g with the mild restriction of homogeneous non-degeneracy, a criteria is established for B to be isomorphic to the crossed product B-1 x(Theta) G for some twisted partial action of G on B-1. The equality BgBg-1 B-g = B-g (for all g is an element of G) is one of the ingredients of the criteria, and if it holds and, moreover, B has enough local units, then it is shown that B is stably isomorphic to a crossed product by a twisted partial action of G. (c) 2008 Elsevier Inc. All rights reserved.

Efeitos não-gaussianos em astrofísica e cosmologia

The recent astronomical observations indicate that the universe has null spatial curvature, is accelerating and its matter-energy content is composed by circa 30% of matter (baryons + dark matter) and 70% of dark energy, a relativistic component with negative pressure. However, in order to built more realistic models it is necessary to consider the evolution of small density perturbations for explaining the richness of observed structures in the scale of galaxies and clusters of galaxies. The structure formation process was pioneering described by Press and Schechter (PS) in 1974, by means of the galaxy cluster mass function. The PS formalism establishes a Gaussian distribution for the primordial density perturbation field. Besides a serious normalization problem, such an approach does not explain the recent cluster X-ray data, and it is also in disagreement with the most up-to-date computational simulations. In this thesis, we discuss several applications of the nonextensive q-statistics (non-Gaussian), proposed in 1988 by C. Tsallis, with special emphasis in the cosmological process of the large structure formation. Initially, we investigate the statistics of the primordial fluctuation field of the density contrast, since the most recent data from the Wilkinson Microwave Anisotropy Probe (WMAP) indicates a deviation from gaussianity. We assume that such deviations may be described by the nonextensive statistics, because it reduces to the Gaussian distribution in the limit of the free parameter q = 1, thereby allowing a direct comparison with the standard theory. We study its application for a galaxy cluster catalog based on the ROSAT All-Sky Survey (hereafter HIFLUGCS). We conclude that the standard Gaussian model applied to HIFLUGCS does not agree with the most recent data independently obtained by WMAP. Using the nonextensive statistics, we obtain values much more aligned with WMAP results. We also demonstrate that the Burr distribution corrects the normalization problem. The cluster mass function formalism was also investigated in the presence of the dark energy. In this case, constraints over several cosmic parameters was also obtained. The nonextensive statistics was implemented yet in 2 distinct problems: (i) the plasma probe and (ii) in the Bremsstrahlung radiation description (the primary radiation from X-ray clusters); a problem of considerable interest in astrophysics. In another line of development, by using supernova data and the gas mass fraction from galaxy clusters, we discuss a redshift variation of the equation of state parameter, by considering two distinct expansions. An interesting aspect of this work is that the results do not need a prior in the mass parameter, as usually occurs in analyzes involving only supernovae data.Finally, we obtain a new estimate of the Hubble parameter, through a joint analysis involving the Sunyaev-Zeldovich effect (SZE), the X-ray data from galaxy clusters and the baryon acoustic oscillations. We show that the degeneracy of the observational data with respect to the mass parameter is broken when the signature of the baryon acoustic oscillations as given by the Sloan Digital Sky Survey (SDSS) catalog is considered. Our analysis, based on the SZE/X-ray data for a sample of 25 galaxy clusters with triaxial morphology, yields a Hubble parameter in good agreement with the independent studies, provided by the Hubble Space Telescope project and the recent estimates of the WMAP

Extended class of exact twistons and crystalline polyethylene

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The Yang-Lee edge singularity in spin models on connected and non-connected rings

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Generalized partition function zeros of 1D spin models and their critical behavior at edge singularities

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Unusual Yang-Lee edge singularity in the one-dimensional axial-next-to-nearest-neighbor Ising model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Critical behavior at edge singularities in one-dimensional spin models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Degenerate and critical Bloch branes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Spinless bosons embedded in a vector Duffin-Kemmer-Petiau oscillator

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Índice de aromaticidade baseado na deslocalização, degenerescência e densidade (D3BIA) para acenos e moléculas homoaromáticas

The aromaticity index is an important tool for the investigation of aromatic molecules. This work consists on new applications of the aromaticity index developed by teacher Caio Lima Firme, so-called D3BIA (density, delocalization, degeneracy-based index of aromaticity). It was investigated its correlation with other well-known aromaticity indexes, such as HOMA (harmonic oscillator model of aromaticity), NICS (nucleus independent chemical shielding), PDI (para-delocalization index), magnetic susceptibility (), and energetic factor in the study of aromaticity of acenes and homoaromatic species based on bisnoradamantanyl cage. The density functional theory (DFT) was used for optimization calculations and for obtaining energetic factors associated with aromaticity and indexes HOMA and NICS. From quantum theory of atoms in molecules (QTAIM) it was obtained the indexes D3BIA, PDI and . For acenes, when the over-mentioned indexes were applied it was observed no correlation except for D3BIA and HOMA (R2=0.752). For bisnoradamantenyl dication and its derivatives, it was obtained a good correlation between D3BIA and NICS. Moreover, it was evaluated solely one of the factors used on D3BIA calculation, the delocalization index uniformity (DIU), so as to investigate its possible influence on stability of chemical species. Then, the DIU was compared with the formation Gibbs free energy of some pairs of carbocations, isomers or not, which each pair had small difference in point group symmetry and no difference among other well-known stability factors. The obtained results indicate that DIU is a new stability factor related to carbocations, that is, the more uniform the electron density delocalization, the more stable the is carbocation. The results of this work validate D3BIA and show its importance on the concept of aromaticity, indicating that it can be understood from degeneracy of atoms belonging the aromatic site, the electronic density in the aromatic site and the degree of uniformity of electron delocalization

Parameter degeneracies in neutrino oscillation measurement of leptonic CP and T violation

The measurement of the mixing angle theta(13), sign of Deltam(13)(2), and the CP or T violating phase delta is fraught with ambiguities in neutrino oscillation. In this paper we give an analytic treatment of the paramater degeneracies associated with measuring the nu(mu)-->nu(e) probability and its CP and/or T conjugates. For CP violation, we give explicit solutions to allow us to obtain the regions where there exist twofold and fourfold degeneracies. We calculate the fractional differences, (Deltatheta/(θ) over bar), between the allowed solutions which may be used to compare with the expected sensitivities of the experiments. For T violation we show that there is always a complete degeneracy between solutions with positive and negative Deltam(13)(2) which arises due to a symmetry and cannot be removed by observing one neutrino oscillation probability and its T conjugate. Thus there is always a fourfold parameter degeneracy apart from exceptional points. Explicit solutions are also given and the fractional differences are computed. The biprobability CP/T trajectory diagrams are extensively used to illuminate the nature of the degeneracies.

Black hole entropy associated with the supersymmetric sigma model

By means of an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the N-fold symmetric product (SX)-X-N of X ((SX)-X-N=X-N/S-N, where S-N is the symmetric group of N elements) to the partition function of a second-quantized string theory, we derive the asymptotic expansion of the partition function as well as the asymptotic for the degeneracy of spectrum in string theory. The asymptotic expansion for the state counting reproduces the logarithmic correction to the black hole entropy.

Dilatonic current-carrying cosmic strings

We investigate the nature of ordinary cosmic vortices in some scalar-tensor extensions of gravity. We find solutions for which the dilaton field condenses inside the vortex core. These solutions can be interpreted as raising the degeneracy between the eigenvalues of the effective stress-energy tensor, namely, the energy per unit length U and the tension T, by picking a privileged spacelike or timelike coordinate direction; in the latter case, a phase frequency threshold occurs that is similar to what is found in ordinary neutral current-carrying cosmic strings. We find that the dilaton contribution for the equation of state, once averaged along the string worldsheet, vanishes, leading to an effective Nambu-Goto behavior of such a string network in cosmology, i.e. on very large scales. It is found also that on small scales, the energy per unit length and tension depend on the string internal coordinates in such a way as to permit the existence of centrifugally supported equilibrium configuration, also known as vortons, whose stability, depending on the very short distance (unknown) physics, can lead to catastrophic consequences on the evolution of the Universe.

The signature of dark energy perturbations in galaxy cluster surveys

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)