Maximal Subgroups of Compact Lie Groups

This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial type, which are simply defined as inverse images of maximal subgroups of the corresponding component group under the canonical projection and whose classification constitutes a problem in finite group theory, (2) those of normal type, whose connected one-component is a normal subgroup, and (3) those of normalizer type, which are the normalizers of their own connected one-component. It is also shown how to reduce the classification of maximal subgroups of the last two types to: (2) the classification of the finite maximal $\Sigma$-invariant subgroups of center-free connected compact simple Lie groups and (3) the classification of the $\Sigma$-primitive subalgebras of compact simple Lie algebras, where $\Sigma$ is a subgroup of the corresponding outer automorphism group. In the second part, we explicitly compute the normalizers of the primitive subalgebras of the compact classical Lie algebras (in the corresponding classical groups), thus arriving at the complete classification of all (non-discrete) maximal subgroups of the compact classical Lie groups.Comment: 83 pages. Final versio

Protein synthesis driven by dynamical stochastic transcription

In this manuscript we propose a mathematical framework to couple transcription and translation in which mRNA production is described by a set of master equations while the dynamics of protein density is governed by a random differential equation. The coupling between the two processes is given by a stochastic perturbation whose statistics satisfies the master equations. In this approach, from the knowledge of the analytical time dependent distribution of mRNA number, we are able to calculate the dynamics of the probability density of the protein population.Comment: 20 pages, 3 figure

A Kolmogorov-Smirnov test for the molecular clock on Bayesian ensembles of phylogenies

Divergence date estimates are central to understand evolutionary processes and depend, in the case of molecular phylogenies, on tests of molecular clocks. Here we propose two non-parametric tests of strict and relaxed molecular clocks built upon a framework that uses the empirical cumulative distribution (ECD) of branch lengths obtained from an ensemble of Bayesian trees and well known non-parametric (one-sample and two-sample) Kolmogorov-Smirnov (KS) goodness-of-fit test. In the strict clock case, the method consists in using the one-sample Kolmogorov-Smirnov (KS) test to directly test if the phylogeny is clock-like, in other words, if it follows a Poisson law. The ECD is computed from the discretized branch lengths and the parameter $\lambda$ of the expected Poisson distribution is calculated as the average branch length over the ensemble of trees. To compensate for the auto-correlation in the ensemble of trees and pseudo-replication we take advantage of thinning and effective sample size, two features provided by Bayesian inference MCMC samplers. Finally, it is observed that tree topologies with very long or very short branches lead to Poisson mixtures and in this case we propose the use of the two-sample KS test with samples from two continuous branch length distributions, one obtained from an ensemble of clock-constrained trees and the other from an ensemble of unconstrained trees. Moreover, in this second form the test can also be applied to test for relaxed clock models. The use of a statistically equivalent ensemble of phylogenies to obtain the branch lengths ECD, instead of one consensus tree, yields considerable reduction of the effects of small sample size and provides again of power.Comment: 14 pages, 9 figures, 8 tables. Minor revision, additin of a new example and new title. Software: https://github.com/FernandoMarcon/PKS_Test.gi

Action of the Metalloproteinases in Gonadal Remodeling during Sex Reversal in the Sequential Hermaphroditism of the Teleostei Fish Synbranchus marmoratus (Synbranchiformes: Synbranchidae)

Teleostei present great plasticity regarding sex change. During sex reversal, the whole gonadincluding the germinal epithelium undergoes significant changes, remodeling, and neoformation.However, there is no information on the changes that occur within the interstitial compartment.Considering the lack of information, especially on the role played by metalloproteinases (MMPs)in fish gonadal remodeling, the aim of this study was to evaluate the action of MMPs on gonadsof sex reversed females of Synbranchus marmoratus, a fresh water protogynic diandric fish. Gonadswere processed for light microscopy and blood samples were used for the determination of plasmasex steroid levels. During sex reversal, degeneration of the ovaries occurred and were graduallyreplaced by the germinal tissue of the male. The action of the MMPs induces significant changesin the interstitial compartment, allowing the reorganization of germinal epithelium. Leydig cellsalso showed an important role in female to male reversion. The gonadal transition coincides withchanges in circulating sex steroid levels throughout sex reversion. The action of the MMPs, in thegonadal remodeling, especially on the basement membrane, is essential for the establishment of anew functional germinal epithelium.Fil: Mazzoni, Talita Sarah. Universidade Estadual Paulista Julio de Mesquita Filho; BrasilFil: Lo Nostro, Fabiana Laura. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Biodiversidad y Biología Experimental. Laboratorio de Ecotoxicología Acuática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Biodiversidad y Biología Experimental y Aplicada. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Biodiversidad y Biología Experimental y Aplicada; ArgentinaFil: Antoneli, Fernanda. Universidade Estadual de Campinas; BrasilFil: Quagio-Grassiotto, Irani. Universidade Estadual Paulista Julio de Mesquita Filho; Brasi

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