The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras

We address two problems with the structure and representation theory of finite W-algebras associated with general linear Lie algebras. Finite W-algebras can be defined using either Kostant`s Whittaker modules or a quantum Hamiltonian reduction. Our first main result is a proof of the Gelfand-Kirillov conjecture for the skew fields of fractions of finite W-algebras. The second main result is a parameterization of finite families of irreducible Gelfand-Tsetlin modules using Gelfand-Tsetlin subalgebra. As a corollary, we obtain a complete classification of generic irreducible Gelfand-Tsetlin modules for finite W-algebras. (C) 2009 Elsevier Inc. All rights reserved.

Galois orders in skew monoid rings

We introduce a new class of noncommutative rings - Galois orders, realized as certain subrings of invariants in skew semigroup rings, and develop their structure theory. The class of Calms orders generalizes classical orders in noncommutative rings and contains many important examples, such as the Generalized Weyl algebras, the universal enveloping algebra of the general linear Lie algebra, associated Yangians and finite W-algebras (C) 2010 Elsevier Inc All rights reserved

Mixed multiplicities and the minimal number of generator of modules

Let (R, m) be a d-dimensional Noetherian local ring. In this work we prove that the mixed Buchsbaum-Rim multiplicity for a finite family of R-submodules of R(p) of finite colength coincides with the Buchsbaum-Rim multiplicity of the module generated by a suitable superficial sequence, that is, we generalize for modules the well-known Risler-Teissier theorem. As a consequence, we give a new proof of a generalization for modules of the fundamental Rees` mixed Multiplicity theorem, which was first proved by Kirby and Rees in (1994, [8]). We use the above result to give an upper bound for the minimal number of generators of a finite colength R-submodule of R(p) in terms of mixed multiplicities for modules, which generalize a similar bound obtained by Cruz and Verma in (2000, [5]) for m-primary ideals. (C) 2009 Elsevier B.V. All rights reserved.

LIMITS OF TILTING MODULES

We study the problem of when a direct limit of tilting modules is still a tilting module.

The first group (co)homology of a group G with coefficients in some G-modules

Let G be a group. We give some formulas for the first group homology and cohomology of a group G with coefficients in an arbitrary G-module (Z) over tilde. More explicit calculations are done in the special cases of free groups, abelian groups and nilpotent groups. We also perform calculations for certain G-module M, by reducing it to the case where the coefficient is a G-module (Z) over tilde. As a result of the well known equalities H-1(X, M) = H-1(pi(1)(X), M) and H-1(X, M) = H-1(pi(1) (X), M), for any G-module M, we are able to calculate the first homology and cohomology groups of topological spaces with certain local system of coefficients.

Torsion theories induced from commutative subalgebras

We begin a study of torsion theories for representations of finitely generated algebras U over a field containing a finitely generated commutative Harish-Chandra subalgebra Gamma. This is an important class of associative algebras, which includes all finite W-algebras of type A over an algebraically closed field of characteristic zero, in particular, the universal enveloping algebra of gl(n) (or sl(n)) for all n. We show that any Gamma-torsion theory defined by the coheight of the prime ideals of Gamma is liftable to U. Moreover, for any simple U-module M, all associated prime ideals of M in Spec Gamma have the same coheight. Hence, the coheight of these associated prime ideals is an invariant of a given simple U-module. This implies the stratification of the category of U-modules controlled by the coheight of the associated prime ideals of Gamma. Our approach can be viewed as a generalization of the classical paper by Block (1981) [4]; it allows, in particular, to study representations of gl(n) beyond the classical category of weight or generalized weight modules. (C) 2011 Elsevier B.V. All rights reserved.

Description of costandard modules for Schur superalgebra S(2 vertical bar 1) in positive characteristic

We describe the characters of simple modules and composition factors of costandard modules for S(2 vertical bar 1) in positive characteristics and verify a conjecture of La Scala-Zubkov regarding polynomial superinvariants for GL(2 vertical bar 1).

A Character Formula for the Category (O)over-tilde of Modules for Affine sl(2)

One may construct, for any function on the integers, an irreducible module of level zero for affine sl(2) using the values of the function as structure constants. The modules constructed using exponential-polynomial functions realize the irreducible modules with finite-dimensional weight spaces in the category (O) over tilde of Chari. In this work, an expression for the formal character of such a module is derived using the highest weight theory of truncations of the loop algebra.

Evaluation of Recycled Tiles and OSB Ceiling Materials in Closed Broiler House Prototypes

This study aimed at evaluating the thermal performance of a modular ceiling system for poultry houses. The reduced- and distorted-scale prototypes used ceiling modules made of reforested wood and were covered with recycled long-life package tiles. The following parameters were measured for 21 days: the internal surface temperature (ST), globe temperature and humidity index (WBGT), and radiant heat load (RHL). Measurements were made at times of highest heat load (11:00 am, 13:00 pm, and 03:00 pm). Collected data were analyzed by ""R"" statistics software. Means were compared by multiple comparison test (Tukey) and linear regression was performed, both at 5% significance level. The results showed that the prototype with the ceiling was more efficient to reduce internal tile surface temperature; however, this was not sufficient to provide a comfortable environment for broilers during the growout. Therefore, other techniques to provide proper cooling are required in addition to the ceiling

The modularity of seed dispersal: differences in structure and robustness between bat- and bird-fruit networks

In networks of plant-animal mutualisms, different animal groups interact preferentially with different plants, thus forming distinct modules responsible for different parts of the service. However, what we currently know about seed dispersal networks is based only on birds. Therefore, we wished to fill this gap by studying bat-fruit networks and testing how they differ from bird-fruit networks. As dietary overlap of Neotropical bats and birds is low, they should form distinct mutualistic modules within local networks. Furthermore, since frugivory evolved only once among Neotropical bats, but several times independently among Neotropical birds, greater dietary overlap is expected among bats, and thus connectance and nestedness should be higher in bat-fruit networks. If bat-fruit networks have higher nestedness and connectance, they should be more robust to extinctions. We analyzed 1 mixed network of both bats and birds and 20 networks that consisted exclusively of either bats (11) or birds (9). As expected, the structure of the mixed network was both modular (M = 0.45) and nested (NODF = 0.31); one module contained only birds and two only bats. In 20 datasets with only one disperser group, bat-fruit networks (NODF = 0.53 +/- A 0.09, C = 0.30 +/- A 0.11) were more nested and had a higher connectance than bird-fruit networks (NODF = 0.42 +/- A 0.07, C = 0.22 +/- A 0.09). Unexpectedly, robustness to extinction of animal species was higher in bird-fruit networks (R = 0.60 +/- A 0.13) than in bat-fruit networks (R = 0.54 +/- A 0.09), and differences were explained mainly by species richness. These findings suggest that a modular structure also occurs in seed dispersal networks, similar to pollination networks. The higher nestedness and connectance observed in bat-fruit networks compared with bird-fruit networks may be explained by the monophyletic evolution of frugivory in Neotropical bats, among which the diets of specialists seem to have evolved from the pool of fruits consumed by generalists.

Analysis of a hyper-diverse seed dispersal network: modularity and underlying mechanisms

Mutualistic interactions involving pollination and ant-plant mutualistic networks typically feature tightly linked species grouped in modules. However, such modularity is infrequent in seed dispersal networks, presumably because research on those networks predominantly includes a single taxonomic animal group (e.g. birds). Herein, for the first time, we examine the pattern of interaction in a network that includes multiple taxonomic groups of seed dispersers, and the mechanisms underlying modularity. We found that the network was nested and modular, with five distinguishable modules. Our examination of the mechanisms underlying such modularity showed that plant and animal trait values were associated with specific modules but phylogenetic effect was limited. Thus, the pattern of interaction in this network is only partially explained by shared evolutionary history. We conclude that the observed modularity emerged by a combination of phylogenetic history and trait convergence of phylogenetically unrelated species, shaped by interactions with particular types of dispersal agents.

Skull Modularity in Neotropical Marsupials and Monkeys: Size Variation and Evolutionary Constraint and Flexibility

An organism is built through a series of contingent factors, yet it is determined by historical, physical, and developmental constraints. A constraint should not be understood as an absolute obstacle to evolution, as it may also generate new possibilities for evolutionary change. Modularity is, in this context, an important way of organizing biological information and has been recognized as a central concept in evolutionary biology bridging on developmental, genetics, morphological, biochemical, and physiological studies. In this article, we explore how modularity affects the evolution of a complex system in two mammalian lineages by analyzing correlation, variance/covariance, and residual matrices (without size variation). We use the multivariate response to selection equation to simulate the behavior of Eutheria and Metharia skulls in terms of their evolutionary flexibility and constraints. We relate these results to classical approaches based on morphological integration tests based on functional/developmental hypotheses. Eutherians (Neotropical primates) showed smaller magnitudes of integration compared with Metatheria (didelphids) and also skull modules more clearly delimited. Didelphids showed higher magnitudes of integration and their modularity is strongly influenced by within-groups size variation to a degree that evolutionary responses are basically aligned with size variation. Primates still have a good portion of the total variation based on size; however, their enhanced modularization allows a broader spectrum of responses, more similar to the selection gradients applied (enhanced flexibility). Without size variation, both groups become much more similar in terms of modularity patterns and magnitudes and, consequently, in their evolutionary flexibility. J. Exp. Zool. (Mol. Dev. Evol.) 314B:663-683, 2010. (C) 2010 Wiley-Liss, Inc.

The Evolution of Modularity in the Mammalian Skull I: Morphological Integration Patterns and Magnitudes

Morphological integration refers to the modular structuring of inter-trait relationships in an organism, which could bias the direction and rate of morphological change, either constraining or facilitating evolution along certain dimensions of the morphospace. Therefore, the description of patterns and magnitudes of morphological integration and the analysis of their evolutionary consequences are central to understand the evolution of complex traits. Here we analyze morphological integration in the skull of several mammalian orders, addressing the following questions: are there common patterns of inter-trait relationships? Are these patterns compatible with hypotheses based on shared development and function? Do morphological integration patterns and magnitudes vary in the same way across groups? We digitized more than 3,500 specimens spanning 15 mammalian orders, estimated the correspondent pooled within-group correlation and variance/covariance matrices for 35 skull traits and compared those matrices among the orders. We also compared observed patterns of integration to theoretical expectations based on common development and function. Our results point to a largely shared pattern of inter-trait correlations, implying that mammalian skull diversity has been produced upon a common covariance structure that remained similar for at least 65 million years. Comparisons with a rodent genetic variance/covariance matrix suggest that this broad similarity extends also to the genetic factors underlying phenotypic variation. In contrast to the relative constancy of inter-trait correlation/covariance patterns, magnitudes varied markedly across groups. Several morphological modules hypothesized from shared development and function were detected in the mammalian taxa studied. Our data provide evidence that mammalian skull evolution can be viewed as a history of inter-module parcellation, with the modules themselves being more clearly marked in those lineages with lower overall magnitude of integration. The implication of these findings is that the main evolutionary trend in the mammalian skull was one of decreasing the constraints to evolution by promoting a more modular architecture.

The Evolution of Modularity in the Mammalian Skull II: Evolutionary Consequences

Changes in patterns and magnitudes of integration may influence the ability of a species to respond to selection. Consequently, modularity has often been linked to the concept of evolvability, but their relationship has rarely been tested empirically. One possible explanation is the lack of analytical tools to compare patterns and magnitudes of integration among diverse groups that explicitly relate these aspects to the quantitative genetics framework. We apply such framework here using the multivariate response to selection equation to simulate the evolutionary behavior of several mammalian orders in terms of their flexibility, evolvability and constraints in the skull. We interpreted these simulation results in light of the integration patterns and magnitudes of the same mammalian groups, described in a companion paper. We found that larger magnitudes of integration were associated with a blur of the modules in the skull and to larger portions of the total variation explained by size variation, which in turn can exert a strong evolutionary constraint, thus decreasing the evolutionary flexibility. Conversely, lower overall magnitudes of integration were associated with distinct modules in the skull, to smaller fraction of the total variation associated with size and, consequently, to weaker constraints and more evolutionary flexibility. Flexibility and constraints are, therefore, two sides of the same coin and we found them to be quite variable among mammals. Neither the overall magnitude of morphological integration, the modularity itself, nor its consequences in terms of constraints and flexibility, were associated with absolute size of the organisms, but were strongly associated with the proportion of the total variation in skull morphology captured by size. Therefore, the history of the mammalian skull is marked by a trade-off between modularity and evolvability. Our data provide evidence that, despite the stasis in integration patterns, the plasticity in the magnitude of integration in the skull had important consequences in terms of evolutionary flexibility of the mammalian lineages.

Complement 4 phenotypes and genotypes in Brazilian patients with classical 21-hydroxylase deficiency

The aim of this work was to analyse C4 genotypes, C4 protein levels, phenotypes and genotypes in patients with the classical form of 21-hydroxylase deficiency. Fifty-four patients from 46 families (36 female, 18 male; mean age 10.8 years) with different clinical manifestations (31 salt-wasting; 23 simple-virilizing) were studied. Taq I Southern blotting was used to perform molecular analysis of the C4/CYP21 gene cluster and the genotypes were defined according to gene organization within RCCX modules. Serum C4 isotypes were assayed by enzyme-linked immunosorbent assay. The results revealed 12 different haplotypes of the C4/CYP21 gene cluster. Total functional activity of the classical pathway (CH50) was reduced in individuals carrying different genotypes because of low C4 concentrations (43% of all patients) to complete or partial C4 allotype deficiency. Thirteen of 54 patients presented recurrent infections affecting the respiratory and/or the urinary tracts, none of them with severe infections. Low C4A or C4B correlated well with RCCX monomodular gene organization, but no association between C4 haplotypes and recurrent infections or autoimmunity was observed. Considering this redundant gene cluster, C4 seems to be a well-protected gene segment along the evolutionary process.