Estudo de alterações estruturais cerebrais em pacientes com esquizofrenia crônica e de primeiro episódio através de imagens por ressonância magnética com morfometria baseada no voxel

Introdução: Embora alterações estruturais cerebrais na esquizofrenia venham sendo repetidamente demonstradas em estudos de ressonância magnética (RM), ainda permanece incerto se tais alterações são estáticas ou progressivas. Enquanto estudos longitudinais são tradicionalmente utilizados na avaliação da questão da progressão, estudos transversais de neuroimagem comparando diretamente pacientes com esquizofrenia crônica e de primeiro episódio a controles saudáveis têm sido bastante raros até o presente. Com o recente interesse em meganálises combinando dados multicêntricos de RM visando-se a maior poder estatístico, o presente estudo multicêntrico de morfometria baseada no voxel (VBM) foi realizado para avaliar os padrões de alterações estruturais cerebrais segundo os diferentes estágios da doença, bem como para avaliar quais (se alguma) dessas alterações se correlacionariam especificamente a moderadores clínicos potenciais, tais como exposição cumulativa a antipsicóticos, tempo de doença e gravidade da doença. Métodos: Selecionou-se uma ampla amostra de pacientes com esquizofrenia (161, sendo 99 crônicos e 62 de primeiro episódio) e controles (151) a partir de quatro estudos prévios de RM (1,5T) realizados na mesma região do Brasil. O processamento e análise das imagens foi realizado usando-se o software Statistical Parametric Mapping (SPM8) com emprego do algoritmo DARTEL (diffeomorphic anatomical registration through exponentiated Lie algebra). Os efeitos de grupo sobre os volumes regionais de substância cinzenta (SC) foram analisados através de comparações voxel-a-voxel por análises de covariância em modelos lineares gerais, inserindo-se, em todas as análises, o volume total de SC, protocolo do scanner, idade e sexo como variáveis de confusão. Por fim, foram realizadas análises de correlação entre os aludidos moderadores clínicos potenciais e os volumes cerebrais globais e regionais. Resultados: Os pacientes com esquizofrenia de primeiro episódio apresentaram reduções volumétricas sutis em comparação aos controles, em um circuito neural circunscrito e identificável apenas em análises SVC (small volume correction) [p < 0.05, com correção family-wise error (FWE)], incluindo a ínsula, estruturas têmporo-límbicas e corpo estriado. Os pacientes crônicos, por outro lado, apresentaram um padrão de alterações extensas comparativamente aos controles, envolvendo os córtices frontais orbitais, superiores e inferiores bilateralmente, córtex frontal médio direito, ambos os córtices cingulados anteriores, ambas as ínsulas, e os córtices temporais superior e médio direitos (p < 0.05, análises whole-brain com correção FWE). Foram encontradas correlações negativas significantes entre exposição cumulativa a antipsicóticos e volumes globais de SC e substância branca nos pacientes com esquizofrenia, embora as correlações com reduções regionais não tenham sido significantes. Detectaram-se, ainda, correlações negativas significantes entre tempo de doença e volumes regionais relativos da ínsula esquerda, córtex cingulado anterior direito e córtices pré-frontais dorsolaterais nas análises SVC para os grupos conjuntos (esquizofrenia crônica e de primeiro episódio). Conclusão: Os achados supracitados indicam que: a) as alterações estruturais associadas com o diagnóstico de esquizofrenia são mais disseminadas na forma crônica em comparação à de primeiro episódio; b) reduções volumétricas regionais em áreas específicas do cérebro podem variar em função do tempo de doença; c) a exposição cumulativa a antipsicóticos associou-se a alterações volumétricas globais, e não regionais

The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30

The ranks of the homotopy groups of odd degree of a finite complex

Special Issue in honor of Prof. Hans-Bjørn Foxby

Credit risk & forward price models

Doutoramento em Gestão

Connected Hopf algebras of finite Gelfand-Kirillov dimension

Following the seminal work of Zhuang, connected Hopf algebras of finite GK-dimension over algebraically closed fields of characteristic zero have been the subject of several recent papers. This thesis is concerned with continuing this line of research and promoting connected Hopf algebras as a natural, intricate and interesting class of algebras. We begin by discussing the theory of connected Hopf algebras which are either commutative or cocommutative, and then proceed to review the modern theory of arbitrary connected Hopf algebras of finite GK-dimension initiated by Zhuang. We next focus on the (left) coideal subalgebras of connected Hopf algebras of finite GK-dimension. They are shown to be deformations of commutative polynomial algebras. A number of homological properties follow immediately from this fact. Further properties are described, examples are considered and invariants are constructed. A connected Hopf algebra is said to be "primitively thick" if the difference between its GK-dimension and the vector-space dimension of its primitive space is precisely one . Building on the results of Wang, Zhang and Zhuang,, we describe a method of constructing such a Hopf algebra, and as a result obtain a host of new examples of such objects. Moreover, we prove that such a Hopf algebra can never be isomorphic to the enveloping algebra of a semisimple Lie algebra, nor can a semisimple Lie algebra appear as its primitive space. It has been asked in the literature whether connected Hopf algebras of finite GK-dimension are always isomorphic as algebras to enveloping algebras of Lie algebras. We provide a negative answer to this question by constructing a counterexample of GK-dimension 5. Substantial progress was made in determining the order of the antipode of a finite dimensional pointed Hopf algebra by Taft and Wilson in the 1970s. Our final main result is to show that the proof of their result can be generalised to give an analogous result for arbitrary pointed Hopf algebras.

The solvable Lie group N_{6, 28}: an example of an almost C_0(\mathcal{K})-C*-algebra

Motivated by the description of the C*-algebra of the affine automorphism group N6,28 of the Siegel upper half-plane of degree 2 as an algebra of operator fields defined over the unitary dual View the MathML source of the group, we introduce a family of C*-algebras, which we call almost C0(K), and we show that the C*-algebra of the group N6,28 belongs to this class.

A Computer Algebra Application to Determination of Lie Symmetries of Partial Differential Equations

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Embedding Of Non-Simple Lie-Groups, Coupling-Constant Relations And Non-Uniqueness Of Models Of Unification

A general derivation of the coupling constant relations which result on embedding a non-simple group like SU L (2) @ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin~0=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons like E 6, while addition of extra charged fermion singlets can reduce the value of sin ~ 0 to 1/4. We point out that at the present time the models of grand unification are far from unique.

Brisure de symétrie par la réduction des groupes de Lie simples à leurs sous-groupes de Lie réductifs maximaux

Dans ce travail, nous exploitons des propriétés déjà connues pour les systèmes de poids des représentations afin de les définir pour les orbites des groupes de Weyl des algèbres de Lie simples, traitées individuellement, et nous étendons certaines de ces propriétés aux orbites des groupes de Coxeter non cristallographiques. D'abord, nous considérons les points d'une orbite d'un groupe de Coxeter fini G comme les sommets d'un polytope (G-polytope) centré à l'origine d'un espace euclidien réel à n dimensions. Nous introduisons les produits et les puissances symétrisées de G-polytopes et nous en décrivons la décomposition en des sommes de G-polytopes. Plusieurs invariants des G-polytopes sont présentés. Ensuite, les orbites des groupes de Weyl des algèbres de Lie simples de tous types sont réduites en l'union d'orbites des groupes de Weyl des sous-algèbres réductives maximales de l'algèbre. Nous listons les matrices qui transforment les points des orbites de l'algèbre en des points des orbites des sous-algèbres pour tous les cas n<=8 ainsi que pour plusieurs séries infinies des paires d'algèbre-sous-algèbre. De nombreux exemples de règles de branchement sont présentés. Finalement, nous fournissons une nouvelle description, uniforme et complète, des centralisateurs des sous-groupes réguliers maximaux des groupes de Lie simples de tous types et de tous rangs. Nous présentons des formules explicites pour l'action de tels centralisateurs sur les représentations irréductibles des algèbres de Lie simples et montrons qu'elles peuvent être utilisées dans le calcul des règles de branchement impliquant ces sous-algèbres.

Lie properties of symmetric elements in group rings

Let * be an involution of a group G extended linearly to the group algebra KG. We prove that if G contains no 2-elements and K is a field of characteristic p, 0 2, then the *-symmetric elements of KG are Lie nilpotent (Lie n-Engel) if and only if KG is Lie nilpotent (Lie n-Engel). (C) 2008 Elsevier Inc. All rights reserved.

Lie properties of crossed products

Let F-sigma(lambda)vertical bar G vertical bar be a crossed product of a group G and the field F. We study the Lie properties of F-sigma(lambda)vertical bar G vertical bar in order to obtain a characterization of those crossed products which are upper (lower) Lie nilpotent and Lie (n, m)-Engel. (C) 2008 Elsevier Inc. All rights reserved.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.

THE ALGEBRA OF NONLOCAL CHARGES IN NONLINEAR SIGMA-MODELS

We obtain the exact classical algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group O(N). As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, now containing a calculable correction of order one unit lower. The relation with Yangians and the role of the results in the context of Lie-Poisson algebras are also discussed.