Classification of simple weight modules for the N=2N=2 superconformal algebra

In this paper, we classify all simple weight modules with finite dimensional weight spaces over the $N=2$ superconformal algebra.Comment: 18 pages, Latex, in this version we delete the Section 7 for application to the $N=1$ superconformal algebr

A Cohomological Characterization of Leibniz Central Extensions of Lie Algebras

Mainly motivated by Pirashvili's spectral sequences on a Leibniz algebra, a cohomological characterization of Leibniz central extensions of Lie algebras is given based on Corollary 3.3 and Theorem 3.5. In particular, as applications, we obtain the cohomological version of Gao's main Theorem in \cite{Gao2} for Kac-Moody algebras and answer a question in \cite{LH}.Comment: 12 pages. Proc. Amer.Math.Soc. (to appear in a simplified version

Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra

In this paper we investigate Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra. With the classifications of Lie bialgebra structures on the Virasoro algebra, we determined such structures on the twisted Heisenberg-Virasoro algebra. Moreover, some general and useful results are obtained. With our methods and results we also can easily to determine such structures on some Lie algebras related to the twisted Heisenberg-Virasoro algebra.Comment: Latex 18page. arXiv admin note: text overlap with arXiv:0901.133

Significance Analysis for Pairwise Variable Selection in Classification

The goal of this article is to select important variables that can distinguish one class of data from another. A marginal variable selection method ranks the marginal effects for classification of individual variables, and is a useful and efficient approach for variable selection. Our focus here is to consider the bivariate effect, in addition to the marginal effect. In particular, we are interested in those pairs of variables that can lead to accurate classification predictions when they are viewed jointly. To accomplish this, we propose a permutation test called Significance test of Joint Effect (SigJEff). In the absence of joint effect in the data, SigJEff is similar or equivalent to many marginal methods. However, when joint effects exist, our method can significantly boost the performance of variable selection. Such joint effects can help to provide additional, and sometimes dominating, advantage for classification. We illustrate and validate our approach using both simulated example and a real glioblastoma multiforme data set, which provide promising results.Comment: 28 pages, 7 figure