A general framework based on majorization, Schur-concavity, and concavity is given that facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed diversity measures useful for best basis selection. Admissible sparsity measures are given by the Schur-concave functions, which are the class of functions consistent with the partial ordering on vecto...

The product sμsν of two Schur functions is one of the most famous examples of a Schur-positive function, i.e. a symmetric function which, when written as a linear combination of Schur functions, has all positive coefficients. We ask when expressions of the form sλsρ − sμsν are Schur-positive. This general question seems to be a difficult one, but a conjecture of Fomin, Fulton, Li and Poon says ...

Each finite p-perfect group G (p a prime) has a universal central p-extension coming from the p part of its Schur multiplier. Serre gave a StiefelWhitney class approach to analyzing spin covers of alternating groups (p = 2) aimed at geometric covering space problems that included their regular realization for the Inverse Galois Problem. A special case of a general result is that any finite simp...

Lossless systems have many applications in systems and control theory, including signal processing, filter design, system identification, system approximation, and the parameterization of classes of linear systems. In this survey paper we address the issue of parameterization of the space of rational lossless matrix functions by successfully combining two approaches. The first approach proceeds...

Each finite p-perfect group G (p a prime) has a universal central p-extension coming from the p part of its Schur multiplier. Serre gave a StiefelWhitney class approach to analyzing spin covers of alternating groups (p = 2) aimed at geometric covering space problems that included their regular realization for the Inverse Galois Problem. A special case of a general result is that any finite simp...

This paper introduces a robust preconditioner for general sparse symmetric matrices, that is based on low-rank approximations of the Schur complement in a Domain Decomposition (DD) framework. In this “Schur Low Rank” (SLR) preconditioning approach, the coefficient matrix is first decoupled by DD, and then a low-rank correction is exploited to compute an approximate inverse of the Schur compleme...