Full-rank affine invariant submanifolds

Full Rank Affine Invariant Submanifolds

Affine Invariant Multivariate Rank Tests for Several Samples

Affine invariant analogues of the two-sample Mann-Whitney-Wilcoxon rank sum test and the c-sample Kruskal-Wallis test for the multivariate location model are introduced. The definition of a multivariate (centered) rank function in the development is based on the Oja criterion function. This work extends bivariate rank methods discussed by Brown and Hettmansperger (1987a,b) and multivariate sign...

Affine-Invariant Online Optimization and the Low-rank Experts Problem

We present a new affine-invariant optimization algorithm calledOnline Lazy Newton. The regret of Online Lazy Newton is independent of conditioning: the algorithm’s performance depends on the best possible preconditioning of the problem in retrospect and on its intrinsic dimensionality. As an application, we show how Online Lazy Newton can be used to achieve an optimal regret of order √ rT for t...

Invariant submanifolds of Sasakian manifolds

In this paper, the geometry of invariant submanifolds of a Sasakian manifold are studied. Necessary and sufficient conditions are given on an submanifold of a Sasakian manifold to be invariant submanifold and the invariant case is considered. In this case, we investigate further properties of invariant submanifolds of a Sasakian manifold. M.S.C. 2000: 53C42, 53C15.

The Field of Definition of Affine Invariant Submanifolds of the Moduli Space of Abelian Differentials

The field of definition of an affine invariant submanifold M is the smallest subfield of R such that M can be defined in local period coordinates by linear equations with coefficients in this field. We show that the field of definition is equal to the intersection of the holonomy fields of translation surfaces inM, and is a real number field of degree at most the genus. We show that the project...