The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem to modules.

We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any black-box routine for ridge regression. By avoiding explicit principal component analysis (PCA), our algorithm is the first with no runtime dependen...

Note that SPSS does not provide statistical significance tests for any of the estimated parameters (such as loadings), nor does it provide confidence intervals. Judgments about the adequacy of a oneor two-component model are not made based on statistical significance tests, but by making arbitrary judgments whether the model that is limited to just one or two components does an adequate job of ...

Let G be a split reductive p-adic group. In this paper, we establish an explicit link between principal nilpotent orbits of G and the irreducible constituents of principal series of G. A geometric characterization of certain irreducible constituents is also provided.

The principal frame and principal quadric form a fundamental description of a smooth surface at a point. This paper is concerned with estimating these from the 3D data acquired by a sensor such as a structured light system. Eight diierent estimation methods are described and a comparison of their performance is presented.