Minimax rank estimation for subspace tracking

Rank estimation is a classical model order selection problem that arises in a variety of important statistical signal and array processing systems, yet is addressed relatively infrequently in the extant literature. Here we present sample covariance asymptotics stemming from random matrix theory, and bring them to bear on the problem of optimal rank estimation in the context of the standard array observation model with additive white Gaussian noise. The most significant of these results demonstrates the existence of a phase transition threshold, below which eigenvalues and associated eigenvectors of the sample covariance fail to provide any information on population eigenvalues. We then develop a decision-theoretic rank estimation framework that leads to a simple ordered selection rule based on thresholding; in contrast to competing approaches, however, it admits asymptotic minimax optimality and is free of tuning parameters. We analyze the asymptotic performance of our rank selection procedure and conclude with a brief simulation study demonstrating its practical efficacy in the context of subspace tracking.Comment: 10 pages, 4 figures; final versio

Light Mesons from Heavy B and Hyperon Decays

Decays of heavy mesons and of heavy hyperons are used to provide tests of the standard model and information about new mixing schemes for the $\eta$ and $\eta^{'}$ mesons. These include the two body decays $B_s \to J / \psi M$ and $B_d \to J / \psi M$, $B \to \eta (\eta ^{'})K(K^\ast)$ and $\Lambda_b \to \Lambda \eta (\eta ^{'})$, semileptonic $D$ decays, and properties of radially excited mesons.Comment: Four pages. Talk given at the Fifth International Conference on Hyperons, Charm and Beauty Hadrons, Vancouver, BC, Canada, July 25-29, 200

Examining the Role of Courts in Canada\u27s Policy-Making Process

This piece explores the apparent disjuncture between the prescribed duties of both the judicial and legislative branches of the Canadian government, and the genuine means by which such duties are attended to regardless of codified jurisdiction. Namely, this piece conducts a dual analysis - including both normative and descriptive components - in order to consider whether or not the Supreme Court of Canada has unduly encroached upon both the Provincial Legislature\u27s and the Federal Parliament\u27s duty to formulate legislation through their exercising of judicial review. In assessing the judiciary\u27s role in policy-making, abstract considerations - such as the inherently undemocratic nature of the judiciary - are examined alongside more practical items, such as the courts\u27 veritable ability to craft sound policy in the first place. Ultimately, this piece concludes that the adoption of a conventional coordinate model would serve best as both a means through which to make sound policy in both a normative and descriptive sense