Estimating Common Principal Components in High Dimensions

We consider the problem of minimizing an objective function that depends on an orthonormal matrix. This situation is encountered when looking for common principal components, for example, and the Flury method is a popular approach. However, the Flury method is not effective for higher dimensional problems. We obtain several simple majorization-minizmation (MM) algorithms that provide solutions to this problem and are effective in higher dimensions. We then use simulated data to compare them with other approaches in terms of convergence and computational time

The distributional effect of the 2008 Pre-Budget Report

The Pre-Budget Report given by the Chancellor on 24th November 2008 contained a number of changes to the tax and benefit system to come into effect at various points over the next three years. This briefing note expands on the information provided at a briefing given by IFS researchers on the day after the Pre-Budget Report1. It gives details of the changes to taxes, benefits and tax credits directly affecting households, and the total distributional impact of measures announced in PBR 2008 together with pre-announced changes, by income and expenditure decile and household type, at three points in time – January 2009, April 2009 and April 2011. It also discusses what PBR 2008 does to our impression of all tax and benefit changes under this Government. Finally, it discusses what PBR 08 did for child poverty in 2010/11 and the likely effects of the income tax changes for those earning more than £100,000 a year

How good must single photon sources and detectors be for efficient linear optical quantum computation?

We present a scheme for linear optical quantum computation (LOQC) which is highly robust to imperfect single photon sources and inefficient detectors. In particular we show that if the product of the detector efficiency with the source efficiency is greater than 2/3, then efficient LOQC is possible. This threshold is many orders of magnitude more relaxed than those which could be inferred by application of standard results in fault tolerance. The result is achieved within the cluster state paradigm for quantum computation.Comment: New version contains an Added Appendi

Interaction of Ising-Bloch fronts with Dirichlet Boundaries

We study the Ising-Bloch bifurcation in two systems, the Complex Ginzburg Landau equation (CGLE) and a FitzHugh Nagumo (FN) model in the presence of spatial inhomogeneity introduced by Dirichlet boundary conditions. It is seen that the interaction of fronts with boundaries is similar in both systems, establishing the generality of the Ising-Bloch bifurcation. We derive reduced dynamical equations for the FN model that explain front dynamics close to the boundary. We find that front dynamics in a highly non-adiabatic (slow front) limit is controlled by fixed points of the reduced dynamical equations, that occur close to the boundary.Comment: 10 pages, 8 figures, submitted to Phys. Rev.

Mixtures of Common Skew-t Factor Analyzers

A mixture of common skew-t factor analyzers model is introduced for model-based clustering of high-dimensional data. By assuming common component factor loadings, this model allows clustering to be performed in the presence of a large number of mixture components or when the number of dimensions is too large to be well-modelled by the mixtures of factor analyzers model or a variant thereof. Furthermore, assuming that the component densities follow a skew-t distribution allows robust clustering of skewed data. The alternating expectation-conditional maximization algorithm is employed for parameter estimation. We demonstrate excellent clustering performance when our model is applied to real and simulated data.This paper marks the first time that skewed common factors have been used