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

Mixtures of Skew-t Factor Analyzers

In this paper, we introduce a mixture of skew-t factor analyzers as well as a family of mixture models based thereon. The mixture of skew-t distributions model that we use arises as a limiting case of the mixture of generalized hyperbolic distributions. Like their Gaussian and t-distribution analogues, our mixture of skew-t factor analyzers are very well-suited to the model-based clustering of high-dimensional data. Imposing constraints on components of the decomposed covariance parameter results in the development of eight flexible models. The alternating expectation-conditional maximization algorithm is used for model parameter estimation and the Bayesian information criterion is used for model selection. The models are applied to both real and simulated data, giving superior clustering results compared to a well-established family of Gaussian mixture models

ARCS, The Arcminute Radio Cluster-lens Search - I. Selection Criteria and Initial Results

We present the results of an unbiased radio search for gravitational lensing events with image separations between 15 and 60 arcsec, which would be associated with clusters of galaxies with masses >10^{13-14}M_{\sun}. A parent population of 1023 extended radio sources stronger than 35 mJy with stellar optical identifications was selected using the FIRST radio catalogue at 1.4 GHz and the APM optical catalogue. The FIRST catalogue was then searched for companions to the parent sources stronger than 7 mJy and with separation in the range 15 to 60 arcsec. Higher resolution observations of the resulting 38 lens candidates were made with the VLA at 1.4 GHz and 5 GHz, and with MERLIN at 5 GHz in order to test the lens hypothesis in each case. None of our targets was found to be a gravitational lens system. These results provide the best current constraint on the lensing rate for this angular scale, but improved calculations of lensing rates from realistic simulations of the clustering of matter on the relevant scales are required before cosmologically significant constraints can be derived from this null result. We now have an efficient, tested observational strategy with which it will be possible to make an order-of-magnitude larger unbiased search in the near future.Comment: Accepted for publication in MNRAS. 12 pages, 29 included PostScript figure

Loss tolerant linear optical quantum memory by measurement-based quantum computing

We give a scheme for loss tolerantly building a linear optical quantum memory which itself is tolerant to qubit loss. We use the encoding recently introduced in Varnava et al 2006 Phys. Rev. Lett. 97 120501, and give a method for efficiently achieving this. The entire approach resides within the 'one-way' model for quantum computing (Raussendorf and Briegel 2001 Phys. Rev. Lett. 86 5188–91; Raussendorf et al 2003 Phys. Rev. A 68 022312). Our results suggest that it is possible to build a loss tolerant quantum memory, such that if the requirement is to keep the data stored over arbitrarily long times then this is possible with only polynomially increasing resources and logarithmically increasing individual photon life-times