On using block principal component analysis for reducing gene-expression data dimensions

Since a microarray gene expression database contains a large number of variables and a relatively small number of samples, using and analyzing the databases require an intense, large-dimension computation method. Principal component analysis (PCA) is a useful tool to reduce the number of dimensions, and therefore, the complexity. PCA allows us to analyze the gene expression database with a relatively small data dimension without losing relevant information and increases the analytic visibility of the data. The initial computation using PCA, however, involves calculating a high-dimension covariance or correlation matrix and requires time and hardware resources which are limited in most real situations; In this thesis, we propose to use a Block Principal Component Analysis (Block PCA) method, introduced by Liu et al. (2002), to produce a subset that can explain a large amount of variation and propose criterion to find the most appropriate subsets; The gene expression data typically is highly correlated and the covariance matrix becomes highly ill-conditioned. The Mahalanobis distances resulting from the application of software packages such as SAS are not reliable in such cases. We investigate the effect of ill-conditioning on Discriminant Analysis of gene expression data from a DNA microarray. Bioinformatics literature recommends forming blocks of variables that are correlated with another. We proposed the method of Partial Least Square (PLS) to form the block of correlated variables for use in Block PCA

P-Cygni Type Lya from Starburst Galaxies

P-Cygni type Lya profiles exhibited in nearly half of starburst galaxies, both nearby and high-z, are believed to be formed by an expanding supershell surrounding a star-forming region. We apply the Monte Carlo code which was developed previously for static and plane-parallel medium to calculate the Lya line transfer in a supershell of neutral hydrogen which are expanding radially in a spherical bulk flow. We consider typical cases that the supershell has the Lya line-centre optical depth of $\tau_0=10^5-10^7$, a radial expansion velocity of $V_exp = 300 km/s, and the turbulence of b=40 km/s. We find that there appear a few emission peaks at the frequencies corresponding to (2N-1) V_exp, where the order of back scatterings N > 1. As V_exp -> b, the emergent profiles become similar to those for the static medium and the peaks are less prominent. We also investigate the effects of column density of the supershell on the emergent Lya profiles. We find that the number and the flux ratios of emission peaks are determined by interplay of$\tau_0$ and V_exp of the supershell. We discuss the effects of dust extinction and the implication of our works in relation to recent spectroscopic observations of starburst galaxies.Comment: 15 pages, 6 figures, submitted to MNRA

Highly efficient source for frequency-entangled photon pairs generated in a 3rd order periodically poled MgO-doped stoichiometric LiTaO3 crystal

We present a highly efficient source for discrete frequency-entangled photon pairs based on spontaneous parametric down-conversion using 3rd order type-0 quasi-phase matching in a periodically poled MgO-doped stoichiometric LiTaO3 crystal pumped by a 355.66 nm laser. Correlated two-photon states were generated with automatic conservation of energy and momentum in two given spatial modes. These states have a wide spectral range, even under small variations in crystal temperature, which consequently results in higher discreteness. Frequency entanglement was confirmed by measuring two-photon quantum interference fringes without any spectral filtering.Comment: 4 pages, 4 figures, to be published in Optics Letter