Separation of the largest eigenvalues in eigenanalysis of genotype data from discrete subpopulations

We present a mathematical model, and the corresponding mathematical analysis, that justifies and quantifies the use of principal component analysis of biallelic genetic marker data for a set of individuals to detect the number of subpopulations represented in the data. We indicate that the power of the technique relies more on the number of individuals genotyped than on the number of markers.Comment: Corrected typos in Section 3.1 (M=120, N=2500) and proof of Lemma

Eigen-Inference for Energy Estimation of Multiple Sources

In this paper, a new method is introduced to blindly estimate the transmit power of multiple signal sources in multi-antenna fading channels, when the number of sensing devices and the number of available samples are sufficiently large compared to the number of sources. Recent advances in the field of large dimensional random matrix theory are used that result in a simple and computationally efficient consistent estimator of the power of each source. A criterion to determine the minimum number of sensors and the minimum number of samples required to achieve source separation is then introduced. Simulations are performed that corroborate the theoretical claims and show that the proposed power estimator largely outperforms alternative power inference techniques.Comment: to appear in IEEE Trans. on Information Theory, 17 pages, 13 figure

Study of resonance light scattering for remote optical probing

Enhanced scattering and fluorescence processes in the visible and UV were investigated which will enable improved remote measurements of gas properties. The theoretical relationship between scattering and fluorescence from an isolated molecule in the approach to resonance is examined through analysis of the time dependence of re-emitted light following excitation of pulsed incident light. Quantitative estimates are developed for the relative and absolute intensities of fluorescence and resonance scattering. New results are obtained for depolarization of scattering excited by light at wavelengths within a dissociative continuum. The experimental work was performed in two separate facilities. One of these utilizes argon and krypton lasers, single moded by a tilted etalon, and a 3/4 meter double monochromator. This facility was used to determine properties of the re-emission from NO2, I2 and O3 excited by visible light. The second facility involves a narrow-line dye laser, and a 3/4 meter single monochromator. The dye laser produces pulsed light with 5 nsec pulse duration and 0.005 nm spectral width

Robust Estimates of Covariance Matrices in the Large Dimensional Regime

This article studies the limiting behavior of a class of robust population covariance matrix estimators, originally due to Maronna in 1976, in the regime where both the number of available samples and the population size grow large. Using tools from random matrix theory, we prove that, for sample vectors made of independent entries having some moment conditions, the difference between the sample covariance matrix and (a scaled version of) such robust estimator tends to zero in spectral norm, almost surely. This result can be applied to various statistical methods arising from random matrix theory that can be made robust without altering their first order behavior.Comment: to appear in IEEE Transactions on Information Theor