Random action of compact Lie groups and minimax estimation of a mean pattern

This paper considers the problem of estimating a mean pattern in the setting of Grenander's pattern theory. Shape variability in a data set of curves or images is modeled by the random action of elements in a compact Lie group on an infinite dimensional space. In the case of observations contaminated by an additive Gaussian white noise, it is shown that estimating a reference template in the setting of Grenander's pattern theory falls into the category of deconvolution problems over Lie groups. To obtain this result, we build an estimator of a mean pattern by using Fourier deconvolution and harmonic analysis on compact Lie groups. In an asymptotic setting where the number of observed curves or images tends to infinity, we derive upper and lower bounds for the minimax quadratic risk over Sobolev balls. This rate depends on the smoothness of the density of the random Lie group elements representing shape variability in the data, which makes a connection between estimating a mean pattern and standard deconvolution problems in nonparametric statistics

PERT: A Method for Expression Deconvolution of Human Blood Samples from Varied Microenvironmental and Developmental Conditions

The cellular composition of heterogeneous samples can be predicted using an expression deconvolution algorithm to decompose their gene expression profiles based on pre-defined, reference gene expression profiles of the constituent populations in these samples. However, the expression profiles of the actual constituent populations are often perturbed from those of the reference profiles due to gene expression changes in cells associated with microenvironmental or developmental effects. Existing deconvolution algorithms do not account for these changes and give incorrect results when benchmarked against those measured by well-established flow cytometry, even after batch correction was applied. We introduce PERT, a new probabilistic expression deconvolution method that detects and accounts for a shared, multiplicative perturbation in the reference profiles when performing expression deconvolution. We applied PERT and three other state-of-the-art expression deconvolution methods to predict cell frequencies within heterogeneous human blood samples that were collected under several conditions (uncultured mono-nucleated and lineage-depleted cells, and culture-derived lineage-depleted cells). Only PERT's predicted proportions of the constituent populations matched those assigned by flow cytometry. Genes associated with cell cycle processes were highly enriched among those with the largest predicted expression changes between the cultured and uncultured conditions. We anticipate that PERT will be widely applicable to expression deconvolution strategies that use profiles from reference populations that vary from the corresponding constituent populations in cellular state but not cellular phenotypic identity

A method for spatial deconvolution of spectra

A method for spatial deconvolution of spectra is presented. It follows the same fundamental principles as the ``MCS image deconvolution algorithm'' (Magain, Courbin, Sohy, 1998) and uses information contained in the spectrum of a reference Point Spread Function (PSF) to spatially deconvolve spectra of very blended sources. An improved resolution rather than an infinite one is aimed at, overcoming the well known problem of ``deconvolution artefacts''. As in the MCS algorithm, the data are decomposed into a sum of analytical point sources and a numerically deconvolved background, so that the spectrum of extended sources in the immediate vicinity of bright point sources may be accurately extracted and sharpened. The algorithm has been tested on simulated data including seeing variation as a function of wavelength and atmospheric refraction. It is shown that the spectra of severely blended point sources can be resolved while fully preserving the spectrophotometric properties of the data. Extended objects ``hidden'' by bright point sources (up to 4-5 magnitudes brighter) can be accurately recovered as well, provided the data have a sufficiently high total signal-to-noise ratio (200-300 per spectral resolution element). Such spectra are relatively easy to obtain, even down to faint magnitudes, within a few hours of integration time with 10m class telescopes.Comment: 18 pages, 6 postscript figures, in press in Ap

The detection of Gravitational Waves

This chapter is concerned with the question: how do gravitational waves (GWs) interact with their detectors? It is intended to be a theory review of the fundamental concepts involved in interferometric and acoustic (Weber bar) GW antennas. In particular, the type of signal the GW deposits in the detector in each case will be assessed, as well as its intensity and deconvolution. Brief reference will also be made to detector sensitivity characterisation, including very summary data on current state of the art GW detectors.Comment: 33 pages, 12 figures, LaTeX2e, Springer style files --included. For Proceedings of the ERE-2001 Conference (Madrid, September 2001

Doppler imaging of the young late-type star LO Pegasi (BD +22 4409) in September 2003

A Doppler image of the ZAMS late-type rapidly rotating star LO Pegasi, based on spectra acquired between 12 and 15 September 2003, is presented. The Least Square Deconvolution technique is applied to enhance the signal-to-noise ratio of the mean rotational broadened line profiles extracted from the observed spectra. In the present application, a unbroadened spectrum is used as a reference, instead of a simple line list, to improve the deconvolution technique applied to extract the mean profiles. The reconstructed image is similar to those previously obtained from observations taken in 1993 and 1998, and shows that LO Peg photospheric activity is dominated by high-latitude spots with a non-uniform polar cap. The latter seems to be a persistent feature as it has been observed since 1993 with little modifications. Small spots, observed between ~ 10 and ~ 60 degrees of latitude, appears to be different with respect to those present in the 1993 and 1998 maps.Comment: 21 pages, 10 figures, accepted by Monthly Notices of the Royal Astronomical Societ