Empirical Bayes selection of wavelet thresholds

This paper explores a class of empirical Bayes methods for level-dependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavy-tailed density. The mixing weight, or sparsity parameter, for each level of the transform is chosen by marginal maximum likelihood. If estimation is carried out using the posterior median, this is a random thresholding procedure; the estimation can also be carried out using other thresholding rules with the same threshold. Details of the calculations needed for implementing the procedure are included. In practice, the estimates are quick to compute and there is software available. Simulations on the standard model functions show excellent performance, and applications to data drawn from various fields of application are used to explore the practical performance of the approach. By using a general result on the risk of the corresponding marginal maximum likelihood approach for a single sequence, overall bounds on the risk of the method are found subject to membership of the unknown function in one of a wide range of Besov classes, covering also the case of f of bounded variation. The rates obtained are optimal for any value of the parameter p in (0,\infty], simultaneously for a wide range of loss functions, each dominating the L_q norm of the \sigmath derivative, with \sigma\ge0 and 0<q\le2.Comment: Published at http://dx.doi.org/10.1214/009053605000000345 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Physical Limit to the Magnetic Fields of T Tauri Stars

Recent estimates of magnetic field strengths in T Tauri stars yield values $B=1$--$4\,{\rm kG}$. In this paper, I present an upper limit to the photospheric values of $B$ by computing the equipartition values for different surface gravities and effective temperatures. The values of $B$ derived from the observations exceed this limit, and I examine the possible causes for this discrepancy

ASCA and ROSAT observations of nearby cluster cooling flows

We present a detailed analysis of the X-ray properties of the cooling flows in a sample of nearby, X-ray bright clusters of galaxies using high-quality ASCA spectra and ROSAT X-ray images. We demonstrate the need for multiphase models to consistently explain the spectral and imaging X-ray data for the clusters. The mass deposition rates of the cooling flows, independently determined from the ASCA spectra and ROSAT images, exhibit reasonable agreement. We confirm the presence of intrinsic X-ray absorption in the clusters using a variety of spectral models. We also report detections of extended $100\mu$m infrared emission, spatially coincident with the cooling flows, in several of the systems studied. The observed infrared fluxes and flux limits are in good agreement with the predicted values due to reprocessed X-ray emission from the cooling flows. We present precise measurements of the abundances of iron, magnesium, silicon and sulphur in the central regions of the Virgo and Centaurus clusters. Our results firmly favour models in which a high mass fraction (70-80 per cent) of the iron in the X-ray gas in these regions is due to Type Ia supernovae. Finally, we present a series of methods which may be used to measure the ages of cooling flows from the X-ray data. The results for the present sample of clusters indicate ages of between 2.5 and 7 Gyr. If the ages of cooling flows are primarily set by subcluster merger events, then our results suggest that in the largest clusters, mergers with subclusters with masses of approximately 30 per cent of the final cluster mass are likely to disrupt cooling flows.Comment: Final version. MNRAS, in press. 36 pages, 9 figs, 14 tables in MNRAS LaTex styl

Measuring the difference between actual and reported food intakes in the context of energy balance under laboratory conditions

Acknowledgements The present study was funded by the Food Standards Agency, UK. The Food Standards Agency had no role in the design, analysis or writing of this article. The authors’ responsibilities were as follows: R. J. S., L. M. O’R. and G. W. H. designed the research; L. M. O’R. and Z. F. conducted the research and analysed the data; G. W. H. performed the statistical analyses; P. R. carried out the DLW analysis; R. J. S. had primary responsibility for the final content; R. J. S., L. M. O’R., Z. F., S. W. and M. B. E. L. wrote the paper.Peer reviewedPublisher PD

Effect of the beam-beam interactions on the dynamic aperture of the LHC at collision

The dynamic aperture of the LHC at collision energy is limited by the field errors in the IR quadrupoles being built at FNAL and KEK. The 300 mu rad crossing angle, incorporated in the design to reduce the effect of the long-range beam beam interactions, enhances the effect of the multipoles on the dynamic aperture. We have investigated the possibility of a different crossing angle with a more accurate modelling of the long-range interactions. Tune scans have been done to determine if a better choice of the tunes exists. (7 refs)

New times, new politics: history and memory during the final years of the CPGB

This article examines the relationship between collective memory, historical interpretation and political identity. It focuses on the dissolution of the Communist Party of Great Britain (CPGB) as constructed through collective narrative memory, and on Marxist interpretations of history. The divisions within the party and the wider Marxist community, stretching from 1956 until 1991, were often framed around questions of historical interpretation. The events of 1989–1991 created an historical and mnemonic crisis for CPGB members who struggled to reconcile their past identities with their present situation. Unlike the outward-facing revisionism of other political parties, this was an intensely personal affair. The solution for many was to emphasise the need to find new ways to progress socialist aims, without relying on a discredited grand narrative. In contrast, other Communist parties, such as the Communist Party of Britain, which had been established (or ‘re-established’) in 1988, fared rather better. By adhering to the international party line of renewal and continued struggle, the party was able to hold its narrative together, condemning the excesses of totalitarian regimes, while reaffirming the need for international class struggle

A Deep Look at the Emission-Line Nebula in Abell 2597

The close correlation between cooling flows and emission-line nebulae in clusters of galaxies has been recognized for over a decade and a half, but the physical reason for this connection remains unclear. Here we present deep optical spectra of the nebula in Abell 2597, one of the nearest strong cooling-flow clusters. These spectra reveal the density, temperature, and metal abundances of the line-emitting gas. The abundances are roughly half-solar, and dust produces an extinction of at least a magnitude in V. The absence of [O III] 4363 emission rules out shocks as a major ionizing mechanism, and the weakness of He II 4686 rules out a hard ionizing source, such as an active galactic nucleus or cooling intracluster gas. Hot stars are therefore the best candidate for producing the ionization. However, even the hottest O stars cannot power a nebula as hot as the one we see. Some other nonionizing source of heat appears to contribute a comparable amount of power. We show that the energy flux from a confining medium can become important when the ionization level of a nebula drops to the low levels seen in cooling-flow nebulae. We suggest that this kind of phenomenon, in which energy fluxes from the surrounding medium augment photoelectric heating, might be the common feature underlying the diverse group of objects classified as LINERS.Comment: 33 Latex pages, including 16 Postscript figures, to appear in 1997 September 1 Astrophysical Journa