Bayesian threshold selection for extremal models using measures of surprise

Statistical extreme value theory is concerned with the use of asymptotically motivated models to describe the extreme values of a process. A number of commonly used models are valid for observed data that exceed some high threshold. However, in practice a suitable threshold is unknown and must be determined for each analysis. While there are many threshold selection methods for univariate extremes, there are relatively few that can be applied in the multivariate setting. In addition, there are only a few Bayesian-based methods, which are naturally attractive in the modelling of extremes due to data scarcity. The use of Bayesian measures of surprise to determine suitable thresholds for extreme value models is proposed. Such measures quantify the level of support for the proposed extremal model and threshold, without the need to specify any model alternatives. This approach is easily implemented for both univariate and multivariate extremes.Comment: To appear in Computational Statistics and Data Analysi

Theory of Direct Scattering, Trapping and Desorption in Atom-Surface Collisions

When gas atoms or molecules collide with clean and ordered surfaces, under many circumstances the energy-resolved scattering spectra exhibit two clearly distinct features due to direct scattering and to trapping in the physisorption well with subsequent desorption. James Clerk Maxwell is credited with being the first to describe this situation by invoking the simple assumption that when an impinging gas beam is scattered from a surface it can be divided into a part that exchanges no energy and specularly reflects and another part that equilibrates or accommodates completely and then desorbs with an equilibrium distribution. In this paper a scattering theory is developed, using an iterative algorithm and classical mechanics for the collision process, that describes both direct scattering and trapping-desorption of the incident beam. The initially trapped fraction of particles can be followed as they continue to make further interactions with the surface until they are all eventually promoted back into the positive energy continuum and leave the surface region. Consequently, this theory allows a rigorous test of the Maxwell assumption and determines the conditions under which it is valid. The theory also gives quantitative explanations of recent experimental measurements which exhibit both a direct scattering contribution and a trapping-desorption fraction in the energy-resolved spectra.Comment: 46 pages including 14 figure

Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.Comment: 4 pages no figur

Inlet protein aggregation: a new mechanism for lubricating film formation with model synovial fluids.

This paper reports a fundamental study of lubricant film formation with model synovial fluid components (proteins) and bovine serum (BS). The objective was to investigate the role of proteins in the lubrication process. Film thickness was measured by optical interferometry in a ball-on-disc device (mean speed range of 2-60 mm/s). A commercial cobalt-chromium (CoCrMo) metal femoral head was used as the stationary component. The results for BS showed complex time-dependent behaviour, which was not representative of a simple fluid. After a few minutes sliding BS formed a thin adherent film of 10-20 nm, which was attributed to protein absorbance at the surface. This layer was augmented by a hydrodynamic film, which often increased at slow speeds. At the end of the test deposited surface layers of 20-50 nm were measured. Imaging of the contact showed that at slow speeds an apparent 'phase boundary' formed in the inlet just in front of the Hertzian zone. This was associated with the formation of a reservoir of high-viscosity material that periodically moved through the contact forming a much thicker film. The study shows that proteins play an important role in the film-forming process and current lubrication models do not capture these mechanisms

Solar Modulation of the Galactic Helium Spectrum Above 30 Mev Per Nucleon

Time measurements of differential energy spectra and flux of primary helium nuclei by use of charged particle telescope