Advanced mean field methods:theory and practice

A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.

Online approximations for wind-field models

We study online approximations to Gaussian process models for spatially distributed systems. We apply our method to the prediction of wind fields over the ocean surface from scatterometer data. Our approach combines a sequential update of a Gaussian approximation to the posterior with a sparse representation that allows to treat problems with a large number of observations.

Field experiments on the dispersal, establishment and colonization of lichens on a slate rock surface

A sample of run-off water from a vertical, slate rock surface in Wales, U.K. contained abundant fragments of the lichen Parmelia glabratula ssp. fuliginosa from about 0.6 to 8.0 mm in diameter, a few fragments of Parmelia conspersa from 0.6 to 4.0 mm in diameter and a large number of unidentified propagules from 0.2 to 0.5 mm in diameter. The colonization of permanent plots on the rock surface was studied over six years. At the end of the experiment relatively few thalli of Parmelia conspersa, Parmelia glabratula ssp. fuliginosa and Buellia aethalea had established in plots on undisturbed and newly-exposed slate. Fragments (2 mm in diameter) of Parmelia conspersa placed on horizontal pieces of slate survived up to 120 days in cracks, 20 days on a thin smear of bird droppings but only 2-3 days on smooth slate, against small joints in the rock or in small holes. Isidia of Parmelia conspersa placed on horizontal pieces of slate established equally in plots on smooth undisturbed slate and in plots on the surface exposed after the removal of large Parmelia conspersa thalli, but less well on newly-exposed slate. These results suggest that lichen propagules are abundant in run-off water but establishment is a hazardous process. This may be attributable to a shortage of suitable sites on the substratum for attachment of propagules.

Analysis of plasmid profiles of Aeromonas salmonicida isolates by pulsed field gel electrophoresis

Plasmid constitutions of Aeromonas salmonicida isolates were characterised by flat-bed and pulsed field gel electrophoresis. Resolution of plasmids by pulsed field gel electrophoresis was greater and more consistent than that achieved by flat-bed gel electrophoresis. The number of plasmids separated by pulsed field gel electrophoresis varied between A. salmonicida isolates, with five being the most common number present in the isolates used in this study. Plasmid profiles were diverse and the reproducibility of the distances migrated facilitated the use of principal components analysis for the characterisation of the isolates. Isolates were grouped according to the number of plasmids supported. Further principal components analysis of groups of isolates supporting five and seven plasmids showed a spatial separation of plasmids based upon distance migrated. Principal components analysis of plasmid profiles and antimicrobial minimum inhibitory concentrations could not be correlated suggesting that resistance to antimicrobial agents is not associated with either one plasmid or a particular plasmid constitution.

Flow field analysis of some mixing and conveying screw element regions, within a closely intermeshing, co-rotating twin-screw extruder.

Grafting of antioxidants and other modifiers onto polymers by reactive extrusion, has been performed successfully by the Polymer Processing and Performance Group at Aston University. Traditionally the optimum conditions for the grafting process have been established within a Brabender internal mixer. Transfer of this batch process to a continuous processor, such as an extruder, has, typically, been empirical. To have more confidence in the success of direct transfer of the process requires knowledge of, and comparison between, residence times, mixing intensities, shear rates and flow regimes in the internal mixer and in the continuous processor.The continuous processor chosen for the current work in the closely intermeshing, co-rotating twin-screw extruder (CICo-TSE). CICo-TSEs contain screw elements that convey material with a self-wiping action and are widely used for polymer compounding and blending. Of the different mixing modules contained within the CICo-TSE, the trilobal elements, which impose intensive mixing, and the mixing discs, which impose extensive mixing, are of importance when establishing the intensity of mixing. In this thesis, the flow patterns within the various regions of the single-flighted conveying screw elements and within both the trilobal element and mixing disc zones of a Betol BTS40 CICo-TSE, have been modelled using the computational fluid dynamics package Polyflow. A major obstacle encountered when solving the flow problem within all of these sets of elements, arises from both the complex geometry and the time-dependent flow boundaries as the elements rotate about their fixed axes. Simulation of the time dependent boundaries was overcome by selecting a number of sequential 2D and 3D geometries, used to represent partial mixing cycles. The flow fields were simulated using the ideal rheological properties of polypropylene and characterised in terms of velocity vectors, shear stresses generated and a parameter known as the mixing efficiency. The majority of the large 3D simulations were performed on the Cray J90 supercomputer situated at the Rutherford-Appleton laboratories, with pre- and postprocessing operations achieved via a Silicon Graphics Indy workstation. A mechanical model was constructed consisting of various CICo-TSE elements rotating within a transparent outer barrel. A technique has been developed using coloured viscous clays whereby the flow patterns and mixing characteristics within the CICo-TSE may be visualised. In order to test and verify the simulated predictions, the patterns observed within the mechanical model were compared with the flow patterns predicted by the computational model. The flow patterns within the single-flighted conveying screw elements in particular, showed good agreement between the experimental and simulated results.

Relationships between fundus image quantification and visual field status in age-related macular degeneration

Presentation Purpose:To relate structural change to functional change in age-related macular degeneration (AMD) in a cross-sectional population using fundus imaging and the visual field status. Methods:10 degree standard and SWAP visual fields and other standard functional clinical measures were acquired in 44 eyes of 27 patients at various stages of AMD, as well as fundus photographs. Retro-mode SLO images were captured in a subset of 29 eyes of 19 of the patients. Drusen area, measured by automated drusen segmentation software (Smith et al. 2005) was correlated with visual field data. Visual field defect position was compared to the position of the imaged drusen and deposits using custom software. Results:The effect of AMD stage on drusen area within the 6000µm was significant (One-way ANOVA: F = 17.231, p < 0.001), however the trend was not strong across all stages. There were significant linear relationships between visual field parameters and drusen area. The mean deviation (MD) declined by 3.00dB and 3.92dB for each log % drusen area for standard perimetry and SWAP, respectively. The visual field parameters of focal loss displayed the strongest correlations with drusen area. The number of pattern deviation (PD) defects increased by 9.30 and 9.68 defects per log % drusen area for standard perimetry and SWAP, respectively. Weaker correlations were found between drusen area and visual acuity, contrast sensitivity, colour vision and reading speed. 72.6% of standard PD defects and 65.2% of SWAP PD defects coincided with retinal signs of AMD on fundus photography. 67.5% of standard PD defects and 69.7% of SWAP PD defects coincided with deposits on retro-mode images. Conclusions:Perimetry exhibited a stronger relationship with drusen area than other measures of visual function. The structure-function relationship between visual field parameters and drusen area was linear. Overall the indices of focal loss had a stronger correlation with drusen area in SWAP than in standard perimetry. Visual field defects had a high coincidence proportion with retinal manifestations of AMD.Smith R.T. et al. (2005) Arch Ophthalmol 123:200-206.

Asymptotic theory of wall-attached convection in a horizontal fluid layer with a vertical magnetic field

A horizontal fluid layer heated from below in the presence of a vertical magnetic field is considered. A simple asymptotic analysis is presented which demonstrates that a convection mode attached to the side walls of the layer sets in at Rayleigh numbers much below those required for the onset of convection in the bulk of the layer. The analysis complements an earlier analysis by Houchens [J. Fluid Mech. 469, 189 (2002)] which derived expressions for the critical Rayleigh number for the onset of convection in a vertical cylinder with an axial magnetic field in the cases of two aspect ratios. © 2008 American Institute of Physics.