Variational Markov Chain Monte Carlo for Bayesian smoothing of non-linear niffusions

In this paper we develop set of novel Markov chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. Flexible blocking strategies are introduced to further improve mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample, applications the algorithm is accurate except in the presence of large observation errors and low observation densities, which lead to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient.

The influence of non-metallic inclusions upon the properties of linepipe steels

The principal aim of this work was to determine the role of non-metallic inclusions in the process of hydrogen stepwise cracking (SWC). Additionally, the influence of inclusions upon the notch ductility of hydrogen charged (HC) and uncharged (UN) tensile specimens was examined. To obtain a basis for experiment a series of low carbon-manganese steels were prepared by induction melting. In order to produce variations in the composition, morphology, volume fraction, size and distribution of the inclusions the steel chemistry was adjusted prior to casting by additions of deoxidiser and Ca-Si injection. Sections of each ingot were hot rolled. Metallography, image analysis, mechanical tests and hydrogen SWC tests were then carried out. The volume fraction, morphology, and shape of inclusions influenced the tensile ductility of the steels. Marked anisotropy was found in the steels containing type II MnS inclusions at all rolling temperatures, whereas the fully Ca treated steel was isotropic. It was found that several inclusion parameters (projected length PL, mean free distance MFD, nearest-neighbour distance NND) correlated with fracture strain. An increase in inclusion volume fraction and/or the dimension of inclusions on a plane parallel to the plane of fracture led to a decrease in fracture strain. The inclusion parameters did not correlate with the fracture strains for the HC tensile specimens. However, large or clusters of inclusions acted as the principal sites for crack initiation. `Fisheyes' or areas of `flat' fracture were often found on these fracture surfaces. The criteria for SWC initiation was found to be either large inclusions or clusters of inclusions. As the PL of inclusions increased the probability of large SWCs occurring increased. SWC initiation at inclusions was believed to occur at a critical concentration of hydrogen. Factors which assisted the concentration of hydrogen at inclusions were discussed. None of the proposed mechanisms of hydrogen embrittlement could be identified as the single cause of SWC.

The influence of the chemical nature of dispersed phase on stability in oil-in-water emulsions

Some of the problems arising from the inherent instability of emulsions are discussed. Aspects of emulsion stability are described and particular attention is given to the influence of the chemical nature of the dispersed phase on adsorbed film structure and stability, Emulsion stability has been measured by a photomicrographic technique. Electrophoresis, interfacial tension and droplet rest-time data were also obtained. Emulsions were prepared using a range of oils, including aliphatic and aromatic hydrocarbons, dispersed In a solution of sodium dodecyl sulphate. In some cases a small amount of alkane or alkanol was incorporated into the oil phase. In general the findings agree with the classical view that the stability of oil-in-water emulsions is favoured by a closely packed interfacial film and appreciable electric charge on the droplets. The inclusion of non-ionic alcohol leads to enhanced stability, presumably owing to the formation of a "mixed" interfacial film which is more closely packed and probably more coherent than that of the anionic surfactant alone. In some instances differences in stability cannot he accounted for simply by differences in interfacial adsorption or droplet charge. Alternative explanations are discussed and it is postulated that the coarsening of emulsions may occur not only hy coalescence but also through the migration of oil from small droplets to larger ones by molecular diffusion. The viability of using the coalescence rates of droplets at a plane interface as a guide to emulsion stability has been researched. The construction of a suitable apparatus and the development of a standard testing procedure are described. Coalescence-time distributions may be correlated by equations similar to those presented by other workers, or by an analysis based upon the log-normal function. Stability parameters for a range of oils are discussed in terms of differences in film drainage and the natl1re of the interfacial film. Despite some broad correlations there is generally poor agreement between droplet and emulsion stabilities. It is concluded that hydrodynamic factors largely determine droplet stability in the systems studied. Consequently droplet rest-time measurements do not provide a sensible indication of emulsion stability,

Consideration of the efficacy of non-ionic vesicles in the targeted delivery of oral vaccines

The fundamentals of this research were to exploit non-ionic surfactant technology for delivery and administration of vaccine antigens across the oral route and to gain a better understanding of vaccine trafficking. Using a newly developed method for manufacture of non-ionic surfactant vesicles (niosomes and bilosomes) lower process temperatures were adopted thus reducing antigen exposure to potentially damaging conditions. Vesicles prepared by this method offered high protection to enzymatic degradation, with only ~10 % antigen loss measured when vesicles incorporating antigen were exposed to enzyme digestion. Interestingly, when formulated using this new production method, the addition of bile salt to the vesicles offered no advantage in terms of stability within simulated gastro-intestinal conditions. Considering their ability to deliver antigen to their target site, results demonstrated that incorporation of antigen within vesicles enhanced delivery and targeting of the antigen to the Peyer's Patch, again with niosomes and bilosomes offering similar efficiency. Delivery to both the Peyer's patches and mesentery lymphatics was shown to be dose dependent at lower concentrations, with saturation kinetics applying at higher concentrations. This demonstrates that in the formulation of vaccine delivery systems, the lipid/antigen dose ratio is not only a key factor in production cost, but is equally a key factor in the kinetics of delivery and targeting of a vaccine system. © 2013 Controlled Release Society.

Consideration of the efficacy of non-ionic vesicles in the targeted delivery of oral vaccines

The fundamentals of this research were to exploit non-ionic surfactant technology for delivery and administration of vaccine antigens across the oral route and to gain a better understanding of vaccine trafficking. Using a newly developed method for manufacture of non-ionic surfactant vesicles (niosomes and bilosomes) lower process temperatures were adopted thus reducing antigen exposure to potentially damaging conditions. Vesicles prepared by this method offered high protection to enzymatic degradation, with only ~10 % antigen loss measured when vesicles incorporating antigen were exposed to enzyme digestion. Interestingly, when formulated using this new production method, the addition of bile salt to the vesicles offered no advantage in terms of stability within simulated gastro-intestinal conditions. Considering their ability to deliver antigen to their target site, results demonstrated that incorporation of antigen within vesicles enhanced delivery and targeting of the antigen to the Peyer's Patch, again with niosomes and bilosomes offering similar efficiency. Delivery to both the Peyer's patches and mesentery lymphatics was shown to be dose dependent at lower concentrations, with saturation kinetics applying at higher concentrations. This demonstrates that in the formulation of vaccine delivery systems, the lipid/antigen dose ratio is not only a key factor in production cost, but is equally a key factor in the kinetics of delivery and targeting of a vaccine system. © 2013 Controlled Release Society.

Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

In this paper we develop set of novel Markov Chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. The novel diffusion bridge proposal derived from the variational approximation allows the use of a flexible blocking strategy that further improves mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample applications the algorithm is accurate except in the presence of large observation errors and low to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient. © 2011 Springer-Verlag.