Modelling conditional probability distributions for periodic variables

Most of the common techniques for estimating conditional probability densities are inappropriate for applications involving periodic variables. In this paper we introduce two novel techniques for tackling such problems, and investigate their performance using synthetic data. We then apply these techniques to the problem of extracting the distribution of wind vector directions from radar scatterometer data gathered by a remote-sensing satellite.

Modelling conditional probability distributions for periodic variables

Most of the common techniques for estimating conditional probability densities are inappropriate for applications involving periodic variables. In this paper we apply two novel techniques to the problem of extracting the distribution of wind vector directions from radar catterometer data gathered by a remote-sensing satellite.

Modelling conditional probability distributions for periodic variables

Most conventional techniques for estimating conditional probability densities are inappropriate for applications involving periodic variables. In this paper we introduce three related techniques for tackling such problems, and investigate their performance using synthetic data. We then apply these techniques to the problem of extracting the distribution of wind vector directions from radar scatterometer data gathered by a remote-sensing satellite.

Bayesian invariant measurements of generalisation for discrete distributions

Neural network learning rules can be viewed as statistical estimators. They should be studied in Bayesian framework even if they are not Bayesian estimators. Generalisation should be measured by the divergence between the true distribution and the estimated distribution. Information divergences are invariant measurements of the divergence between two distributions. The posterior average information divergence is used to measure the generalisation ability of a network. The optimal estimators for multinomial distributions with Dirichlet priors are studied in detail. This confirms that the definition is compatible with intuition. The results also show that many commonly used methods can be put under this unified framework, by assume special priors and special divergences.

Bayesian invariant measurements of generalisation for continuous distributions

A family of measurements of generalisation is proposed for estimators of continuous distributions. In particular, they apply to neural network learning rules associated with continuous neural networks. The optimal estimators (learning rules) in this sense are Bayesian decision methods with information divergence as loss function. The Bayesian framework guarantees internal coherence of such measurements, while the information geometric loss function guarantees invariance. The theoretical solution for the optimal estimator is derived by a variational method. It is applied to the family of Gaussian distributions and the implications are discussed. This is one in a series of technical reports on this topic; it generalises the results of ¸iteZhu95:prob.discrete to continuous distributions and serve as a concrete example of a larger picture ¸iteZhu95:generalisation.

Robust control of nonlinear stochastic systems by modelling conditional distributions of control signals

We introduce a novel inversion-based neuro-controller for solving control problems involving uncertain nonlinear systems that could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. In this work a novel robust inverse control approach is obtained based on importance sampling from these distributions. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The performance of the new algorithm is illustrated through simulations with example systems.

Velocity distributions in a plate heat exchanger channel

The development of a Laser Doppler Anemometer technique to measure the velocity distribution in a commercial plate heat exchanger is described. Detailed velocity profiles are presented and a preliminary investigation is reported on flow behaviour through a single cell in the channel matrix. The objective of the study was to extend previous investigations of plate heat exchanger flow patterns in the laminar range with the eventual aim of establishing the effect of flow patterns on heat transfer performance, thus leading to improved plate heat exchanger design and design methods. Accurate point velocities were obtained by Laser Anemometry in a perspex replica of the metal channel. Oil was used as a circulating liquid with a refractive index matched to that of the perspex so that the laser beams were not distorted. Cell-by-cell velocity measurements over a range of Reynolds number up to ten showed significant liquid mal-distribution. Local cell velocities were found to be as high as twenty seven times average velocity, contrary to the previously held belief of four times. The degree of mal-distribution varied across the channel as well as in the vertical direction, and depended on the upward or downward direction of flow. At Reynolds numbers less than one, flow zig-zagged from one side of the channel to the other in wave form, but increases in Reynolds number improved liquid distribution. A detailed examination of selected cells showed velocity variations in different directions, together with variation within individual cells. Experimental results are also reported on the flow split when passing through a single cell in a section of a channel . These observations were used to explain mal-distribution in the perspex channel itself.

Stock price distributions and news:evidence from index options

We estimate the shape of the distribution of stock prices using data from options on the underlying asset, and test whether this distribution is distorted in a systematic manner each time a particular news event occurs. In particular we look at the response of the FTSE100 index to market wide announcements of key macroeconomic indicators and policy variables. We show that the whole distribution of stock prices can be distorted on an event day. The shift in distributional shape happens whether the event is characterized as an announcement occurrence or as a measured surprise. We find that larger surprises have proportionately greater impact, and that higher moments are more sensitive to events however characterised.

Size frequency distributions of abnormal protein deposits in Alzheimer’s disease and variant Creutzfeldt-Jakob disease

TThe size frequency distributions of ß-amyloid (Aß) and prion protein (PrPsc) deposits were studied in Alzheimer’s disease (AD) and the variant form of Creutzfeldt-Jakob disease (vCJD) respectively. All size distributions were unimodal and positively skewed. Aß deposits reached a greater maximum size and their distributions were significantly less skewed than the PrPsc deposits. All distributions were approximately log-normal in shape but only the diffuse PrPsc deposits did not deviate significantly from a log-normal model. There were fewer larger classic Aß deposits than predicted and the florid PrPsc deposits occupied a more restricted size range than predicted by a log-normal model. Hence, Aß deposits exhibit greater growth than the corresponding PrPsc deposits. Surface diffusion may be particularly important in determining the growth of the diffuse PrPsc deposits. In addition, there are factors limiting the maximum size of the Aß and florid PrPsc deposits.

Size frequency distributions of the florid prion protein aggregates in variant Creutzfeldt-Jakob disease follow a power-law function

The objective was to test the hypothesis that the size frequency distributions of the prion protein (PrP) plaques in cases of variant Creutzfeldt-Jakob disease (vCJD) follow a power-law function. The design was a retrospective neuropathological study. The patients were 11 cases of clinically and neuropathologically verified vCJD. Size distributions of the diffuse and florid-type plaques were measured in several areas of the cerebral cortex and hippocampus from each case and a power-law function fitted to each distribution. The size distributions of the florid and diffuse plaques were fitted successfully by a powerlaw function in 100% and 42% of brain areas investigated respectively. Processes of aggregation/disaggregation may be more important than surface diffusion in the pathogenesis of the florid plaques. By contrast, surface diffusion may be a more significant factor in the development of the diffuse plaques. © Springer-Verlag Italia 2006.

Sequence distributions in free-radical polymers

This thesis is concerned with demonstrating how the visual representation of the sequence distribution of individual monomer units, of a polymer, that would be observed upon polymerisation, may be utilised in designing and synthesizing polymers with relatively low cell adhesion characteristics, The initial part of this thesis is concerned with demonstrating the use of a computer simulation technique, in illustrating the sequence distribution that would be observed upon the polymerisation of a set of monomers. The power of the computer simulation technique has been demonstrated through the simulation of the sequence distributions of some generic contact lens materials. These generic contact lens materials were chosen simply because in the field of biomaterials their compositions are amongst the most systematically regulated and they present a wide range of compositions. The validity of the computer simulation technique has been assessed through the synthesis and analysis of linear free-radical polymers at different conversions. Two main parameters were examined, that of composition and the number-average sequence lengths of individual monomer units, at various conversions. The polymers were synthesized through the solution polymerisation process. The monomer composition was determined by elemental analysis and 13C nuclear magnetic analysis (NMR). Number-average sequence lengths were determined exclusively through 13C NMR. Although the computer simulation technique provides a visual representation of the monomer sequence distribution up to 100% conversion, these assessments were made on linear polymers at a reasonably high conversion (above 50%) but below 100% conversion of ease for analysis. The analyses proved that the computer simulation technique was reasonably accurate in predicting the sequence distribution of monomer units, upon polymerisation, in the polymer.An approach has been presented which allows one to manipulate the use of monomers, with their reactivity ratios, thereby enabling us to design polymers with controlled sequence distributions.Hydrogel membranes, with relatively controlled sequence distributions and polymerised to 100% conversion, were synthesized to represent prospective biomaterials. Cell adhesion studies were used as a biological probe to investigate the susceptibility of the surface of these membranes to cell adhesion. This was necessary in order to assess the surface biocompatibility or biotolerance of these prospective biomaterials.

The size frequency distributions of beta-amyloid deposit subtypes in Alzheimer's disease

The size frequency distributions of diffuse, primitive and classic beta/A4 deposits was studied in single sections in the hippocampus, parahippocampal gyrus (PHG) and lateral occipitotemporal gyrus (LOT) in five cases of Alzheimer's disease. In most brain regions, the size distribution of the diffuse deposits was significantly different from that of the primitive and classic deposits. The data suggested that larger diffuse deposits appeared to be converted less often into primitive and classic deposits. Significant differences in the size distribution of primitive deposits were commonly observed between brain regions in which there was no difference in the size distribution of the diffuse deposits. Hence, local brain factors may influence the size of diffuse deposit which can be converted into mature amyloid deposit.