A principled approach to interactive hierarchical non-linear visualization of high-dimensional data

Hierarchical visualization systems are desirable because a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex high-dimensional data sets. We extend an existing locally linear hierarchical visualization system PhiVis [1] in several directions: bf(1) we allow for em non-linear projection manifolds (the basic building block is the Generative Topographic Mapping -- GTM), bf(2) we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree, bf(3) we describe folding patterns of low-dimensional projection manifold in high-dimensional data space by computing and visualizing the manifold's local directional curvatures. Quantities such as magnification factors [3] and directional curvatures are helpful for understanding the layout of the nonlinear projection manifold in the data space and for further refinement of the hierarchical visualization plot. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. We demonstrate the visualization system principle of the approach on a complex 12-dimensional data set and mention possible applications in the pharmaceutical industry.

Models of gas-liquid solubilities

A recent method for phase equilibria, the AGAPE method, has been used to predict activity coefficients and excess Gibbs energy for binary mixtures with good accuracy. The theory, based on a generalised London potential (GLP), accounts for intermolecular attractive forces. Unlike existing prediction methods, for example UNIFAC, the AGAPE method uses only information derived from accessible experimental data and molecular information for pure components. Presently, the AGAPE method has some limitations, namely that the mixtures must consist of small, non-polar compounds with no hydrogen bonding, at low moderate pressures and at conditions below the critical conditions of the components. Distinction between vapour-liquid equilibria and gas-liquid solubility is rather arbitrary and it seems reasonable to extend these ideas to solubility. The AGAPE model uses a molecular lattice-based mixing rule. By judicious use of computer programs a methodology was created to examine a body of experimental gas-liquid solubility data for gases such as carbon dioxide, propane, n-butane or sulphur hexafluoride which all have critical temperatures a little above 298 K dissolved in benzene, cyclo-hexane and methanol. Within this methodology the value of the GLP as an ab initio combining rule for such solutes in very dilute solutions in a variety of liquids has been tested. Using the GLP as a mixing rule involves the computation of rotationally averaged interactions between the constituent atoms, and new calculations have had to be made to discover the magnitude of the unlike pair interactions. These numbers have been seen as significant in their own right in the context of the behaviour of infinitely-dilute solutions. A method for extending this treatment to "permanent" gases has also been developed. The findings from the GLP method and from the more general AGAPE approach have been examined in the context of other models for gas-liquid solubility, both "classical" and contemporary, in particular those derived from equations-of-state methods and from reference solvent methods.

Neural network enhanced self tuning adaptive control application for non-linear control of dynamic systems

The main theme of research of this project concerns the study of neutral networks to control uncertain and non-linear control systems. This involves the control of continuous time, discrete time, hybrid and stochastic systems with input, state or output constraints by ensuring good performances. A great part of this project is devoted to the opening of frontiers between several mathematical and engineering approaches in order to tackle complex but very common non-linear control problems. The objectives are: 1. Design and develop procedures for neutral network enhanced self-tuning adaptive non-linear control systems; 2. To design, as a general procedure, neural network generalised minimum variance self-tuning controller for non-linear dynamic plants (Integration of neural network mapping with generalised minimum variance self-tuning controller strategies); 3. To develop a software package to evaluate control system performances using Matlab, Simulink and Neural Network toolbox. An adaptive control algorithm utilising a recurrent network as a model of a partial unknown non-linear plant with unmeasurable state is proposed. Appropriately, it appears that structured recurrent neural networks can provide conveniently parameterised dynamic models for many non-linear systems for use in adaptive control. Properties of static neural networks, which enabled successful design of stable adaptive control in the state feedback case, are also identified. A survey of the existing results is presented which puts them in a systematic framework showing their relation to classical self-tuning adaptive control application of neural control to a SISO/MIMO control. Simulation results demonstrate that the self-tuning design methods may be practically applicable to a reasonably large class of unknown linear and non-linear dynamic control systems.

Agent Based Models of Competition and Collaboration

Swarm intelligence is a popular paradigm for algorithm design. Frequently drawing inspiration from natural systems, it assigns simple rules to a set of agents with the aim that, through local interactions, they collectively solve some global problem. Current variants of a popular swarm based optimization algorithm, particle swarm optimization (PSO), are investigated with a focus on premature convergence. A novel variant, dispersive PSO, is proposed to address this problem and is shown to lead to increased robustness and performance compared to current PSO algorithms. A nature inspired decentralised multi-agent algorithm is proposed to solve a constrained problem of distributed task allocation. Agents must collect and process the mail batches, without global knowledge of their environment or communication between agents. New rules for specialisation are proposed and are shown to exhibit improved eciency and exibility compared to existing ones. These new rules are compared with a market based approach to agent control. The eciency (average number of tasks performed), the exibility (ability to react to changes in the environment), and the sensitivity to load (ability to cope with differing demands) are investigated in both static and dynamic environments. A hybrid algorithm combining both approaches, is shown to exhibit improved eciency and robustness. Evolutionary algorithms are employed, both to optimize parameters and to allow the various rules to evolve and compete. We also observe extinction and speciation. In order to interpret algorithm performance we analyse the causes of eciency loss, derive theoretical upper bounds for the eciency, as well as a complete theoretical description of a non-trivial case, and compare these with the experimental results. Motivated by this work we introduce agent "memory" (the possibility for agents to develop preferences for certain cities) and show that not only does it lead to emergent cooperation between agents, but also to a signicant increase in efficiency.

Developing accurate models of the human airways

Objectives Particle delivery to the airways is an attractive prospect for many potential therapeutics, including vaccines. Developing strategies for inhalation of particles provides a targeted, controlled and non-invasive delivery route but, as with all novel therapeutics, in vitro and in vivo testing are needed prior to clinical use. Whilst advanced vaccine testing demands the use of animal models to address safety issues, the production of robust in vitro cellular models would take account of the ethical framework known as the 3Rs (Replacement, Reduction and Refinement of animal use), by permitting initial screening of potential candidates prior to animal use. There is thus a need for relevant, realistic in vitro models of the human airways. Key findings Our laboratory has designed and characterised a multi-cellular model of human airways that takes account of the conditions in the airways and recapitulates many salient features, including the epithelial barrier and mucus secretion. Summary Our human pulmonary models recreate many of the obstacles to successful pulmonary delivery of particles and therefore represent a valid test platform for screening compounds and delivery systems.