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Sensible heat flux, a key component of the surface energy balance, is difficult to estimate in practice. This study was conducted to see if backpropagation neural networks could estimate sensible heat flux by using horizontal wind speed, air temperature, radiometric surface temperature, net radiation, and time as input. Ground measurements from the First ISLSCP (International Satellite Land Surface Climatology Project) Field Experiment (FIFE), collected in 1987 and 1989 over a prairie grassland in Kansas, were used for network training and validation. Networks trained on part of the data from a narrow range of space-time coordinates performed well over the other part, with error (root mean square error divided by mean of observations) values as low as 0.24. This indicates the potential in neural networks for linking sensible heat flux to routinely measured meteorological variables and variables amenable to remote sensing. When the networks were tested with data from other space-times, performance varied from good to poor, with average error values around 1.26. This was mainly due to lack of input variables parameterizing canopy morphology and soil moisture, indicating that such variables should be incorporated in the design of future networks intended for large scale applications.

Knowledge-based Cascade-correlation is a neural network algorithm that combines inductive learning and knowledge transfer (Shultz & Rivest, 2001). In the present thesis, this algorithm is tested on several real-world and artificial problems, and extended in several ways. The first extension consists in the incorporation of the Knowledge-based Artificial Neural Network (KBANN; Shavlik, 1994) technique for generating rule-based (RBCC) networks. The second extension consists of the adaptation of the Optimal Brain Damage (OBD; LeCun, Denker, & Solla, 1990) pruning technique to remove superfluous connection weights. Finally, the third extension consists in a new objective function based on information theory for controlling the distribution of knowledge attributed to subnetworks. A simulation of lexical ambiguity resolution is proposed. In this study, the use of RBCC networks is motivated from a cognitive and neurophysiological perspective.

I obtain a number of results for the dynamics of several disordered spin systems, of successively greater complexity. I commence with the generalised Hopfield model trained with an intensive number of patterns, where in the thermodynamic limit macroscopic, deterministic equations of motion can be derived exactly for both the synchronous discrete time and asynchronous continuous time dynamics. I show that for symmetric embedding matrices Lyapunov functions exist at the macroscopic level of description in terms of pattern overlaps. I then show that for asymmetric embedding matrices several types of bifurcation phenomena to complex non-transient dynamics occur, even in this simplest model. Extending a recent result of Coolen and Sherrington, I show how the dynamics of the generalised Hopfield model trained with extensively many patterns and non-trivial embedding matrix can be described by the evolution of a small number of overlaps and the disordered contribution to the 'energy', upon calculation of a noise distribution by the replica method. The evaluation of the noise distribution requires two key assumptions: that the flow equations are self averaging, and that equipartitioning of probability occurs within the macroscopic sub-shells of the ensemble. This method is inexact on intermediate time scales, due to the microscopic information integrated out in order to derive a closed set of equations. I then show how this theory can be improved in a systematic manner by introducing an order parameter function - the joint distribution of spins and local alignment fields, which evolves in time deterministically, according to a driven diffusion type equation. I show how the coefficients in this equation can be evaluated for the generalised Sherrington-Kirkpatrick model, both within the replica symmetric ansatz, and using Parisi's ultrametric ansatz for the replica matrices, upon making once again the two key assumptions (self averaging and equipartitioning). Since the order parameter is now a continuous function, however, the assumption of equipartitioning within the macroscopic sub-shells is much less restricting.

Neural networks have recently been applied to real-world speech recognition problems with a great deal of success. This thesis developes a strategy for optimising a neural network known as the Radial Basis Function classifier (RBF), on a large spoken letter recognition problem designed by British Telecom Research Laboratories. The strategy developed can be viewed as a compromise between a fully adaptive approach involving prohibitively large amounts of computation, and a heuristic approach resulting in poor generalisation. A value for the optimal number of kernel functions is suggested, and methods for determining the positions of the centres and the values of the width parameters are provided. During the evolution of the optimisation strategy it was demonstrated that spatial organisation of the centres does not adversely affect the ability of the classifier to generalise. An RBF employing the optimisation strategy achieved a lower error rate than a multilayer perceptron and two traditional static pattern classifiers on the same problem. The error rate of the RBF was very close to the theoretical minimum error rate obtainable with an optimal Bayes classifier. In addition to error rate, the performance of the classifiers was assessed in terms of the computational requirements of training and classification, illustrating the significant trade-off between computational investment in training and level of generalisation achieved. The error rate of the RBF was compared with that of a well established method of dynamic classification to examine whether non-linear time normalisation of word patterns was advantageous to generalisation. It was demonstrated that the dynamic classifier was better suited to small-scale speech recognition problems, and the RBF to speaker-independent speech recognition problems. The dynamic classifier was then combined with a neural network algorithm, greatly reducing its computational requirement without significantly increasing its error rate. This system was then extended into a novel system for visual feedback therapy in which speech is visualised as a moving trajectory on a computer screen.