This thesis is about the automatic acquisition of a particular kind of lexical knowledge, namely the knowledge of which noun senses can fill the argument slots of predicates. The knowledge is represented using probabilities, which agrees with the intuition that there are no absolute constraints on the arguments of predicates, but that the constraints are satisfied to a certain degree; thus the problem of knowledge acquisition becomes the problem of probability estimation from corpus data. The problem with defining a probability model in terms of senses is that this involves a huge number of parameters, which results in a sparse data problem. The proposal here is to define a probability model over senses in a semantic hierarchy, and exploit the fact that senses can be grouped into classes consisting of semantically similar senses. A novel class-based estimation technique is developed, together with a procedure that determines a suitable class for a sense (given a predicate and argument position). The problem of determining a suitable class can be thought of as finding a suitable level of generalisation in the hierarchy. The generalisation procedure uses a statistical test to locate areas consisting of semantically similar senses, and, as well as being used for probability estimation, is also employed as part of a re-estimation algorithm for estimating sense frequencies from incomplete data. The rest of the thesis considers how the lexical knowledge can be used to resolve structural ambiguities, and provides empirical evaluations. The estimation techniques are first integrated into a parse selection system, using a probabilistic dependency model to rank the alternative parses for a sentence. Then, a PP-attachment task is used to provide an evaluation which is more focussed on the class-based estimation technique, and, finally, a pseudo disambiguation task is used to compare the estimation technique with alternative approaches.

Throughout the past decade, interest has grown in the use of boundary-fitted coordinate systems in many areas of computational fluid dynamics. The boundary-fitted technique provides an exact method of implementing finite-difference numerical schemes in curved flow geometries and offers an alternative solution procedure to the finite-element method. The unavoidable large bandwidth of the global stiffness matrix, employed in finite-element algorithms, means that they are computationally less efficient than corresponding finite-difference schemes. As a consequence, the boundary-fitted method offers a more efficient process for solving partial differential flow equations in awkwardly shaped regions. This thesis describes a versatile finite-difference numerical scheme for the solution of the shallow water equations on arbitrary boundary-fitted non-orthogonal curvilinear grids. The model is capable of simulating flows in irregular geometries typically encountered in river basin management. Validation tests have been conducted against the severe condition of jet-forced flow in a circular reservoir with vertical side walls, where initial reflections of free surface waves pose major problems in achieving a stable solution. Furthermore, the validation exercises have been designed to test the computer model for artificial diffusion which may be a consequence of the numerical scheme adopted to stabilise the shallow water equations. The thesis also describes two subsidiary numerical studies of jet-forced recirculating flow in circular cylinders. The first of these implements a Biot-Savart discrete vortex method for simulating the vorticity in the shear layers of the inflow jet, whereas the second employs a stream function/vorticity-transport finite-difference procedure for solving the two-dimensional Navier-Stokes equations on a distorted orthogonal polar mesh. Although the predictions from the stream function/vorticity-transport model are confined to low Reynolds number flows, they provide a valuable set of benchmark velocity fields which are used to confirm the validity of the boundary-fitted shallow water equation solver.

published_or_final_version / abstract / Computer Science / Doctoral / Doctor of Philosophy

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