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The increase in demand for the radio spectrum over the last twenty or so years has been huge, largely due to the surge development of mobile and wireless technologies. Interference between two sets of radio equipment can be a prohibiting factor if the tliei~ respective frequency assignments are not sufficiently separated on the radio spectrum. However, the radio spectrum is a finite resource and as such must be carefully .assigned to avoid excessive and unnecessary use while satisfying as many request of use for radio equipment as possible. This thesis is the result of an investigation into combinatorial optimisation methodologies applied to frequency assignment problems in which we study data, bounds, special cases, representations and algorithms. rvlost of our work concerns the minimum span problem in which an interference free assignment that satisfies frequency separation requirements is required. A comprehensive literature review is presented to give a thorough overview of the work done to date which serves as a basis for the remaining aspects of the thesis. Following this we consider the nature of frequency assignment problems by studying he benchmark data sets and classify them according to some of their inherent properties. This facilitates the generation of artificial data with properties that reflect real-life instances. Further to this we study the concept of 'robustness' of frequency assignments and study the effect of changing networks over time. It is noted that often frequency assignment problems have conflicting objectives. Vve study this in detail by considering the effect of combining objectives. Vve define a bi-criteria frequency assignment problem related to the span of an assignment using a· goal programming approach. We provide a mathematical analysis for this problem and consider the implications of restricting potential interference to co-channel and adjacent channel only. In addition, we provide an optimal solution when the co-channel subgraph has a particular structure. Our primary contribution is the useof a new representation for the minimum span frequency assignment problem that relates the number of acyclic orientations of a graph representing a radio nehvork to the span of frequency assignments. Vve provide results concerning the expected number of acyclic orientations of a graph and show that the solution space of this representation can be significantly smaller than other representations presented in the literature. In addition we define a new Hamming distance for graph orientations that is more suitable for frequency assignments than others proposed in the literature. We demonstrate the viability of this representation computationally by designing a set of simple genetic algorithms for the problem. A comprehensive set of experiments are designed and our algorithms are tested against approaches reported in the literature.

This thesis is concerned with the approximations of prediction error and predictive distribution of the best reserve estimate produced by the models which combine information from multiple data sets. Two models are studied . ~; within the GLM framework, i.e. SClmieper's: model proposed by Schnieper (1991) and the MeL method introduced by Quargand Mack (2004). Theoretical and empirical approximation approaches for the MSEP of these two models are discussed and compared. This includes derivations of closed formulae following the approaches introduced by· both Mack (1993) and Murphy (1994) and also the empirical approach, i.e. the bootstrap method. And finally, various models which combine information from multiple data sets are investigated and compared, providing new insights to the claims .reserving area.

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Wave run-up and overtopping of coastal structures have been extensively studied over the last 30 years to provide guidance for the construction of sea defences. Numerical models based on fluid flow equations can provide a useful aid in the design of these coastal defences. Computers have now advanced sufficiently to enable programs written to solve the flow equations to run on hardware that is readily available (e.g., desktop or laptop computers), thus giving engineers the ability to conduct multiple runs of an experiment, reconfigure the bathymetry, change the wave conditions and collect data from anywhere in the solution domain. An existing numerical model, AMAZON, based on the non-linear Shallow \Vater Equations (S\VE) was used to give wave height and overtopping discharges for a series of violent overtopping experiments. A second-order accurate highresolution finite-volume method was used to solve the SWE. The source terms that model the bed topography were treated using the Surface Gradient Method (SGM). The numerical model gave overtopping predictions to within 20% of the experimental overtopping discharges for cases where the wave ~onditions at the sea wall were not severely impacting. However, wave height comparisons showed that the SWE could not model wave propagation in intermediate depth water. The Boussinesq class of equations was chosen to extend the numerical modelling of wave propagation, run-up and overtopping into intermediate depth water. A hybrid finite-volumejfinite-difference solver was used to solve two different extended Boussinesq formulations, one of which was chosen to model a range of run-up and overtopping experiments. It was found'that the numerical model was able to model wave propagation where the typical depth to wavelength ratio was less than 0.35 for both regular and irregular waves. However, the numerical model was not able to accurately model breaking waves. Comparisons between overtopping discharges from the physical experiments and the numerical model showed that, in the majority of cases, the numerical model was able to provide predictions to within an absolute relative error of 3. It was found that as the gradient of the seawall increa'3ed, so did the accuracy of the numerical overtopping predictions.