The species–area relationship (SAR) has been applied to predict species richness declines as area is converted to human-dominated land covers.In many areas of the world, however, many species persist in human-dominated areas, including threatened species. Because SARs are decelerating nonlinear, small extents of natural habitat can be converted to human use with little expected loss of associated species, but with the addition of more species that are associated with human land uses. Decelerating SARs suggest that, as area is converted to human-dominated forms, more species will be added to the rare habitat than are lost from the common one. This should lead to a peaked relationship between richness and natural area. I found that the effect of natural area on avian richness across Ontario was consistent with the sum of SARs for natural habitat species and human-dominated habitat species, suggesting that almost half the natural area can be converted to human-dominated forms before richness declines. However, I found that this spatial relationship did not remain consistent through time: bird richness increased when natural cover was removed (up to 4%), irrespective of its original extent. The inclusion of metapopulation processes in predictive models of species presence improves predictions of diversity change through time dramatically. Variability in site occupancy was common among bird species evaluated in this study, likely resulting from local extinction-colonization dynamics. Likelihood of species presence declined when few neighbouring sites were previously occupied by the species. Site occupancy was also less likely when little suitable habitat was present. Consistent with expectations that larger habitats are easier targets for colonists, habitat area was more important for more isolated sites. Accounting for the effect of metapopulation dynamics on site occupancy predicted change in richness better than land cover change and increased the strength of the regional richness–natural area relationship to levels observed for continental richness–environment relationships suggesting that these metapopulation processes “scale up” to modify regional species richness patterns making them more difficult to predict. It is the existence of absences in otherwise suitable habitat within species’ ranges that appears to weaken regional richness–environment relationships.

Copulas are multivariate probability distributions, as well as functions which link marginal distributions to their joint distribution. These functions have been used extensively in finance and more recently in other disciplines, for example hydrology and genetics. This study has two components, (a) the development of copula-based mathematical tools for use in all industries, and (b) the application of distorted copulas in structured finance. In the first part of this study, copulabased conditional expectation formulae are described and are applied to small data sets from medicine and hydrology. In the second part of this study we develop a method of improving the estimation of default risk in the context of collateralized debt obligations. Credit risk is a particularly important application of copulas, and given the current global financial crisis, there is great motivation to improve the way these functions are applied. We compose distortion functions with copula functions in order to obtain greater flexibility and accuracy in existing pricing algorithms. We also describe an n-dimensional dynamic copula, which takes into account temporal and spatial changes. / Thesis (Ph.D.) - University of Adelaide, School of Mathematical sciences, 2009

Partial saturation of porous rock by two fluids substantially affects compressional wave propagation. In particular, partial saturation causes significant attenuation and dispersion due to wave-induced fluid flow. Such flow arises when a passing wave induces different fluid pressures in regions of rock saturated by different fluids. When partial saturation is mesoscopic, i.e. existing on a length scale much greater than pore scale but less than wavelength scale, significant attenuation can arise for frequencies 10-1000 Hz. Models for attenuation and dispersion due to mesoscale heterogeneities mostly assume fluids are distributed in a regular way. Recent experiments indicate mesoscopic heterogeneities have less idealised distributions and distribution affects attenuation/dispersion. Thus, theoretical models are required to simulate effects due to realistic fluid distributions. / The thesis focus is to model attenuation and dispersion due to realistic mesoscopic fluid distributions and fluid contrasts. First X-ray tomographic images of partially saturated rock are analysed statistically to identify spatial measures useful for describing fluid distribution patterns. The correlation function and associated correlation length for a specific fluid type are shown to be of greatest utility. Next a new model, called 3DCRM (CRM stands for continuous random media) is derived, utilizing a correlation function to describe the fluid distribution pattern. It is a random media model, is accurate for small fluid contrast and approximate for large fluid contrast. Using 3DCRM attenuation and dispersion are shown to depend on fluid distribution. / Next a general framework for partial saturation called APS (acoustics of partial saturation) is extended enabling estimation of attenuation and dispersion due to arbitrary 1D/3D fluid distributions. The intent is to construct a versatile model enabling attenuation and dispersion to be estimated for arbitrary fluid distributions, contrasts and saturations. Two crucial parameters within APS called shape and frequency scaling parameters are modified via asymptotic analysis using several random media models (which are accurate for only certain contrasts in fluid bulk moduli and percent saturation). For valid fluid contrasts and saturations, which satisfy certain random media conditions there is good correspondence between modified APS and the random media models, hence showing that APS can be utilized to model attenuation and dispersion due to more realistic fluid distributions. / Finally I devise a numerical method to test the accuracy of the analytical shape parameters for a range of fluid distributions, saturations and contrasts. In particular, the analytical shape parameter for randomly distributed spheres was shown to be accurate for a large range of saturations and fluid contrasts.

The underlying aim of this research is to investigate the mathematical descriptions of homogeneous textures in digital images for the purpose of segmentation and recognition. The research covers the problem of testing these mathematical descriptions by using them to generate synthetic realisations of the homogeneous texture for subjective and analytical comparisons with the source texture from which they were derived. The application of this research is in analysing satellite or airborne images of the Earth's surface. In particular, Synthetic Aperture Radar (SAR) images often exhibit regions of homogeneous texture, which if segmented, could facilitate terrain classification. In this thesis we present noncausal, nonparametric, multiscale, Markov random field (MRF) models for recognising and synthesising texture. The models have the ability to capture the characteristics of, and to synthesise, a wide variety of textures, varying from the highly structured to the stochastic. For texture synthesis, we introduce our own novel multiscale approach incorporating a new concept of local annealing. This allows us to use large neighbourhood systems to model complex natural textures with high order statistical characteristics. The new multiscale texture synthesis algorithm also produces synthetic textures with few, if any, phase discontinuities. The power of our modelling technique is evident in that only a small source image is required to synthesise representative examples of the source texture, even when the texture contains long-range characteristics. We also show how the high-dimensional model of the texture may be modelled with lower dimensional statistics without compromising the integrity of the representation. We then show how these models -- which are able to capture most of the unique characteristics of a texture -- can be for the ``open-ended'' problem of recognising textures embedded in a scene containing previously unseen textures. Whilst this technique was developed for the practical application of recognising different terrain types from Synthetic Aperture Radar (SAR) images, it has applications in other image processing tasks requiring texture recognition.

Thesis (Ph. D.)--University of Sydney, 2002. / Title from title screen (viewed Apr. 28, 2008). Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the School of Mathematics and Statistics, Faculty of Science. Includes bibliography. Also available in print form.

Thesis (Ph.D.)--University of Wollongong, 2004. / Typescript. Includes bibliographical references: leaf 106-117.

Thesis (M. A.)--University of Notre Dame, 2005. / Thesis directed by Ke-Hai Yuan for the Department of Psychology. "October 2005." Includes bibliographical references (leaves 60-63).

Thesis (Ph. D.)--Ohio State University, 2007. / Full text release at OhioLINK's ETD Center delayed at author's request

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 115-121).

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 180-183).