In many previous physiological and psychoacoustic studies, Schroeder-phase masking (using Schroeder harmonic complexes to mask other sounds) has proven useful in understanding different aspects of cochlear function, particularly the phase curvature of the cochlea and cochlear nonlinearity. The common method of measuring Schroeder-phase masking functions uses a very time consuming three-alternative forced choice (3AFC) process, which limits its research and clinical usefulness. This thesis describes a fast method for measuring Schroeder-phase masking functions that we developed to address this problem. By adapting the Békésy tracking technique, we demonstrate how the measurement time can be reliably shortened by almost 80% in comparison to the commonly-used method. Using the fast method, we have demonstrated that the difference in masking effectiveness produced by different phases of Schroeder maskers (known as the ‘phase effect’) is reduced in conditions where cochlear non-linearity is expected to be reduced (i.e. at low intensity levels and in sensorineural hearing loss subjects) – findings which are consistent with previous studies. The possible involvement of other mechanisms in producing the Schroeder phase effect (particularly the medial olivocochlear (MOC) reflex) is discussed. Given the shorter testing time and higher resolution data it can give, the fast method can be a useful tool in estimating cochlear phase curvature. The reduction in testing time in particular may significantly aid the investigation of different aspects of cochlear function which might have been limited by the long testing time given by the commonly-used method.

The ring of polynomials over a finite field has many arithmetic properties similar to those of the ring of rational integers. In this thesis, we apply the Hardy-Littlewood circle method to investigate the density of rational points on certain algebraic varieties in function fields. The aim is to establish asymptotic relations that are relatively robust to changes in the characteristic of the base finite field. More notably, in the case when the characteristic is "small", the results are sharper than their integer analogues.

Šiame darbe nagrinėjama atsitiktinio dydžio X skirstinio aproksimacijos sudėtiniu Puasono dėsniu netolygūs įverčiai. / In this paper we analyze nonuniform estimates in approximation by the compound Poisson distribution.

In phylogenetic analysis, an important issue is to construct the confidence region for gene trees from DNA sequences. Usually estimation of the trees is the initial step. Maximum likelihood methods are widely applied but few tests are based on distance methods. In this thesis, we propose a new test based on balanced minimum evolution. We first examine the normality assumption of pairwise distance estimates under various model misspeci cations and also examine their variances, MSEs and squared biases. Then we compare the BME method with the WLS method in true tree reconstruction under different variance structures and model pairs. Finally, we develop a new test for finding a confidence region for the tree based on the BME method and demonstrate its effectiveness through simulation.

In this thesis, the numerical solution of time-dependent partial differential equations (PDE) is studied. In particular high-order finite difference methods on Summation-by-parts (SBP) form are analysed and applied to model problems as well as the PDEs governing aerodynamics. The SBP property together with an implementation of boundary conditions called SAT (Simultaneous Approximation Term), yields stability by energy estimates. The first derivative SBP operators were originally derived for Cartesian grids. Since aerodynamic computations are the ultimate goal, the scheme must also be stable on curvilinear grids. We prove that stability on curvilinear grids is only achieved for a subclass of the SBP operators. Furthermore, aerodynamics often requires addition of artificial dissipation and we derive an SBP version. With the SBP-SAT technique it is possible to split the computational domain into a multi-block structure which simplifies grid generation and more complex geometries can be resolved. To resolve extremely complex geometries an unstructured discretisation method must be used. Hence, we have studied a finite volume approximation of the Laplacian. It can be shown to be on SBP form and a new boundary treatment is derived. Based on the Laplacian scheme, we also derive an SBP artificial dissipation for finite volume schemes. We derive a new set of boundary conditions that leads to an energy estimate for the linearised three-dimensional Navier-Stokes equations. The new boundary conditions will be used to construct a stable SBP-SAT discretisation. To obtain an energy estimate for the discrete equation, it is necessary to discretise all the second derivatives by using the first derivative approximation twice. According to previous theory that would imply a degradation of formal accuracy but we present a proof that this is not the case.

The efficacy of a Marine Protected Area (MPA) is contingent on it having a design appropriate for the species it is intended to protect. Hector�s dolphin (Cephalorhynchus hectori), a coastal delphinid endemic to New Zealand, is endangered due to bycatch in gillnets. Analyses of survival rate and population viability suggest that the Banks Peninsula population is most likely still declining despite the presence of the Banks Peninsula Marine Mammal Sanctuary (BPMMS), where gillnetting is regulated. More data on distribution and movements of dolphins are therefore required to improve the design of the BPMMS. On aerial surveys of Hector�s dolphin distribution at Banks Peninsula over three years, sightings were made up to 19 n.mi. offshore. On average, 19% of dolphins were sighted outside the BPMMS�s 4 n.mi. offshore boundary in summer, compared to 56% in winter. On similar surveys of the South Island�s west coast, all dolphins were sighted within 6 n.mi. of the coast and there was no seasonal change in distribution. At each location, Mantel tests indicated that distance offshore had the strongest and most consistent effect on distribution. However, a logistic regression model using the combined datasets suggested that distribution was most strongly defined by water depth, with all sightings made inside the 90 m isobath. Boat surveys were carried out at Banks Peninsula (2002 to 2006) to continue the long-term photo-ID project. Using the 22 year dataset, alongshore home-range of the 20 most frequently sighted dolphins was estimated by univariate kernel methods. Mean alongshore range was 49.69 km (SE = 5.29), 60% larger than the previous estimate. Fifteen percent of these individuals had ranges extending beyond the northern boundary of the BPMMS. An acoustic data logger, the T-POD, was trialled for passive acoustic monitoring of Hector�s dolphins. Simultaneous T-POD/theodolite surveys revealed that T-PODs reliably detected dolphins within 200m. No detections were made beyond 500m. To monitor inshore habitat use, T-PODs were deployed in three locations at Banks Peninsula (n = 431 days). A GLM analysis of Detection Positive Minutes (DPM) per day indicated that season had the largest effect on detection rate, with over twice as many DPMs per day in summer (x̄ = 99.8) as winter (x̄ = 47.6). The new findings on Hector�s dolphin distribution and ranging can be used to improve the design of the BPMMS. It is recommended that the offshore boundary of the BPMMS is extended to 20 n.mi. (37 km), the northern boundary is moved 12 km north and recreational gillnetting is prohibited year round. In areas where distribution of Hector�s dolphin has not been studied, the offshore boundary of MPAs should enclose the 100 m isobath.

The results of this thesis are motivated by the investigation of abstract Cauchy problems. Our primary contribution is encapsulated in two new theorems. The first main theorem is a generalisation of a result of E. M. Stein. In particular, we show that every symmetric diffusion semigroup acting on a complex-valued Lebesgue space has a tensor product extension to a UMD-valued Lebesgue space that can be continued analytically to sectors of the complex plane. Moreover, this analytic continuation exhibits pointwise convergence almost everywhere. Both conclusions hold provided that the UMD space satisfies a geometric condition that is weak enough to include many classical spaces. The theorem is proved by showing that every symmetric diffusion semigroup is dominated by a positive symmetric diffusion semigoup. This allows us to obtain (a) the existence of the semigroup's tensor extension, (b) a vector-valued version of the Hopf--Dunford--Schwartz ergodic theorem and (c) an holomorphic functional calculus for the extension's generator. The ergodic theorem is used to prove a vector-valued version of a maximal theorem by Stein, which, when combined with the functional calculus, proves the pointwise convergence theorem. The second part of the thesis proves the existence of abstract Strichartz estimates for any evolution family of operators that satisfies an abstract energy and dispersive estimate. Some of these Strichartz estimates were already announced, without proof, by M. Keel and T. Tao. Those estimates which are not included in their result are new, and are an abstract extension of inhomogeneous estimates recently obtained by D. Foschi. When applied to physical problems, our abstract estimates give new inhomogeneous Strichartz estimates for the wave equation, extend the range of inhomogeneous estimates obtained by M. Nakamura and T. Ozawa for a class of Klein--Gordon equations, and recover the inhomogeneous estimates for the Schr??dinger equation obtained independently by Foschi and M. Vilela. These abstract estimates are applicable to a range of other problems, such as the Schr??dinger equation with a certain class of potentials.

[Abstract]: Since early settlement, agriculture has been one of the main industries contributing to the livelihoods of most rural communities in Australia. The wheat grain industry is Australia’s second largest agricultural export commodity, with an average value of $3.5 billion per annum. Climate variability and change, higher input costs, and world commodity markets have put increased pressure on the sustainability of the grain industry. This has lead to an increasing demand for accurate, objective and near real-time crop production information by industry. To generate such production estimates, it is essential to determine crop area planted at the desired spatial and temporal scales. However, such information at regional scale is currently not available in Australia.The aim of this study was to determine broadacre crop area estimates through the use of multi-temporal satellite imagery for major Australian winter crops. Specifically, the objectives were to: (i) assess the ability of a range of approaches to using multi-temporal Moderate Resolution Imaging Spectroradiometer (MODIS) imagery to estimate total end-of-season winter crop area; (ii) determine the discriminative ability of such remote sensing approaches in estimating planted area for wheat, barley and chickpea within a specific cropping season; (iii) develop and evaluate the methodology for determining the predictability of crop area estimates well before harvest; and (iv) validate the ability of multi-temporal MODIS approaches to determine the pre-harvest and end-of-season winter crop area estimates for different seasons and regions.MODIS enhanced vegetation index (EVI) was used as a surrogate measure for crop canopy health and architecture, for two contiguous shires in the Darling Downs region of Queensland, Australia. Multi-temporal approaches comprising principal component analysis (PCA), harmonic analysis of time series (HANTS), multi-date MODIS EVI during the crop growth period (MEVI), and two curve fitting procedures (CF1, CF2) were derived and applied. These approaches were validated against the traditional single-date approach. Early-season crop area estimates were derived through the development and application of a metric, i.e. accumulation of consecutive 16-day EVI values greater than or equal to 500, at different periods before flowering. Using ground truth data, image classification was conducted by applying supervised (maximum likelihood) and unsupervised (K-means) classification algorithms. The percent correctly classified and kappa coefficient statistics from the error matrix were used to assess pixel-scale accuracy, while shire-scale accuracy was determined using the percent error (PE) statistic. A simple linear regression of actual shire-scale data against predicted data was used to assess accuracy across regions and seasons. Actual shire-scale data was acquired from government statistical reports for the period 2000, 2001, 2003 and 2004 for the Darling Downs, and 2005 and 2006 for the entire Queensland cropping region.Results for 2003 and 2004 showed that multi-temporal HANTS, MEVI, CF1, CF2 and PCA methods achieved high overall accuracies ranging from 85% to 97% to discriminate between crops and non-crops. The accuracies for discriminating between specific crops at pixel scale were less, but still moderate, especially for wheat and barley (lowest at 57%). The HANTS approach had the smallest mean absolute percent error of 27% at shire-scale compared to other multi-temporal approaches. For early-season prediction, the 16-day EVI values greater than or equal to 500 metric showed high accuracy (94% to 98%) at a pixel scale and high R2 (0.96) for predicting total winter crop area planted.The rigour of the HANTS and the 16-day EVI values greater than or equal to 500 approaches was assessed when extrapolating over the entire Queensland cropping region for the 2005 and 2006 season. The combined early-season estimate of July and August produced high accuracy at pixel and regional scales with percent error of 8.6% and 26% below the industry estimates for 2005 and 2006 season, respectively. These satellite-derived crop area estimates were available at least four months before harvest, and deemed that such information will be highly sought after by industry in managing their risk. In discriminating among crops at pixel and regional scale, the HANTS approach showed high accuracy. Specific area estimates for wheat, barley and chickpea were, respectively, 9.9%, -5.2% and 10.9% (for 2005) and -2.8%, -78% and 64% (for 2006). Closer investigation suggested that the higher error in 2006 area estimates for barley and chickpea has emanated from the industry figures collected by the government.Area estimates of total winter crop, wheat, barley and chickpea resulted in R2 values of 0.92, 0.89, 0.82 and 0.52, when contrasted against the actual shire-scale data. A significantly high R2 (0.87) was achieved for total winter crop area estimates in Augusts across all shires for the 2006 season. Furthermore, the HANTS approach showed high accuracy in discriminating cropping area from non-cropping area and highlighted the need for accurate and up-to-date land use maps.This thesis concluded that time-series MODIS EVI imagery can be applied successfully to firstly, determine end-of-season crop area estimates at shire scale. Secondly, capturing canopy green-up through a novel metric (i.e. 16-day EVI values greater than or equal to 500) can be utilised effectively to determine early-season crop area estimates well before harvest. Finally, the extrapolability of these approaches to determine total and specific winter crop area estimates showed good utility across larger areas and seasons. Hence, it is envisaged that this technology is transferable to different regions across Australia. The utility of the remote sensing techniques developed in this study will depend on the risk agri-industry operates at within their decision and operating regimes. Trade-off between risk and value will depend on the accuracy and timing of the disseminated crop production forecast.

The average length of life from birth until death in a human population is a single statistic that is often used to characterise the prevailing health status of the population. It is one of many statistics calculated from an analysis that, for each age, combines the number of deaths with the size of the population in which these deaths occur. This analysis is generally known as life table analysis. Life tables have only occasionally been produced specifically for South Australia, although the necessary data has been routinely collected since 1842. In this thesis, the mortality pattern of South Australia over the period of 150 years of European settlement is quantified by using life table analyses and estimates of average length of life. In Chapter 1, a mathematical derivation is given for the lifetime statistical distribution function that is the basis of life table analysis, and from which the average length of life or current expected life is calculated. This derivation uses mathematical notation that clearly shows the deficiency of current expected life as a measure of the life expectancy of an existing population. Four statistical estimation procedures are defined, and the computationally intensive method of bootstrapping is discussed as an estimation procedure for the standard error of each of the estimates of expected life. A generalisation of this method is given to examine the robustness of the estimate of current expected life. In Chapter 2, gender and age-specific mortality and population data are presented for twenty five three-year periods; each period encompassing one of the colonial (1841-1901) or post-Federation (1911-96) censuses that have been taken in South Australia. For both genders within a census period, four types of estimate of current expected life, each with a bootstrap standard error, are calculated and compared, and a robustness assessment is made. In Chapter 3, an alternate measure of life expectancy known as generation expected life is considered. Generation expected life is derived by extracting, from official records arranged in temporal order, the mortality pattern of a notional group of individuals who were born in the same calendar year. Several estimates of generation expected life are calculated using South Australian data, and each estimate is compared to the corresponding estimate of current expected life. Additional estimates of generation expected life calculated using data obtained from the Roll of Honour at the Australian War Memorial quantify the reduction in male generation expected life for 1881-1900 as a consequence of military service during World War I, 1914-18, and the Influenza Pandemic, 1919. / Thesis (M.Sc.) -- University of Adelaide, School of Applied Mathematics, 2003.

Abstract This thesis considers some linear and nonlinear time series models. In the linear case, the analysis of a large number of short time series generated by a first order autoregressive type model is considered. The conditional and exact maximum likelihood procedures are developed to estimate parameters. Simulation results are presented and compare the bias and the mean square errors of the parameter estimates. In Chapter 3, five important nonlinear models are considered and their time series properties are discussed. The estimating function approach for nonlinear models is developed in detail in Chapter 4 and examples are added to illustrate the theory. A simulation study is carried out to examine the finite sample behavior of these proposed estimates based on the estimating functions.