Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

Reducing the risk of posttraumatic stress disorder in children following natural disasters

A significant number of children suffer long term psychological disturbance following exposure to a natural disaster. Evidence suggests that a dose-response relationship exists, so that children and adolescents who experience the most intense or extensive exposure to the risk factors for PTSD are likely to develop the most serious and persistent symptoms. Risk factors include gender, age, personality, extent of exposure to the natural disaster, amount of damage to property and infrastructure, witnessing injury or death of others or perceiving a threat to their own life. Knowing these factors enables various strategies to be put in place to decrease the risk of psychological disturbance following the aftermath of traumatic events. Re-establishing a sense of safety, security and normality is important in the aftermath of a natural disaster, and promoting social connectedness, positive family functioning, and effective coping mechanisms can make children more resilient in the face of catastrophic events. This paper examines the risk and protective factors associated with the development of post traumatic stress disorder (PTSD), and considers how schools can use this knowledge to contribute to the recovery effort, and reduce the prevalence of PTSD amongst pupils in the wake of a natural disaster.

Bootstrap approaches for estimation and confidence intervals of long term memory processes

In this work, we investigate an alternative bootstrap approach based on a result of Ramsey [F.L. Ramsey, Characterization of the partial autocorrelation function, Ann. Statist. 2 (1974), pp. 1296-1301] and on the Durbin-Levinson algorithm to obtain a surrogate series from linear Gaussian processes with long range dependence. We compare this bootstrap method with other existing procedures in a wide Monte Carlo experiment by estimating, parametrically and semi-parametrically, the memory parameter d. We consider Gaussian and non-Gaussian processes to prove the robustness of the method to deviations from normality. The approach is also useful to estimate confidence intervals for the memory parameter d by improving the coverage level of the interval.

The Impact of Globalization and Corruption on Extraordinary Wealth: An Empirical Analysis

The billionaires of the world attract significant attention from the media and the public. The popular press is full of books selling formulas on how to become rich. Surprisingly, only a limited number of studies have explored empirically the determinants of extraordinary wealth. Using a large data set we explore whether globalization and corruption affect extreme wealth accumulation. We find evidence that an increase in globalization increases super-richness. In addition, we also find that an increase in corruption leads to an increase in the creation of super fortune. This supports the argument that in kleptocracies large sums are transferred into the hands of a small group of individuals.

In Bed with Autobiography: Unravelling the Fabric of Gender and Genre in Women’s Bed(room) Confessions

This thesis consists of a confessional narrative, What My Mother Doesn’t Know, and an accompanying exegesis, And Why I Should (Maybe) Tell Her. The creative piece employs the confessional mode as a subversive device in three separate narratives, each of which situates the bed as a site of resistance. The exegesis investigates how this self-disclosure in a domestic space flouts the governing rules of self-representation, specifically: telling the truth, respecting privacy and displaying normalcy. The female confession, I argue, creates an alternative space in women’s autobiography where notions of truth-telling can be undermined, the political dimensions of personal experience can be uncovered and the discourse of normality can be negotiated. In particular, women’s confessions told in, on or about the bed, dismantle the genre’s illusion of self and confirm the representative aspects of women’s experience. Framed within these parameters of power and powerlessness, the exegesis includes textual analyses of Charlotte Perkins Gilman’s The Yellow Wallpaper (1892), Tracey Emin’s My Bed (1999) and Lauren Slater’s Lying (2000), each of which exposes in a bedroom space, the author’s most obscure, intimate and traumatic experiences. Situated firmly within and against the genre’s traditional masculine domain, the exegesis also includes mediations on the creative work that validate the bed as my fabric for confession.

Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

Compliance, normality and the patient on peritoneal dialysis

Monitoring and enhancing patient compliance with peritoneal dialysis (PD) is a recurring and problematic theme in the renal literature. A growing body of literature also argues that a failure to understand the patient's perspective of compliance may be contributing to these problems. The aim of this study was to understand the concept of compliance with PD from the patient's perspective. Using the case study approach recommended by Stake (1995), five patients on PD consented to in-depth interviews that explored the meaning of compliance in the context of PD treatment and lifestyle regimens recommended by health professionals. Participants also discussed factors that influenced their choices to follow, disregard, or refine these regimens. Results indicate that health professionals acting in alignment with individual patient needs and wishes, and demonstrating an awareness of the constraints under which patients operate and the strengths they bring to their treatment, may be the most significant issues to consider with respect to definitions of PD compliance and the development of related compliance interventions. Aspects of compliance that promoted relative normality were also important to the participants in this study and tended to result in greater concordance with health professionals' advice.

Multi-criteria assessment of innovative technology in the beef industry

In Australia rural research and development corporations and companies expended over $AUS500 million on agricultural research and development. A substantial proportion of this is invested in R&D in the beef industry. The Australian beef industry exports almost $AUS5billionof product annually and invest heavily in new product development to improve the beef quality and improve production efficiency. Review points are critical for effective new product development, yet many research and development bodies, particularly publicly funded ones, appear to ignore the importance of assessing products prior to their release. Significant sums of money are invested in developing technological innovations that have low levels and rates of adoption. The adoption rates could be improved if the developers were more focused on technology uptake and less focused on proving their technologies can be applied in practice. Several approaches have been put forward in an effort to improve rates of adoption into operational settings. This paper presents a study of key technological innovations in the Australian beef industry to assess the use of multiple criteria in evaluating the potential uptake of new technologies. Findings indicate that using multiple criteria to evaluate innovations before commercializing a technology enables researchers to better understand the issues that may inhibit adoption.

Robust tracking control of autonomous underwater vehicles in the presence of disturbance inputs

An autonomous underwater vehicle (AUV) is expected to operate in an ocean in the presence of poorly known disturbance forces and moments. The uncertainties of the environment makes it difficult to apply open-loop control scheme for the motion planning of the vehicle. The objective of this paper is to develop a robust feedback trajectory tracking control scheme for an AUV that can track a prescribed trajectory amidst such disturbances. We solve a general problem of feedback trajectory tracking of an AUV in SE(3). The feedback control scheme is derived using Lyapunov-type analysis. The results obtained from numerical simulations confirm the asymptotic tracking properties of the feedback control law. We apply the feedback control scheme to different mission scenarios, with the disturbances being initial errors in the state of the AUV.

Comparison of scoring systems for invasive pests using ROC analysis and Monte Carlo simulation

Different international plant protection organisations advocate different schemes for conducting pest risk assessments. Most of these schemes use structured questionnaire in which experts are asked to score several items using an ordinal scale. The scores are then combined using a range of procedures, such as simple arithmetic mean, weighted averages, multiplication of scores, and cumulative sums. The most useful schemes will correctly identify harmful pests and identify ones that are not. As the quality of a pest risk assessment can depend on the characteristics of the scoring system used by the risk assessors (i.e., on the number of points of the scale and on the method used for combining the component scores), it is important to assess and compare the performance of different scoring systems. In this article, we proposed a new method for assessing scoring systems. Its principle is to simulate virtual data using a stochastic model and, then, to estimate sensitivity and specificity values from these data for different scoring systems. The interest of our approach was illustrated in a case study where several scoring systems were compared. Data for this analysis were generated using a probabilistic model describing the pest introduction process. The generated data were then used to simulate the outcome of scoring systems and to assess the accuracy of the decisions about positive and negative introduction. The results showed that ordinal scales with at most 5 or 6 points were sufficient and that the multiplication-based scoring systems performed better than their sum-based counterparts. The proposed method could be used in the future to assess a great diversity of scoring systems.

On the empirical eigenvalue distribution of slotted amplify-and-forward relaying protocol model

In this paper we consider the case of large cooperative communication systems where terminals use the protocol known as slotted amplify-and-forward protocol to aid the source in its transmission. Using the perturbation expansion methods of resolvents and large deviation techniques we obtain an expression for the Stieltjes transform of the asymptotic eigenvalue distribution of a sample covariance random matrix of the type HH† where H is the channel matrix of the transmission model for the transmission protocol we consider. We prove that the resulting expression is similar to the Stieltjes transform in its quadratic equation form for the Marcenko-Pastur distribution.

Practical stability of approximating discrete-time filters with respect to model mismatch using relative entropy concepts

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Using local consistency assumption, the practical stability established is in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Significantly, these practical stability results do not require the approximating model to be of the same model type as the true system. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.