The renormalization group: A perturbation method for the graduate curriculum

In this paper the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. Lett., 73 (1994), pp.1311-1315; Phys. Rev. E, 54 (1996), pp.376-394] is presented in a pedagogical way to increase its visibility in applied mathematics and to argue favorably for its incorporation into the corresponding graduate curriculum.The method is illustrated by some linear and nonlinear singular perturbation problems. Key word. © 2012 Society for Industrial and Applied Mathematics.

A Combined Renormalization Group-Multiple Scale Method for Singularly Perturbed Problems

This paper introduces a straightforward method to asymptotically solve a variety of initial and boundary value problems for singularly perturbed ordinary differential equations whose solution structure can be anticipated. The approach is simpler than conventional methods, including those based on asymptotic matching or on eliminating secular terms. © 2010 by the Massachusetts Institute of Technology.

Reduction of amplitude equations by the renormalization group approach

This article elucidates and analyzes the fundamental underlying structure of the renormalization group (RG) approach as it applies to the solution of any differential equation involving multiple scales. The amplitude equation derived through the elimination of secular terms arising from a naive perturbation expansion of the solution to these equations by the RG approach is reduced to an algebraic equation which is expressed in terms of the Thiele semi-invariants or cumulants of the eliminant sequence { Zi } i=1 . Its use is illustrated through the solution of both linear and nonlinear perturbation problems and certain results from the literature are recovered as special cases. The fundamental structure that emerges from the application of the RG approach is not the amplitude equation but the aforementioned algebraic equation. © 2008 The American Physical Society.

The renormalization group and the implicit function theorem for amplitude equations

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

Secular series and renormalization group for amplitude equations

We have developed a technique that circumvents the process of elimination of secular terms and reproduces the uniformly valid approximations, amplitude equations, and first integrals. The technique is based on a rearrangement of secular terms and their grouping into the secular series that multiplies the constants of the asymptotic expansion. We illustrate the technique by deriving amplitude equations for standard nonlinear oscillator and boundary-layer problems. © 2008 The American Physical Society.

Renormalization group interpretation of the Born and Rytov approximations

In this paper the method of renormalization group (RG) [Phys. Rev. E 54, 376 (1996)] is related to the well-known approximations of Rytov and Born used in wave propagation in deterministic and random media. Certain problems in linear and nonlinear media are examined from the viewpoint of RG and compared with the literature on Born and Rytov approximations. It is found that the Rytov approximation forms a special case of the asymptotic expansion generated by the RG, and as such it gives a superior approximation to the exact solution compared with its Born counterpart. Analogous conclusions are reached for nonlinear equations with an intensity-dependent index of refraction where the RG recovers the exact solution. © 2008 Optical Society of America.

A non-malleable group key exchange protocol robust against active insiders

In this paper we make progress towards solving an open problem posed by Katz and Yung at CRYPTO 2003. We propose the first protocol for key exchange among n ≥2k+1 parties which simultaneously achieves all of the following properties: 1. Key Privacy (including forward security) against active attacks by group outsiders, 2. Non-malleability — meaning in particular that no subset of up to k corrupted group insiders can ‘fix’ the agreed key to a desired value, and 3. Robustness against denial of service attacks by up to k corrupted group insiders. Our insider security properties above are achieved assuming the availability of a reliable broadcast channel.

Parent's socio-economic status and social support as risks for child mortality : consideration of health equity in The Gambia

A matched case-control study of mortality to children under age five was conducted to consider associations with parents' socio-economic status and social support in the Farafenni Demographic Surveillance Site (DSS). Cases and controls were selected from Farafenni DSS, matched on date of birth, and parents were interviewed about personal resources and social networks. Parents with the lowest personal socio-economic status and social support were identified. Multivariate multinomial regression was used to consider whether the children of these parents were at increased risk of either infant or 1-4 mortality, in separate models using either parents' characteristics. There was no benefit found for higher SES or better social support with respect to child mortality. Children of fathers who had the poorest social support had lower 1-4 mortality risk (OR=0.52, p=0.037). Given that socio-economic status was not associated with child mortality, it seems unlikely that the explanation for the link between father's social support and mortality is linked to resource availability. Explanations for the risk effect of father's social ties may lie in decision-making around health maintenance and health care for children.

Writing Indigenous vampires: Aboriginal gothic or Aboriginal fantastic?

The usual postmodern suspicions about diligently deciphering authorial intent or stridently seeking fixed meaning/s and/or binary distinctions in an artistic work aside, this self-indulgent essay pushes the boundaries regarding normative academic research, for it focusses on my own (minimally celebrated) published creative writing’s status as a literary innovation. Dedicated to illuminating some of the less common denominators at play in Australian horror, my paper recalls the creative writing process involved when I set upon the (arrogant?) goal of creating a new genre of creative writing: that of the ‘Aboriginal Fantastic’. I compare my work to the literary output of a small but significant group (2.5% of the population), of which I am a member: Aboriginal Australians. I narrow my focus even further by examining that creative writing known as Aboriginal horror. And I reduce the sample size of my study to an exceptionally small number by restricting my view to one type of Aboriginal horror literature only: the Aboriginal vampire novel, a genre to which I have contributed professionally with the 2011 paperback and 2012 e-book publication of That Blackfella Bloodsucka Dance! However, as this paper hopefully demonstrates, and despite what may be interpreted by some cynical commentators as the faux sincerity of my taxonomic fervour, Aboriginal horror is a genre noteworthy for its instability and worthy of further academic interrogation. (first paragraph)

Testing the international linkage in the platinum-group metal futures markets

This study tests whether an international market exists in the platinum-group metal (PGM) futures markets. For this purpose, we tested the law of one price (LOP) and the causality between the U.S. and Japanese platinum and palladium futures markets. We also performed the test when structural breaks are considered. Long-run price relationships were found in both platinum and palladium markets but the LOP only sustained in the palladium market. The causality test revealed that it is the U.S. market that leads the price to transmit information between the U.S. and Japanese markets. Structural breaks had large impacts on the test results, suggesting that incorporating breaks is important when investigating the international price linkage in the PGM futures markets.

Sentencing and public confidence in Australia: The dynamics and foci of small group deliberations

This study is the first of its kind in Australia to use the deliberative small group methodology to explore participants’ deeper, nuanced thoughts on specific criminal justice issues in order to gain insight into the underlying beliefs that influence people’s opinions on sentencing. The use of small group discussions allows an analysis of the dynamics of people’s interactions and the potential of these to elicit deeper, more thoughtful deliberation. Participants’ comments around two policy areas – mandatory sentencing and the use of alternatives to imprisonment – were founded on concerns about the need for judges to tailor the sentence to fit the specific circumstances of each case. The methodology itself has shown that people may change their initial opinions on complex issues when given the opportunity to discuss and reflect on their beliefs.

The story of the men’s white shirt

The classic white dress shirt is familiar and omnipresent in men’s fashion. As a result, we tend to be unaware that for more than 200 years this singular item of apparel, which is essentially unadulterated in form from the late 19th century, has been able to define and represent status, wealth and fashion norms. The history underlying this garment is rich and, in the main part, untold.

Clinical utility of exhaled nitric oxide

Lower airway inflammation is generally classified as eosinophilic or neutrophilic. In conditions where eosinophilic inflammation predominates such as asthma in children, corticosteroids are usually beneficial. Traditionally, lower airway eosinophilia is measured using cellular count (through bronchoalveolar lavage or induced sputum). Both methods have limited applicability in children. When instruments to measure fractional exhaled nitric oxide (FeNO) became available, it presented an attractive option as it provided a non-invasive method of measuring eosinophilic inflammation suitable for children and adult. Not surprisingly, proposals have been made that FeNO measurement can be clinically used in many scenarios including monitoring the response to anti-inflammatory medications, to verify the adherence to treatment, and to predict upcoming asthma exacerbations. This thesis addresses the utility of FeNO levels in various scenarios, specifically in relation to asthma control and cough, a contentious aspect of the diagnosis of asthma. The thesis consists of a series of systematic reviews (related to the main question) and original studies in children. The over-arching aim of the thesis is to determine if FeNO is a clinically useful tool in the management of asthma and common asthma symptoms. The specific aims of the thesis were, to: 1. Determine if children with asthma have more severe acute respiratory symptoms at presentation with an asthma exacerbation and at days 7, 10 and 14 using validated scales. We also examined if children with asthma were more likely to have a persistent cough on day 14 than children with protracted bronchitis and/or controls. 2. Evaluate the efficacy of tailoring asthma interventions based on sputum analysis in comparison to clinical symptoms (with or without spirometry/peak flow) for asthma related outcomes in children and adults. 3. Evaluate the efficacy of tailoring asthma interventions based on exhaled nitric oxide in comparison to clinical symptoms (with or without spirometry/peak flow) for asthma related outcomes in children and adults. 4. Determine if adjustment of asthma medications based on FeNO levels (compared to management based on clinical symptoms) reduces severe exacerbations in children with asthma. 5. Examine the relationship between FeNO and exercise induced broncho-constriction and cough in children The aims above are addressed in respective chapters and all but one has been published/submitted. A synopsis of the findings are: In study-1 (Aim 1), we found that children with protracted bronchitis had the most severe acute respiratory infection symptoms and higher percentage of respiratory morbidity at day 14 in comparison to children with asthma and healthy controls. The systematic review of study-2 (Aim 2) included 246 randomised adult participants (no children) with 221 completing the trials. In the meta-analysis, a significant reduction in number of participants who had one or more asthma exacerbations occurred when treatment was based on sputum eosinophils in comparison to clinical symptoms. In the systematic review of study-3 (Aim 3), we found no significant difference between the intervention group (treatment adjusted based on FeNO) and control group (treatment adjusted based on clinical symptoms) for the primary outcome of asthma exacerbations or for the other outcomes (clinical symptoms, FeNO level and spirometry). In post-hoc analysis, a significant reduction in mean final daily dose ICS per adult was found in the group where treatment was based on FeNO in comparison to clinical symptoms. In contrast, in the paediatric studies, there was a significant increase in ICS dose in the FeNO strategy arm. Thus, controversy remains of the benefit or otherwise of utilising exhaled nitric oxide (FeNO) in routine clinical practice. FeNO levels are dependent on atopy and none of the 7 published trials have considered atopic status in FeNO levels when medications were adjusted. In study-4 (Aim 4), 64 children with asthma were recruited. Their asthma medications were adjusted according to either FeNO levels or usual clinical care utilising a management hierarchy taking into account atopy. It was concluded that tailoring of asthma medications in accordance to FeNO levels (compared to usual management), taking into account atopy status, reduced the number of children with severe exacerbations. However, a FeNO-based strategy resulted in higher daily ICS doses and had no benefit on asthma control. In study-5 (Aim 5), 33 children with cough and 17 controls were recruited. They were randomised to undertake an exercise challenge on day 1, or dry powder mannitol challenge on day 1 (with alternative challenge being done on day 2). In addition, a 24 hour cough meter, skin prick test, capsaicin cough sensitivity test and cough diary were undertaken. The change in cough frequency post exercise was significantly increased in the children with cough. FeNO decreases post exercise regardless of whether EIB is present or not. Limitations in the studies were addressed in the respective chapters. In summary, the studies from this thesis have provided new information on: • The severity of respiratory symptoms was increased in the early phase of the asthma exacerbation but not in the later recovery phase when compared with controls. • The utility of FeNO in the management of children with asthma. • The relationship of FeNO, cough and EIB in children. • Systematic reviews on the efficacy of tailoring asthma interventions based on eosinophilic inflammatory markers (sputum analysis and FeNO) in comparison to clinical symptoms.

‘It's all scientific to me’ : focus group insights into why young people do not apply safe-sex knowledge

Despite rising levels of safe-sex knowledge in Australia, sexually transmitted infection notifications continue to increase. A culture-centred approach suggests it is useful in attempting to reach a target population first to understand their perspective on the issues. Twenty focus groups were conducted with 89 young people between the ages of 14 and 16 years. Key findings suggest that scientific information does not articulate closely with everyday practice, that young people get the message that sex is bad and they should not be preparing for it and that it is not appropriate to talk about sex. Understanding how young people think about these issues is particularly important because the focus groups also found that young people disengage from sources of information that do not match their own experiences.

Advance Care Planning in palliative care : a systematic literature review of the contextual factors influencing its uptake 2008-2012

Background: Advance Care Planning is an iterative process of discussion, decision-making and documentation about end-of-life care. Advance Care Planning is highly relevant in palliative care due to intersecting clinical needs. To enhance the implementation of Advance Care Planning, the contextual factors influencing its uptake need to be better understood. Aim: To identify the contextual factors influencing the uptake of Advance Care Planning in palliative care as published between January 2008 and December 2012. Methods: Databases were systematically searched for studies about Advance Care Planning in palliative care published between January 2008 and December 2012. This yielded 27 eligible studies, which were appraised using National Institute of Health and Care Excellence Quality Appraisal Checklists. Iterative thematic synthesis was used to group results. Results: Factors associated with greater uptake included older age, a college degree, a diagnosis of cancer, greater functional impairment, being white, greater understanding of poor prognosis and receiving or working in specialist palliative care. Barriers included having non-malignant diagnoses, having dependent children, being African American, and uncertainty about Advance Care Planning and its legal status. Individuals’ previous illness experiences, preferences and attitudes also influenced their participation. Conclusion: Factors influencing the uptake of Advance Care Planning in palliative care are complex and multifaceted reflecting the diverse and often competing needs of patients, health professionals, legislature and health systems. Large population-based studies of palliative care patients are required to develop the sound theoretical and empirical foundation needed to improve uptake of Advance Care Planning in this setting.