On the probability density function of the product of Rayleigh distributed random variables

In this paper we investigate the distribution of the product of Rayleigh distributed random variables. Considering the Mellin-Barnes inversion formula and using the saddle point approach we obtain an upper bound for the product distribution. The accuracy of this tail-approximation increases as the number of random variables in the product increase.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

Social signal processing for pain monitoring using a hidden conditional random field

utomatic pain monitoring has the potential to greatly improve patient diagnosis and outcomes by providing a continuous objective measure. One of the most promising methods is to do this via automatically detecting facial expressions. However, current approaches have failed due to their inability to: 1) integrate the rigid and non-rigid head motion into a single feature representation, and 2) incorporate the salient temporal patterns into the classification stage. In this paper, we tackle the first problem by developing a “histogram of facial action units” representation using Active Appearance Model (AAM) face features, and then utilize a Hidden Conditional Random Field (HCRF) to overcome the second issue. We show that both of these methods improve the performance on the task of pain detection in sequence level compared to current state-of-the-art-methods on the UNBC-McMaster Shoulder Pain Archive.

Using variable speed limits for motorway off-ramp queue protection

Motorway off-ramps are a significant source of traffic congestion and collisions. Heavy diverging traffic to off-ramps slows down the mainline traffic speed. When the off-ramp queue spillbacks onto the mainline, it leads to a major breakdown of the motorway capacity and a significant threat to the traffic safety. This paper proposes using Variable Speed Limits (VSL) for protection of the motorway off-ramp queue and thus to promote safety in congested diverging areas. To support timely activation of VSL in advance of queue spillover, a proactive control strategy is proposed based on a real-time off-ramp queue estimation and prediction. This process determines the estimated queue size in the near-term future, on which the decision to change speed limits is made. VSL can effectively slow down traffic as it is mandatory that drivers follow the changed speed limits. A collateral benefit of VSL is its potential effect on drivers making them more attentive to the surrounding traffic conditions, and prepared for a sudden braking of the leading car. This paper analyses and quantifies these impacts and potential benefits of VSL on traffic safety and efficiency using the microsimulation approach.

Conserved and variable features of gag structure and arrangement in immature retrovirus particles

The assembly of retroviruses is driven by oligomerization of the Gag polyprotein. We have used cryo-electron tomography together with subtomogram averaging to describe the three-dimensional structure of in vitro-assembled Gag particles from human immunodeficiency virus, Mason-Pfizer monkey virus, and Rous sarcoma virus. These represent three different retroviral genera: the lentiviruses, betaretroviruses and alpharetroviruses. Comparison of the three structures reveals the features of the supramolecular organization of Gag that are conserved between genera and therefore reflect general principles of Gag-Gag interactions and the features that are specific to certain genera. All three Gag proteins assemble to form approximately spherical hexameric lattices with irregular defects. In all three genera, the N-terminal domain of CA is arranged in hexameric rings around large holes. Where the rings meet, 2-fold densities, assigned to the C-terminal domain of CA, extend between adjacent rings, and link together at the 6-fold symmetry axis with a density, which extends toward the center of the particle into the nucleic acid layer. Although this general arrangement is conserved, differences can be seen throughout the CA and spacer peptide regions. These differences can be related to sequence differences among the genera. We conclude that the arrangement of the structural domains of CA is well conserved across genera, whereas the relationship between CA, the spacer peptide region, and the nucleic acid is more specific to each genus.

A variable step-size FxLMS algorithm for feedforward active noise control systems based on a new online secondary path modelling technique

Several approaches have been introduced in literature for active noise control (ANC) systems. Since FxLMS algorithm appears to be the best choice as a controller filter, researchers tend to improve performance of ANC systems by enhancing and modifying this algorithm. This paper proposes a new version of FxLMS algorithm. In many ANC applications an online secondary path modelling method using a white noise as a training signal is required to ensure convergence of the system. This paper also proposes a new approach for online secondary path modelling in feedfoward ANC systems. The proposed algorithm stops injection of the white noise at the optimum point and reactivate the injection during the operation, if needed, to maintain performance of the system. Benefiting new version of FxLMS algorithm and not continually injection of white noise makes the system more desirable and improves the noise attenuation performance. Comparative simulation results indicate effectiveness of the proposed approach.

Sex discrimination and non-random sampling in the Australian labour market

Historically a significant gap between male and female wages has existed in the Australian labour market. Indeed this wage differential was institutionalised in the 1912 arbitration decision which determined that the basic female wage would be set at between 54 and 66 per cent of the male wage. More recently however, the 1969 and 1972 Equal Pay Cases determined that male/female wage relativities should be based upon the premise of equal pay for work of equal value. It is important to note that the mere observation that average wages differ between males and females is not sine qua non evidence of sex discrimination. Economists restrict the definition of wage discrimination to cases where two distinct groups receive different average remuneration for reasons unrelated to differences in productivity characteristics. This paper extends previous studies of wage discrimination in Australia (Chapman and Mulvey, 1986; Haig, 1982) by correcting the estimated male/female wage differential for the existence of non-random sampling. Previous Australian estimates of male/female human capital basedwage specifications together with estimates of the corresponding wage differential all suffer from a failure to address this issue. If the sample of females observed to be working does not represent a random sample then the estimates of the male/female wage differential will be both biased and inconsistent.

Immigrant wage differentials and the role of self-employment in Australia

Immigration has played an important role in the historical development of Australia. Thus, it is no surprise that a large body of empirical work has developed, which focuses upon how migrants fare in the land of opportunity. Much of the literature is comparatively recent, i.e. the last ten years or so, encouraged by the advent of public availability of Australian crosssection micro data. Several different aspects of migrant welfare have been addressed, with major emphasis being placed upon earnings and unemployment experience. For recent examples see Haig (1980), Stromback (1984), Chiswick and Miller (1985), Tran-Nam and Nevile (1988) and Beggs and Chapman (1988). The present paper contributes to the literature by providing additional empirical evidence on the native/migrant earnings differential. The data utilised are from the rather neglected Australian Bureau of Statistics, ABS Special Supplementary Survey No.4. 1982, otherwise known as the Family Survey. The paper also examines the importance of distinguishing between the wage and salary sector and the self-employment sector when discussing native/migrant differentials. Separate earnings equations for the two labour market groups are estimated and the native/migrant earnings differential is broken down by employment status. This is a novel application in the Australian context and provides some insight into the earnings of the selfemployed, a group that despite its size (around 20 per cent of the labour force) is frequently ignored by economic research. Most previous empirical research fails to examine the effect of employment status on earnings. Stromback (1984) includes a dummy variable representing self-employment status in an earnings equation estimated over a pooled sample of paid and self-employed workers. The variable is found to be highly significant, which leads Stromback to question the efficacy of including the self-employed in the estimation sample. The suggestion is that part of self-employed earnings represent a return to non-human capital investment, i.e. investments in machinery, buildings etc, the structural determinants of earnings differ significantly from those for paid employees. Tran-Nam and Nevile (1988) deal with differences between paid employees and the selfemployed by deleting the latter from their sample. However, deleting the self-employed from the estimation sample may lead to bias in the OLS estimation method (see Heckman 1979). The desirable properties of OLS are dependent upon estimation on a random sample. Thus, the 'Ran-Nam and Nevile results are likely to suffer from bias unless individuals are randomly allocated between self-employment and paid employment. The current analysis extends Tran-Nam and Nevile (1988) by explicitly treating the choice of paid employment versus self-employment as being endogenously determined. This allows an explicit test for the appropriateness of deleting self-employed workers from the sample. Earnings equations that are corrected for sample selection are estimated for both natives and migrants in the paid employee sector. The Heckman (1979) two-step estimator is employed. The paper is divided into five major sections. The next section presents the econometric model incorporating the specification of the earnings generating process together with an explicit model determining an individual's employment status. In Section 111 the data are described. Section IV draws together the main econometric results of the paper. First, the probit estimates of the labour market status equation are documented. This is followed by presentation and discussion of the Heckman two-stage estimates of the earnings specification for both native and migrant Australians. Separate earnings equations are estimated for paid employees and the self-employed. Section V documents estimates of the nativelmigrant earnings differential for both categories of employees. To aid comparison with earlier work, the Oaxaca decomposition of the earnings differential for paid-employees is carried out for both the simple OLS regression results as well as the parameter estimates corrected for sample selection effects. These differentials are interpreted and compared with previous Australian findings. A short section concludes the paper.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative

Rayleigh–Stokes problems have in recent years received much attention due to their importance in physics. In this article, we focus on the variable-order Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative. Implicit and explicit numerical methods are developed to solve the problem. The convergence, stability of the numerical methods and solvability of the implicit numerical method are discussed via Fourier analysis. Moreover, a numerical example is given and the results support the effectiveness of the theoretical analysis.

Numerical approximation for a variable-order nonlinear reaction–subdiffusion equation

Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A numerical approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved numerical approximation. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

Advice to consult a general medical practitioner in Western Australia : Could it be cancer?

Background: Many people will consult a medical practitioner about lower bowel symptoms, and the demand for access to general practitioners (GPs) is growing. We do not know if people recognise the symptoms of lower bowel cancer when advising others about the need to consult a doctor. A structured vignette survey was conducted in Western Australia. Method: Participants were recruited from the waiting rooms at five general practices. Respondents were invited to complete self-administered questionnaires containing nine vignettes chosen at random from a pool of 64 based on six clinical variables. Twenty-seven vignettes described high-risk bowel cancer scenarios. Respondents were asked if they would recommend a medical consultation for the case described and whether they believed the scenario was a cancer presentation. Logistic regression was used to estimate the independent effects of each variable on the respondent's judgement. Two-hundred and sixty-eight completed responses were collected over eight weeks. Results: The majority (61%) of respondents were female, aged 40 years and older. A history of rectal bleeding, six weeks of symptoms, and weight loss independently increased the odds of recommending a consultation with a medical practitioner by a factor of 7.64, 4.11 and 1.86, respectively. Most cases that were identified as cancer (75.2%) would not be classified as such on current research evidence. Factors that predict recognition of cancer presentations include rectal bleeding, weight loss and diarrhoea.

Targeted control of feral pigs in far north Queensland : defining management units using molecular techniques

The feral pig, Sus scrofa, is a widespread and abundant invasive species in Australia. Feral pigs pose a significant threat to the environment, agricultural industry, and human health, and in far north Queensland they endanger World Heritage values of the Wet Tropics. Historical records document the first introduction of domestic pigs into Australia via European settlers in 1788 and subsequent introductions from Asia from 1827 onwards. Since this time, domestic pigs have been accidentally and deliberately released into the wild and significant feral pig populations have become established, resulting in the declaration of this species as a class 2 pest in Queensland. The overall objective of this study was to assess the population genetic structure of feral pigs in far north Queensland, in particular to enable delineation of demographically independent management units. The identification of ecologically meaningful management units using molecular techniques can assist in targeting feral pig control to bring about effective long-term management. Molecular genetic analysis was undertaken on 434 feral pigs from 35 localities between Tully and Innisfail. Seven polymorphic and unlinked microsatellite loci were screened and fixation indices (FST and analogues) and Bayesian clustering methods were used to identify population structure and management units in the study area. Sequencing of the hyper-variable mitochondrial control region (D-loop) of 35 feral pigs was also examined to identify pig ancestry. Three management units were identified in the study at a scale of 25 to 35 km. Even with the strong pattern of genetic structure identified in the study area, some evidence of long distance dispersal and/or translocation was found as a small number of individuals exhibited ancestry from a management unit outside of which they were sampled. Overall, gene flow in the study area was found to be influenced by environmental features such as topography and land use, but no distinct or obvious natural or anthropogenic geographic barriers were identified. Furthermore, strong evidence was found for non-random mating between pigs of European and Asian breeds indicating that feral pig ancestry influences their population genetic structure. Phylogenetic analysis revealed two distinct mitochondrial DNA clades, representing Asian domestic pig breeds and European breeds. A significant finding was that pigs of Asian origin living in Innisfail and south Tully were not mating randomly with European breed pigs populating the nearby Mission Beach area. Feral pig control should be implemented in each of the management units identified in this study. The control should be coordinated across properties within each management unit to prevent re-colonisation from adjacent localities. The adjacent rainforest and National Park Estates, as well as the rainforest-crop boundary should be included in a simultaneous control operation for greater success.

Exploring empathy as a variable in the evaluation of professional development programmes for palliative care nurses

Research indicates that empathy, a quality regarded as fundamentally important to nursing practice, is a teachable skill. Because empathic nurse-patient relationships are particularly important in the care of the terminally ill, this has direct relevance to the professional development of palliative care nurses. This article discusses the place of empathy as a criterion variable in the evaluation of a professional development program for palliative care nurses introduced at the Centre for Mental Health Nursing Research at Queensland University of Technology, Brisbane, Australia. A modified version of the Staff-Patient Interaction Response Scale (SPIRS) was used as a pre- and postintervention measure to assess the expressed empathy of the participating nurses. The modifications to SPIR and its coding system to make it suitable for palliative care nursing, and the mechanisms for improving and evaluating the reliability of this instrument will be discussed. The full description of this particular modification of SPIRS for palliative care research is provided as an example of how this instrument could be used in projects for which nurses undertake the difficult task of providing compassionate care to the terminally ill.