An external field prior for the hidden Potts model with application to cone-beam computed tomography

In images with low contrast-to-noise ratio (CNR), the information gain from the observed pixel values can be insufficient to distinguish foreground objects. A Bayesian approach to this problem is to incorporate prior information about the objects into a statistical model. A method for representing spatial prior information as an external field in a hidden Potts model is introduced. This prior distribution over the latent pixel labels is a mixture of Gaussian fields, centred on the positions of the objects at a previous point in time. It is particularly applicable in longitudinal imaging studies, where the manual segmentation of one image can be used as a prior for automatic segmentation of subsequent images. The method is demonstrated by application to cone-beam computed tomography (CT), an imaging modality that exhibits distortions in pixel values due to X-ray scatter. The external field prior results in a substantial improvement in segmentation accuracy, reducing the mean pixel misclassification rate for an electron density phantom from 87% to 6%. The method is also applied to radiotherapy patient data, demonstrating how to derive the external field prior in a clinical context.

A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation

This paper aims to develop a meshless approach based on the Point Interpolation Method (PIM) for numerical simulation of a space fractional diffusion equation. Two fully-discrete schemes for the one-dimensional space fractional diffusion equation are obtained by using the PIM and the strong-forms of the space diffusion equation. Numerical examples with different nodal distributions are studied to validate and investigate the accuracy and efficiency of the newly developed meshless approach.

Estimation of inhaled ultrafine particle surface area dose for urban environments

There is considerable scientific interest in personal exposure to ultrafine particles. Owing to their small size, these particles are able to penetrate deep into the lungs, where they may cause adverse respiratory, pulmonary and cardiovascular health effects. This article presents Bayesian hierarchical models for estimating and comparing inhaled particle surface area in the lung.

Ultrafine Particles from Traffic Emissions and Children’s Health (UPTECH) in Brisbane, Queensland (Australia): Study design and implementation

Ultrafine particles are particles that are less than 0.1 micrometres (µm) in diameter. Due to their very small size they can penetrate deep into the lungs, and potentially cause more damage than larger particles. The Ultrafine Particles from Traffic Emissions and Children’s Health (UPTECH) study is the first Australian epidemiological study to assess the health effects of ultrafine particles on children’s health in general and peripheral airways in particular. The study is being conducted in Brisbane, Australia. Continuous indoor and outdoor air pollution monitoring was conducted within each of the twenty five participating school campuses to measure particulate matter, including in the ultrafine size range, and gases. Respiratory health effects were evaluated by conducting the following tests on participating children at each school: spirometry, forced oscillation technique (FOT) and multiple breath nitrogen washout test (MBNW) (to assess airway function), fraction of exhaled nitric oxide (FeNO, to assess airway inflammation), blood cotinine levels (to assess exposure to second-hand tobacco smoke), and serum C-reactive protein (CRP) levels (to measure systemic inflammation). A pilot study was conducted prior to commencing the main study to assess the feasibility and reliably of measurement of some of the clinical tests that have been proposed for the main study. Air pollutant exposure measurements were not included in the pilot study.

A semi-alternating direction method for a 2-D fractional FitzHugh–Nagumo monodomain model on an approximate irregular domain

A FitzHugh-Nagumo monodomain model has been used to describe the propagation of the electrical potential in heterogeneous cardiac tissue. In this paper, we consider a two-dimensional fractional FitzHugh-Nagumo monodomain model on an irregular domain. The model consists of a coupled Riesz space fractional nonlinear reaction-diffusion model and an ordinary differential equation, describing the ionic fluxes as a function of the membrane potential. Secondly, we use a decoupling technique and focus on solving the Riesz space fractional nonlinear reaction-diffusion model. A novel spatially second-order accurate semi-implicit alternating direction method (SIADM) for this model on an approximate irregular domain is proposed. Thirdly, stability and convergence of the SIADM are proved. Finally, some numerical examples are given to support our theoretical analysis and these numerical techniques are employed to simulate a two-dimensional fractional Fitzhugh-Nagumo model on both an approximate circular and an approximate irregular domain.

A statistical model for combustion resonance from a DI diesel engine with applications

Introduced in this paper is a Bayesian model for isolating the resonant frequency from combustion chamber resonance. The model shown in this paper focused on characterising the initial rise in the resonant frequency to investigate the rise of in-cylinder bulk temperature associated with combustion. By resolving the model parameters, it is possible to determine: the start of pre-mixed combustion, the start of diffusion combustion, the initial resonant frequency, the resonant frequency as a function of crank angle, the in-cylinder bulk temperature as a function of crank angle and the trapped mass as a function of crank angle. The Bayesian method allows for individual cycles to be examined without cycle-averaging|allowing inter-cycle variability studies. Results are shown for a turbo-charged, common-rail compression ignition engine run at 2000 rpm and full load.

The mathematical modelling of cheese ripening

A mathematical model is developed for the ripening of cheese. Such models may assist predicting final cheese quality using measured initial composition. The main constituent chemical reactions are described with ordinary differential equations. Numerical solutions to the model equations are found using Matlab. Unknown parameter values have been fitted using experimental data available in the literature. The results from the numerical fitting are in good agreement with the data. Statistical analysis is performed on near infrared data provided to the MISG. However, due to the inhomogeneity and limited nature of the data, not many conclusions can be drawn from the analysis. A simple model of the potential changes in acidity of cheese is also considered. The results from this model are consistent with cheese manufacturing knowledge, in that the pH of cheddar cheese does not significantly change during ripening.

Enhancing the teaching and learning of mathematical visual images

The literacy demands of mathematics are very different to those in other subjects (Gough, 2007; O'Halloran, 2005; Quinnell, 2011; Rubenstein, 2007) and much has been written on the challenges that literacy in mathematics poses to learners (Abedi and Lord, 2001; Lowrie and Diezmann, 2007, 2009; Rubenstein, 2007). In particular, a diverse selection of visuals typifies the field of mathematics (Carter, Hipwell and Quinnell, 2012), placing unique literacy demands on learners. Such visuals include varied tables, graphs, diagrams and other representations, all of which are used to communicate information.

Remaining useful life prediction of rotating equipment using covariate-based hazard models : industry applications

The ability to estimate the expected Remaining Useful Life (RUL) is critical to reduce maintenance costs, operational downtime and safety hazards. In most industries, reliability analysis is based on the Reliability Centred Maintenance (RCM) and lifetime distribution models. In these models, the lifetime of an asset is estimated using failure time data; however, statistically sufficient failure time data are often difficult to attain in practice due to the fixed time-based replacement and the small population of identical assets. When condition indicator data are available in addition to failure time data, one of the alternate approaches to the traditional reliability models is the Condition-Based Maintenance (CBM). The covariate-based hazard modelling is one of CBM approaches. There are a number of covariate-based hazard models; however, little study has been conducted to evaluate the performance of these models in asset life prediction using various condition indicators and data availability. This paper reviews two covariate-based hazard models, Proportional Hazard Model (PHM) and Proportional Covariate Model (PCM). To assess these models’ performance, the expected RUL is compared to the actual RUL. Outcomes demonstrate that both models achieve convincingly good results in RUL prediction; however, PCM has smaller absolute prediction error. In addition, PHM shows over-smoothing tendency compared to PCM in sudden changes of condition data. Moreover, the case studies show PCM is not being biased in the case of small sample size.

Discrete families of Saffman–Taylor fingers with exotic shapes

The mathematical problem of determining the shape of a steadily propagating Saffman–Taylor finger in a rectangular Hele-Shaw cell is known to have a countably infinite number of solutions for each fixed surface tension value. For sufficiently large surface tension values, we find that fingers on higher solution branches are non-convex. The tips of the fingers have increasingly exotic shapes as the branch number increases.

Wake angle for surface gravity waves on a finite depth fluid

Linear water wave theory suggests that wave patterns caused by a steadily moving disturbance are contained within a wedge whose half-angle depends on the depth-based Froude number $F_H$. For the problem of flow past an axisymmetric pressure distribution in a finite-depth channel, we report on the apparent angle of the wake, which is the angle of maximum peaks. For moderately deep channels, the dependence of the apparent wake angle on the Froude number is very different to the wedge angle, and varies smoothly as $F_H$ passes through the critical value $F_H=1$. For shallow water, the two angles tend to follow each other more closely, which leads to very large apparent wake angles for certain regimes.

Are there generalizable trends in the release of airborne synthetic clay nanoparticles from a jet milling process?

Despite recent efforts to assess the release of nanoparticles to the workplace during different nanotechnology activities, the existence of a generalizable trend in the particle release has yet to be identified. This study aimed to characterize the release of synthetic clay nanoparticles from a laboratory-based jet milling process by quantifying the variations arising from primary particle size and surface treatment of the material used, as well as the feed rate of the machine. A broad range of materials were used in this study, and the emitted particles mass (PM2.5) and number concentrations (PNC) were measured at the release source. Analysis of variance, followed by linear mixed-effects modeling, was applied to quantify the variations in PM2.5 and PNC of the released particles caused by the abovementioned factors. The results confirmed that using materials of different primary size and surface treatment affects the release of the particles from the same process by causing statistically-significant variations in PM2.5 and PNC. The interaction of these two factors should also be taken into account as it resulted in variations in the measured particles release properties. Furthermore, the feed rate of the milling machine was confirmed to be another influencing parameter. Although this research does not identify a specific pattern in the release of synthetic clay nanoparticles from the jet milling process generalizable to other similar settings, it emphasizes that each tested case should be handled individually in terms of exposure considerations.

Airborne culturable fungi in naturally ventilated primary school environments in a subtropical climate

There is currently a lack of reference values for indoor air fungal concentrations to allow for the interpretation of measurement results in subtropical school settings. Analysis of the results of this work established that, in the majority of properly maintained subtropical school buildings, without any major affecting events such as floods or visible mould or moisture contamination, indoor culturable fungi levels were driven by outdoor concentration. The results also allowed us to benchmark the “baseline range” concentrations for total culturable fungi, Penicillium spp., Cladosporium spp. and Aspergillus spp. in such school settings. The measured concentration of total culturable fungi and three individual fungal genera were estimated using Bayesian hierarchical modelling. Pooling of these estimates provided a predictive distribution for concentrations at an unobserved school. The results indicated that “baseline” indoor concentration levels for indoor total fungi, Penicillium spp., Cladosporium spp. and Aspergillus spp. in such school settings were generally ≤ 1450, ≤ 680, ≤ 480 and ≤ 90 cfu/m3, respectively, and elevated levels would indicate mould damage in building structures. The indoor/outdoor ratio for most classrooms had 95% credible intervals containing 1, indicating that fungi concentrations are generally the same indoors and outdoors at each school. Bayesian fixed effects regression modeling showed that increasing both temperature and humidity resulted in higher levels of fungi concentration.

Inhaled particle surface area dose: Stationary vs personal monitoring

The aim of this paper is to determine the suitability of solely stationary measurements for exposure assessment and management applications. For this purpose, quantified inhaled particle surface area (IPSA) doses using both stationary and personal particle exposure monitors were evaluated and compared.

Characterisation and sources of ultrafine particles in an inner city urban area

Exposure to atmospheric ultrafine particles (UFPs, D<100 nm) has been an increasingly concern because of their potential impact one health. Motor vehicle emissions are considered as one of the major source of UFPin urban airshed, as the combustion of both petrol and diesel engine leads to emission of particles which are predominantly in this size range (Ban-Weiss et al, 2010; Morawska et al, 2008). New particle formations (NPFs) and major facilities such as airport or seaport has also been identified as major sources of UFPs in urban airshed (Cheung et al, 2010; González et al, 2011; Mazaheri et al, 2013). However, contribution of those urban sources to ambient UFP concentrations has not been comprehensively characterized.