Mathematical models of calcium and tight junctions in normal and reconstructed epidermis

This project investigated the calcium distributions of the skin, and the growth patterns of skin substitutes grown in the laboratory, using mathematical models. The research found that the calcium distribution in the upper layer of the skin is controlled by three different mechanisms, not one as previously thought. The research also suggests that tight junctions, which are adhesions between neighbouring skin cells, cannot be solely responsible for the differences in the growth patterns of skin substitutes and normal skin.

Using genomic data to make indirect (and unauthorized) estimates of disease risk

The number of genetic factors associated with common human traits and disease is increasing rapidly, and the general public is utilizing affordable, direct-to-consumer genetic tests. The results of these tests are often in the public domain. A combination of factors has increased the potential for the indirect estimation of an individual's risk for a particular trait. Here we explain the basic principals underlying risk estimation which allowed us to test the ability to make an indirect risk estimation from genetic data by imputing Dr. James Watson's redacted apolipoprotein E gene (APOE) information. The principles underlying risk prediction from genetic data have been well known and applied for many decades, however, the recent increase in genomic knowledge, and advances in mathematical and statistical techniques and computational power, make it relatively easy to make an accurate but indirect estimation of risk. There is a current hazard for indirect risk estimation that is relevant not only to the subject but also to individuals related to the subject; this risk will likely increase as more detailed genomic data and better computational tools become available.

Achieving a national sample of nursing homes: Balancing probability techniques and practicalities

Sampling design is critical to the quality of quantitative research, yet it does not always receive appropriate attention in nursing research. The current article details how balancing probability techniques with practical considerations produced a representative sample of Australian nursing homes (NHs). Budgetary, logistical, and statistical constraints were managed by excluding some NHs (e.g., those too difficult to access) from the sampling frame; a stratified, random sampling methodology yielded a final sample of 53 NHs from a population of 2,774. In testing the adequacy of representation of the study population, chi-square tests for goodness of fit generated nonsignificant results for distribution by distance from major city and type of organization. A significant result for state/territory was expected and was easily corrected for by the application of weights. The current article provides recommendations for conducting high-quality, probability-based samples and stresses the importance of testing the representativeness of achieved samples.

Mathematical modelling of human corneal oxygenation and cell kinetics in corneal epithelial wound healing

Healthy transparent cornea depends upon the regulation of fluid, nutrient and oxygen transport through the tissue to sustain cell metabolism and other critical processes for normal functioning. This research considers the corneal geometry and investigates oxygen distribution using a two-dimensional Monod kinetic model, showing that previous studies make assumptions that lead to predictions of near-anoxic levels of oxygen tension in the limbal regions of the cornea. It also considers the comparison of experimental spatial and temporal data with the predictions of novel mathematical models with respect to distributed mitotic rates during corneal epithelial wound healing.

Sonography of paediatric appendicitis and its secondary signs

Sonographic diagnosis of appendicitis in children is an important clinical tool, often obviating the need for potentially harmful ionising radiation from computed tomography (CT) scans and unnecessary appendectomies. Established criteria do not commonly account for the sonographic secondary signs of acute appendicitis as an adjunct or corollary to an identifiably inflamed appendix. If one of, or combinations of these secondary signs are a reliable positive and/or negative indicator of the condition, diagnostic accuracy may be improved. This will be of particular importance in cases where the appendix cannot be easily identified, possibly providing referring clinicians with a less equivocal diagnosis. Acute appendicitis (AA) is the most common emergency presentation requiring surgical intervention among both adults and children. During 2010-11 in Australia 25000 appendicectomies were performed on adults and children, more than double the number of the next most common surgical procedure [1]. Ultrasound has been commonly used to diagnose AA since the 1980s, however the best imaging modality or combination of modalities to accurately and cost-effectively diagnose the condition is still debated. A study by Puylaert advocated ultrasound in all presentations [2], whereas others suggested it only as a first line modality [3–5]. Conversely, York et al state that it is not appropriate as it delays treatment [6]. CT has been shown to more accurately diagnose AA than ultrasound, however its inherent radiation risks warrant cautionary use in children [7]. Improved accuracy in the diagnosis of suspected AA using ultrasound would enable surgeons to make a decision without the need to expose children to the potentially harmful effects of CT. Secondary signs of appendicitis are well established [8], although research into their predictive values has only recently been undertaken [9,10] indicating their potential diagnostic benefit in the absence of an identifiable appendix. The purpose of this review is to examine the history of appendiceal sonography, established sonographic criteria, paediatric specific techniques and the predictive value of secondary signs.

Open-pit block sequencing optimization: A mathematical model and solution technique

This study presents a comprehensive mathematical formulation model for a short-term open-pit mine block sequencing problem, which considers nearly all relevant technical aspects in open-pit mining. The proposed model aims to obtain the optimum extraction sequences of the original-size (smallest) blocks over short time intervals and in the presence of real-life constraints, including precedence relationship, machine capacity, grade requirements, processing demands and stockpile management. A hybrid branch-and-bound and simulated annealing algorithm is developed to solve the problem. Computational experiments show that the proposed methodology is a promising way to provide quantitative recommendations for mine planning and scheduling engineers.

Unmanned Aerial Vehicles (UAVs) and artificial intelligence revolutionizing wildlife monitoring and conservation

Surveying threatened and invasive species to obtain accurate population estimates is an important but challenging task that requires a considerable investment in time and resources. Estimates using existing ground-based monitoring techniques, such as camera traps and surveys performed on foot, are known to be resource intensive, potentially inaccurate and imprecise, and difficult to validate. Recent developments in unmanned aerial vehicles (UAV), artificial intelligence and miniaturized thermal imaging systems represent a new opportunity for wildlife experts to inexpensively survey relatively large areas. The system presented in this paper includes thermal image acquisition as well as a video processing pipeline to perform object detection, classification and tracking of wildlife in forest or open areas. The system is tested on thermal video data from ground based and test flight footage, and is found to be able to detect all the target wildlife located in the surveyed area. The system is flexible in that the user can readily define the types of objects to classify and the object characteristics that should be considered during classification.

Mathematical modelling and numerical simulation of phosphine flow during grain fumigation in leaky cylindrical silos

The phosphine distribution in a cylindrical silo containing grain is predicted. A three-dimensional mathematical model, which accounts for multicomponent gas phase transport and the sorption of phosphine into the grain kernel is developed. In addition, a simple model is presented to describe the death of insects within the grain as a function of their exposure to phosphine gas. The proposed model is solved using the commercially available computational fluid dynamics (CFD) software, FLUENT, together with our own C code to customize the solver in order to incorporate the models for sorption and insect extinction. Two types of fumigation delivery are studied, namely, fan- forced from the base of the silo and tablet from the top of the silo. An analysis of the predicted phosphine distribution shows that during fan forced fumigation, the position of the leaky area is very important to the development of the gas flow field and the phosphine distribution in the silo. If the leak is in the lower section of the silo, insects that exist near the top of the silo may not be eradicated. However, the position of a leak does not affect phosphine distribution during tablet fumigation. For such fumigation in a typical silo configuration, phosphine concentrations remain low near the base of the silo. Furthermore, we find that half-life pressure test readings are not an indicator of phosphine distribution during tablet fumigation.

A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area

Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical evidence that self-intersection is possible for non-convex initial conditions, distinguishing between pinch-off and coalescence of the curve interior.

Computational methods for the prediction of the structure and interactions of coiled-coil peptides

The past several years have seen significant advances in the development of computational methods for the prediction of the structure and interactions of coiled-coil peptides. These methods are generally based on pairwise correlations of amino acids, helical propensity, thermal melts and the energetics of sidechain interactions, as well as statistical patterns based on Hidden Markov Model (HMM) and Support Vector Machine (SVM) techniques. These methods are complemented by a number of public databases that contain sequences, motifs, domains and other details of coiled-coil structures identified by various algorithms. Some of these computational methods have been developed to make predictions of coiled-coil structure on the basis of sequence information; however, structural predictions of the oligomerisation state of these peptides still remains largely an open question due to the dynamic behaviour of these molecules. This review focuses on existing in silico methods for the prediction of coiled-coil peptides of functional importance using sequence and/or three-dimensional structural data.

Deploying speaker verification techniques to vision-based RPA detect and avoid

Detect and Avoid (DAA) technology is widely acknowledged as a critical enabler for unsegregated Remote Piloted Aircraft (RPA) operations, particularly Beyond Visual Line of Sight (BVLOS). Image-based DAA, in the visible spectrum, is a promising technological option for addressing the challenges DAA presents. Two impediments to progress for this approach are the scarcity of available video footage to train and test algorithms, in conjunction with testing regimes and specifications which facilitate repeatable, statistically valid, performance assessment. This paper includes three key contributions undertaken to address these impediments. In the first instance, we detail our progress towards the creation of a large hybrid collision and near-collision encounter database. Second, we explore the suitability of techniques employed by the biometric research community (Speaker Verification and Language Identification), for DAA performance optimisation and assessment. These techniques include Detection Error Trade-off (DET) curves, Equal Error Rates (EER), and the Detection Cost Function (DCF). Finally, the hybrid database and the speech-based techniques are combined and employed in the assessment of a contemporary, image based DAA system. This system includes stabilisation, morphological filtering and a Hidden Markov Model (HMM) temporal filter.

Aircraft trajectory clustering techniques using circular statistics

This paper presents a statistical aircraft trajectory clustering approach aimed at discriminating between typical manned and expected unmanned traffic patterns. First, a resampled version of each trajectory is modelled using a mixture of Von Mises distributions (circular statistics). Second, the remodelled trajectories are globally aligned using tools from bioinformatics. Third, the alignment scores are used to cluster the trajectories using an iterative k-medoids approach and an appropriate distance function. The approach is then evaluated using synthetically generated unmanned aircraft flights combined with real air traffic position reports taken over a sector of Northern Queensland, Australia. Results suggest that the technique is useful in distinguishing between expected unmanned and manned aircraft traffic behaviour, as well as identifying some common conventional air traffic patterns.

Mathematical modelling of rock-bed solar thermal storage tank

An important application of thermal storage is solar energy for power generation or process heating. Low temperature thermal storage in a packed rock bed is considered best option for thermal storage for solar drying applications. In this paper, mathematical formulations for conical and cylindrical rock bed storage tanks have been developed. The model equations are solved numerically for charging/discharging cycles. From the simulated results, it was observed that for the same aspect ratio between the diameter and the length of the thermal storages, the conical thermal storage had better performance. The temperature distribution was found to be more uniform in the truncated conical shape rock bed storage. Also, the pressure drop over long period of time in the conical thermal storage was lower than that of the cylindrical thermal storage. Hence, the amount of power required from a centrifugal fan was lower.

A semi-analytical solution for multilayer diffusion in a composite medium consisting of a large number of layers

Diffusion in a composite slab consisting of a large number of layers provides an ideal prototype problem for developing and analysing two-scale modelling approaches for heterogeneous media. Numerous analytical techniques have been proposed for solving the transient diffusion equation in a one-dimensional composite slab consisting of an arbitrary number of layers. Most of these approaches, however, require the solution of a complex transcendental equation arising from a matrix determinant for the eigenvalues that is difficult to solve numerically for a large number of layers. To overcome this issue, in this paper, we present a semi-analytical method based on the Laplace transform and an orthogonal eigenfunction expansion. The proposed approach uses eigenvalues local to each layer that can be obtained either explicitly, or by solving simple transcendental equations. The semi-analytical solution is applicable to both perfect and imperfect contact at the interfaces between adjacent layers and either Dirichlet, Neumann or Robin boundary conditions at the ends of the slab. The solution approach is verified for several test cases and is shown to work well for a large number of layers. The work is concluded with an application to macroscopic modelling where the solution of a fine-scale multilayered medium consisting of two hundred layers is compared against an “up-scaled” variant of the same problem involving only ten layers.