A hybrid model for studying spatial aspects of infectious diseases

We consider a hybrid model, created by coupling a continuum and an agent-based model of infectious disease. The framework of the hybrid model provides a mechanism to study the spread of infection at both the individual and population levels. This approach captures the stochastic spatial heterogeneity at the individual level, which is directly related to deterministic population level properties. This facilitates the study of spatial aspects of the epidemic process. A spatial analysis, involving counting the number of infectious agents in equally sized bins, reveals when the spatial domain is nonhomogeneous.

Tactically-driven nonmonotone travelling waves

Models of cell invasion incorporating directed cell movement up a gradient of an external substance and carrying capacity-limited proliferation give rise to travelling wave solutions. Travelling wave profiles with various shapes, including smooth monotonically decreasing, shock-fronted monotonically decreasing and shock-fronted nonmonotone shapes, have been reported previously in the literature. The existence of tacticallydriven shock-fronted nonmonotone travelling wave solutions is analysed for the first time. We develop a necessary condition for nonmonotone shock-fronted solutions. This condition shows that some of the previously reported shock-fronted nonmonotone solutions are genuine while others are a consequence of numerical error. Our results demonstrate that, for certain conditions, travelling wave solutions can be either smooth and monotone, smooth and nonmonotone or discontinuous and nonmonotone. These different shapes correspond to different invasion speeds. A necessary and sufficient condition for the travelling wave with minimum wave speed to be nonmonotone is presented. Several common forms of the tactic sensitivity function have the potential to satisfy the newly developed condition for nonmonotone shock-fronted solutions developed in this work.

Stable strong order 1.0 schemes for solving stochastic ordinary differential equations

The Balanced method was introduced as a class of quasi-implicit methods, based upon the Euler-Maruyama scheme, for solving stiff stochastic differential equations. We extend the Balanced method to introduce a class of stable strong order 1. 0 numerical schemes for solving stochastic ordinary differential equations. We derive convergence results for this class of numerical schemes. We illustrate the asymptotic stability of this class of schemes is illustrated and is compared with contemporary schemes of strong order 1. 0. We present some evidence on parametric selection with respect to minimising the error convergence terms. Furthermore we provide a convergence result for general Balanced style schemes of higher orders.

Minimum important difference between patients with rheumatoid arthritis : the patient's perspective

OBJECTIVE: To determine the point at which differences in clinical assessment scores on physical ability, pain and overall condition are sufficiently large to correspond to a subjective perception of a meaningful difference from the perspective of the patient. METHODS: Forty patients with a diagnosis of rheumatoid arthritis participated in an evening of clinical assessment and one-on-one conversations with each other regarding their arthritic condition. The assessments included tender and swollen joint counts, clinician and patient global assessments, participant assessment of pain and the Health Assessment Questionnaire (HAQ) on physical ability. After each conversation, participants rated themselves relative to their conversational partner on physical ability, pain and overall condition. These subjective comparative ratings were compared to the differences of the individual clinical assessments. RESULTS: In total there were 120 conversations. Generally participants judged themselves as less disabled than others. They rated themselves as "somewhat better" than their conversation partner when they had a (mean) 7% better score on the HAQ, 6% less pain, and 9% better global assessment. In contrast, they rated themselves as "somewhat worse" when they had a (mean) 16% worse score on the HAQ, 16% more pain, and 29% worse global assessment. CONCLUSIONS: Patients view clinically important differences in an asymmetric manner. These results can provide guidance in interpreting results and planning clinical trials.

A novel numerical approximation for the space fractional advection-dispersion equation

In this paper, we consider a space fractional advection–dispersion equation. The equation is obtained from the standard advection–diffusion equation by replacing the first- and second-order space derivatives by the Riesz fractional derivatives of order β1 ∈ (0, 1) and β2 ∈ (1, 2], respectively. The fractional advection and dispersion terms are approximated by using two fractional centred difference schemes. A new weighted Riesz fractional finite-difference approximation scheme is proposed. When the weighting factor θ equals 12, a second-order accuracy scheme is obtained. The stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

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.

Some practical issues in the design and analysis of computer experiments

Deterministic computer simulations of physical experiments are now common techniques in science and engineering. Often, physical experiments are too time consuming, expensive or impossible to conduct. Complex computer models or codes, rather than physical experiments lead to the study of computer experiments, which are used to investigate many scientific phenomena of this nature. A computer experiment consists of a number of runs of the computer code with different input choices. The Design and Analysis of Computer Experiments is a rapidly growing technique in statistical experimental design. This thesis investigates some practical issues in the design and analysis of computer experiments and attempts to answer some of the questions faced by experimenters using computer experiments. In particular, the question of the number of computer experiments and how they should be augmented is studied and attention is given to when the response is a function over time.

Exercising QS: Quantitative skills in an exercise science course

This study seeks to bring the discipline of exercise science into the discussion of Quantitative Skills (QS) in Science. The author’s experiences of providing learning support to students and working with educators in the field are described, demonstrating the difficulty of encouraging students to address their skills deficit. A survey of students’ perceptions of their own QS and of that required for their course, demonstrates the difficulties faced by students who do not have the prescribed assumed knowledge for the course. Limited results from academics suggest that their perceptions of students’ QS deficits are even more dire than those of the under-prepared students.

From science to management : using Bayesian networks to learn about Lyngbya

Toxic blooms of Lyngbya majuscula occur in coastal areas worldwide and have major ecological, health and economic consequences. The exact causes and combinations of factors which lead to these blooms are not clearly understood. Lyngbya experts and stakeholders are a particularly diverse group, including ecologists, scientists, state and local government representatives, community organisations, catchment industry groups and local fishermen. An integrated Bayesian Network approach was developed to better understand and model this complex environmental problem, identify knowledge gaps, prioritise future research and evaluate management options.

Modeling the viability of the free-ranging cheetah population in Namibia : an object-oriented Bayesian network approach

Conservation of free-ranging cheetah (Acinonyx jubatus) populations is multi faceted and needs to be addressed from an ecological, biological and management perspective. There is a wealth of published research, each focusing on a particular aspect of cheetah conservation. Identifying the most important factors, making sense of various (and sometimes contrasting) findings, and taking decisions when little or no empirical data is available, are everyday challenges facing conservationists. Bayesian networks (BN) provide a statistical modeling framework that enables analysis and integration of information addressing different aspects of conservation. There has been an increased interest in the use of BNs to model conservation issues, however the development of more sophisticated BNs, utilizing object-oriented (OO) features, is still at the frontier of ecological research. We describe an integrated, parallel modeling process followed during a BN modeling workshop held in Namibia to combine expert knowledge and data about free-ranging cheetahs. The aim of the workshop was to obtain a more comprehensive view of the current viability of the free-ranging cheetah population in Namibia, and to predict the effect different scenarios may have on the future viability of this free-ranging cheetah population. Furthermore, a complementary aim was to identify influential parameters of the model to more effectively target those parameters having the greatest impact on population viability. The BN was developed by aggregating diverse perspectives from local and independent scientists, agents from the national ministry, conservation agency members and local fieldworkers. This integrated BN approach facilitates OO modeling in a multi-expert context which lends itself to a series of integrated, yet independent, subnetworks describing different scientific and management components. We created three subnetworks in parallel: a biological, ecological and human factors network, which were then combined to create a complete representation of free-ranging cheetah population viability. Such OOBNs have widespread relevance to the effective and targeted conservation management of vulnerable and endangered species.

The epidemiology of invasive group A streptococcal disease in Victoria, Australia

Objective To estimate the incidence and severity of invasive group A streptococcal infection in Victoria, Australia. Design Prospective active surveillance study. Setting Public and private laboratories, hospitals and general practitioners throughout Victoria. Patients eople in Victoria diagnosed with group A streptococcal disease notified to the surveillance system between 1 March 2002 and 31 August 2004. Main outcome measure Confirmed invasive group A streptococcal disease. Results We identified 333 confirmed cases: an average annualised incidence rate of 2.7 (95% CI, 2.3-3.2) per 100000 population per year. Rates were highest in people aged 65 years and older and those younger than 5 years. The case-fatality rate was 7.8%. Streptococcal toxic shock syndrome occurred in 48 patients (14.4%), with a case-fatality rate of 23%. Thirty cases of necrotising fasciitis were reported; five (17%) of these patients died. Type 1 (23%) was the most frequently identified emm sequence type in all, age groups. All tested isolates were susceptible to penicillin and clindamycin. Two isolates (4%) were resistant to erythromycin. Conclusion The incidence of invasive group A streptococcal disease in temperate Australia is greater than previously appreciated and warrants greater public health attention, including its designation as a notifiable disease.

Ignition delay of bio-fuels in a common-rail compression ignition engine

The utility of a novel technique for determining the ignition delay in a compression ignition engine has been shown. This method utilises statistical modelling in the Bayesian paradigm to accurately resolve the start of combustion from a band-pass in-cylinder pressure signal. Applied to neat diesel and six biofuels, including four fractionations of palm oil of varying carbon chain length and degree of unsaturation, the relationships between ignition delay, cetane number and oxygen content have been explored. It is noted that the expected negative relationship between ignition delay and cetane number held, as did the positive relationship between ignition delay and oxygen content. The degree of unsaturation was also identified as a potential factor influencing the ignition delay.

The impact of spatial scales and spatial smoothing on the outcome of Bayesian spatial model

Discretization of a geographical region is quite common in spatial analysis. There have been few studies into the impact of different geographical scales on the outcome of spatial models for different spatial patterns. This study aims to investigate the impact of spatial scales and spatial smoothing on the outcomes of modelling spatial point-based data. Given a spatial point-based dataset (such as occurrence of a disease), we study the geographical variation of residual disease risk using regular grid cells. The individual disease risk is modelled using a logistic model with the inclusion of spatially unstructured and/or spatially structured random effects. Three spatial smoothness priors for the spatially structured component are employed in modelling, namely an intrinsic Gaussian Markov random field, a second-order random walk on a lattice, and a Gaussian field with Matern correlation function. We investigate how changes in grid cell size affect model outcomes under different spatial structures and different smoothness priors for the spatial component. A realistic example (the Humberside data) is analyzed and a simulation study is described. Bayesian computation is carried out using an integrated nested Laplace approximation. The results suggest that the performance and predictive capacity of the spatial models improve as the grid cell size decreases for certain spatial structures. It also appears that different spatial smoothness priors should be applied for different patterns of point data.

An Artificial Neutral Network (ANN) model for predicting biodiesel kinetic viscosity as a function of temperature and chemical compositions

An Artificial Neural Network (ANN) is a computational modeling tool which has found extensive acceptance in many disciplines for modeling complex real world problems. An ANN can model problems through learning by example, rather than by fully understanding the detailed characteristics and physics of the system. In the present study, the accuracy and predictive power of an ANN was evaluated in predicting kinetic viscosity of biodiesels over a wide range of temperatures typically encountered in diesel engine operation. In this model, temperature and chemical composition of biodiesel were used as input variables. In order to obtain the necessary data for model development, the chemical composition and temperature dependent fuel properties of ten different types of biodiesels were measured experimentally using laboratory standard testing equipments following internationally recognized testing procedures. The Neural Networks Toolbox of MatLab R2012a software was used to train, validate and simulate the ANN model on a personal computer. The network architecture was optimised following a trial and error method to obtain the best prediction of the kinematic viscosity. The predictive performance of the model was determined by calculating the absolute fraction of variance (R2), root mean squared (RMS) and maximum average error percentage (MAEP) between predicted and experimental results. This study found that ANN is highly accurate in predicting the viscosity of biodiesel and demonstrates the ability of the ANN model to find a meaningful relationship between biodiesel chemical composition and fuel properties at different temperature levels. Therefore the model developed in this study can be a useful tool in accurately predict biodiesel fuel properties instead of undertaking costly and time consuming experimental tests.

Lattice-based certificateless public-key encryption in the standard model

The notion of certificateless public-key encryption (CL-PKE) was introduced by Al-Riyami and Paterson in 2003 that avoids the drawbacks of both traditional PKI-based public-key encryption (i.e., establishing public-key infrastructure) and identity-based encryption (i.e., key escrow). So CL-PKE like identity-based encryption is certificate-free, and unlike identity-based encryption is key escrow-free. In this paper, we introduce simple and efficient CCA-secure CL-PKE based on (hierarchical) identity-based encryption. Our construction has both theoretical and practical interests. First, our generic transformation gives a new way of constructing CCA-secure CL-PKE. Second, instantiating our transformation using lattice-based primitives results in a more efficient CCA-secure CL-PKE than its counterpart introduced by Dent in 2008.