Analysis of Melanoma Onset: Assessing Familial Aggregation by Using Estimating Equations and Fitting Variance Components via Bayesian Random Effects Models

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.

Implicit stochastic Runge-Kutta methods for stochastic differential equations

In this paper we construct implicit stochastic Runge-Kutta (SRK) methods for solving stochastic differential equations of Stratonovich type. Instead of using the increment of a Wiener process, modified random variables are used. We give convergence conditions of the SRK methods with these modified random variables. In particular, the truncated random variable is used. We present a two-stage stiffly accurate diagonal implicit SRK (SADISRK2) method with strong order 1.0 which has better numerical behaviour than extant methods. We also construct a five-stage diagonal implicit SRK method and a six-stage stiffly accurate diagonal implicit SRK method with strong order 1.5. The mean-square and asymptotic stability properties of the trapezoidal method and the SADISRK2 method are analysed and compared with an explicit method and a semi-implicit method. Numerical results are reported for confirming convergence properties and for comparing the numerical behaviour of these methods.

Prediction of the growth of wear-type rail corrugation

The growth behaviour of the vibrational wear phenomenon known as rail corrugation is investigated analytically and numerically using mathematical models. A simplified feedback model for wear-type rail corrugation that includes a wheel pass time delay is developed with an aim to analytically distil the most critical interaction occurring between the wheel/rail structural dynamics, rolling contact mechanics and rail wear. To this end, a stability analysis on the complete system is performed to determine the growth of wear-type rail corrugations over multiple wheelset passages. This analysis indicates that although the dynamical behaviour of the system is stable for each wheel passage, over multiple wheelset passages, the growth of wear-type corrugations is shown to be the result of instability due to feedback interaction between the three primary components of the model. The corrugations are shown analytically to grow for all realistic railway parameters. From this analysis an analytical expression for the exponential growth rate of corrugations in terms of known parameters is developed. This convenient expression is used to perform a sensitivity analysis to identify critical parameters that most affect corrugation growth. The analytical predictions are shown to compare well with results from a benchmarked time-domain finite element model. (C) 2004 Elsevier B.V. All rights reserved.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.

Growth performance and management of a mixed rainforest tree plantation

Monoculture plantations of Pinus, Eucalyptus and Acacia have been established oil rainforest lands throughout the world. However, this type of reforestation generally supplies low quality timber and contributes to landscape simplification. Alternatives to exotic monoculture plantations are now beginning to gain momentum with farmers and landholders attempting to establish a variety of rainforest trees in small plantations. When compared to the well studied commercial species, knowledge concerning the growth and management of many of these rainforest species is in its infancy. To help expand this limited knowledge base an experimental plantation of 16 rainforest tree species in a randomised design was established near Mt. Mee, in south-eastern Queensland, Australia. Changes in growth, form (based on stem straightness, branch size and branchiness), crown diameters and leaf area of each species were examined over 5 years. Patterns of height growth were also measured monthly for 31 months. Species in this trial could be separated into three groups based on their overall growth after 5 years and their growth patterns. Early successional status, low timber density, high maximum photosynthetic rates and large total leaf areas were generally correlated to rapid height growth. Several species (including Araucaria cunninghamii, Elaeocarpus grandis, Flindersia brayleyana, Grevillea robusta and Khaya nyasica) had above average form and growth, while all species in the trial had considerable potential to have increased productivity through tree selection. As canopy closure occurred at the site between years four and five, growth increments declined. To reduce stand competition a number of different thinning techniques could be employed. However, simple geometric or productivity based thinnings appear to be inappropriate management techniques for this mixed species stand as they would either remove many of the best performing trees or nearly half the species in the trial. Alternatively, a form based thinning would maintain the site's diversity, increase the average form of the plantation and provide some productivity benefits.

Solvability of singular second order m-point boundary value problems of Dirichlet type

Let f : [0, 1] x R2 -> R be a function satisfying the Caxatheodory conditions and t(1 - t)e(t) epsilon L-1 (0, 1). Let a(i) epsilon R and xi(i) (0, 1) for i = 1,..., m - 2 where 0 < xi(1) < xi(2) < (...) < xi(m-2) < 1 - In this paper we study the existence of C[0, 1] solutions for the m-point boundary value problem [GRAPHICS] The proof of our main result is based on the Leray-Schauder continuation theorem.

Costs of learning: the dynamics of mixed-prey exploitation by silver perch, Bidyanus bidyanus (Mitchell, 1838)

Although generalist predators have been reported to forage less efficiently than specialists, there is little information on the extent to which learning can improve the efficiency of mixed-prey foraging. Repeated exposure of silver perch to mixed prey (pelagic Artemia and benthic Chironomus larvae) led to substantial fluctuations in reward rate over relatively long (20-day) timescales. When perch that were familiar with a single prey type were offered two prey types simultaneously, the rate at which they captured both familiar and unfamiliar prey dropped progressively over succeeding trials. This result was not predicted by simple learning paradigms, but could be explained in terms of an interaction between learning and attention. Between-trial patterns in overall intake were complex and differed between the two prey types, but were unaffected by previous prey specialization. However, patterns of prey priority (i.e. the prey type that was preferred at the start of a trial) did vary with previous prey training. All groups of fish converged on the most profitable prey type (chironomids), but this process took 15-20 trials. In contrast, fish offered a single prey type reached asymptotic intake rates within five trials and retained high capture abilities for at least 5 weeks. Learning and memory allow fish to maximize foraging efficiency on patches of a single prey type. However, when foragers are faced with mixed prey populations, cognitive constraints associated with divided attention may impair efficiency, and this impairment can be exacerbated by experience. (c) 2005 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

Liquid-phase adsorption of n-paraffins on type 5A molecular sieves

As a basis for the commercial separation of normal paraffins a detailed study has been made of factors affecting the adsorption of binary liquid mixtures of high molecular weight normal paraffins (C12, C16, and C20) from isooctane on type 5A molecular sieves. The literature relating to molecular sieve properties and applications, and to liquid-phase adsorption of high molecular weight normal paraffin compounds by zeolites, was reviewed. Equilibrium isotherms were determined experimentally for the normal paraffins under investigation at temperatures of 303oK, 323oK and 343oK and showed a non-linear, favourable- type of isotherm. A higher equilibrium amount was adsorbed with lower molecular weight normal paraffins. An increase in adsorption temperature resulted in a decrease in the adsorption value. Kinetics of adsorption were investigated for the three normal paraffins at different temperatures. The effective diffusivity and the rate of adsorption of each normal paraffin increased with an increase in temperature in the range 303 to 343oK. The value of activation energy was between 2 and 4 kcal/mole. The dynamic properties of the three systems were investigated over a range of operating conditions (i.e. temperature, flow rate, feed concentration, and molecular sieve size in the range 0.032 x 10-3 to 2 x 10-3m) with a packed column. The heights of adsorption zones calculated by two independent equations (one based on a constant width, constant velocity and adsorption zone and the second on a solute material balance within the adsorption zone) agreed within 3% which confirmed the validity of using the mass transfer zone concept to provide a simple design procedure for the systems under study. The dynamic capacity of type 5A sieves for n-eicosane was lower than for n-hexadecane and n-dodecane corresponding to a lower equilibrium loading capacity and lower overall mass transfer coefficient. The values of individual external, internal, theoretical and experimental overall mass transfer coefficient were determined. The internal resistance was in all cases rate-controlling. A mathematical model for the prediction of dynamic breakthrough curves was developed analytically and solved from the equilibrium isotherm and the mass transfer rate equation. The experimental breakthrough curves were tested against both the proposed model and a graphical method developed by Treybal. The model produced the best fit with mean relative percent deviations of 26, 22, and 13% for the n-dodecane, n-hexadecane, and n-eicosane systems respectively.

Dynamic simulation of chemical plant

This thesis describes the design and implementation of a new dynamic simulator called DASP. It is a computer program package written in standard Fortran 77 for the dynamic analysis and simulation of chemical plants. Its main uses include the investigation of a plant's response to disturbances, the determination of the optimal ranges and sensitivities of controller settings and the simulation of the startup and shutdown of chemical plants. The design and structure of the program and a number of features incorporated into it combine to make DASP an effective tool for dynamic simulation. It is an equation-oriented dynamic simulator but the model equations describing the user's problem are generated from in-built model equation library. A combination of the structuring of the model subroutines, the concept of a unit module, and the use of the connection matrix of the problem given by the user have been exploited to achieve this objective. The Executive program has a structure similar to that of a CSSL-type simulator. DASP solves a system of differential equations coupled to nonlinear algebraic equations using an advanced mixed equation solver. The strategy used in formulating the model equations makes it possible to obtain the steady state solution of the problem using the same model equations. DASP can handle state and time events in an efficient way and this includes the modification of the flowsheet. DASP is highly portable and this has been demonstrated by running it on a number of computers with only trivial modifications. The program runs on a microcomputer with 640 kByte of memory. It is a semi-interactive program, with the bulk of all input data given in pre-prepared data files with communication with the user is via an interactive terminal. Using the features in-built in the package, the user can view or modify the values of any input data, variables and parameters in the model, and modify the structure of the flowsheet of the problem during a simulation session. The program has been demonstrated and verified using a number of example problems.

Premature cardiovascular events and mortality in south Asians with type 2 diabetes in the United Kingdom Asian Diabetes Study - effect of ethnicity on risk

Background/Aim - People of south Asian origin have an excessive risk of morbidity and mortality from cardiovascular disease. We examined the effect of ethnicity on known risk factors and analysed the risk of cardiovascular events and mortality in UK south Asian and white Europeans patients with type 2 diabetes over a 2 year period. Methods - A total of 1486 south Asian (SA) and 492 white European (WE) subjects with type 2 diabetes were recruited from 25 general practices in Coventry and Birmingham, UK. Baseline data included clinical history, anthropometry and measurements of traditional risk factors – blood pressure, total cholesterol, HbA1c. Multiple linear regression models were used to examine ethnicity differences in individual risk factors. Ten-year cardiovascular risk was estimated using the Framingham and UKPDS equations. All subjects were followed up for 2 years. Cardiovascular events (CVD) and mortality between the two groups were compared. Findings - Significant differences were noted in risk profiles between both groups. After adjustment for clustering and confounding a significant ethnicity effect remained only for higher HbA1c (0.50 [0.22 to 0.77]; P?=?0.0004) and lower HDL (-0.09 [-0.17 to -0.01]; P?=?0.0266). Baseline CVD history was predictive of CVD events during follow-up for SA (P?type 2 diabetes in the UK have a higher cardiovascular risk and present with cardiovascular events at a significantly younger age than white Europeans. Enhanced and ethnicity specific targets and effective treatments are needed if these inequalities are to be reduced.

A variational method and approximations of a Cauchy problem for elliptic equations

A Cauchy problem for general elliptic second-order linear partial differential equations in which the Dirichlet data in H½(?1 ? ?3) is assumed available on a larger part of the boundary ? of the bounded domain O than the boundary portion ?1 on which the Neumann data is prescribed, is investigated using a conjugate gradient method. We obtain an approximation to the solution of the Cauchy problem by minimizing a certain discrete functional and interpolating using the finite diference or boundary element method. The minimization involves solving equations obtained by discretising mixed boundary value problems for the same operator and its adjoint. It is proved that the solution of the discretised optimization problem converges to the continuous one, as the mesh size tends to zero. Numerical results are presented and discussed.

An integral equation method for a mixed initial boundary value problem for unsteady Stokes system in a doubly-connected domain

We present a novel numerical method for a mixed initial boundary value problem for the unsteady Stokes system in a planar doubly-connected domain. Using a Laguerre transformation the unsteady problem is reduced to a system of boundary value problems for the Stokes resolvent equations. Employing a modied potential approach we obtain a system of boundary integral equations with various singularities and we use a trigonometric quadrature method for their numerical solution. Numerical examples are presented showing that accurate approximations can be obtained with low computational cost.

An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.

Illness perceptions, beliefs and prevention of Type 2 Diabetes among British Pakistani mothers and young British Pakistani women

The prevalence rates of type2 diabetes mellitus (T2DM) continues to rise among British Pakistanis. The aim of this project was to explore T2DM perceptions and any preventative intentions among British Pakistani women and to discover whether they are doing anything to prevent the onset in themselves and their families. Initially a systematic review was conducted to investigate 20 existing prevention interventions and to assess their effectiveness (n=12,419). Mixed methods approach was adopted and three studies were conducted. The first study consisted of two focus groups with T2DM mothers (n=8) and three focus groups with non-T2DM mothers (n=17). The second study consisted of four focus groups young British Pakistani females (n=11). All focus groups were transcribed verbatim and analysed using thematic analysis. Following these a quantitative study was undertaken comprising of a questionnaire survey; 12 prevention-perception items (derived from the qualitative data) and the Illness-Perception Questionnaire Revised (IPQ-R) using participants from the same populations: T2DM mothers (n=41), non-T2DM mother (n=47) and young women (n=42). Results were analysed using multiple/hierarchical regression. The systematic review highlighted that the most effective prevention programmes focussed on behaviour and lifestyle with a combination of support and education to participants. The research studies demonstrated that T2DM was seen as an older person’s disease to be dealt with if/when it happens. T2DM mothers demonstrated knowledge and prevention understanding. There were non-significant relationships between prevention perceptions and T2DM illness perceptions across all three groups. The finding of this thesis emphasised that lifestyle interventions are crucial to aiding T2DM preventions as a good healthy diet and regular physical activity are the key components to T2DM prevention, and the importance of personal experience in perceived severity and lay-beliefs regarding T2DM and on family/cultural influences in British-Pakistanis. The findings of this project can be used to design culturally specific interventions towards preventing T2DM in the British Pakistani community.