Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

Latent variable models in statistical genetics

Understanding the complexities that are involved in the genetics of multifactorial diseases is still a monumental task. In addition to environmental factors that can influence the risk of disease, there is also a number of other complicating factors. Genetic variants associated with age of disease onset may be different from those variants associated with overall risk of disease, and variants may be located in positions that are not consistent with the traditional protein coding genetic paradigm. Latent Variable Models are well suited for the analysis of genetic data. A latent variable is one that we do not directly observe, but which is believed to exist or is included for computational or analytic convenience in a model. This thesis presents a mixture of methodological developments utilising latent variables, and results from case studies in genetic epidemiology and comparative genomics. Epidemiological studies have identified a number of environmental risk factors for appendicitis, but the disease aetiology of this oft thought useless vestige remains largely a mystery. The effects of smoking on other gastrointestinal disorders are well documented, and in light of this, the thesis investigates the association between smoking and appendicitis through the use of latent variables. By utilising data from a large Australian twin study questionnaire as both cohort and case-control, evidence is found for the association between tobacco smoking and appendicitis. Twin and family studies have also found evidence for the role of heredity in the risk of appendicitis. Results from previous studies are extended here to estimate the heritability of age-at-onset and account for the eect of smoking. This thesis presents a novel approach for performing a genome-wide variance components linkage analysis on transformed residuals from a Cox regression. This method finds evidence for a dierent subset of genes responsible for variation in age at onset than those associated with overall risk of appendicitis. Motivated by increasing evidence of functional activity in regions of the genome once thought of as evolutionary graveyards, this thesis develops a generalisation to the Bayesian multiple changepoint model on aligned DNA sequences for more than two species. This sensitive technique is applied to evaluating the distributions of evolutionary rates, with the finding that they are much more complex than previously apparent. We show strong evidence for at least 9 well-resolved evolutionary rate classes in an alignment of four Drosophila species and at least 7 classes in an alignment of four mammals, including human. A pattern of enrichment and depletion of genic regions in the profiled segments suggests they are functionally significant, and most likely consist of various functional classes. Furthermore, a method of incorporating alignment characteristics representative of function such as GC content and type of mutation into the segmentation model is developed within this thesis. Evidence of fine-structured segmental variation is presented.

A multicast routing scheme for efficient safety message dissemination in VANET

Vehicular ad hoc network (VANET) is a wireless ad hoc network that operates in a vehicular environment to provide communication between vehicles. VANET can be used by a diverse range of applications to improve road safety. Cooperative collision warning system (CCWS) is one of the safety applications that can provide situational awareness and warning to drivers by exchanging safety messages between cooperative vehicles. Currently, the routing strategies for safety message dissemination in CCWS are scoped broadcast. However, the broadcast schemes are not efficient as a warning message is sent to a large number of vehicles in the area, rather than only the endangered vehicles. They also cannot prioritize the receivers based on their critical time to avoid collision. This paper presents a more efficient multicast routing scheme that can reduce unnecessary transmissions and also use adaptive transmission range. The multicast scheme involves methods to identify an abnormal vehicle, the vehicles that may be endangered by the abnormal vehicle, and the latest time for each endangered vehicle to receive the warning message in order to avoid the danger. We transform this multicast routing problem into a delay-constrained minimum Steiner tree problem. Therefore, we can use existing algorithms to solve the problem. The advantages of our multicast routing scheme are mainly its potential to support various road traffic scenarios, to optimize the wireless channel utilization, and to prioritize the receivers.

Validation of an Australian sign language instrument of outcome measurement for adults in mental health settings

Objective: There are currently no adult mental health outcome measures that have been translated into Australian sign language (Auslan). Without a valid and reliable Auslan outcome measure, empirical research into the efficacy of mental health interventions for sign language users is unattainable. To address this research problem the Outcome Rating Scale (ORS), a measure of general functioning, was translated into Auslan and recorded on to digital video disk for use in clinical settings. The purpose of the present study was therefore to examine the reliability, validity and acceptability of an Auslan version of the ORS (ORS-Auslan). Method: The ORS-Auslan was administered to 44 deaf people who use Auslan as their first language and who identify as members of a deaf community (termed ‘Deaf’ people) on their first presentation to a mental health or counselling facility and to 55 Deaf people in the general community. The community sample also completed an Auslan version of the Depression Anxiety Stress Scale-21 (DASS-21). Results: t-Tests indicated significant differences between the mean scores for the clinical and community sample. Internal consistency was acceptable given the low number of items in the ORS-Auslan. Construct validity was established by significant correlations between total scores on the DASS-21-Auslan and ORS-Auslan. Acceptability of ORS-Auslan was evident in the completion rate of 93% compared with 63% for DASS-21-Auslan. Conclusions: This is the only Auslan outcome measure available that can be used across a wide variety of mental health and clinical settings. The ORS-Auslan provides mental health clinicians with a reliable and valid, brief measure of general functioning that can significantly distinguish between clinical and non-clinical presentations for members of the Deaf community.

An empirical study of data collection protocols for wireless sensor networks

In the past few years, numerous data collection protocols have been developed for wireless sensor networks (WSNs). However, there has been no comparison of their relative performance in realistic environments. Here we report the results of an empirical study using a Fleck3 sensor network testbed for four different data collection protocols: One phase pull Directed Diffusion (DD), Expected Number of Transmissions (ETX), ETX with explicit acknowledgment (ETX-eAck), and ETX with implicit acknowledgment (ETX-iAck). Our empirical study provides useful insights for future sensor network deployments. When the required application end-to-end reliability is not strict (e.g., 70%) and link quality is good, DD and ETX are the best options because of their simplicity and low routing overhead. Both ETX-eAck and ETX-iAck achieve more than 90% end-to-end reliability when the link quality is reasonable (less than 25% packet loss). When the link quality is good, ETX-iAck introduces significantly less routing overhead (up to 50%) than ETX-eAck. However, if the radio transceiver supports variable packet length, ETX-eAck can outperform ETX-iAck when the link quality is poor. The important message from this paper is that choice of data collection protocol should come after the operating environment is understood. This understanding must include the characteristics of the radio transceiver, and link loss statistics from a long-term (across seasons and weather variation) radio survey of the site.

A two-Dimensional finite volume method for variable density flow and solute transport through saturated-unsaturated media

Extensive groundwater withdrawal has resulted in a severe seawater intrusion problem in the Gooburrum aquifers at Bundaberg, Queensland, Australia. Better management strategies can be implemented by understanding the seawater intrusion processes in those aquifers. To study the seawater intrusion process in the region, a two-dimensional density-dependent, saturated and unsaturated flow and transport computational model is used. The model consists of a coupled system of two non-linear partial differential equations. The first equation describes the flow of a variable-density fluid, and the second equation describes the transport of dissolved salt. A two-dimensional control volume finite element model is developed for simulating the seawater intrusion into the heterogeneous aquifer system at Gooburrum. The simulation results provide a realistic mechanism by which to study the convoluted transport phenomena evolving in this complex heterogeneous coastal aquifer.

Models of collective cell spreading with variable cell aspect ratio : a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multi-scale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (pme). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the pme to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.

Variable structure control for power systems stabilization

The application of variable structure control (VSC) for power systems stabilization is studied in this paper. It is the application, aspects and constraints of VSC which are of particular interest. A variable structure control methodology has been proposed for power systems stabilization. The method is implemented using thyristor controlled series compensators. A three machine power system is stabilized using a switching line control for large disturbances which becomes a sliding control as the disturbance becomes smaller. The results demonstrate the effectiveness of the methodology proposed as an useful tool to suppress the oscillations in power systems.

Calibration and operational analysis of variable speed limits for high flow condition

Variable Speed Limits (VSL) is a control tool of Intelligent Transportation Systems (ITS) which can enhance traffic safety and which has the potential to contribute to traffic efficiency. This study presents the results of a calibration and operational analysis of a candidate VSL algorithm for high flow conditions on an urban motorway of Queensland, Australia. The analysis was done using a framework consisting of a microscopic simulation model combined with runtime API and a proposed efficiency index. The operational analysis includes impacts on speed-flow curve, travel time, speed deviation, fuel consumption and emission.

Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy