Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Mining patterns and factors contributing to crash severity on road curves

Road curves are an important feature of road infrastructure and many serious crashes occur on road curves. In Queensland, the number of fatalities is twice as many on curves as that on straight roads. Therefore, there is a need to reduce drivers’ exposure to crash risk on road curves. Road crashes in Australia and in the Organisation for Economic Co-operation and Development(OECD) have plateaued in the last five years (2004 to 2008) and the road safety community is desperately seeking innovative interventions to reduce the number of crashes. However, designing an innovative and effective intervention may prove to be difficult as it relies on providing theoretical foundation, coherence, understanding, and structure to both the design and validation of the efficiency of the new intervention. Researchers from multiple disciplines have developed various models to determine the contributing factors for crashes on road curves with a view towards reducing the crash rate. However, most of the existing methods are based on statistical analysis of contributing factors described in government crash reports. In order to further explore the contributing factors related to crashes on road curves, this thesis designs a novel method to analyse and validate these contributing factors. The use of crash claim reports from an insurance company is proposed for analysis using data mining techniques. To the best of our knowledge, this is the first attempt to use data mining techniques to analyse crashes on road curves. Text mining technique is employed as the reports consist of thousands of textual descriptions and hence, text mining is able to identify the contributing factors. Besides identifying the contributing factors, limited studies to date have investigated the relationships between these factors, especially for crashes on road curves. Thus, this study proposed the use of the rough set analysis technique to determine these relationships. The results from this analysis are used to assess the effect of these contributing factors on crash severity. The findings obtained through the use of data mining techniques presented in this thesis, have been found to be consistent with existing identified contributing factors. Furthermore, this thesis has identified new contributing factors towards crashes and the relationships between them. A significant pattern related with crash severity is the time of the day where severe road crashes occur more frequently in the evening or night time. Tree collision is another common pattern where crashes that occur in the morning and involves hitting a tree are likely to have a higher crash severity. Another factor that influences crash severity is the age of the driver. Most age groups face a high crash severity except for drivers between 60 and 100 years old, who have the lowest crash severity. The significant relationship identified between contributing factors consists of the time of the crash, the manufactured year of the vehicle, the age of the driver and hitting a tree. Having identified new contributing factors and relationships, a validation process is carried out using a traffic simulator in order to determine their accuracy. The validation process indicates that the results are accurate. This demonstrates that data mining techniques are a powerful tool in road safety research, and can be usefully applied within the Intelligent Transport System (ITS) domain. The research presented in this thesis provides an insight into the complexity of crashes on road curves. The findings of this research have important implications for both practitioners and academics. For road safety practitioners, the results from this research illustrate practical benefits for the design of interventions for road curves that will potentially help in decreasing related injuries and fatalities. For academics, this research opens up a new research methodology to assess crash severity, related to road crashes on curves.

Transaction mining for fraud detection in ERP Systems

Despite all attempts to prevent fraud, it continues to be a major threat to industry and government. Traditionally, organizations have focused on fraud prevention rather than detection, to combat fraud. In this paper we present a role mining inspired approach to represent user behaviour in Enterprise Resource Planning (ERP) systems, primarily aimed at detecting opportunities to commit fraud or potentially suspicious activities. We have adapted an approach which uses set theory to create transaction profiles based on analysis of user activity records. Based on these transaction profiles, we propose a set of (1) anomaly types to detect potentially suspicious user behaviour, and (2) scenarios to identify inadequate segregation of duties in an ERP environment. In addition, we present two algorithms to construct a directed acyclic graph to represent relationships between transaction profiles. Experiments were conducted using a real dataset obtained from a teaching environment and a demonstration dataset, both using SAP R/3, presently the predominant ERP system. The results of this empirical research demonstrate the effectiveness of the proposed approach.