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Integrable Functional and Delay Differential Equations. Major challenges such as predicting epidemics or modelling the dynamics of human movement, rely on our understanding of functional and delay differential equations. This research will provide new methods for prediction and analysis of such models.
New mathematical and statistical methods that inform the control of infectious disease outbreaks. Emerging infectious diseases are an ever-present threat to our community, as highlighted by the recent SARS epidemic and current fears concerning avian influenza. The research proposed by this project will help policy makers implement effective border control and outbreak control against a variety of emerging and re-emerging infectious diseases, including SARS, influenza and the deliberate release o ....New mathematical and statistical methods that inform the control of infectious disease outbreaks. Emerging infectious diseases are an ever-present threat to our community, as highlighted by the recent SARS epidemic and current fears concerning avian influenza. The research proposed by this project will help policy makers implement effective border control and outbreak control against a variety of emerging and re-emerging infectious diseases, including SARS, influenza and the deliberate release of an infectious disease such as smallpox. The project will enhance preparedness through a better understanding of the relative merits of different control strategies, and provide new methodology that can dynamically guide border and outbreak control in the midst of an outbreak by making effective use of data. Read moreRead less
Stochastic methods for studying models of infection and abundance. The outcomes of this project will have immense benefit to Australia. They impact upon two areas of national importance, namely ensuring an environmentally sustainable Australia, and safeguarding Australia. In particular, the project will provide models, methodology and optimal strategies for sustainable use of Australia's biodiversity, for protecting Australia from invasive diseases and pests, and for protecting Australia from te ....Stochastic methods for studying models of infection and abundance. The outcomes of this project will have immense benefit to Australia. They impact upon two areas of national importance, namely ensuring an environmentally sustainable Australia, and safeguarding Australia. In particular, the project will provide models, methodology and optimal strategies for sustainable use of Australia's biodiversity, for protecting Australia from invasive diseases and pests, and for protecting Australia from terrorism and crime. Special focus will be given to the control of invasive species, the control of emerging infections, and the optimal allocation of resources. The current risks posed by invasive diseases and pests, and the alarming rate of destruction of biodiversity, warrant urgent funding of this project.Read moreRead less
Modelling and estimation techniques for the transmission and control of Tuberculosis with new and existing vaccines. Most Tuberculosis in Australia is seen in foreign-born people. Australia has an important role in providing leadership in the Asia-Pacific region in Tuberculosis control, which will have flow-on benefits to TB control in this country. Using mathematical models, this project will assess the use of vaccines for Tuberculosis in the developing world. Rising levels of extremely drug r ....Modelling and estimation techniques for the transmission and control of Tuberculosis with new and existing vaccines. Most Tuberculosis in Australia is seen in foreign-born people. Australia has an important role in providing leadership in the Asia-Pacific region in Tuberculosis control, which will have flow-on benefits to TB control in this country. Using mathematical models, this project will assess the use of vaccines for Tuberculosis in the developing world. Rising levels of extremely drug resistant infections make this a timely and important study with significant policy implications, both externally and in the Australian context. Read moreRead less
COMPLEX NETWORKS: DYNAMICS, OPTIMIZATION AND CONTROL. Complex networks such large power grids, the Internet, transportation networks and co-operation networks of all kinds provide challenges for frontier technologies particularly computing, communication and control. In particular, advanced societies have become dependent on large infrastructure networks to an extent beyond our capability to plan and control them. The recent spate of collapses in power grids and virus attacks on the Internet i ....COMPLEX NETWORKS: DYNAMICS, OPTIMIZATION AND CONTROL. Complex networks such large power grids, the Internet, transportation networks and co-operation networks of all kinds provide challenges for frontier technologies particularly computing, communication and control. In particular, advanced societies have become dependent on large infrastructure networks to an extent beyond our capability to plan and control them. The recent spate of collapses in power grids and virus attacks on the Internet illustrate the need for research on modelling, analysis of behaviour, planning and control in such networks. This project aims to establish research in this area for Australia's benefit.Read moreRead less
Dynamics and Security Control of Complex Networks. The research will yield basic techniques to analyse, design and operate complex networks so that security, as well as performance, is achieved. These techniques will be further developed towards particular applications including power grids and telecommunication networks. However, the emphasis is on providing basic ideas and techniques.
Geometric structures in representation theory. Mathematics underpins every aspect of people's interactions with nature (e.g. physics) and with each other (e.g. finance). Its uses range from formulating physical laws in order to understand and predict nature, to analysis of financial concepts and transactions. This project will formulate and develop three new fundamental mathematical concepts: cellular algebras, eigenspace geometries, and diagram algebras. Benefits include enhancement of Australi ....Geometric structures in representation theory. Mathematics underpins every aspect of people's interactions with nature (e.g. physics) and with each other (e.g. finance). Its uses range from formulating physical laws in order to understand and predict nature, to analysis of financial concepts and transactions. This project will formulate and develop three new fundamental mathematical concepts: cellular algebras, eigenspace geometries, and diagram algebras. Benefits include enhancement of Australia's position at the very frontier of world class mathematical research, and a myriad of potential applications to physics, coding theory, information technology, electronic security and experimental design.Read moreRead less
The geometry of exotic nilpotent cones. This research will describe the geometry of some important objects which sit at the boundary of algebra, geometry, and combinatorics. It has intrinsic value as a significant addition to the heritage of mathematical thought, and will strengthen Australian traditions in these areas of mathematics.
Increasing the effectiveness of quantitative verification. The ability to analyse the performance of complex systems and protocols is a vital part of the development of large-scale computer applications. Methods that improve the effectiveness of the analysis task would increase the competitiveness of the software industry, and would attract future development work (in complex systems) to Australia. The results of this project will have a direct influence on currently available design tools; the ....Increasing the effectiveness of quantitative verification. The ability to analyse the performance of complex systems and protocols is a vital part of the development of large-scale computer applications. Methods that improve the effectiveness of the analysis task would increase the competitiveness of the software industry, and would attract future development work (in complex systems) to Australia. The results of this project will have a direct influence on currently available design tools; the fact that Australian institutions will be (in part) responsible for key theoretical results in this growing field will strengthen Australia's position worldwide as an international centre for computer science.Read moreRead less
Control of Markov jumping processes with constraints. The project outcomes will constitute the set of tools for modelling and optimisation of complex stochastic systems and will lead to new and more precise characterisations of optimal behaviour of complex controllable systems arising in Resource Management, Engineering and Telecommunications. Therefore, the project fits to the research priority areas Breakthrough Science and Frontier Technologies in the topic of mathematical modelling and optim ....Control of Markov jumping processes with constraints. The project outcomes will constitute the set of tools for modelling and optimisation of complex stochastic systems and will lead to new and more precise characterisations of optimal behaviour of complex controllable systems arising in Resource Management, Engineering and Telecommunications. Therefore, the project fits to the research priority areas Breakthrough Science and Frontier Technologies in the topic of mathematical modelling and optimisation of Complex Systems.Read moreRead less