Operator algebras associated to product systems, and higher-rank-graph algebras. Operator algebras are used to study a wide range of physical systems in quantum physics and quantum computing, and in electrical engineering. The clearer our picture of how operator algebras work, the better we are able to predict and explain how these physical systems will behave. The proposed research project is aimed at showing that we can describe operator algebras in terms of simple coloured diagrams rather tha ....Operator algebras associated to product systems, and higher-rank-graph algebras. Operator algebras are used to study a wide range of physical systems in quantum physics and quantum computing, and in electrical engineering. The clearer our picture of how operator algebras work, the better we are able to predict and explain how these physical systems will behave. The proposed research project is aimed at showing that we can describe operator algebras in terms of simple coloured diagrams rather than abstract mathematical symbols. Consequently, the project will lead to a simpler and less technical approach to the physical problems which operator algebras are used to study.Read moreRead less
ARC Centre for Complex Dynamic Systems & Control. Complex dynamic systems are an inescapable feature of the world we live in. Modelling, analysing and optimizing complex behaviour is crucial for environment, process industry, biomedical, energy distribution, transportation and other applications. The Centre for Complex Dynamic Systems and Control will become an international authority in the analysis, design and optimization of complex dynamic systems, pursuing both outstanding fundamental and c ....ARC Centre for Complex Dynamic Systems & Control. Complex dynamic systems are an inescapable feature of the world we live in. Modelling, analysing and optimizing complex behaviour is crucial for environment, process industry, biomedical, energy distribution, transportation and other applications. The Centre for Complex Dynamic Systems and Control will become an international authority in the analysis, design and optimization of complex dynamic systems, pursuing both outstanding fundamental and cutting edge applied research outcomes. These outcomes will be of specific benefit to partner organizations including minerals, process, metal forming, and automotive industries.Read moreRead less
Centre for Mathematical and Statistical Modelling of Complex Systems. This Centre, formed by a group of high-profile researchers, brings expertise from linked but hitherto disparate areas together. It will place Australia at the forefront of research into complex systems.
The mission of the Centre is to stimulate research in mathematical and statistical modelling of complex systems and to encourage cross-fertilisation of ideas and techniques. The specific objectives are
- to formulate and ana ....Centre for Mathematical and Statistical Modelling of Complex Systems. This Centre, formed by a group of high-profile researchers, brings expertise from linked but hitherto disparate areas together. It will place Australia at the forefront of research into complex systems.
The mission of the Centre is to stimulate research in mathematical and statistical modelling of complex systems and to encourage cross-fertilisation of ideas and techniques. The specific objectives are
- to formulate and analyse mathematical and statistical models for natural and artificial complex systems,
- to use these models to develop an understanding of the behaviour of these systems
- to incorporate this understanding into strategies for management and control.Read moreRead less
Sustaining Australia's sheep industry under climate change: modelling Australia's sheep flock response to climatic and economic constraints. This project aims to provide a quantitative assessment of the impact of climate change and economic conditions on the Australian sheep industry. This will be achieved by constructing a robust dynamic model of the Australian sheep flock capable of integrating biophysical and economic constraints across regional and national scales. Using historical and proje ....Sustaining Australia's sheep industry under climate change: modelling Australia's sheep flock response to climatic and economic constraints. This project aims to provide a quantitative assessment of the impact of climate change and economic conditions on the Australian sheep industry. This will be achieved by constructing a robust dynamic model of the Australian sheep flock capable of integrating biophysical and economic constraints across regional and national scales. Using historical and projected biophysical and economic inputs it will enhance the capacity of the Australian sheep industry for strategic planning in the face of projected climate change. This capacity is being actively sought by the peak sheep industry bodies in conjunction with our industry partner the Bureau of Rural Sciences.Read moreRead less
A Dynamical Systems Approach to Mapping Southern Ocean Circulation Pathways. Climate change can be expected to have complex, long-term consequences for Australia's biodiversity, for our agricultural and marine production systems, and for regional communities. The Southern Ocean is a critical driver of global climate, connecting the three major oceanic basins. Using sophisticated mathematics to analyse state-of-the-art global ocean models, this project will create a detailed picture of hitherto i ....A Dynamical Systems Approach to Mapping Southern Ocean Circulation Pathways. Climate change can be expected to have complex, long-term consequences for Australia's biodiversity, for our agricultural and marine production systems, and for regional communities. The Southern Ocean is a critical driver of global climate, connecting the three major oceanic basins. Using sophisticated mathematics to analyse state-of-the-art global ocean models, this project will create a detailed picture of hitherto invisible Southern Ocean circulation 'pathways'. The newly discovered pathways will greatly enhance our understanding of the Southern Ocean circulation, lead to improved coupled climate models, and increase our ability to predict future climate change and threats to marine populations. Read moreRead less
The dynamics of viral latency in chronic infection. Although many acute infections can now be controlled, we still suffer from a large number of chronic infections such as HIV or herpes that cannot be eradicated. Many of these infections persist because they can lie dormant in a 'latent' state. How this latent state is established, and how long it lasts are important to understand if we want to control these infections. We have assembled a team of mathematicians, immunologists and virologists in ....The dynamics of viral latency in chronic infection. Although many acute infections can now be controlled, we still suffer from a large number of chronic infections such as HIV or herpes that cannot be eradicated. Many of these infections persist because they can lie dormant in a 'latent' state. How this latent state is established, and how long it lasts are important to understand if we want to control these infections. We have assembled a team of mathematicians, immunologists and virologists in order to study latent infection at the cellular level, and within infected monkeys. This will provide the first insights into the dynamics of latency - how these cells are produced and die - and should lead to novel approaches to controlling chronic infection.Read moreRead less
Green functions, correlation functions and differential equations. Classical and quantum exact solutions are established cornerstones in Australian applied mathematical research. In this project, we will:- 1). Address long standing open problems, whose resolution will add to mathematical knowledge and enhance Australia's reputation as a leading contributor to these topics; 2). List concrete and tractable sub-projects that will engage young scientists, whose training we are particularly keen on, ....Green functions, correlation functions and differential equations. Classical and quantum exact solutions are established cornerstones in Australian applied mathematical research. In this project, we will:- 1). Address long standing open problems, whose resolution will add to mathematical knowledge and enhance Australia's reputation as a leading contributor to these topics; 2). List concrete and tractable sub-projects that will engage young scientists, whose training we are particularly keen on, in vigorous and internationally competitive research; 3). Facilitate collaborations between various Australian research groups, all of whom are very well positioned to contribute to it; 4). Bring leading scientists to visit Australia to the benefit of the entire Australian mathematical community.Read moreRead less
Extension of representations and homogeneous spaces. The CI is an early-career researcher who is establishing her research program. The proposed project will allow her to broaden the scope of this program by involving other young Australians, including students. The project involves taking a new approach to a classical problem in representation theory; the outcomes will be of interest to a broad range of the mathematical community in Australia and overseas.
New mathematics of fractional diffusion for understanding cognitive impairment at the neuronal level. As Australia's population ages, cognitive impairment due to cortical ageing and neurodegeneration is looming as the nation's greatest health problem. The project will deliver new, more realistic, mathematical models for a mechanistic understanding of cognitive impairment at the neuronal level. This understanding is a vital first step in targeting drugs, e.g., to influence neuronal spine proper ....New mathematics of fractional diffusion for understanding cognitive impairment at the neuronal level. As Australia's population ages, cognitive impairment due to cortical ageing and neurodegeneration is looming as the nation's greatest health problem. The project will deliver new, more realistic, mathematical models for a mechanistic understanding of cognitive impairment at the neuronal level. This understanding is a vital first step in targeting drugs, e.g., to influence neuronal spine properties, for preventative health care. The project will maintain international collaborations, between applied mathematicians at UNSW, Sydney and biomathematicians and neuroscientists at Mount Sinai School of Medicine, New York, providing ongoing training opportunities for Australian scientists in this cutting edge biomathematical research.Read moreRead less
Modelling, forecasting, and control for econometrics based on generalized dynamic factor models: a system theoretic approach. The project will provide a tool that will assist organizations wishing to understand the dynamics of a national economy to model it, and to forecast future econometric time series values. Such ability will provide another tool to econometric managers, including the Reserve Bank , Treasury and fund managers, that should benefit the Australian nation.