Global Behaviour of Integrable Complex Systems. Complex systems as diverse as the weather and the solar system are modelled by non-linear equations that have elusive, unstable solutions. An infinitesimally small change in the state of the system at one place can lead to a vast change in its behaviour far away. Such extreme sensitivity is often take to be a sign of chaos, but it also occurs in completely ordered, integrable systems. Our main aim is to tackle the immense challenge of describing th ....Global Behaviour of Integrable Complex Systems. Complex systems as diverse as the weather and the solar system are modelled by non-linear equations that have elusive, unstable solutions. An infinitesimally small change in the state of the system at one place can lead to a vast change in its behaviour far away. Such extreme sensitivity is often take to be a sign of chaos, but it also occurs in completely ordered, integrable systems. Our main aim is to tackle the immense challenge of describing the global behaviour of such elusive solutions, particularly when the systems depend on many variables.Read moreRead less
Iwasawa N Groups. Semisimple Lie groups and related objects are important in mathematics, theoretical physics (e.g., quantum mechanics and string theory), theoretical computer science (e.g., construction of expanders), and many other areas. They may be studied from different points of view---algebraic, analytic, geometric and representation theoretic---and these different studies find different applications. The project aims to synthesize the different points of view, to understand their funda ....Iwasawa N Groups. Semisimple Lie groups and related objects are important in mathematics, theoretical physics (e.g., quantum mechanics and string theory), theoretical computer science (e.g., construction of expanders), and many other areas. They may be studied from different points of view---algebraic, analytic, geometric and representation theoretic---and these different studies find different applications. The project aims to synthesize the different points of view, to understand their fundamental unity, and to allow results of one type to be translated into another context.Read moreRead less
Investigating evidence of control system dynamics in visuomotor skill acquisition using multimodal functional magnetic resonance imaging. This project brings together mathematical and engineering methods with cognitive neuroscience in a novel way to better understand the fundamental processes associated with brain imaging, and the acquisition of motor skills. An improved understanding of the function of regions within the motor network will have a direct benefit for the rehabilitation of patient ....Investigating evidence of control system dynamics in visuomotor skill acquisition using multimodal functional magnetic resonance imaging. This project brings together mathematical and engineering methods with cognitive neuroscience in a novel way to better understand the fundamental processes associated with brain imaging, and the acquisition of motor skills. An improved understanding of the function of regions within the motor network will have a direct benefit for the rehabilitation of patients suffering motor deficits from developmental causes, following traumatic brain injuries, and after stroke and other neurodegenerative diseases. The outcomes of the research will also contribute to our understanding of the complexity of brain networks involved in motor skill acquisition.Read moreRead less
Equivalence Relations, Group Actions, and Descriptive Set Theory. This project is a contribution to basic and foundational research in the area of Pure Mathematics generally and Mathematical Logic specifically. Logic in particular appears in disciplines as diverse as Computer Science,Linguistics, and Philosophy, and the development of logic in these fields has been profoundly influenced by the foundational work of mathematical logicians. The innovative techniques introduced in this proposal will ....Equivalence Relations, Group Actions, and Descriptive Set Theory. This project is a contribution to basic and foundational research in the area of Pure Mathematics generally and Mathematical Logic specifically. Logic in particular appears in disciplines as diverse as Computer Science,Linguistics, and Philosophy, and the development of logic in these fields has been profoundly influenced by the foundational work of mathematical logicians. The innovative techniques introduced in this proposal will enable Australia to maintain a position at the forefront of Pure Mathematics, and by recruiting a recent winner of the highly prestigious Karp prize the country will be instantly established as one of the leading centers of Mathematical Logic.Read moreRead less
Special Research Initiatives - Grant ID: SR0354727
Funder
Australian Research Council
Funding Amount
$20,000.00
Summary
Mathematics for Government, Industry and Community -- The *Magic* Network. The *Magic* network will promote the use of mathematics by government, industry and community to analyse real problems and implement practical solutions. It will connect the most promising young Australian mathematicians to experienced researchers with strong research teams linked directly to the broader community. Our program will demand research excellence, emphasise a sustainable society, support outstanding young mat ....Mathematics for Government, Industry and Community -- The *Magic* Network. The *Magic* network will promote the use of mathematics by government, industry and community to analyse real problems and implement practical solutions. It will connect the most promising young Australian mathematicians to experienced researchers with strong research teams linked directly to the broader community. Our program will demand research excellence, emphasise a sustainable society, support outstanding young mathematicians and create opportunities for promising postgraduate students. We will offer scholarships for professional development and fund research visits and exchanges. *Magic* will provide tangible incentives for young Australian mathematicians and a new generation of researchers and research leaders.Read moreRead less
Who acquires infection from whom across international borders? New approaches for control of emerging infections through understanding travel patterns. Mathematical modelling of data on travellers traversing Australia's borders and their contact patterns can be used to understand the pathways by which infectious diseases enter and spread in Australia. Currently available social contact data which informs models are inadequate and outdated. Gathering new data relevant to modern society will help ....Who acquires infection from whom across international borders? New approaches for control of emerging infections through understanding travel patterns. Mathematical modelling of data on travellers traversing Australia's borders and their contact patterns can be used to understand the pathways by which infectious diseases enter and spread in Australia. Currently available social contact data which informs models are inadequate and outdated. Gathering new data relevant to modern society will help control future infectious disease threats to our society. Our aim is to collect detailed, unique data on demography, behavioural and social patterns of travellers and residents, and use this to develop mathematical models to evaluate effective control measures for emerging infections in Australia. This study will make a unique contribution to national disease control policy.Read moreRead less
Bayesian choice modelling. Discrete choice models are important as they provide tools to help understand choice processes of decision makers. It remains a challenge to specify models with covariance structures flexible enough to capture complex patterns of cross-substitution between choices while being able to capture heterogeneity present in individual behaviour. We will develop a Bayesian approach to choice modelling that uses covariance selection to overcome these problems. This will train re ....Bayesian choice modelling. Discrete choice models are important as they provide tools to help understand choice processes of decision makers. It remains a challenge to specify models with covariance structures flexible enough to capture complex patterns of cross-substitution between choices while being able to capture heterogeneity present in individual behaviour. We will develop a Bayesian approach to choice modelling that uses covariance selection to overcome these problems. This will train researchers and raise the profile of Australia in an active research area that is important in the social sciences; substantive applications will be in health economics, but developments will also be relevant to cognate areas of biostatistics, epidemiology, and ecology.Read moreRead less
How do macroeconomic fluctuations affect the educational choices of young Australians? The 1990-1991 recession, recent evidence, and econometric issues. The educational choices of young people are crucial for any nation's future. The project's empirical findings will inform public policy, particularly in the areas of education and training and youth unemployment. The research will help policy makers target people who need extra support in tough times and help determine the demand for different k ....How do macroeconomic fluctuations affect the educational choices of young Australians? The 1990-1991 recession, recent evidence, and econometric issues. The educational choices of young people are crucial for any nation's future. The project's empirical findings will inform public policy, particularly in the areas of education and training and youth unemployment. The research will help policy makers target people who need extra support in tough times and help determine the demand for different kinds of education. The findings have implications for future policies aimed at reducing inequality. The project's methodological contributions will lead to better and more reliable research in economics and other fields such as biology and engineering. The findings will be suitable for the top economics journals and contribute to Australia's standing in the academic community.Read moreRead less
Entanglement renormalization: a new route to strongly correlated fermions and novel states of matter in two dimensions. The expected outcome of the research program is a significant boost in our understanding of strongly correlated fermion systems, which will reinforce Australia's competitiveness and international profile in aspects of breakthrough science and frontier technologies. By strengthening both the underpinning theory and innovative computational tools to study fermion systems, and by ....Entanglement renormalization: a new route to strongly correlated fermions and novel states of matter in two dimensions. The expected outcome of the research program is a significant boost in our understanding of strongly correlated fermion systems, which will reinforce Australia's competitiveness and international profile in aspects of breakthrough science and frontier technologies. By strengthening both the underpinning theory and innovative computational tools to study fermion systems, and by applying them to specific problems of recognized importance, this program will have direct implications in condensed matter physics and will exert significant influence in areas such as quantum chemistry, particle, nuclear and atomic physics, quantum computing, quantum atom optics and nanotechnology.Read moreRead less
Choice experiments to improve predictive power for policy makers. In the current economic climate, Australian governments will benefit from superior choice experiments which will lead to improved prediction of the potential public benefit of proposed policy changes. The choice experiments developed here will have a substantial effect on the development of strategies for the promotion and maintenance of a strong health care system as well as being relevant to the maintenance of a sustainable envi ....Choice experiments to improve predictive power for policy makers. In the current economic climate, Australian governments will benefit from superior choice experiments which will lead to improved prediction of the potential public benefit of proposed policy changes. The choice experiments developed here will have a substantial effect on the development of strategies for the promotion and maintenance of a strong health care system as well as being relevant to the maintenance of a sustainable environment, both designated National Research Priority areas. The innovative research proposed will tap into and build strong links with international research networks, advancing Australia's research reputation and providing a rich environment for the training of research graduates.Read moreRead less