An optimisation-based framework for non-classical Chebyshev approximation. This project aims to solve open mathematical problems in multivariate and piecewise polynomial approximations, two directions that correspond to fundamental obstacles to extending classical approximation results. Through an innovative combination of optimisation and algebraic technique, the project intends to develop foundations for new results in approximation theory, and new insights into other areas of mathematics, mos ....An optimisation-based framework for non-classical Chebyshev approximation. This project aims to solve open mathematical problems in multivariate and piecewise polynomial approximations, two directions that correspond to fundamental obstacles to extending classical approximation results. Through an innovative combination of optimisation and algebraic technique, the project intends to develop foundations for new results in approximation theory, and new insights into other areas of mathematics, most notably optimisation. The techniques and methods developed should also have significant benefits in the many disciplines where approximation problems appear, such as engineering, physics or data mining. The research outputs resulting from this project will be used in a wide range of fields to help implement programs, policies and improve decision making.Read moreRead less
Expanding and linking random matrix theory. Fundamental to random matrix theory are certain universality laws, holding in scaling limits to infinite matrix size. A basic question is to quantify the rate of convergence to the universal laws. The analysis of data for the Riemann zeros from prime number theory, and of the spectral form factor probe of chaos in black hole physics, are immediate applications. An analysis involving integrable structures holding for finite matrix size and their asympt ....Expanding and linking random matrix theory. Fundamental to random matrix theory are certain universality laws, holding in scaling limits to infinite matrix size. A basic question is to quantify the rate of convergence to the universal laws. The analysis of data for the Riemann zeros from prime number theory, and of the spectral form factor probe of chaos in black hole physics, are immediate applications. An analysis involving integrable structures holding for finite matrix size and their asymptotics is proposed, allowing the rate to be quantified for a large class of model
ensembles, and providing predictions in the various applied settings. The broad project is to be networked with researchers in the Asia-Oceania region, with the aim of establishing leadership status for Australia.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE170100171
Funder
Australian Research Council
Funding Amount
$360,000.00
Summary
Towards a mathematical description of magneto-hydrodynamic turbulence. The project aims to better predict magneto-hydrodynamic turbulence than existing empirical models. Turbulence in high-speed flows of electrically conductive fluid sustains magnetic fields in various engineering, geophysical, and astrophysical flows. However, investigations into magneto-hydrodynamic flows have been limited to slow flows, and the application of the results to the actual problems hindered. This project aims to i ....Towards a mathematical description of magneto-hydrodynamic turbulence. The project aims to better predict magneto-hydrodynamic turbulence than existing empirical models. Turbulence in high-speed flows of electrically conductive fluid sustains magnetic fields in various engineering, geophysical, and astrophysical flows. However, investigations into magneto-hydrodynamic flows have been limited to slow flows, and the application of the results to the actual problems hindered. This project aims to improve magneto-hydrodynamic flow control in future energy-generating technology, using theoretical and numerical tools that are mathematically consistent with the high-speed limit of the governing equations. More efficient electric generators could improve Australia’s future energy supply with fewer emissions of global warming gases.Read moreRead less
The Sakai scheme-Askey table correspondence, analogues of isomonodromy and determinantal point processes. The Australian mathematical sciences enjoys two research groups with active interests on Painleve equations in applied mathematics which are able to address difficult problems. Such a problem is to give a formulation of Sakai's 2001 classification of the Painleve equations in a form most suitable for applications. For this links will be made with a seemingly distinct area of mathematics - t ....The Sakai scheme-Askey table correspondence, analogues of isomonodromy and determinantal point processes. The Australian mathematical sciences enjoys two research groups with active interests on Painleve equations in applied mathematics which are able to address difficult problems. Such a problem is to give a formulation of Sakai's 2001 classification of the Painleve equations in a form most suitable for applications. For this links will be made with a seemingly distinct area of mathematics - the Askey table from the theory of hypergeometric orthogonal polynomials. A number of tractable PhD projects are suggested by this proposal.Read moreRead less
Construction of utility functions from observations of consumer behaviour with application to resource modelling and water management strategies. The optimisation techniques developed will be on the forefront of applied mathematical sciences and will increase the prestige of the Australian mathematical community. The expected results will also be of value because they can be used to improve the CGE modelling technique. The implementation of the CGE model of one of Victoria's agricultural regions ....Construction of utility functions from observations of consumer behaviour with application to resource modelling and water management strategies. The optimisation techniques developed will be on the forefront of applied mathematical sciences and will increase the prestige of the Australian mathematical community. The expected results will also be of value because they can be used to improve the CGE modelling technique. The implementation of the CGE model of one of Victoria's agricultural regions will be used to improve the accuracy of regional economic models and will contribute to efficient regional resource management. This has the potential to positively affect the economic growth and employment in the region. The expected outcomes of the project are especially important taking into account the need for predicting the socio-economic consequences of the 1994 COAG water reforms. Read moreRead less
Bayesian estimation of flexible spatial models with applications in medical imaging and econometric modeling. This project aims to develop statistical methodology for estimating flexible highly parameterised Bayesian spatial models. The flexible models examined will include regression, choice and time series models for data that is spatially registered. Spatial smoothing of parameters in the models will involve application of hierarchical spatial prior distributions. The resulting methodology wi ....Bayesian estimation of flexible spatial models with applications in medical imaging and econometric modeling. This project aims to develop statistical methodology for estimating flexible highly parameterised Bayesian spatial models. The flexible models examined will include regression, choice and time series models for data that is spatially registered. Spatial smoothing of parameters in the models will involve application of hierarchical spatial prior distributions. The resulting methodology will be applied to the analysis of medical imaging data and to the estimation of spatial econometric models of residential real estate prices. The expected outcomes include developments in the frontier framework of Bayesian computational estimation methodology, improved methods for medical image processing and estimation of high resolution spatial models of residential real estate prices in Australian metropolitan centres.Read moreRead less
Natural resources and ecosystem services in productivity measurement. This project aims to understand sources of productivity growth through addressing theoretical and practical problems in the economics of natural resources and ecosystem services. It will study the valuation of non-renewable resources and ecosystem services, acknowledging their contributions to economic activity and the effect on national income from their depletion and degradation. It will develop approaches to incorporating n ....Natural resources and ecosystem services in productivity measurement. This project aims to understand sources of productivity growth through addressing theoretical and practical problems in the economics of natural resources and ecosystem services. It will study the valuation of non-renewable resources and ecosystem services, acknowledging their contributions to economic activity and the effect on national income from their depletion and degradation. It will develop approaches to incorporating natural resource depletion and degradation into productivity analysis with the aim of better informing environmental, innovation and industry policy.Read moreRead less
Estimation and Inference in Weakly Identified Models. Economic and social systems are made up of interacting components leading to complex structures that are difficult to predict and manage. Consequently policy analysis and decision-making must be informed by statistical analysis of data. In many situations the informational content of observations is minimal; examples of such situations are found in the areas of education, health, finance and various aspects of macroeconomic analysis. This pro ....Estimation and Inference in Weakly Identified Models. Economic and social systems are made up of interacting components leading to complex structures that are difficult to predict and manage. Consequently policy analysis and decision-making must be informed by statistical analysis of data. In many situations the informational content of observations is minimal; examples of such situations are found in the areas of education, health, finance and various aspects of macroeconomic analysis. This project aims to develop methods of estimation and inference that make more efficient use of the information available in data. This will lead to more precise statistical analyses, resulting in a clearer understanding of economic and social systems, and better informed policy analysis and decision-making.Read moreRead less
Modelling the Transmission of International Monetary Policy Shocks: Implications for Australian Asset Markets. Three main outcomes of the project are as follows. First, the relative strengths of the transmission mechanisms linking monetary policy and asset markets will be better identified. This will lead to a better understanding of monetary policy thereby enabling the Reserve Bank to achieve its policy goals of inflation operating at or near the target rate, and for currency markets to exhibit ....Modelling the Transmission of International Monetary Policy Shocks: Implications for Australian Asset Markets. Three main outcomes of the project are as follows. First, the relative strengths of the transmission mechanisms linking monetary policy and asset markets will be better identified. This will lead to a better understanding of monetary policy thereby enabling the Reserve Bank to achieve its policy goals of inflation operating at or near the target rate, and for currency markets to exhibit stability. Second, a number of empirical puzzles relating to monetary policy and asset markets in general, that exist in the empirical literature, will be solved. Third, the project will lead to a number of international papers which will add to the international reputation of Australia as a leading research nation.Read moreRead less