Classification methods for providing personalised and class decisions. This project provides a novel approach to the clustering of multivariate samples on entities in a class that automatically matches the sample clusters across the entities, allowing for inter-sample variation between the samples in a class. The project aims to develop a widely applicable, mixture-model-based framework for the simultaneous clustering of multivariate samples with inter-sample variation in a class and for the mat ....Classification methods for providing personalised and class decisions. This project provides a novel approach to the clustering of multivariate samples on entities in a class that automatically matches the sample clusters across the entities, allowing for inter-sample variation between the samples in a class. The project aims to develop a widely applicable, mixture-model-based framework for the simultaneous clustering of multivariate samples with inter-sample variation in a class and for the matching of the clusters across the entities in the class. The project will use a statistical approach to automatically match the clusters, since the overall mixture model provides a template for the class. It will provide a basis for discriminating between different classes in addition to the identification of atypical data points within a sample and of anomalous samples within a class. Key applications include biological image analysis and the analysis of data in flow cytometry which is one of the fundamental research tools for the life scientist.Read moreRead less
New Directions in Bayesian Statistics: formulation, computation and application to exemplar challenges. Bayesian statistics is a fundamental statistical and machine learning approach for density estimation, data analysis and inference. However, there remain open questions regarding the formulation of the model, the likelihood and priors, and efficient computation. This project proposes new approaches that address these issues, and applies them to two exemplar challenges: the impact of climate ch ....New Directions in Bayesian Statistics: formulation, computation and application to exemplar challenges. Bayesian statistics is a fundamental statistical and machine learning approach for density estimation, data analysis and inference. However, there remain open questions regarding the formulation of the model, the likelihood and priors, and efficient computation. This project proposes new approaches that address these issues, and applies them to two exemplar challenges: the impact of climate change on the Great Barrier Reef and better understanding neurological diseases related aging, in particular Parkinson's Disease. Read moreRead less
Understanding dissipation, thermal conduction and diffusion in superionic conductors using ab initio nonequilibrium molecular dynamics simulation. Lithium ion batteries are widely used in computers, cars and more recently in aircraft. However they may exhibit thermal runaway leading to fire. Recently these problems have grounded the fleet of Boeing 787 aircraft, worldwide. Understanding superionic conduction is of thus of considerable technological importance. The project will focus on understa ....Understanding dissipation, thermal conduction and diffusion in superionic conductors using ab initio nonequilibrium molecular dynamics simulation. Lithium ion batteries are widely used in computers, cars and more recently in aircraft. However they may exhibit thermal runaway leading to fire. Recently these problems have grounded the fleet of Boeing 787 aircraft, worldwide. Understanding superionic conduction is of thus of considerable technological importance. The project will focus on understanding mass and heat flow in superionic conductors using a new molecular simulation technique that the team has recently developed. This technique combines nonequilibrium statistical mechanics and ab initio molecular dynamics simulation. The project will learn how heat is generated and conducted through these materials and how temperature influences these processes, and how heat and mass flow couple together.Read moreRead less
Heterogeneity, Wage Inequality, Unemployment, and Economic Growth. This project would provide the first internally consistent theory of wage inequality, unemployment and economic growth - and the roles that government policy variables play in determining them. It would use and extend frontier developments in theory, and identify the settings of policy variables (unemployment insurance, tax structures, education policies) that maximise social welfare, given that governments must satisfy their bud ....Heterogeneity, Wage Inequality, Unemployment, and Economic Growth. This project would provide the first internally consistent theory of wage inequality, unemployment and economic growth - and the roles that government policy variables play in determining them. It would use and extend frontier developments in theory, and identify the settings of policy variables (unemployment insurance, tax structures, education policies) that maximise social welfare, given that governments must satisfy their budget constraints. It also aims to uncover the relationship between the innate abilities of workers and their education choices - and the consequences for macro economies and public policy.Read moreRead less
Categorical symmetries in representation theory. This project aims to develop categorical symmetries of central objects in mathematics such as braid groups, the Hilbert scheme of points, and the Virasoro algebra. The concept of symmetry is an important organising principle in science. Representation theory is the field of mathematics concerned with studying symmetries. The problems proposed have connections to many different areas including algebra, geometry, topology, and mathematical physics. ....Categorical symmetries in representation theory. This project aims to develop categorical symmetries of central objects in mathematics such as braid groups, the Hilbert scheme of points, and the Virasoro algebra. The concept of symmetry is an important organising principle in science. Representation theory is the field of mathematics concerned with studying symmetries. The problems proposed have connections to many different areas including algebra, geometry, topology, and mathematical physics. This project expects to advance pure mathematics and provide potential benefit in many related fields.Read moreRead less
Threshold models in micro-econometrics with applications to empirical models of health. The aim of this project is to develop and apply new statistical approaches to endogenously identify non-linear relationships between explanatory variable(s) and the response variable in non-linear econometric models and to illustrate these with applications important to empirical health economics. Literature proliferates in linear models with non-linear effects, but in health economics non-linear models domin ....Threshold models in micro-econometrics with applications to empirical models of health. The aim of this project is to develop and apply new statistical approaches to endogenously identify non-linear relationships between explanatory variable(s) and the response variable in non-linear econometric models and to illustrate these with applications important to empirical health economics. Literature proliferates in linear models with non-linear effects, but in health economics non-linear models dominate. This project will generalise these techniques to allow for various forms of the threshold variable(s), including categorical and continuous, endogenous and exogenous, and those measured with error.Read moreRead less
Modelling Income Distributions over Space and Time: 1985-2010. The aim of this project is to develop and use interpolation and extrapolation methods, designed to overcome data scarcity, to estimate annual income distributions for countries, regions and the world for the period 1985 to 2010, facilitating measurement and comparison of changes in inequality, per capita income, poverty, and pro-poor growth, at national, regional and global levels. Reliable estimates of these welfare measures provide ....Modelling Income Distributions over Space and Time: 1985-2010. The aim of this project is to develop and use interpolation and extrapolation methods, designed to overcome data scarcity, to estimate annual income distributions for countries, regions and the world for the period 1985 to 2010, facilitating measurement and comparison of changes in inequality, per capita income, poverty, and pro-poor growth, at national, regional and global levels. Reliable estimates of these welfare measures provide valuable information for policy advisors and other researchers interested in growth and welfare of society.Read moreRead less
Technological innovation, trade liberalization, unemployment, and policy design. Australia, like all economies, is heavily influenced by technological changes and shifting trade patterns. Understanding these influences, and the impact they have on the distribution of income, the unemployment rate, and the job mix, is very important for the design of appropriate policy initiatives. The proposed research aims to achieve exactly this by developing a mathematical model which incorporates technologic ....Technological innovation, trade liberalization, unemployment, and policy design. Australia, like all economies, is heavily influenced by technological changes and shifting trade patterns. Understanding these influences, and the impact they have on the distribution of income, the unemployment rate, and the job mix, is very important for the design of appropriate policy initiatives. The proposed research aims to achieve exactly this by developing a mathematical model which incorporates technological change, trade, and unemployment. The model will be used to analyse the effects of these changes and, thus, to design optimal policy. The results from this project should also stimulate policy discussions both within Australia and abroad - enriching academic relations between domestic and international universities.Read moreRead less
Macdonald polynomials: Combinatorics and representations. This proposal is part of the aim to build a world class research team in algebraic combinatorics and combinatorial representation theory at the University of Melbourne, led by the two CI.
These fields are currently experiencing very rapid growth and development, and a strong Australia based team will further enhance the country's strong reputation in combinatorics and algebra.
The project will also provide a perfect training ground fo ....Macdonald polynomials: Combinatorics and representations. This proposal is part of the aim to build a world class research team in algebraic combinatorics and combinatorial representation theory at the University of Melbourne, led by the two CI.
These fields are currently experiencing very rapid growth and development, and a strong Australia based team will further enhance the country's strong reputation in combinatorics and algebra.
The project will also provide a perfect training ground for Higher Degree Students with interests in pure mathematics as well as computer
algebra and symbolic computation.Read moreRead less
Economic efficiency and the provision of incentives for information acquisition and disclosure: a mechanism design approach. By uncovering what determines information acquisition, highlighting what allows experts and insiders to manipulate market outcomes, and studying the efficiency gains obtainable with the use of a variety of incentives schemes, this research will provide valuable insights for public policy concerning information diffusion and market transparency.