Efficient Design for Generalized Linear Models. In industrial, commercial and social research, we collect data in order to predict the outcome of a process based on the inputs to that process. We want to maximize the information that is gained from the data. Good planning is crucially important to achieve this. This project will determine how best to select the inputs to the process for many situations that occur in research. A computer package to answer these questions will be written. The nati ....Efficient Design for Generalized Linear Models. In industrial, commercial and social research, we collect data in order to predict the outcome of a process based on the inputs to that process. We want to maximize the information that is gained from the data. Good planning is crucially important to achieve this. This project will determine how best to select the inputs to the process for many situations that occur in research. A computer package to answer these questions will be written. The nation will benefit from a fundamental increase in efficiency of research and, therefore, in efficient use of research dollars.Read moreRead less
Robust Reformulation Methods. Many decision problems in engineering, business and economics are modeled as nonlinear continuous optimization problems. Often these are made difficult by the existence of constraints. In this project, we reformulate such problems as constrained nonsmooth equations, rather than optimization problems, and develop generalized Newton and quasi-Newton methods for solving them. The expected outcomes of this project include a systematic theory of reformulation methods, ....Robust Reformulation Methods. Many decision problems in engineering, business and economics are modeled as nonlinear continuous optimization problems. Often these are made difficult by the existence of constraints. In this project, we reformulate such problems as constrained nonsmooth equations, rather than optimization problems, and develop generalized Newton and quasi-Newton methods for solving them. The expected outcomes of this project include a systematic theory of reformulation methods, and robust and efficient algorithms for solving some important nonlinear continuous optimization problems. There is high potential for applications in engineering, business and finance.Read moreRead less
Harmonic analysis on Lie groups via hypergroup convolution structures. This project studies convolution structures for conjugacy classes
of nilpotent and compact Lie groups and the connections with fusion rule algebras. The aims are to establish a suitable theory of almost periodic functions on a nilpotent Lie group to allow a
wrapping theorem to be formulated, to describe precisely the
class hypergroup of a compact Lie group, and to clarify the relations of the latter with fusion rule algebr ....Harmonic analysis on Lie groups via hypergroup convolution structures. This project studies convolution structures for conjugacy classes
of nilpotent and compact Lie groups and the connections with fusion rule algebras. The aims are to establish a suitable theory of almost periodic functions on a nilpotent Lie group to allow a
wrapping theorem to be formulated, to describe precisely the
class hypergroup of a compact Lie group, and to clarify the relations of the latter with fusion rule algebras. This will result in further understanding of the Kirillov orbit method and the have applications to conformal field theory.Read moreRead less
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
Trans-dimensional and Approximate Bayesian Computation. Many applied scientists in Australia, particularly those in the biological, medical and environmental sciences are now interested in incorporating Bayesian statistical methodologies into their research.
The development of more generic and efficient Bayesian statistical methods will not only benefit applied statisticians but also the more occasional users of statistics in other disciplinary areas. The success of this project will enhance Au ....Trans-dimensional and Approximate Bayesian Computation. Many applied scientists in Australia, particularly those in the biological, medical and environmental sciences are now interested in incorporating Bayesian statistical methodologies into their research.
The development of more generic and efficient Bayesian statistical methods will not only benefit applied statisticians but also the more occasional users of statistics in other disciplinary areas. The success of this project will enhance Australia's reputation as a strong contributor to the development of Bayesian methodologies. Two PhD students will also be provided training in computational Bayesian statistics.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
Implementing Feferman-Landin Logic. The objective of this project is to utilise computer based verification tools (such as PVS and Rewritting Logic) to develop a software engineering environment for specifying and verifying systems written in high-level programming languages such as Java, Scheme, and ML. The project will thus subtantially advance the use of formal computer based tools to develop reliable programs and specifications for life-critical systems. The project will also develop form ....Implementing Feferman-Landin Logic. The objective of this project is to utilise computer based verification tools (such as PVS and Rewritting Logic) to develop a software engineering environment for specifying and verifying systems written in high-level programming languages such as Java, Scheme, and ML. The project will thus subtantially advance the use of formal computer based tools to develop reliable programs and specifications for life-critical systems. The project will also develop formally
based interoperability between the PVS and Maude systems, two widely
used computer tools for reasoning about complex systems.Read moreRead less
New Bayesian methodology for understanding complex systems using hidden Markov models and expert opinion, environmental, robotics and genomics applications. This project aims to merge four areas of intense international interest in describing complex systems: hidden Markov models and mixtures, semi-parametric and nonparametric approaches, true combination of expert opinion with data, and new Bayesian computational methods based on perfect sampling and particle sampling. The project will signific ....New Bayesian methodology for understanding complex systems using hidden Markov models and expert opinion, environmental, robotics and genomics applications. This project aims to merge four areas of intense international interest in describing complex systems: hidden Markov models and mixtures, semi-parametric and nonparametric approaches, true combination of expert opinion with data, and new Bayesian computational methods based on perfect sampling and particle sampling. The project will significantly contribute to statistical methodology and its ability to inform about real-world problems. A strong focus on applications to genomics, robotics and environmental modelling will bring immediate research and monetary benefit for industry. Expected outcomes include enhanced cross-disciplinary and international linkages, publications, industry-funded projects and highly trained graduates.Read moreRead less
Computer Assisted Research Mathematics and its Applications. The mathematics community will benefit from infusion of new computer-assisted techniques and modalities for research and training post-graduate students, both from my pure research project and through development of an associated research centre. Ultimately, this should also help more school students learn mathematics well and so play a part in addressing Australia's skill shortage. Also, the work on optimization algorithms promises to ....Computer Assisted Research Mathematics and its Applications. The mathematics community will benefit from infusion of new computer-assisted techniques and modalities for research and training post-graduate students, both from my pure research project and through development of an associated research centre. Ultimately, this should also help more school students learn mathematics well and so play a part in addressing Australia's skill shortage. Also, the work on optimization algorithms promises to improve the performance and quality of many practical signal reconstruction methods. These are used by varied Australian industries from telecommunication to mining and by researchers in the digital arts and fields such as astronomy, physics, chemistry, bioscience, geoscience, engineering and medicine.Read moreRead less
Dynamic Equations on Measure Chains. Boundary value problems (BVPs) on ``measure chains''are new and useful mathematical equations that describe the world around. This project aims to answer some imporotant and fundamental mathematical questions such as
(i) Under what conditions do BVPs on measure chains actually have solutions?
(ii) If solutions do exist, then what are their properties?
The approach is to use modern tools from mathematical analysis, including topological transversality ....Dynamic Equations on Measure Chains. Boundary value problems (BVPs) on ``measure chains''are new and useful mathematical equations that describe the world around. This project aims to answer some imporotant and fundamental mathematical questions such as
(i) Under what conditions do BVPs on measure chains actually have solutions?
(ii) If solutions do exist, then what are their properties?
The approach is to use modern tools from mathematical analysis, including topological transversality and Leray-Schauder degree.
The project outcomes will
(a) significantly advance current mathematical theory for BVPs on measure chains
(b) unify the theory of BVPs for differential and difference equations
(c) potentially apply to many real-world phenomena.Read moreRead less