Optimal Transforms of Random Vectors. This proposal focusses on development of optimal transforms to describe and model nonlinear phenomena when only statistical information is known. An optimal transform is a mathematical procedure that enables us to process information in a way that is most suited to the task in hand. These transforms have been successfully used in approximation, information theory, communications, control theory and signal and image processing. Applications include modelli ....Optimal Transforms of Random Vectors. This proposal focusses on development of optimal transforms to describe and model nonlinear phenomena when only statistical information is known. An optimal transform is a mathematical procedure that enables us to process information in a way that is most suited to the task in hand. These transforms have been successfully used in approximation, information theory, communications, control theory and signal and image processing. Applications include modelling of physical, chemical and biological systems, filtering and compression of signals and data classification and clustering. We propose two new hybrid models for realistic transforms in a general structural framework.
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Sparse grid approximations and fitting using generalised combination techniques. Sparse grid techniques provide an effective tool to deal with the
computational curse of dimensionality which is a constant challenge in
modelling complex data. The proposed research is aimed at the
development and analysis of algorithms for data fitting with sparse
grids using variants of the combination technique. The outcome of the
research is a theory which will provide insights in the applicability,
limit ....Sparse grid approximations and fitting using generalised combination techniques. Sparse grid techniques provide an effective tool to deal with the
computational curse of dimensionality which is a constant challenge in
modelling complex data. The proposed research is aimed at the
development and analysis of algorithms for data fitting with sparse
grids using variants of the combination technique. The outcome of the
research is a theory which will provide insights in the applicability,
limitations and the convergence properties of the proposed
algorithms. The outcomes will be widely applicable in modelling of
large scale and complex data as is encountered in areas of
bioinformatics, physics and experimental studies of complex systems.
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Modelling, Identification and Control of Complex Networks. Australia has been well known for its leading research in systems and control and many real-world applications in, for instance, telecommunications, defence, power grids and life sciences. This project will further promote Australia's leading position in the emerging new research field - complex networks by theoretical breakthrough in modelling, identification and control of complex networks, and cutting-edge platform technology that can ....Modelling, Identification and Control of Complex Networks. Australia has been well known for its leading research in systems and control and many real-world applications in, for instance, telecommunications, defence, power grids and life sciences. This project will further promote Australia's leading position in the emerging new research field - complex networks by theoretical breakthrough in modelling, identification and control of complex networks, and cutting-edge platform technology that can help Australian energy industry to reduce greenhouse emissions. It will also result in education of the next generation research leaders in this emerging field.Read moreRead less
Continued Fractions and Torsion on Hyperelliptic Curves. Scientific advance should not blindly add to our knowledge; a true advance brings insights that collapse different issues into one. Understanding more is to need to remember less. For an important class of examples, this project identifies the study of a fundamental invariant of a quadratic number field, its regulator and hence its class number, with maximum torsion on the Jacobian variety of an hyperelliptic curve. The investigator's meth ....Continued Fractions and Torsion on Hyperelliptic Curves. Scientific advance should not blindly add to our knowledge; a true advance brings insights that collapse different issues into one. Understanding more is to need to remember less. For an important class of examples, this project identifies the study of a fundamental invariant of a quadratic number field, its regulator and hence its class number, with maximum torsion on the Jacobian variety of an hyperelliptic curve. The investigator's methods will surprise some longstanding problems into submission and in particular will lead them to reveal full data on torsion on hyperelliptic curves of low genus.
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Studying Discretisation Behaviours in Variable Structure Control Systems. Variable structure control is a technology that helps build very simple and effective switching control devices for dealing with environmental uncertainties, which are widely used, for example, in industrial control systems/processes. The outcomes from this research will help the understanding of control performance deterioration due to discretisation and developing effective measures for protection from possible ill beha ....Studying Discretisation Behaviours in Variable Structure Control Systems. Variable structure control is a technology that helps build very simple and effective switching control devices for dealing with environmental uncertainties, which are widely used, for example, in industrial control systems/processes. The outcomes from this research will help the understanding of control performance deterioration due to discretisation and developing effective measures for protection from possible ill behaviours of these control devices. This research will place Australia in the forefront of the development of this new technology, resulting in enhanced reliability of control devices, improved productivity and cost saving for industries, and consequent improvement in quality of life.Read moreRead less
Algebraic Properties of Cryptographic Components and their Cryptanalysis. The outcomes will enhance information and communication security, which is absolutely crucial for the rapidly growing e-commerce and e-government services in Australia. International collaboration will be strengthened by reciprocal exchange of researchers and postgraduate students leading to more attractive and productive research environment. Our project will help to maintain a high profile of Australian researchers, to i ....Algebraic Properties of Cryptographic Components and their Cryptanalysis. The outcomes will enhance information and communication security, which is absolutely crucial for the rapidly growing e-commerce and e-government services in Australia. International collaboration will be strengthened by reciprocal exchange of researchers and postgraduate students leading to more attractive and productive research environment. Our project will help to maintain a high profile of Australian researchers, to increase the capacity for consultancy and contract work, and provide a cutting-edge information technology for the Australian telecommunications industry, business and government.Read moreRead less
Generalised Linear Mixed Models: Theory, Methods and New Areas of Application. This project will aid the analysis of complex data sets throughout Australia. The ensuing methodology and software products will be applicable to data arising from longitudinal and geo-referenced public health and biomedical studies being conducted in Australia. It will also aid analysis of complex survey data from the Australian Bureau of Statistics and other agencies. Part of this project is geared towards smart inf ....Generalised Linear Mixed Models: Theory, Methods and New Areas of Application. This project will aid the analysis of complex data sets throughout Australia. The ensuing methodology and software products will be applicable to data arising from longitudinal and geo-referenced public health and biomedical studies being conducted in Australia. It will also aid analysis of complex survey data from the Australian Bureau of Statistics and other agencies. Part of this project is geared towards smart information use in Australian industries and will help foster collaboration between mathematical scientists and members of the Australian business sector. Cancer research in Australia will also benefit from this project.Read moreRead less
Fast, practical and effective algorithms for clustering with advice. To maintain a safe and healthy society, government and industry need high quality immunization and national security databases. Since we cannot afford to have duplicate, incomplete and conflicting records that refer to the same person, we unify them by identifying clusters of related records.
In the emerging field of functional genomics, diagnosis of certain diseases is enhanced by determining which genes act together. Diffe ....Fast, practical and effective algorithms for clustering with advice. To maintain a safe and healthy society, government and industry need high quality immunization and national security databases. Since we cannot afford to have duplicate, incomplete and conflicting records that refer to the same person, we unify them by identifying clusters of related records.
In the emerging field of functional genomics, diagnosis of certain diseases is enhanced by determining which genes act together. Different experimental runs might result in different clusterings of genes: we need one consensus clustering that summarizes the experimental outcomes.
Cleaning databases and combining clusterings by hand would require vast amounts of time. This project will result in faster and more accurate computational procedures.Read moreRead less
A study of the potential for the public to be involved in the design of large scale public works. Public acceptability of infrastructure such as desalination plants or new public spaces, is a concern for the Australian Commonwealth and State Governments. However, tensions exist between the need for expedient planning and development of critical public infrastructure and Australian principles of democratic social and economic participation. The instrument developed by this research will inform pu ....A study of the potential for the public to be involved in the design of large scale public works. Public acceptability of infrastructure such as desalination plants or new public spaces, is a concern for the Australian Commonwealth and State Governments. However, tensions exist between the need for expedient planning and development of critical public infrastructure and Australian principles of democratic social and economic participation. The instrument developed by this research will inform public policy to negotiate and understand arrangements that balance social participation with Government objectives.Read moreRead less
Managing and Mining Evolving Ontologies through combining Patterns Languages and Data Mining. Data mining offers insight into the substantial and growing repositories of medical data while pattern languages offer the ability to provide a high level conceptual designs of an artifact or process. This project thus promises to facilitate, on the one hand, the discovery of medical knowledge from large quantities of clinical or epidemiological data, while also providing a better way of constructing a ....Managing and Mining Evolving Ontologies through combining Patterns Languages and Data Mining. Data mining offers insight into the substantial and growing repositories of medical data while pattern languages offer the ability to provide a high level conceptual designs of an artifact or process. This project thus promises to facilitate, on the one hand, the discovery of medical knowledge from large quantities of clinical or epidemiological data, while also providing a better way of constructing and validating medically oriented design patterns which can then be used in medical data collection systems.Read moreRead less