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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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
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
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
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
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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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
Efficient Synchronisation of Large Repositories. Accuracy and maintenance of vast quantities of data are essential for any modern society. The economy, health institutes and industries, and our defence and legal systems rely on having data being distributed widely and securely, and on queries being answered accurately and quickly. Complete synchronisation of databases is often impossible due to the limitations of internet bandwidth. Better compression techniques have the potential to allow crit ....Efficient Synchronisation of Large Repositories. Accuracy and maintenance of vast quantities of data are essential for any modern society. The economy, health institutes and industries, and our defence and legal systems rely on having data being distributed widely and securely, and on queries being answered accurately and quickly. Complete synchronisation of databases is often impossible due to the limitations of internet bandwidth. Better compression techniques have the potential to allow critical data to be distributed much more efficiently; we anticipate in some applications that the size of a compressed file could be reduced tenfold or more compared to previous best methods, leading to dramatic savings.Read moreRead less
Algorithms for change detection based on finite sample system identification theory. Detection of abrupt changes has many important applications. One particular application that will be investigated is leak detection in irrigation channels. As agriculture accounts for about 80% of Australia's water usage, the timely detection of leaks means that corrective actions can be taken early which will lead to large water savings and significant environmental benefits. The developed methods can be design ....Algorithms for change detection based on finite sample system identification theory. Detection of abrupt changes has many important applications. One particular application that will be investigated is leak detection in irrigation channels. As agriculture accounts for about 80% of Australia's water usage, the timely detection of leaks means that corrective actions can be taken early which will lead to large water savings and significant environmental benefits. The developed methods can be designed with any false alarm rate. This is important since frequent false alarms lead to wasted resources and operators will stop using the system. The technology once developed can be transferred to many other application areas such as urban water supplies, pipelines for oil and gas, and the process and manufacturing industries.Read moreRead less