Emerging applications of advanced computational methods and discrete mathematics. Ongoing improvements in computer performance are revolutionising research in combinatorial discrete mathematics, and leading to exciting new applications in information technology and the biological and chemical sciences. As a result, substantial international research effort, both at universities and in commercial and industrial organisations, is being channelled into high-performance computation and theoretical p ....Emerging applications of advanced computational methods and discrete mathematics. Ongoing improvements in computer performance are revolutionising research in combinatorial discrete mathematics, and leading to exciting new applications in information technology and the biological and chemical sciences. As a result, substantial international research effort, both at universities and in commercial and industrial organisations, is being channelled into high-performance computation and theoretical problems in combinatorial mathematics. Our aim is to develop and apply advanced computational methods through the study of several unsolved theoretical problems in design theory and practical problems in exact matrix computation and drug design.Read moreRead less
Cycle decompositions of graphs. The benefits to Australia of fundamental research in core disciplines such as mathematics are well documented. This project aims to solve long-standing and significant open problems in the field of mathematics known as graph theory. Solving such problems will undoubtedly bring Australian research in this field to the fore, and help to enhance Australia's international research profile generally. The project offers substantial postgraduate training in the form of t ....Cycle decompositions of graphs. The benefits to Australia of fundamental research in core disciplines such as mathematics are well documented. This project aims to solve long-standing and significant open problems in the field of mathematics known as graph theory. Solving such problems will undoubtedly bring Australian research in this field to the fore, and help to enhance Australia's international research profile generally. The project offers substantial postgraduate training in the form of three excellent PhD projects in discrete mathematics. The computer age has ensured that this is a booming discipline and an increasing component of undergraduate syllabi around the world. It is thus a crucial area in which to be providing quality research training.Read moreRead less
New computational methods study on protein function prediction. The proposed research aims to develop new computational methods to solve one of the most important bioinformatics problems in the post-genome era. This project will expand the knowledge on protein sequence-structure-function relationship, provide new analysis methods and predict the functions of novel proteins. This project will strengthen Australia's reputation for research excellence.
Statistical Methods for Discovering Ribonucleic acids (RNAs) contributing to human diseases and phenotypes. Identifying the causative genetic factors involved in quantitative phenotypes and diseases is a major goal of biology in the 21st century and beyond. A crucial step towards this goal is identifying and classifying the functional non-protein-coding Ribonucleic acids (RNAs) encoded in the human genome. This project will make major contributions to international efforts in this area by identi ....Statistical Methods for Discovering Ribonucleic acids (RNAs) contributing to human diseases and phenotypes. Identifying the causative genetic factors involved in quantitative phenotypes and diseases is a major goal of biology in the 21st century and beyond. A crucial step towards this goal is identifying and classifying the functional non-protein-coding Ribonucleic acids (RNAs) encoded in the human genome. This project will make major contributions to international efforts in this area by identifying RNA molecules that contribute to quantitative phenotypes including susceptibility to disease. As such, it will directly benefit fundamental science via the discovery and classification of new molecules. Indirectly, it will lead to breakthroughs in biology, and consequently to major medical and pharmaceutical advances in the diagnosis and treatment of genetic disease.Read moreRead less
Quantum entanglement and its role in complex quantum systems. Quantum entanglement - non-classical correlations in quantum states - is the physical resource at the heart of modern applications of quantum technology, such as absolutely secure communication, and teleportation of quantum states from one location to another. This project aims to deepen our theoretical understanding of entanglement by characterizing the type and amount of entanglement present in the ground and thermal states of a ge ....Quantum entanglement and its role in complex quantum systems. Quantum entanglement - non-classical correlations in quantum states - is the physical resource at the heart of modern applications of quantum technology, such as absolutely secure communication, and teleportation of quantum states from one location to another. This project aims to deepen our theoretical understanding of entanglement by characterizing the type and amount of entanglement present in the ground and thermal states of a general physical system. These results will enable us to study the central role entanglement plays in quantum phase transitions - the change of a physical system from one state of matter to another, different, state of matter, one with a truly quantum character.Read moreRead less
Multi-scale modelling of cell migration in developmental biology. Interpretative and predictive tools are needed for the comprehensive understanding of directed cell migration in the medical sciences. Mathematical models and modelling methodologies developed in this project will make a significant contribution to the investigation of cell migration and the testing and generation of hypotheses. Such models are needed to understand observed cellular patterns. This project will contribute to knowle ....Multi-scale modelling of cell migration in developmental biology. Interpretative and predictive tools are needed for the comprehensive understanding of directed cell migration in the medical sciences. Mathematical models and modelling methodologies developed in this project will make a significant contribution to the investigation of cell migration and the testing and generation of hypotheses. Such models are needed to understand observed cellular patterns. This project will contribute to knowledge of normal and abnormal developmental processes, especially in embryonic growth. Understanding these processes should lead to prediction and treatment of congenital disorders and contribute to a healthy start to life.Read moreRead less
Security Applications of Combinatorial Puzzles. This project provides a basis for improving the implementation and maintenance of key management systems. The application of discrete mathematics to information security will help safeguard Australia, will provide opportunities for Australians to take a leading role in an important area and will develop a research network, bridging both theoretical and practical aspects of mathematics and computer science. The project will enhance Australia's inter ....Security Applications of Combinatorial Puzzles. This project provides a basis for improving the implementation and maintenance of key management systems. The application of discrete mathematics to information security will help safeguard Australia, will provide opportunities for Australians to take a leading role in an important area and will develop a research network, bridging both theoretical and practical aspects of mathematics and computer science. The project will enhance Australia's international reputation by establishing collaborations with well-respected international mathematicians and computer scientists. The proposal contains topics suitable for the training of new graduates, allowing them to make high quality original research contributions in a novel and important area. Read moreRead less
Timed Commitment Schemes to Smooth Internet Bottlenecks, Defend against Denial of Service Attacks, and Bypass Some Legal Problems of Enccryption. Bottlenecks on the Internet and Denial of Service attacks on a server are both caused by excessive demands made on a system. This proposal is to reduce the ill-effects of either by building on our previous theoretical work on strongboxes of combinatorial designs. In the case of bottlenecks, the demands are legitimate but badly timed, and our approach ....Timed Commitment Schemes to Smooth Internet Bottlenecks, Defend against Denial of Service Attacks, and Bypass Some Legal Problems of Enccryption. Bottlenecks on the Internet and Denial of Service attacks on a server are both caused by excessive demands made on a system. This proposal is to reduce the ill-effects of either by building on our previous theoretical work on strongboxes of combinatorial designs. In the case of bottlenecks, the demands are legitimate but badly timed, and our approach will redistribute the demands more evenly. In the case of Denial of Service attacks, the demands are malicious, and our approach will respond in such a way as to deplete the resources of the attacker.Read moreRead less
Statistical methods for detection of non-coding RNAs in eukaryote genomes. Understanding how eukaryotic cells work is a major goal of 21st century biology. A crucial step will be to catalogue the functional components of eukaryotic genomes. Australian researchers must be involved in this process at an early stage, in order to maximise commercial opportunities, attract quality researchers and position ourselves for further advances. This project will make major contributions to international effo ....Statistical methods for detection of non-coding RNAs in eukaryote genomes. Understanding how eukaryotic cells work is a major goal of 21st century biology. A crucial step will be to catalogue the functional components of eukaryotic genomes. Australian researchers must be involved in this process at an early stage, in order to maximise commercial opportunities, attract quality researchers and position ourselves for further advances. This project will make major contributions to international efforts in this area, via the development of statistical methods for segmenting genomes, classification of those segments, and study of the resulting classes. In the long term, enhanced understanding of eukaryotic cells will lead to breakthroughs in biology, and to medical, pharmaceutical, agricultural and scientific advances.Read moreRead less
A multi-scale approach for modelling coupled transport in heterogeneous and anisotropic porous media. Mathematical Sciences foster interdisciplinary collaboration and underpin fundamental understanding of significant national/international research priorities in science and technology. This world-class team will advance knowledge in modelling complex systems ensuring the competitiveness of Australian research in this important field. A key outcome is a multi-scale computational strategy that can ....A multi-scale approach for modelling coupled transport in heterogeneous and anisotropic porous media. Mathematical Sciences foster interdisciplinary collaboration and underpin fundamental understanding of significant national/international research priorities in science and technology. This world-class team will advance knowledge in modelling complex systems ensuring the competitiveness of Australian research in this important field. A key outcome is a multi-scale computational strategy that can be used by engineers in Australia and France to simulate transport phenomena in porous media, which have significant environmental impact. The research will lead to publications in scientific journals and communications at national/international conferences. Research training of postdocs and PhD students is another excellent outcome of the project.Read moreRead less