Explicit Construction of Global Function Fields with Many Rational Places. The use of error-correcting codes and cryptosystems is fundamental to the secure and reliable operation of many technological devices that we depend upon in our everyday lives. Essentially invisible, both coding theory and cryptography are essential for banking (ATM machines, e-banking), commerce (e-commerce), defense (cryptography) and entertainment (digital TV and radio, music CDs, DVDs). While certain families of "goo ....Explicit Construction of Global Function Fields with Many Rational Places. The use of error-correcting codes and cryptosystems is fundamental to the secure and reliable operation of many technological devices that we depend upon in our everyday lives. Essentially invisible, both coding theory and cryptography are essential for banking (ATM machines, e-banking), commerce (e-commerce), defense (cryptography) and entertainment (digital TV and radio, music CDs, DVDs). While certain families of "good" codes and cryptosystems can be constructed from specific function fields whose existence is guaranteed by abstract theory, often no actual construction for the function field is currently known. We aim to close this gap, making a greater range of "good" codes and cryptosystems available for practical applications.
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Chromatic polynomials, random graphs, and error-correcting codes: a unified approach to graph colouring problems. Through a unified approach involving cutting-edge results on chromatic polynomials, random graphs, matroids, and error-correcting codes, this project will establish the foundations for a rigorous mathematical framework for attempting to provide a short, transparent and illuminating solution to the Four Colour Problem. The project will support developments in computer science and sta ....Chromatic polynomials, random graphs, and error-correcting codes: a unified approach to graph colouring problems. Through a unified approach involving cutting-edge results on chromatic polynomials, random graphs, matroids, and error-correcting codes, this project will establish the foundations for a rigorous mathematical framework for attempting to provide a short, transparent and illuminating solution to the Four Colour Problem. The project will support developments in computer science and statistical mechanics and is likely to have flow-on effects in real-world disciplines such as network communication. This project will also strengthen Australia's international presence in discrete mathematics and will further strengthen ties between Australian and international mathematicians.Read moreRead less
Information security and digital watermarking with Latin squares. The importance of digital information is increasing constantly. Audio, video, and still image data dominate our daily lives. Such information has commercial and strategic importance. It is invaluable in crime prevention: for example, video from security cameras. The protection of commercially valuable material against piracy and sensitive information against security breaches is vital to our economy and our safety. This project ad ....Information security and digital watermarking with Latin squares. The importance of digital information is increasing constantly. Audio, video, and still image data dominate our daily lives. Such information has commercial and strategic importance. It is invaluable in crime prevention: for example, video from security cameras. The protection of commercially valuable material against piracy and sensitive information against security breaches is vital to our economy and our safety. This project addresses these issues, by developing new, secure watermarks and fingerprints to protect digital information. Such watermarks can also protect radio communication channels, which is important due to the rising demand for wireless connectivity.Read moreRead less
New lattice approach for digital broadband communications. A main limiting factor in supplying future broadband communications is overcoming signal dispersion in the transmission channel. Recent preliminary collaboration by the chief investigators has uncovered a novel approach to this problem based on powerful mathematical lattice theory. The techniques have potential to significantly increase bandwidth and reliability compared to current technologies. This project will use lattice theory to pr ....New lattice approach for digital broadband communications. A main limiting factor in supplying future broadband communications is overcoming signal dispersion in the transmission channel. Recent preliminary collaboration by the chief investigators has uncovered a novel approach to this problem based on powerful mathematical lattice theory. The techniques have potential to significantly increase bandwidth and reliability compared to current technologies. This project will use lattice theory to propose, develop, analyse and test new data transmission techniques including joint coding, modulation and equalisation. The research will include theoretical analysis and hardware implementation. The overall aim is to dramatically improve reliability and throughput of data communication systems.Read moreRead less
From Universal Induction to Intelligent Systems. The dream of creating artificial devices that (out)reach human intelligence is an old one. What makes this challenge so interesting? A solution would have enormous implications for our society, and there are arguments that the AI problem might be solved within a couple of decades. Specialized intelligent systems are actually already pervasive (finger print, handwriting, speech, and face recognition; spam filtering; search engines; computer chess; ....From Universal Induction to Intelligent Systems. The dream of creating artificial devices that (out)reach human intelligence is an old one. What makes this challenge so interesting? A solution would have enormous implications for our society, and there are arguments that the AI problem might be solved within a couple of decades. Specialized intelligent systems are actually already pervasive (finger print, handwriting, speech, and face recognition; spam filtering; search engines; computer chess; robots). This decade the first presumably complete mathematical theory of AI has been proposed. By working out this theory, this project will significantly contribute to the foundations of inductive inference and AI, and ultimately lead to smarter software and intelligent systems.Read moreRead less
Geometric structures in representation theory. Mathematics underpins every aspect of people's interactions with nature (e.g. physics) and with each other (e.g. finance). Its uses range from formulating physical laws in order to understand and predict nature, to analysis of financial concepts and transactions. This project will formulate and develop three new fundamental mathematical concepts: cellular algebras, eigenspace geometries, and diagram algebras. Benefits include enhancement of Australi ....Geometric structures in representation theory. Mathematics underpins every aspect of people's interactions with nature (e.g. physics) and with each other (e.g. finance). Its uses range from formulating physical laws in order to understand and predict nature, to analysis of financial concepts and transactions. This project will formulate and develop three new fundamental mathematical concepts: cellular algebras, eigenspace geometries, and diagram algebras. Benefits include enhancement of Australia's position at the very frontier of world class mathematical research, and a myriad of potential applications to physics, coding theory, information technology, electronic security and experimental design.Read moreRead less
The geometry of exotic nilpotent cones. This research will describe the geometry of some important objects which sit at the boundary of algebra, geometry, and combinatorics. It has intrinsic value as a significant addition to the heritage of mathematical thought, and will strengthen Australian traditions in these areas of mathematics.
Increasing the effectiveness of quantitative verification. The ability to analyse the performance of complex systems and protocols is a vital part of the development of large-scale computer applications. Methods that improve the effectiveness of the analysis task would increase the competitiveness of the software industry, and would attract future development work (in complex systems) to Australia. The results of this project will have a direct influence on currently available design tools; the ....Increasing the effectiveness of quantitative verification. The ability to analyse the performance of complex systems and protocols is a vital part of the development of large-scale computer applications. Methods that improve the effectiveness of the analysis task would increase the competitiveness of the software industry, and would attract future development work (in complex systems) to Australia. The results of this project will have a direct influence on currently available design tools; the fact that Australian institutions will be (in part) responsible for key theoretical results in this growing field will strengthen Australia's position worldwide as an international centre for computer science.Read moreRead less
Control of Markov jumping processes with constraints. The project outcomes will constitute the set of tools for modelling and optimisation of complex stochastic systems and will lead to new and more precise characterisations of optimal behaviour of complex controllable systems arising in Resource Management, Engineering and Telecommunications. Therefore, the project fits to the research priority areas Breakthrough Science and Frontier Technologies in the topic of mathematical modelling and optim ....Control of Markov jumping processes with constraints. The project outcomes will constitute the set of tools for modelling and optimisation of complex stochastic systems and will lead to new and more precise characterisations of optimal behaviour of complex controllable systems arising in Resource Management, Engineering and Telecommunications. Therefore, the project fits to the research priority areas Breakthrough Science and Frontier Technologies in the topic of mathematical modelling and optimisation of Complex Systems.Read moreRead less
Non-invasive assessment of hip fracture risk in elderly people. No falls, no fractures - this will be the main benefit of the proposed research. The most significant outcome will be new computational tools to improve current understanding of the biomechanics of falls and bone fragility in elderly people, which, in turn, will help to reduce healthcare costs associated with the treatment and management of hip fractures. Realistic models and computer simulations of human movement can play a pivota ....Non-invasive assessment of hip fracture risk in elderly people. No falls, no fractures - this will be the main benefit of the proposed research. The most significant outcome will be new computational tools to improve current understanding of the biomechanics of falls and bone fragility in elderly people, which, in turn, will help to reduce healthcare costs associated with the treatment and management of hip fractures. Realistic models and computer simulations of human movement can play a pivotal role in three of Australia's largest industries: healthcare, through the diagnosis and treatment of movement disorders; sports, through the development of personalized training programs for elite athletes; and entertainment, through the development of video/digital games and animated films.Read moreRead less