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.
Read moreRead less
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
Parameterized Algorithm Design and Complexity Analysis: New Methods and Strategic Applications in the FPT Algorithmic Server Project. A fundamental discovery of the first decades of computer science is that completely efficient (polynomial time) algorithms probably do not exist for thousands of natural computational problems. The project will result in new methods for designing and analyzing algorithms for hard problems with natural parameters, and in improved
algorithms for these problems.
A new theory for retinotectal map formation. How brains become wired up during development is a question of
importance to both biology and computing. In this project we adopt a
novel computational approach to understanding the development of
topographic maps, a wiring pattern that is ubiquitous in biological
nervous systems. This project will build capacity for research in
computational neuroscience in Australia. It may also lead to
technological benefits such as new ideas for the design o ....A new theory for retinotectal map formation. How brains become wired up during development is a question of
importance to both biology and computing. In this project we adopt a
novel computational approach to understanding the development of
topographic maps, a wiring pattern that is ubiquitous in biological
nervous systems. This project will build capacity for research in
computational neuroscience in Australia. It may also lead to
technological benefits such as new ideas for the design of self-wiring
computing devices, and new insights into
the causes of wiring defects both during normal development and
rewiring after injury.
Read moreRead less
Wiring up the nervous system: how do axons detect molecular gradients? This project will improve our understanding of how the nervous system
becomes wired up during development. This will ultimately allow better
therapies for some types of developmental disorders, and for repairing
damaged connections for instance in the spinal cord. The theoretical
models developed will improve our understanding of the computations
necessary to generate appropriate wiring of the nervous system, which
may ....Wiring up the nervous system: how do axons detect molecular gradients? This project will improve our understanding of how the nervous system
becomes wired up during development. This will ultimately allow better
therapies for some types of developmental disorders, and for repairing
damaged connections for instance in the spinal cord. The theoretical
models developed will improve our understanding of the computations
necessary to generate appropriate wiring of the nervous system, which
may facilitate the development of self-organizing computing
devices. The project will also provide unique research training at the
interface of biology and computation, building capacity for such
interdisciplinary research throughout Australia.
Read moreRead less
Evolutionary multi-objective algorithms for Global Grids. This research investigates alternative software technologies for Grid-based evolutionary multi-objective decision algorithms. By employing the latest adaptive techniques and taking advantage of the low cost Grid infrastructure, new parallel evolutionary systems will be developed that can rapidly supply robust solutions to complex problems. This project will further develop an understanding of scaling issues in parallel evolutionary syste ....Evolutionary multi-objective algorithms for Global Grids. This research investigates alternative software technologies for Grid-based evolutionary multi-objective decision algorithms. By employing the latest adaptive techniques and taking advantage of the low cost Grid infrastructure, new parallel evolutionary systems will be developed that can rapidly supply robust solutions to complex problems. This project will further develop an understanding of scaling issues in parallel evolutionary systems and pave the way for even more widespread application of evolutionary techniques for large scale, data-intensive applications in science and industry.Read moreRead less
Unsupervised learning of finite mixture models in data mining applications. The extraction of useful information from massively large databases is known as data mining. Its broad but vague goal is to find "interesting structure" in the data, which typically leads to breaking the data into clusters. To this end, we consider the fast, efficient, and automatic learning of finite mixture models in hugh data sets without any prior knowledge of the structure. This probabilistic approach to the discove ....Unsupervised learning of finite mixture models in data mining applications. The extraction of useful information from massively large databases is known as data mining. Its broad but vague goal is to find "interesting structure" in the data, which typically leads to breaking the data into clusters. To this end, we consider the fast, efficient, and automatic learning of finite mixture models in hugh data sets without any prior knowledge of the structure. This probabilistic approach to the discovery and validation of group structure in data mining applications will considerably enhance knowledge management and decision support in science, industry, and government.
Read moreRead less