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
Global Lithospheric Architecture Mapping II. The continents have been rifted, or broken up, and collided, or re-assembled, along major zones of weakness many times throughout Earth's history. Boundaries between such continental domains focus large-scale movements of fluids that can produce giant ore deposits. This study will provide new perspectives on the localisation of world-class economic deposits, the Earth resources on which society depends. Innovations in imaging the deep Earth beneath co ....Global Lithospheric Architecture Mapping II. The continents have been rifted, or broken up, and collided, or re-assembled, along major zones of weakness many times throughout Earth's history. Boundaries between such continental domains focus large-scale movements of fluids that can produce giant ore deposits. This study will provide new perspectives on the localisation of world-class economic deposits, the Earth resources on which society depends. Innovations in imaging the deep Earth beneath continents, and in numerical modelling, will maintain our high international profile in research relevant to National Priority 1.6 (Developing Deep Earth Resources). Unique 3D geological maps of regions down to 250km will make the composition of deep Earth regions newly accessible to geoscientists and all potential endusers.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
The Initiation and 3D Evolution of Instabilities in the Deep Continental Lithosphere. This project is part of a new international initiative in the Geodynamics of the Australian Plate bringing together studies of the active tectonics of the boundary regions of our plate and the ancient analogues of these processes which are locked into the stable interior of the Australian continent. The proposed research is a good fit to the Identification and Extraction of Deep Earth Resources priority goal. D ....The Initiation and 3D Evolution of Instabilities in the Deep Continental Lithosphere. This project is part of a new international initiative in the Geodynamics of the Australian Plate bringing together studies of the active tectonics of the boundary regions of our plate and the ancient analogues of these processes which are locked into the stable interior of the Australian continent. The proposed research is a good fit to the Identification and Extraction of Deep Earth Resources priority goal. Detachment of the lithosphere is associated with fertile mantle being emplaced at shallow depth below the crust; an important precursory event for mineralization. The project builds upon AuScope (NCRIS 5.13) to create infrastructure for a new, smart resource exploration and extraction industry based on modelling and simulation.Read moreRead less
Computer simulation to study emergence of material texture in the Earth and Plate Tectonics. Plate tectonics has played a crucial role in the evolution and dynamics of the earth impacting on the diversity of life, mineralisation, and crustal dynamics. Despite its significance, how and under what conditions material texture and plate tectonics emerge from a proto-planet is not well understood. New computational methodologies to simulate the evolution of the plate-mantle system will be used to stu ....Computer simulation to study emergence of material texture in the Earth and Plate Tectonics. Plate tectonics has played a crucial role in the evolution and dynamics of the earth impacting on the diversity of life, mineralisation, and crustal dynamics. Despite its significance, how and under what conditions material texture and plate tectonics emerge from a proto-planet is not well understood. New computational methodologies to simulate the evolution of the plate-mantle system will be used to study how the upper mantle emerges as a thermo-mechanically distinct boundary layer, how this emergent structure relates to anisotropy in the upper mantle, and how it is affected by cross-scale effects controlling fault zone behaviour and crustal dynamics.Read moreRead less
Plate kinematics to plate dynamics: understanding plate boundary processes at the global scale. This proposal aims to create geodynamic models which can be used a basis for a new, smart resource exploration and extraction industry which uses simulation to help characterize regions where traditional geophysical imaging alone is not able to penetrate. It provides essential scientific underpinnings for
The Australian Computational Earth System Simulator Major National Research Facility (ACcESS).
NUMERICAL MODELS OF PLATE TECTONICS, MANTLE CONVECTION AND SLAB DYNAMICS WITH EVOLVING FAULTS. We plan to develop a method for simulating large-scale
geological structures with a much improved treatment
of tectonic faults in 3D.
Current computer models have sharp geological faults at plate
boundaries represented by broad, blurred zones. New techniques
for modeling cracks in engineering structures will be scaled up to
the whole Earth.
This will help us to understand how the Earth's p ....NUMERICAL MODELS OF PLATE TECTONICS, MANTLE CONVECTION AND SLAB DYNAMICS WITH EVOLVING FAULTS. We plan to develop a method for simulating large-scale
geological structures with a much improved treatment
of tectonic faults in 3D.
Current computer models have sharp geological faults at plate
boundaries represented by broad, blurred zones. New techniques
for modeling cracks in engineering structures will be scaled up to
the whole Earth.
This will help us to understand how the Earth's plates move and
interact now and in the past and how the structure of the continents
arose.
Not only is this intrinsically interesting, it
will also be of immediate practical benefit to geological modelers.Read moreRead less