Asynchronous Continuous Time Conditioning. Methodology for reasoning about Asynchronous Temporal Conditional Events (ATCE) obtains, complete with logical calculus for causal relations, reasoning about continuous time belief change, and markov chain algorithms calculating joint distributions of ATCE's.
Current techniques, including bayesian nets, are oblivious to temporal aspects; within our model they can be enhanced to recognize dynamic time changes. Ours is the first such unified model and ....Asynchronous Continuous Time Conditioning. Methodology for reasoning about Asynchronous Temporal Conditional Events (ATCE) obtains, complete with logical calculus for causal relations, reasoning about continuous time belief change, and markov chain algorithms calculating joint distributions of ATCE's.
Current techniques, including bayesian nets, are oblivious to temporal aspects; within our model they can be enhanced to recognize dynamic time changes. Ours is the first such unified model and first to link conditional objects with continuous time constraints.
Need for structures we propose arises in diagnostic reasoning, bayesian learning, temporal databases, and time-dependent data mining. Several commercial products (like Microsoft Office Assistant)could apply them forthwith.Read moreRead less
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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What is the spatial and environmental distribution of phylogenetic diversity in the Australian biota? Almost nothing is known about the geographic distribution of phylogenetic relationships across Australia at fine resolutions of the order of tens of kilometres. The aim of this research is to map the spatial patterns of phylogenetic diversity in the Australian biota and identify possible environmental controls over them. We will analyse five disparate groups at a spatial resolution that is ord ....What is the spatial and environmental distribution of phylogenetic diversity in the Australian biota? Almost nothing is known about the geographic distribution of phylogenetic relationships across Australia at fine resolutions of the order of tens of kilometres. The aim of this research is to map the spatial patterns of phylogenetic diversity in the Australian biota and identify possible environmental controls over them. We will analyse five disparate groups at a spatial resolution that is orders of magnitude finer than previous research, analysing their relationship with possible environmental controls using advanced spatial analysis methods. The knowledge we will generate about the spatial distribution of these relationships is essential to understand and conserve Australia's unique biodiversity.Read moreRead less
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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Statistical Methods for Flow Cytometric Data. The project will aid users of flow cytometry throughout Australia. It will help foster collaborations between the biological and mathematical scientists. Biological research is an important part of Australia's future and is becoming very quantitative. During the course of the project, two PhD students will be provided strong training in Statistics geared towards biological applications. The project is aligned with the 8th Human Leucocyte Differentiat ....Statistical Methods for Flow Cytometric Data. The project will aid users of flow cytometry throughout Australia. It will help foster collaborations between the biological and mathematical scientists. Biological research is an important part of Australia's future and is becoming very quantitative. During the course of the project, two PhD students will be provided strong training in Statistics geared towards biological applications. The project is aligned with the 8th Human Leucocyte Differentiation Antigen workshop to culminate in Adelaide in December 2004 and will aid the fight against blood cell cancers. The project will also aid research on plankton with potential commercial benefits for Australia's marine scallop industry.
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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
Spatial Cognition—Expressive Representation Formalisms and Effective Reasoning Mechanisms. The project will contribute significantly to the advancement of knowledge in breakthrough science in qualitative spatial reasoning and smart information use in geographic information systems. Expressive spatial languages are important in organising spatial knowledge, defining spatial query languages and guiding spatial data mining. Effective spatial reasoning mechanisms bring theory closer to applications ....Spatial Cognition—Expressive Representation Formalisms and Effective Reasoning Mechanisms. The project will contribute significantly to the advancement of knowledge in breakthrough science in qualitative spatial reasoning and smart information use in geographic information systems. Expressive spatial languages are important in organising spatial knowledge, defining spatial query languages and guiding spatial data mining. Effective spatial reasoning mechanisms bring theory closer to applications including consistency checking and spatial query pre-processing. The project will help in extracting knowledge from massive spatial databases, meeting the growing needs of naive users for spatial information and establishing Australia as a major player in spatial cognition research and in the development of geo-location services.Read moreRead less
Investigations into machine learning applications in link analysis. Link analysis is an emerging tool for the detection of patterns in structured data. The detection of pattern in such data can lead to the detection of fraud occurrence, security breaches in computer systems, and patterns of social interactions with a community. It is also popularly applied to applications such as Web search engine designs and marketing analysis. This project aims to advance the area of link analysis by allowing ....Investigations into machine learning applications in link analysis. Link analysis is an emerging tool for the detection of patterns in structured data. The detection of pattern in such data can lead to the detection of fraud occurrence, security breaches in computer systems, and patterns of social interactions with a community. It is also popularly applied to applications such as Web search engine designs and marketing analysis. This project aims to advance the area of link analysis by allowing the incorporation of contextual information which accounts for relationships among actors properly. Advances in link detection will allow improvements in security and Web services on which a wide field of national bodies rely. This project can help to place Australia at the forefront of this research area.Read moreRead less
Knowledge Based Model Updating for the Correctness of Security Protocols. This project will fundamentally provide a new paradigm of the security protocol verification and modification. As such, it will significantly enhance Australia's already leading role in the cutting edge research on information security. By applying the new methodology and technology, Australian IT industry will be able to develop more secure communication systems in real world domains. With a very strong research team acro ....Knowledge Based Model Updating for the Correctness of Security Protocols. This project will fundamentally provide a new paradigm of the security protocol verification and modification. As such, it will significantly enhance Australia's already leading role in the cutting edge research on information security. By applying the new methodology and technology, Australian IT industry will be able to develop more secure communication systems in real world domains. With a very strong research team across different areas such as knowledge reasoning, temporal logics and information security, and a collaborative research training environment, this project will further enhance Australia's international reputation as a leader in computing and IT research.Read moreRead less
Economical and practical design and analysis of probabilistic distributed systems. Complex computing systems composed of communicating processes are
distributed over networks, and interact with embedded hardware
components. They routinely operate in probabilistic environments:
hardware components fail randomly, but at known rates; and tactical
randomisation resolves competition for resources. Effective
specification, development and analysis methods for these systems
is crucial, and probab ....Economical and practical design and analysis of probabilistic distributed systems. Complex computing systems composed of communicating processes are
distributed over networks, and interact with embedded hardware
components. They routinely operate in probabilistic environments:
hardware components fail randomly, but at known rates; and tactical
randomisation resolves competition for resources. Effective
specification, development and analysis methods for these systems
is crucial, and probability makes that particularly difficult.
The focus of this project is to develop new formal methods that are
economical and practical in use. Exploiting our recent advances in
probabilistic program semantics, we will add probability in a new
way to proven techniques in concurrency theory, including
refinement and hierarchical design.Read moreRead less