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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Mathematics of Elliptic Curve Cryptography. The Australian society and economy requires fast, reliable, and secure digital infrastructure. First-generation security solutions cannot support the efficiency and scalability requirements of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined and analysed. Thus developing a new framework in this area is one of the most important and urgent tasks. Besides, the intended wor ....Mathematics of Elliptic Curve Cryptography. The Australian society and economy requires fast, reliable, and secure digital infrastructure. First-generation security solutions cannot support the efficiency and scalability requirements of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined and analysed. Thus developing a new framework in this area is one of the most important and urgent tasks. Besides, the intended work advances our knowledge of the theory and the quality of our culture. As such, it will promote the Australian science and will also have many practical applications in Computer Security and E-Commerce.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
Bayesian choice modelling. Discrete choice models are important as they provide tools to help understand choice processes of decision makers. It remains a challenge to specify models with covariance structures flexible enough to capture complex patterns of cross-substitution between choices while being able to capture heterogeneity present in individual behaviour. We will develop a Bayesian approach to choice modelling that uses covariance selection to overcome these problems. This will train re ....Bayesian choice modelling. Discrete choice models are important as they provide tools to help understand choice processes of decision makers. It remains a challenge to specify models with covariance structures flexible enough to capture complex patterns of cross-substitution between choices while being able to capture heterogeneity present in individual behaviour. We will develop a Bayesian approach to choice modelling that uses covariance selection to overcome these problems. This will train researchers and raise the profile of Australia in an active research area that is important in the social sciences; substantive applications will be in health economics, but developments will also be relevant to cognate areas of biostatistics, epidemiology, and ecology.Read moreRead less
Mathematics of Cryptography. The Australian society and economy requires fast, reliable, and secure communication. First-generation security solutions are not capable of supporting the efficiency and scalability requirements of mass-market adoption of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined. Thus developing new mathematically solid tools in this area is one of the most important and urgent tasks. Besides, ....Mathematics of Cryptography. The Australian society and economy requires fast, reliable, and secure communication. First-generation security solutions are not capable of supporting the efficiency and scalability requirements of mass-market adoption of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined. Thus developing new mathematically solid tools in this area is one of the most important and urgent tasks. Besides, the intended work advances our knowledge of the theory and the quality of our culture. As such, it will promote the Australian science and will also have many practical applications in Cryptography, Computer Security and E-Commerce.Read moreRead less