A Grid based platform for multi-scaled biological simulation. Heart disease currently affects over 3.5 million Australians. In 2006 it claimed the lives of almost 46,000 Australians (34% of all deaths). We will develop enabling technology that underpins cardiac disease research, offering potential for new treatments and pharmaceutical therapies. Even a small improvement in this area can translate into significant national benefit. Further, the mathematical techniques and software tools we will d ....A Grid based platform for multi-scaled biological simulation. Heart disease currently affects over 3.5 million Australians. In 2006 it claimed the lives of almost 46,000 Australians (34% of all deaths). We will develop enabling technology that underpins cardiac disease research, offering potential for new treatments and pharmaceutical therapies. Even a small improvement in this area can translate into significant national benefit. Further, the mathematical techniques and software tools we will develop, whilst focused on heart tissue, will have broader applicability, and may underpin advancements in other disciplines. Finally, we expect that the software solutions and infrastructure will have both commercial and strategic value in their own right.Read moreRead less
'Fixed points': extending and deepening our understanding of mathematical and computational aspects of game theory. This work will extend and deepen our understanding of mathematical and computational aspects of game theory. It will produce computer code embodying new methods of solving systems of nonlinear equations, which is useful in many areas of applied research in economics, in other disciplines such as chemistry, and potentially in the analysis of business operations. The project will a ....'Fixed points': extending and deepening our understanding of mathematical and computational aspects of game theory. This work will extend and deepen our understanding of mathematical and computational aspects of game theory. It will produce computer code embodying new methods of solving systems of nonlinear equations, which is useful in many areas of applied research in economics, in other disciplines such as chemistry, and potentially in the analysis of business operations. The project will also deepen our understanding of the underlying mathematics of such systems, and of other mathematical foundations of economic research. One application will be a new measure of the relative power resulting from voting rules. Such measures assist the design of democratic institutions by allowing the designer to assess the fairness of the outcomes they produce.Read moreRead less
Evidence-based frameworks for security protocol verification. Security protocols are an essential part of secure communication networks. This project aims to develop verification techniques for security protocols that produce independently verifiable formal certificates of correctness. The project's outcome will contribute to the certification processes for secure network systems at the highest level of assurance.
Practical and theoretical aspects of structure enumeration. Many areas of study involve processing of large numbers of
objects in some class. These are countless examples in
chemistry, physics, mathematics, and other disciplines.
Structure Enumeration is the study of methods for efficient
generation and analysis of such objects. The project will
involve exploitation and extension of recent advances, many
due to the CI, which have added orders of magnitude to what
was possible only a few ....Practical and theoretical aspects of structure enumeration. Many areas of study involve processing of large numbers of
objects in some class. These are countless examples in
chemistry, physics, mathematics, and other disciplines.
Structure Enumeration is the study of methods for efficient
generation and analysis of such objects. The project will
involve exploitation and extension of recent advances, many
due to the CI, which have added orders of magnitude to what
was possible only a few years ago. The outcome will be a
combination of theoretical results and practical achievements,
whose usefulness will be demonstrated with some serious
applications in physics and mathematics.
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Structure enumeration, applications and analysis. Structure enumeration and analysis is at the heart of finite mathematics and its many fields of application in diverse scientific disciplines. Australia has a substantial status in this field both in mathematics and physics. This project will enhance that status and develop greater ties with the centres of structure research in other parts of the world.
The arithmetic of supersingular elliptic curves. The proposed research will have substantial benefits both in the area of pure mathematics, and to the standing of number theory within Australia generally. If successful, the investigators envisage: - fundamental advances in the study of both elliptic curves and modular forms; - key progress in our understanding of the final Millenium Prize Problem in Mathematics; - academic software to compute special values of L-functions; - applications to com ....The arithmetic of supersingular elliptic curves. The proposed research will have substantial benefits both in the area of pure mathematics, and to the standing of number theory within Australia generally. If successful, the investigators envisage: - fundamental advances in the study of both elliptic curves and modular forms; - key progress in our understanding of the final Millenium Prize Problem in Mathematics; - academic software to compute special values of L-functions; - applications to computational mathematics, particularly elliptic curve cryptosystems; - a huge boost to the development of number theory Australia-wide.
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Tractable topological computing: Escaping the hardness trap. Computational topology is a young and energetic field that uses computers to solve complex geometric problems driven by pure mathematics, and with diverse applications in biology, signal processing and data mining. A major barrier is that many of these problems are thought to be fundamentally and intractably hard. This project aims to defy such barriers for typical real-world inputs by fusing geometric techniques with technologies from ....Tractable topological computing: Escaping the hardness trap. Computational topology is a young and energetic field that uses computers to solve complex geometric problems driven by pure mathematics, and with diverse applications in biology, signal processing and data mining. A major barrier is that many of these problems are thought to be fundamentally and intractably hard. This project aims to defy such barriers for typical real-world inputs by fusing geometric techniques with technologies from the field of parameterised complexity, creating powerful, practical solutions for these problems. It is expected to shed much-needed light on the vast and puzzling gap between theory and practice, and give researchers fast new software tools for large-scale experimentation and cutting-edge computer proofs.Read moreRead less
Practical Automated Deduction. This project will develop, implement and validate improved methods for automated deduction in decidable fragments of first order logic, also incorporating reasoning in special theories such as arithmetic. It will significantly extend previous work on the model evolution calculus and dynamic semantic resolution, and introduce new techniques that combine these reasoning methods. This work has direct application to reasoning about business rules and about industrial o ....Practical Automated Deduction. This project will develop, implement and validate improved methods for automated deduction in decidable fragments of first order logic, also incorporating reasoning in special theories such as arithmetic. It will significantly extend previous work on the model evolution calculus and dynamic semantic resolution, and introduce new techniques that combine these reasoning methods. This work has direct application to reasoning about business rules and about industrial optimisation problems, and it will motivate and test our systems by means of case studies from both of these areas.Read moreRead less
Three-dimensional magnetotelluric and controlled-source electromagnetic modelling and inversion in isotropic and anisotropic media with Gaussian Quadrature Grids. Electromagnetic methods are widely used by geophysicists in many applications, including mineral, petroleum and geothermal exploration, environmental and groundwater characterisation, and in imaging of Earth and other planets. Large data-sets are routinely collected, but to interpret these carefully we need efficient computer modellin ....Three-dimensional magnetotelluric and controlled-source electromagnetic modelling and inversion in isotropic and anisotropic media with Gaussian Quadrature Grids. Electromagnetic methods are widely used by geophysicists in many applications, including mineral, petroleum and geothermal exploration, environmental and groundwater characterisation, and in imaging of Earth and other planets. Large data-sets are routinely collected, but to interpret these carefully we need efficient computer modelling tools that incorporate the complexity of the subsurface. We will develop a new computer algorithm that uses an innovative approach to model the Earth in three dimensions. Computer codes will be available through the national AuScope infrastructure facilities, so that researchers will have free access to algorithms, largely for the first time, to better interpret their data.Read moreRead less
Practical Identity-Based Cryptography: Efficient and Secure Elliptic Curve Pairings. Bilinear pairings on elliptic curves are a new cryptographic tool and allow novel and improved applications in information security. For example, they have been proposed as a substitute of existing public key infrastructures, an essential element in electronic commerce and a secure Internet. The research will lead to an increase in fundamental knowledge in the area of practical implementation and secure applic ....Practical Identity-Based Cryptography: Efficient and Secure Elliptic Curve Pairings. Bilinear pairings on elliptic curves are a new cryptographic tool and allow novel and improved applications in information security. For example, they have been proposed as a substitute of existing public key infrastructures, an essential element in electronic commerce and a secure Internet. The research will lead to an increase in fundamental knowledge in the area of practical implementation and secure applications of pairings. The results will benefit all users of electronic communications who require security for their information. This includes the financial industries, government, commerce and domestic users. It will also support many new product opportunities aligned with Motorola's business markets.Read moreRead less