'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
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
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 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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Model Update with Localisation, Constraints and Abstraction. This project will fundamentally provide a new paradigm and a system prototype for advanced computer aided system modification. It will significantly enhance Australia's leading role in the cutting edge research in computer aided system development. By applying the new methodology and technology, Australian IT industry will significantly improve its capacity for developing highly complex hardware and software systems for various applica ....Model Update with Localisation, Constraints and Abstraction. This project will fundamentally provide a new paradigm and a system prototype for advanced computer aided system modification. It will significantly enhance Australia's leading role in the cutting edge research in computer aided system development. By applying the new methodology and technology, Australian IT industry will significantly improve its capacity for developing highly complex hardware and software systems for various applications. With a strong research program across different areas such as knowledge system update, model checking and software development, and a collaborative research training environment, this project will strengthen Australia's international reputation as a leader in computing and IT research.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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Constructive Representation Theory and its Applications. The algorithms developed will make it possible to determine the different ways (representations) in which a group of symmetries may be realised as transformations of some space. Such knowledge is required in many areas including differential equations, digital signal processing, engineering ('strut-and-cable' constructions), the design of telephone networks, crystallography and quantum information processing. The high-performance tools fo ....Constructive Representation Theory and its Applications. The algorithms developed will make it possible to determine the different ways (representations) in which a group of symmetries may be realised as transformations of some space. Such knowledge is required in many areas including differential equations, digital signal processing, engineering ('strut-and-cable' constructions), the design of telephone networks, crystallography and quantum information processing. The high-performance tools for linear algebra developed will also find application in cryptography and coding theory. This work represents the latest stage in a long-term project to discover practical algorithms for elucidating the properties of complex algebraic structures - an area where Australia is a world-leader.Read moreRead less
Computational Methods for Matrix Groups and Group Representations. The symmetry of a system is captured mathematically by the notion of a group. A set of matrices closed under multiplication and the taking of inverses is an important example of a group. For instance, the symmetries of many physical systems and other objects are captured by a group of matrices over the complex numbers. This project will develop the computational tools necessary for constructing and analyzing finite matrix groups ....Computational Methods for Matrix Groups and Group Representations. The symmetry of a system is captured mathematically by the notion of a group. A set of matrices closed under multiplication and the taking of inverses is an important example of a group. For instance, the symmetries of many physical systems and other objects are captured by a group of matrices over the complex numbers. This project will develop the computational tools necessary for constructing and analyzing finite matrix groups over infinite fields such as the complex numbers. These methods will find immediate application to many areas of science and engineering and, in particular, to the theory of quantum computation.
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