Massively parallel algorithms for Bayesian inference and decision making. This project uses the graphical processing units of desktop computers, originally developed for games and video, to enhance substantially the quantitative tools used on a daily basis by economists. It will develop procedures and software to enhance the reliability of economic predictions and policy.
Pooling econometric models for prediction and decision making. The project develops methods for combining econometric models with the goal of improving prediction. It applies these methods to macroeconomic models used to improve monetary policy and to asset return models used to improve financial risk management.
Material boundaries in ultrasonics: New methods and in vitro studies in biomedical phantoms. Ultrasound is an indispensable part of healthcare worldwide. The next wave of applications will see ultrasound pulses used to closely probe suspected disease sites and to directly manipulate bioactive agents. For safe and effective use of such techniques it is essential to know the ultrasound field at the disease site. This project will develop simulation methods to achieve the fast, accurate and case-sp ....Material boundaries in ultrasonics: New methods and in vitro studies in biomedical phantoms. Ultrasound is an indispensable part of healthcare worldwide. The next wave of applications will see ultrasound pulses used to closely probe suspected disease sites and to directly manipulate bioactive agents. For safe and effective use of such techniques it is essential to know the ultrasound field at the disease site. This project will develop simulation methods to achieve the fast, accurate and case-specific results required. Community healthcare will benefit, through better diagnostic capabilities and customized treatment. Australia is well placed to profit further from this research, in view of the growing worldwide demand for more sophisticated, knowledge-based techniques in medicine.Read moreRead less
The effect of vessel wall structures on ultrasonic flow velocity measurements. The flow velocity within a nearly cylindrical vessel is often measured using an external ultrasound transducer via the Doppler principle. Thick vessel walls may present acoustically mismatched structures. This project aims to determine how such walls redistribute the energy in an interrogating ultrasound beam, and how this in turn affects the measurement of flow velocities. This is a fundamental issue, especially imp ....The effect of vessel wall structures on ultrasonic flow velocity measurements. The flow velocity within a nearly cylindrical vessel is often measured using an external ultrasound transducer via the Doppler principle. Thick vessel walls may present acoustically mismatched structures. This project aims to determine how such walls redistribute the energy in an interrogating ultrasound beam, and how this in turn affects the measurement of flow velocities. This is a fundamental issue, especially important in vascular disease where blood flow and blood vessels are affected by wall irregularities and lesions. The new knowledge generated by this project will have practical importance and, by identifying achievable outcomes, potentially major cost savings, in medical ultrasound.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
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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New regularisation techniques in electromagnetic diffraction from cavities and related complex scatterers. Modern technology, such as radar and other imaging devices, exploits the information carried by electromagnetic waves. New technology depends centrally upon advances in the mathematics of waves to give precise, reliable and effective means of predicting how objects capture and re-radiate wave energy in the scattering environment. This project aims to develop a new mathematical approach to w ....New regularisation techniques in electromagnetic diffraction from cavities and related complex scatterers. Modern technology, such as radar and other imaging devices, exploits the information carried by electromagnetic waves. New technology depends centrally upon advances in the mathematics of waves to give precise, reliable and effective means of predicting how objects capture and re-radiate wave energy in the scattering environment. This project aims to develop a new mathematical approach to wave scattering by objects with complex scattering mechanisms, as typified by cavity structures. This new formulation is obtained by a process of analytical regularisation of the equations describing the scattering process. It generates algorithms more reliable and computationally accurate than current codes.
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RichProlog, a System for Deducing, Inducing and Learning in the Declarative Programming Paradigm. The aim of the project is to contribute to bridge the gap between learning and logic, theoretically and practically. Our purpose is to extend considerably the scope of the declarative programming paradigm, and build a system that can be used to solve learning or discovery problems as encountered in Artificial Intelligence. The system will enable rapid prototyping when applied to problems involving d ....RichProlog, a System for Deducing, Inducing and Learning in the Declarative Programming Paradigm. The aim of the project is to contribute to bridge the gap between learning and logic, theoretically and practically. Our purpose is to extend considerably the scope of the declarative programming paradigm, and build a system that can be used to solve learning or discovery problems as encountered in Artificial Intelligence. The system will enable rapid prototyping when applied to problems involving deduction, induction, and nonmonotonic reasoning. We intend the system to become a standard tool for tackling a broad range of applications, and the underlying theory to provide new insights on the logical foundations of Artificial Intelligence.
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