'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
Discovery Early Career Researcher Award - Grant ID: DE240100006
Funder
Australian Research Council
Funding Amount
$444,847.00
Summary
Robust Derivative-Free Algorithms for Complex Optimisation Problems. Mathematical optimisation gives a systematic way for optimal decision-making. This project aims to develop new mathematical tools for complex optimisation problems where limited problem information is available. It will generate new foundational theories for alternative optimisation tools, introducing substantial new capability and rigour to the discipline. The project will create significant new mathematical optimisation techn ....Robust Derivative-Free Algorithms for Complex Optimisation Problems. Mathematical optimisation gives a systematic way for optimal decision-making. This project aims to develop new mathematical tools for complex optimisation problems where limited problem information is available. It will generate new foundational theories for alternative optimisation tools, introducing substantial new capability and rigour to the discipline. The project will create significant new mathematical optimisation techniques and create world-leading and publicly available software. These new techniques and software may ultimately be able to solve some of the most complex optimisation problems in research and industry, such as improving long-term climate predictions and designing 3D-printed medical implants.Read moreRead less
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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THE DEVELOPMENT OF MECHANISTIC MODELS FOR BUBBLY FLOWS WITH HEAT AND MASS TRANSFER. Commercially available CFD computer codes are currently widely used in many Australian industrial sectors. It is clearly recognised that the state-of-the-art models for dealing with complex bubbly flows with/without heat and mass transfer in these computer codes require further developments and improvements. This research project will address the prevalent deficiency in many of these computer codes. It is antici ....THE DEVELOPMENT OF MECHANISTIC MODELS FOR BUBBLY FLOWS WITH HEAT AND MASS TRANSFER. Commercially available CFD computer codes are currently widely used in many Australian industrial sectors. It is clearly recognised that the state-of-the-art models for dealing with complex bubbly flows with/without heat and mass transfer in these computer codes require further developments and improvements. This research project will address the prevalent deficiency in many of these computer codes. It is anticipated that through this major development of new models capable of predicting a wide range of industrial bubbly flow problems and implementation thereafter in these computer codes, industries will experience significant benefits especially reduce time and costs in their design and production.Read moreRead less
Experimental and Numerical Modelling of Gas-Liquid Flows. Multiphase flow systems are encountered in many process industries such as chemical, petroleum, mining, energy, food and pharmaceutical, which are fundamental to the Australian economy. Commercially available computer codes for simulating such systems are currently widely used in many Australian industrial sectors. This research project will address the prevalent deficiency in many of these computer codes and develop new models capable of ....Experimental and Numerical Modelling of Gas-Liquid Flows. Multiphase flow systems are encountered in many process industries such as chemical, petroleum, mining, energy, food and pharmaceutical, which are fundamental to the Australian economy. Commercially available computer codes for simulating such systems are currently widely used in many Australian industrial sectors. This research project will address the prevalent deficiency in many of these computer codes and develop new models capable of predicting a wide range of industrial bubbly flow problems. The resultant improved computer codes will provide industries with significant benefits - especially reduced times and costs in their design and production.Read moreRead less
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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Intelligent Model Checking. Real-world systems are typically so complex that software engineers require specialised CAD tools to debug and verify a design. Model checking is a formal method that is used extensively for this purpose, particularly for mission-critical systems. In this work, a new kind of verifying tool, based on model checking, is developed. This new model checker is intelligent because a heuristic search is integrated into the underlying formalism. It is not exhaustive, and is mo ....Intelligent Model Checking. Real-world systems are typically so complex that software engineers require specialised CAD tools to debug and verify a design. Model checking is a formal method that is used extensively for this purpose, particularly for mission-critical systems. In this work, a new kind of verifying tool, based on model checking, is developed. This new model checker is intelligent because a heuristic search is integrated into the underlying formalism. It is not exhaustive, and is more efficient than a traditional model checker during the design phase because it does only a minimum amount of work in its search for a fault.Read moreRead less