Structured barrier and penalty functions in infinite dimensional optimisation and analysis. Very large scale tightly-constrained optimisation problems are ubiquitous and include water management, traffic flow, and imaging at telescopes and hospitals. Massively parallel computers can solve such problems and provide physically realisable solution only if subtle design issues are mastered. Resolving such issues is the goal of this project.
Construction of near optimal oscillatory regimes in singularly perturbed control systems via solutions of Hamilton-Jacobi-Bellman inequalities. Problems of optimal control of systems evolving in multiple time scales arise in a great variety of applications (from diet to environmental modelling). This project addresses the challenge of analytically and numerically constructing rapidly oscillating controls that would 'near optimally coordinate' the slow and fast dynamics.
Perturbations in Complex Systems and Games. This project aims to: advance the perturbation theory of dynamic and stochastic games; further develop approximations of infinite dimensional linear programs by their finite dimensional counterparts, and by finding asymptotic limits of spaces of occupational measures, by solution of successive layers of fundamental equations; explain and quantify the "exceptionality" of instances of systems that are genuinely difficult to solve; and, capitalise on the ....Perturbations in Complex Systems and Games. This project aims to: advance the perturbation theory of dynamic and stochastic games; further develop approximations of infinite dimensional linear programs by their finite dimensional counterparts, and by finding asymptotic limits of spaces of occupational measures, by solution of successive layers of fundamental equations; explain and quantify the "exceptionality" of instances of systems that are genuinely difficult to solve; and, capitalise on the outstanding performance of our Snakes-and-Ladders Heuristic (SLH) for the solution of the Hamiltonian cycle problem to identify its "fixed complexity orbits" and generalise this notion to other NP-complete problems.Read moreRead less
Risk Measures and Management in Finance and Actuarial Science Under Regime-Switching Models. New models for assessing and managing risk of financial products will place Australia at the forefront of risk management. The work will also sustain the competitive edge of Australia as one of the major financial centres in the Asia-Pacific region through enhancing both the theory and practice of financial risk management. The project outcome will also benefit to the country in other areas of risk, for ....Risk Measures and Management in Finance and Actuarial Science Under Regime-Switching Models. New models for assessing and managing risk of financial products will place Australia at the forefront of risk management. The work will also sustain the competitive edge of Australia as one of the major financial centres in the Asia-Pacific region through enhancing both the theory and practice of financial risk management. The project outcome will also benefit to the country in other areas of risk, for example, environment risk, climate change, and energy and security problems.Read moreRead less
Two-price quantitative finance. This project aims to establish a novel field, namely two-price quantitative finance, and explore its applications. The new field will integrate two major schools for modelling and explain the presence of two prices, the buying and selling prices, widely observed in the real-world markets, and the equilibrium approach from the fundamental law of one price. The outcomes would deepen our understanding of the fundamental relationship among liquidity, prices, risk and ....Two-price quantitative finance. This project aims to establish a novel field, namely two-price quantitative finance, and explore its applications. The new field will integrate two major schools for modelling and explain the presence of two prices, the buying and selling prices, widely observed in the real-world markets, and the equilibrium approach from the fundamental law of one price. The outcomes would deepen our understanding of the fundamental relationship among liquidity, prices, risk and the economy. This project expects to bring about long-term impact on quantitative finance and related applications through providing a deep understanding of, and a new perspective for, the design, risk and fairness of the finance, property and insurance markets.Read moreRead less
G-expectation and its applications to nonlinear risk management. This project will develop novel theories and methods for nonlinear risk management based on nonlinear expectations and Backward Stochastic Differential Equations. The expected outcomes of the project will place Australia in the forefront and the leading position of these fields.
Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using pow ....Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using powerful geometric tools from conformal geometry, the project will extend this to less symmetric spaces. The knowledge generated from this project will extend to more general geometric contexts providing a concrete setting for the study of the associated natural equations in curved spaces.Read moreRead less
Equipping Australian teachers today to face AI tomorrow. Applications of Artificial Intelligence (AI) are set to transform society, including how people work and learn. Yet there is very little research about what Australian teachers need to know in order to prepare students to thrive in an AI-rich society and workforce. This study aims to construct a foundational understanding for teaching with and about AI. It will also show how to develop effective networks to empower teachers as active chang ....Equipping Australian teachers today to face AI tomorrow. Applications of Artificial Intelligence (AI) are set to transform society, including how people work and learn. Yet there is very little research about what Australian teachers need to know in order to prepare students to thrive in an AI-rich society and workforce. This study aims to construct a foundational understanding for teaching with and about AI. It will also show how to develop effective networks to empower teachers as active change agents. The expected outcomes will equip teachers with the knowledge and resources to lead the development of Australia’s future AI capability, including through enhanced classroom practices and more creative teacher networks.Read moreRead less
Special Research Initiatives - Grant ID: SR0354693
Funder
Australian Research Council
Funding Amount
$10,000.00
Summary
Australian e-Research Grid. The e-Research Grid program will research and implement core Grid technologies on APAC and partner's deployed HPC resources, to underpin a broad range of Australian research. The computer science CIs will form collaborative links with international programs, adapting developments to local circumstances. The applications-domain CIs will leverage those into their scientific simulations and databases, using grid integrative techniques and portals. Many CIs participate in ....Australian e-Research Grid. The e-Research Grid program will research and implement core Grid technologies on APAC and partner's deployed HPC resources, to underpin a broad range of Australian research. The computer science CIs will form collaborative links with international programs, adapting developments to local circumstances. The applications-domain CIs will leverage those into their scientific simulations and databases, using grid integrative techniques and portals. Many CIs participate in other RNs linking to their motivating applications, enhancing prospects for research and integration. They participate in the APAC Grid program, leveraging 75 HPC staff nationally. A key aim is interoperability with "real-world Grids": eg e-learning & e-health programs.Read moreRead less
Understanding and working with anger in male Indigenous people in prison settings. Anger has links to many important outcomes in the prison environment, including violent behaviour, institutional conflict and self-harm. The nature and consequences of anger have rarely been investigated for imprisoned offenders and little is known about anger in male Indigenous Australians in prison, despite evidence that anger levels in this group are particularly high. This research will explore constitutive, ....Understanding and working with anger in male Indigenous people in prison settings. Anger has links to many important outcomes in the prison environment, including violent behaviour, institutional conflict and self-harm. The nature and consequences of anger have rarely been investigated for imprisoned offenders and little is known about anger in male Indigenous Australians in prison, despite evidence that anger levels in this group are particularly high. This research will explore constitutive, regulatory, procedural and other aspects of anger with male Indigenous prisoners, using both qualitative and quantitative methodologies, leading to the development of an intervention that will improve both the wellbeing and adjustment of Indigenous men in prison and rehabilitation outcomes.Read moreRead less