Liquidity in financial markets. This project aims to develop a theory which models the effect of liquidity on option prices under different market conditions. Economic or financial crises are inevitable and affect economics. During or after a major financial crisis, market liquidity usually becomes risky and needs to be studied. Through both empirical and theoretical explorations, this project will quantify and measure liquidity risk and its effect on the options markets. It will develop a frame ....Liquidity in financial markets. This project aims to develop a theory which models the effect of liquidity on option prices under different market conditions. Economic or financial crises are inevitable and affect economics. During or after a major financial crisis, market liquidity usually becomes risky and needs to be studied. Through both empirical and theoretical explorations, this project will quantify and measure liquidity risk and its effect on the options markets. It will develop a framework to help market regulators manage illiquidity, enhance the efficiency of option trading in illiquid markets and help in the detection of market manipulation.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.
Extending the scope of modular analysis for the validation of large systems. The increasing complexity of computer systems has severe implications for verification and validation, especially for critical systems (e.g. medical supervision, avionics mission systems). The standard approach is to build a formal model of the system and automatically analyse its behaviour. Such models can be captured in a modular, high-level description, but the number of states is usually so large as to preclude an ....Extending the scope of modular analysis for the validation of large systems. The increasing complexity of computer systems has severe implications for verification and validation, especially for critical systems (e.g. medical supervision, avionics mission systems). The standard approach is to build a formal model of the system and automatically analyse its behaviour. Such models can be captured in a modular, high-level description, but the number of states is usually so large as to preclude analysis. The modular analysis proposed in this project matches the analysis technique to the structure of the model. Preliminary results are promising and motivate the extension of the technique to a larger class of modular descriptions.Read moreRead less
Monopoles, instantons and metrics. This Project is pure basic research in the general area of differential geometry or the study of manifolds. Manifolds are higher dimensional analogues of surfaces such as the surface of the sphere or the surface of a doughnut. This Project studies monopoles and instantons which are solutions of partial differential equations arising in physics. These solutions and the so-called moduli spaces of all solutions have been used in the last two decades by the worlds ....Monopoles, instantons and metrics. This Project is pure basic research in the general area of differential geometry or the study of manifolds. Manifolds are higher dimensional analogues of surfaces such as the surface of the sphere or the surface of a doughnut. This Project studies monopoles and instantons which are solutions of partial differential equations arising in physics. These solutions and the so-called moduli spaces of all solutions have been used in the last two decades by the worlds leading mathematicians to revolutionize the study of three and four dimensional manifolds.Read moreRead less
Characterizing and classifying ovoids, flocks and generalized quadrangles. This project lies within the framework of the classification and characterization of fundamental structures in finite geometry. This research area is the site of much international activity, in which the proposed research team plays a central role. The aim of the project is to pursue twin goals: the classification of ovoids in three dimensional projective space, a famous long-standing problem; and the classification of ce ....Characterizing and classifying ovoids, flocks and generalized quadrangles. This project lies within the framework of the classification and characterization of fundamental structures in finite geometry. This research area is the site of much international activity, in which the proposed research team plays a central role. The aim of the project is to pursue twin goals: the classification of ovoids in three dimensional projective space, a famous long-standing problem; and the classification of certain generalized quadrangles. Our approach is novel as it utilises recently discovered links between these areas. The expected outcomes are significant progress towards these goals, as well as the development of new techniques in finite geometry.Read moreRead less
Communication and information storage mechanisms in complex dynamical brain networks. Recordings of electrical activity in the brain often cycle repetitively. The aim of this research is to explain how these brain rhythms assist the brain to coordinate simultaneous activity in several regions. Australian socioeconomic benefits include: (i) contributions to the knowledge base of theoretical neuroscience, enhancing Australia's reputation for cutting-edge research; (ii) strengthening of internation ....Communication and information storage mechanisms in complex dynamical brain networks. Recordings of electrical activity in the brain often cycle repetitively. The aim of this research is to explain how these brain rhythms assist the brain to coordinate simultaneous activity in several regions. Australian socioeconomic benefits include: (i) contributions to the knowledge base of theoretical neuroscience, enhancing Australia's reputation for cutting-edge research; (ii) strengthening of international collaborations with Europe and Japan; (iii) outcomes will ultimately impact on improved medical bionics and future interfaces between brain activity and machines or computers; and (iv) commercialization and technology transfer opportunities, via the transfer of results to biologically inspired engineering.Read moreRead less
Aggregating Generalised Stochastic Petri Nets for improved Performance Analysis. Australia's economy is very dependent on the operation of complex man-made systems. Important examples are telecommunication networks and services (e.g. the Internet), manufacturing plants, organisational processes, military logistics and transport systems (e.g. air traffic control). The performance of these systems is critical to their success. Thus being able to predict performance before systems are implemented i ....Aggregating Generalised Stochastic Petri Nets for improved Performance Analysis. Australia's economy is very dependent on the operation of complex man-made systems. Important examples are telecommunication networks and services (e.g. the Internet), manufacturing plants, organisational processes, military logistics and transport systems (e.g. air traffic control). The performance of these systems is critical to their success. Thus being able to predict performance before systems are implemented is very important in their design. This project will develop leading-edge performance analysis techniques and tools for an important class of practical systems. There is potential to commercialise the resulting tools and methodology and to transfer the expertise to industry.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE130100031
Funder
Australian Research Council
Funding Amount
$333,684.00
Summary
Mathematical modelling of the complex mechanics of biological materials and their role in tissue function and development. The mechanics of biological materials is complicated because they consist of many components such as fibres, proteins and polymers. We aim to use mathematical tools to understand how these components interact in tissues such as the spinal disc which will aid the development of new treatments to reverse the effects of injury, disease or aging.
Advanced Sweep-Line State Space Reduction Methods for Verification of Concurrent and Distributed Systems. The rigorous design and analysis of distributed systems, such as the Internet and its applications, is known to be a difficult problem. This project will develop new techniques for reducing the memory and time required for computer-aided verification of concurrent and distributed systems. The technique will be combined with other reduction techniques to increase their range of applicability. ....Advanced Sweep-Line State Space Reduction Methods for Verification of Concurrent and Distributed Systems. The rigorous design and analysis of distributed systems, such as the Internet and its applications, is known to be a difficult problem. This project will develop new techniques for reducing the memory and time required for computer-aided verification of concurrent and distributed systems. The technique will be combined with other reduction techniques to increase their range of applicability. The reduction techniques will be implemented and evaluated using important transaction protocols for electronic commerce and internet enabled wireless communications. The technique will also be applied to so called 'object-oriented' modelling languages.Read moreRead less
Optimal electromaterial structures for energy applications. This project aims to develop new mathematical and modelling approaches to determine optimal configurations and parameters for material structures created from three-dimensional printing of combined metals and electromaterials. Electromaterials are needed for sustainable energy, but solving coupled-systems of highly nonlinear governing equations is needed for optimal control of spatial arrangement and composition in nano and micro-struct ....Optimal electromaterial structures for energy applications. This project aims to develop new mathematical and modelling approaches to determine optimal configurations and parameters for material structures created from three-dimensional printing of combined metals and electromaterials. Electromaterials are needed for sustainable energy, but solving coupled-systems of highly nonlinear governing equations is needed for optimal control of spatial arrangement and composition in nano and micro-structural domains. Dealing with this mathematical complexity is critical to developing high efficiency energy generation and gas storage systems. This is expected to enhance transport mechanisms within electrochemical devices and create opportunities for industry to use electrofunctional materials.Read moreRead less