Decomposition and Duality: New Approaches to Integer and Stochastic Integer Programming. Because of their rich modelling capabilities, integer programs are widely used in industry for decision making and planning. However their solution algorithms do not have the maturity of their cousins in convex optimisation, where the theory of strong duality is ubiquitous. Efficient methods for convex optimisation under uncertainty do not apply to the integer case, which is highly non-convex. Furthermore, i ....Decomposition and Duality: New Approaches to Integer and Stochastic Integer Programming. Because of their rich modelling capabilities, integer programs are widely used in industry for decision making and planning. However their solution algorithms do not have the maturity of their cousins in convex optimisation, where the theory of strong duality is ubiquitous. Efficient methods for convex optimisation under uncertainty do not apply to the integer case, which is highly non-convex. Furthermore, integer models usually assume the data is known with certainty, which is often not the case in the real world. This project will develop new theory and algorithms to enhance the analysis of integer models, including those that incorporating uncertainty, while also enabling the use of parallel computing paradigms. Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE160100227
Funder
Australian Research Council
Funding Amount
$355,481.00
Summary
Experimentally validated multiphase mathematical models of leg ulcers. The project is designed to develop mathematical models of the complex biological processes of leg ulcer formation and healing. The project intends to combine mathematical techniques from fluid dynamics, mathematical biology, numerical analysis and statistical inference to develop novel, multiphase, validated mathematical models that capture the complex spatiotemporal evolution of cellular and chemical species during the forma ....Experimentally validated multiphase mathematical models of leg ulcers. The project is designed to develop mathematical models of the complex biological processes of leg ulcer formation and healing. The project intends to combine mathematical techniques from fluid dynamics, mathematical biology, numerical analysis and statistical inference to develop novel, multiphase, validated mathematical models that capture the complex spatiotemporal evolution of cellular and chemical species during the formation and healing of a leg ulcer – biological processes which are currently poorly understood. The mathematical models are expected to provide new insight into the underlying biological mechanisms of leg ulcers and may ultimately improve management of chronic wounds.Read moreRead less
Can an anti-HIV gene in blood stem cells protect from immune depletion by HIV? Approximately 15,000 individuals in Australia are currently HIV infected. Gene therapy has the capacity to remove antiretroviral treatment related issues, dramatically decrease treatment costs and simplify treatment of HIV.
In this study we will model a new approach to treat HIV in which the patient's own cells are used as the therapy by incorporating an anti-HIV gene. These cells are then re-introduced into the p ....Can an anti-HIV gene in blood stem cells protect from immune depletion by HIV? Approximately 15,000 individuals in Australia are currently HIV infected. Gene therapy has the capacity to remove antiretroviral treatment related issues, dramatically decrease treatment costs and simplify treatment of HIV.
In this study we will model a new approach to treat HIV in which the patient's own cells are used as the therapy by incorporating an anti-HIV gene. These cells are then re-introduced into the patient.
The strong mathematical focus of this project, and its application to a promising approach against HIV, will place Australia at the forefront of the mathematics of gene research and contribute to the National Priority Area of Promoting and Maintaining Good Health and the Priority Goal of Preventative Healthcare.
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Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in mi ....Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in microscale tissue properties are lacking. The tools developed by this project will be used to generate new magnetic resonance image based maps to convey information on tissue microstructure changes in the human brain. Additionally, the mathematical tools developed will be transferable to other applications where diffusion and transport in heterogeneous porous media play a role.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE200100063
Funder
Australian Research Council
Funding Amount
$394,398.00
Summary
Nonmonotone Algorithms in Operator Splitting, Optimisation and Data Science. This project aims to develop the mathematical foundations for the analysis and development of optimisation algorithms used in data science. Despite their now ubiquitous use, machine learning software packages routinely rely on a number of algorithms from mathematical optimisation which are not properly understood. By moving beyond the traditional realms of Fejér monotone algorithms, this project expects to develop the m ....Nonmonotone Algorithms in Operator Splitting, Optimisation and Data Science. This project aims to develop the mathematical foundations for the analysis and development of optimisation algorithms used in data science. Despite their now ubiquitous use, machine learning software packages routinely rely on a number of algorithms from mathematical optimisation which are not properly understood. By moving beyond the traditional realms of Fejér monotone algorithms, this project expects to develop the mathematical theory required to rigorously justify the use of such algorithms and thereby ensure the integrity of the decision tools they produce. This mathematical framework is also expected to produce new algorithms for optimisation which benefit consumers of data science such as the health-care and cybersecurity sectors.Read moreRead less
Engineering evolving complex network systems through structure intervention. This project aims to create a theory and technology for engineering complex network systems (CSS) through structural intervention. Complex network systems with evolving components are ubiquitous in nature and society. The science of biological networks, the Internet and large-scale power networks demand tools to understand and influence their evolving dynamics. This project could result in a breakthrough theory in netwo ....Engineering evolving complex network systems through structure intervention. This project aims to create a theory and technology for engineering complex network systems (CSS) through structural intervention. Complex network systems with evolving components are ubiquitous in nature and society. The science of biological networks, the Internet and large-scale power networks demand tools to understand and influence their evolving dynamics. This project could result in a breakthrough theory in network science and technology to augment biological systems and power grids. Expected benefits include cost-effective augmentation of power networks injected with renewable energy sources, and advancing basic biology research.Read moreRead less
Modelling large urban transport networks using stochastic cellular automata. Urban traffic congestion is a major social, economic and environmental problem, and to overcome it we need reliable and flexible mathematical models of traffic flow. This project will introduce and study new mathematical traffic models, and use them to study innovative traffic signal systems for our arterial roads, freeways, and tram routes.
Efficient computational methods for worst-case analysis and optimal control of nonlinear dynamical systems. Natural and technological systems can exhibit extremely complicated behaviour in worst-case scenarios. This project will develop efficient mathematical and computational tools that will enable this behaviour to be understood and controlled.