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
Innovations in spherical approximation - construction, analysis and applications. The motivating problems for this project come from geophysics, including climate, weather forecasting, planetary gravitation and magnetism, and from coding theory and molecular chemistry. National benefit is expected to arise both from an improved ability to handle problems of key economic importance, and from an enhanced position in the international scientific world, through public presentation in leading journa ....Innovations in spherical approximation - construction, analysis and applications. The motivating problems for this project come from geophysics, including climate, weather forecasting, planetary gravitation and magnetism, and from coding theory and molecular chemistry. National benefit is expected to arise both from an improved ability to handle problems of key economic importance, and from an enhanced position in the international scientific world, through public presentation in leading journals and international conferences, and from direct collaboration with internationally leading scientists from USA, UK and Germany. The project will also increase the pool of trained mathematicians with expertise in areas important for applications.
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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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Australian Laureate Fellowships - Grant ID: FL210100110
Funder
Australian Research Council
Funding Amount
$3,021,288.00
Summary
New Approaches to Understand How Form and Function Shape Complex Systems. As biology and medicine transform into quantitative sciences, existing mathematical methods are often inadequate to explain the data they generate. This project aims to unlock the potential of such biomedical data through the development of new mathematical approaches that combine concepts from pure and applied mathematics, statistics and data science, and then to investigate their ability to generate mechanistic insight i ....New Approaches to Understand How Form and Function Shape Complex Systems. As biology and medicine transform into quantitative sciences, existing mathematical methods are often inadequate to explain the data they generate. This project aims to unlock the potential of such biomedical data through the development of new mathematical approaches that combine concepts from pure and applied mathematics, statistics and data science, and then to investigate their ability to generate mechanistic insight into fundamental biomedical processes. In this way, the project expects to affect a paradigm shift in mathematical biology while strengthening Australia’s reputation as a world-leader in mathematical biology. An outcome from this project could be new mathematical models that guide decision making in the clinic.Read moreRead less
Enhancing control capabilities and robustness in the engineering of quantum ensembles. This project will develop novel fundamental quantum ensemble control approaches and methodologies that are important to emerging quantum technology. The expected outcomes are new theories and powerful quantum control algorithms which will play an important role in establishing Australian industries based on quantum technology.
Advanced mathematical modelling and computation of fractional sub-diffusion problems in complex domains. Over the past few decades, researchers have observed numerous biological, physical and financial systems in which some key underlying random motion fails to conform to the classical model of diffusion. The project will extend current macroscopic models describing such anomalous sub-diffusion by correctly incorporating the confounding effects of nonlinear reactions, forcing and irregular geome ....Advanced mathematical modelling and computation of fractional sub-diffusion problems in complex domains. Over the past few decades, researchers have observed numerous biological, physical and financial systems in which some key underlying random motion fails to conform to the classical model of diffusion. The project will extend current macroscopic models describing such anomalous sub-diffusion by correctly incorporating the confounding effects of nonlinear reactions, forcing and irregular geometry. A key aspect of the project is the design of new algorithms that will fundamentally improve the accuracy and efficiency of direct numerical simulations of sub-diffusion in challenging applications. Read moreRead less
Exploratory Experimentation and Computation in the Mathematical Sciences: Theory and Practice. Seemingly disparate mathematical research projects rely on subtle experimental mathematics methods, and have unveiled weaknesses in current computer algebra systems and symbolic-numeric-graphic tools. The project attacks issues of efficiency, effectiveness, reliability, and certifiability in high-precision mathematical and scientific computation. This will be done by developing enhanced tools for advan ....Exploratory Experimentation and Computation in the Mathematical Sciences: Theory and Practice. Seemingly disparate mathematical research projects rely on subtle experimental mathematics methods, and have unveiled weaknesses in current computer algebra systems and symbolic-numeric-graphic tools. The project attacks issues of efficiency, effectiveness, reliability, and certifiability in high-precision mathematical and scientific computation. This will be done by developing enhanced tools for advanced computation of special functions driven by pursuit of challenging research problems. The focus is on tractable components that arose in prior research on effective high-precision algorithms for multiple integrals, such as arise throughout mathematical physics, number theory and elsewhere.Read moreRead less
A probabilistic and geometric understanding of transport and metastability in mathematical geophysical flows. Complicated fluid flow is at the heart of physical oceanography and atmospheric science. This project will develop new mathematical technologies to reveal hidden transport barriers around which complicated fluid flow is organised. This project will lead to more accurate circulation predictions from ocean and atmosphere models.
Discovery and tracking of coherent structures in geophysical flows. Coherent structures in geophysical flows play fundamental roles by organising fluid flow and obstructing transport. For example, ocean eddies strongly influence the transportation of heat, nutrients, phytoplankton, and fish larvae, in both the horizontal and vertical direction. Many coherent structures are very difficult to detect and track by direct measurement (for example satellite observations), and current mathematical tech ....Discovery and tracking of coherent structures in geophysical flows. Coherent structures in geophysical flows play fundamental roles by organising fluid flow and obstructing transport. For example, ocean eddies strongly influence the transportation of heat, nutrients, phytoplankton, and fish larvae, in both the horizontal and vertical direction. Many coherent structures are very difficult to detect and track by direct measurement (for example satellite observations), and current mathematical techniques cannot provide an adequate global description. This project aims to create innovative new mathematical theory and numerical methods to discover and track coherent structures over time frames of physical importance, contributing significantly to our understanding of their role in the oceans' biosphere and climate.Read moreRead less
Innovative mathematics using transfer operators to reveal hidden ordered structures in geophysical flows. Complicated fluid flow is at the heart of physical oceanography and atmospheric science. This research will develop new mathematical technologies to reveal hidden ordered structures around which complicated fluid flow is organised. This new analytical approach will lead to more accurate circulation predictions from ocean and atmosphere models.