Discovery Early Career Researcher Award - Grant ID: DE130101191
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Formation of the osteocyte network in bone matrix. The formation of new bone, which occurs throughout life for bone renewal and acutely after fractures, entraps a network of cells that can detect micro-damage and direct repair mechanisms. Mathematical and computational methods will be used to understand how this network can lead to a self-detecting and self-repairing biomaterial.
Individualisation for 3D Audio. The project aim is to allow the general listener to enjoy high-fidelity 3-D sound over headphones. Such 3-D audio is of paramount importance when inter-personal communication requires situational awareness, (eg search and rescue, fire-fighting, and air traffic control). To achieve this, the project aims to address one of the toughest problems in audio signal processing: deriving high-fidelity 3-D audio headphone filters from photos and/or 3D scans of ears. The pro ....Individualisation for 3D Audio. The project aim is to allow the general listener to enjoy high-fidelity 3-D sound over headphones. Such 3-D audio is of paramount importance when inter-personal communication requires situational awareness, (eg search and rescue, fire-fighting, and air traffic control). To achieve this, the project aims to address one of the toughest problems in audio signal processing: deriving high-fidelity 3-D audio headphone filters from photos and/or 3D scans of ears. The project plans to address fundamental research questions in statistical shape and data analysis and to perceptually evaluate the 3-D audio methods developed.Read moreRead less
A new approach to compressed sensing. Compressed sensing is an exciting new paradigm promising vastly improved signal sampling and reconstruction in a wide variety of applications including digital cameras, mobile phones and MRI machines. This project will explore a newly discovered approach to compressed sensing which uses mathematical arrays known as hash families.
Explicit methods in number theory: Computation, theory and application. This project aims to use explicit estimates to unify three problems in number theory: primitive roots, Diophantine quintuples, and linear independence of zeroes of the Riemann zeta-function. It will use computational and analytic number theory to reduce the quintuples problem to a soluble level. Pursuing relations between the zeta zeroes will overhaul many current results. This project will apply its findings about primitive ....Explicit methods in number theory: Computation, theory and application. This project aims to use explicit estimates to unify three problems in number theory: primitive roots, Diophantine quintuples, and linear independence of zeroes of the Riemann zeta-function. It will use computational and analytic number theory to reduce the quintuples problem to a soluble level. Pursuing relations between the zeta zeroes will overhaul many current results. This project will apply its findings about primitive roots to signal processing, cryptography and cybersecurity.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE120100040
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Partitioning and ordering Steiner triple systems. Steiner triple systems are fundamental mathematical objects with many real-world applications. This project will develop deep new insights into these objects, resulting in systems allowing many users to simultaneously use a communication channel, and in schemes for preventing the loss of computer data due to hard disk failures.
System identification of microstructure in the brain using magnetic resonance. Magnetic Resonance Imaging technologies will be exploited to probe the microstructure of the brain, using powerful Bayesian optimisation techniques and innovative uses of magnetic resonance. The project will in particular develop non-invasive imaging methods to quantify iron content in the brain, important for research on dementia and Alzheimer's disease.
Discovery Early Career Researcher Award - Grant ID: DE210101056
Funder
Australian Research Council
Funding Amount
$395,775.00
Summary
Realising the potential of hyperbolic programming. This project aims to develop and analyse new mathematical and algorithmic methods for polynomial optimisation and decision problems. In doing so it expects to generate knowledge and tools in mathematical optimisation that build on recent developments in the theory of hyperbolic polynomials. Expected outcomes include more scalable and/or reliable methods for polynomial optimisation and safety verification of dynamical systems, and theory explain ....Realising the potential of hyperbolic programming. This project aims to develop and analyse new mathematical and algorithmic methods for polynomial optimisation and decision problems. In doing so it expects to generate knowledge and tools in mathematical optimisation that build on recent developments in the theory of hyperbolic polynomials. Expected outcomes include more scalable and/or reliable methods for polynomial optimisation and safety verification of dynamical systems, and theory explaining the power and limitations of these methods when compared with existing approaches. Possible benefits include safer and more reliable complex engineered systems, such as the power grid or interacting autonomous vehicles, verified by methods built on those developed in the project.Read moreRead less
Prediction of inertial particle focusing in curved microfluidic ducts. This project aims to develop mathematical models to predict migration of particles suspended in flow through curved microfluidic ducts and their focusing by size to different regions in the cross-section of the duct. New knowledge in mathematics and engineering will be generated through models that capture the two-way force balance between fluid and particles and by a novel use of asymptotics for computational efficiency. Exp ....Prediction of inertial particle focusing in curved microfluidic ducts. This project aims to develop mathematical models to predict migration of particles suspended in flow through curved microfluidic ducts and their focusing by size to different regions in the cross-section of the duct. New knowledge in mathematics and engineering will be generated through models that capture the two-way force balance between fluid and particles and by a novel use of asymptotics for computational efficiency. Expected outcomes are understanding of the physics that drives particle migration and the parameters that may be used to control particle focusing. This will benefit design and operation of microfluidic devices for particle sorting as required for "liquid biopsy", the isolation of cancer cells in a routine blood sample.Read moreRead less
A New Approach to Sampled-Data Control Design for Nonlinear Systems. This project aims to exploit new sampling and sampled-data modelling insights to bridge the continuous/sampled-data gap in the control of nonlinear systems. The goal is to investigate the impact of these insights on the control design problem and provide a new class of digital control laws for continuous time non-linear systems.
Robust control of power electronics and drives: a synthesis of traditional and model predictive control approaches. This project aims to generate high-performance strategies for the control of power converters. Through the combination of traditional and modern approaches, the project will develop methods which are more reliable and give better energy efficiency than current state of the art techniques.