Beyond Planarity: Algorithms for Visualisation of Sparse Non-Planar Graphs. This project aims to develop new efficient algorithms to enable analysts to visually understand complex data and detect anomalies or patterns. It aims to develop visualisation algorithms for sparse non-planar graphs arising from real-world networks. Specifically, the project plans to investigate structural properties of sparse non-planar topological graphs such as k-planar graphs, k-skew graphs, and k-quasi-planar graphs ....Beyond Planarity: Algorithms for Visualisation of Sparse Non-Planar Graphs. This project aims to develop new efficient algorithms to enable analysts to visually understand complex data and detect anomalies or patterns. It aims to develop visualisation algorithms for sparse non-planar graphs arising from real-world networks. Specifically, the project plans to investigate structural properties of sparse non-planar topological graphs such as k-planar graphs, k-skew graphs, and k-quasi-planar graphs, and design efficient testing algorithms, embedding algorithms, and drawing algorithms. These algorithms will be evaluated with real-world social networks and biological networks. New insights into the mathematical interplay between combinatorial and geometric structures would provide a theoretical foundation for a new generation of complex network visualisation methods with potential applications in social networks, systems biology, health informatics, finance and security.Read moreRead less
Wave-ice models of Antarctic sea ice. This project aims to design and execute autonomous observations above (unmanned aerial vehicles), below (autonomous underwater vehicles) and within (wave-ice interaction buoys) sea ice on international Antarctic research voyages. The project intends to advance the parameterisation of wave-ice interaction, critical to the seasonal advance and retreat of Antarctic sea ice, in climate models that do not reproduce the observed trends in regional Antarctic sea ic ....Wave-ice models of Antarctic sea ice. This project aims to design and execute autonomous observations above (unmanned aerial vehicles), below (autonomous underwater vehicles) and within (wave-ice interaction buoys) sea ice on international Antarctic research voyages. The project intends to advance the parameterisation of wave-ice interaction, critical to the seasonal advance and retreat of Antarctic sea ice, in climate models that do not reproduce the observed trends in regional Antarctic sea ice extent. The project expects to improve prediction of sea ice’s responses and feedbacks to changes in ocean and atmospheric forcing around the Southern Ocean. This work should place Australia at the forefront of polar climate research. Greater accuracy in climate projections will help to optimise the balance between human populations, economic growth and environmental protection in an uncertain future.Read moreRead less
Semiparametric Regression for Streaming Data. Semiparametric regression converts large and complex data-sets into interpretable summaries from which sound decisions can be made. This project tackles semiparametric regression analysis of streaming data - where the data are so voluminous that they may not be storable in standard computer memory and therefore need to be processed rapidly on arrival and then discarded. Effective solutions necessitate a rethinking of semi-parametric regression and ne ....Semiparametric Regression for Streaming Data. Semiparametric regression converts large and complex data-sets into interpretable summaries from which sound decisions can be made. This project tackles semiparametric regression analysis of streaming data - where the data are so voluminous that they may not be storable in standard computer memory and therefore need to be processed rapidly on arrival and then discarded. Effective solutions necessitate a rethinking of semi-parametric regression and new approaches will be developed. The project will also develop novel theory and methodology for robotics applications. It will allow analysis of streaming and massive data sets that would not be possible using currently available methods, opening up new applications.Read moreRead less
Fast approximate inference methods: new algorithms, applications and theory. This project aims to develop new algorithms and theory for fast approximate inference and lay down infrastructure to aid future extensions. Fast approximate inference methods are a principled and extensible means of fitting large and complex statistical models to big data sets. They come into their own in applications where speed is paramount and traditional approaches are not feasible. The project aims to lead to prac ....Fast approximate inference methods: new algorithms, applications and theory. This project aims to develop new algorithms and theory for fast approximate inference and lay down infrastructure to aid future extensions. Fast approximate inference methods are a principled and extensible means of fitting large and complex statistical models to big data sets. They come into their own in applications where speed is paramount and traditional approaches are not feasible. The project aims to lead to practical outcomes from better business decision-making for insurance data warehouses, to improved medical imaging technology.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
Control and Optimization of Distributed Multiagent Formations. The project aims to develop a conceptual framework and algorithms for handling multi-vehicle formation control. Formations of unmanned airborne vehicles are currently used by defence forces and swarms of micro-vehicles are beginning to find increasing use in defence and for civilian emergency response, largely for surveillance purposes. Vehicles must cooperate to achieve a global formation objective, while respecting constraints on s ....Control and Optimization of Distributed Multiagent Formations. The project aims to develop a conceptual framework and algorithms for handling multi-vehicle formation control. Formations of unmanned airborne vehicles are currently used by defence forces and swarms of micro-vehicles are beginning to find increasing use in defence and for civilian emergency response, largely for surveillance purposes. Vehicles must cooperate to achieve a global formation objective, while respecting constraints on sensors, energy, and general mechanical limitations. The project aims to resolve the challenges of deciding what a single vehicle should observe, what and to where it should communicate, and how it should move in relation to what it sees. The conceptual framework developed may also be relevant in guiding future defence acquisitions and civilian applications.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE130100819
Funder
Australian Research Council
Funding Amount
$281,600.00
Summary
Measuring the improbable: optimal Monte Carlo methods for rare event simulation of maxima of dependent random variables. Some events occurring with low frequency can have dramatic consequences: natural catastrophes, economic crises, system malfunctions. Estimating their probabilities is a very difficult problem. This project will develop new simulation methods capable of delivering the most precise and efficient estimators for the probabilities of such events.
New mathematics for multi-extremal optimization and diffusion tensor imaging. This project aims to establish numerically certifiable mathematical theory and methods for semi-algebraic optimisation problems. Numerically certifiable optimisation principles and techniques are vital for the practical use of optimisation technologies because they can be readily implemented by common computer models and algorithms. Yet no such methodologies exist for multi-extremal, semi-algebraic optimisation problem ....New mathematics for multi-extremal optimization and diffusion tensor imaging. This project aims to establish numerically certifiable mathematical theory and methods for semi-algebraic optimisation problems. Numerically certifiable optimisation principles and techniques are vital for the practical use of optimisation technologies because they can be readily implemented by common computer models and algorithms. Yet no such methodologies exist for multi-extremal, semi-algebraic optimisation problems which are common in modern science and medicine. The expected outcomes of this project include enhanced optimisation methods for diffusion tensor imaging, an emerging technology in brain sciences.Read moreRead less
Innovations in sparse optimisation: big data nonsmooth optimisation. This project aims to produce innovative optimisation methods capable of solving a wide range of practical problems that are currently too complex to be solved. Optimisation involving huge data sets is ubiquitous. Sparse optimisation has emerged as a challenging frontier of modern optimisation because it effectively computes an optimal solution with desired low complexity structure so that a resulting solution can be efficiently ....Innovations in sparse optimisation: big data nonsmooth optimisation. This project aims to produce innovative optimisation methods capable of solving a wide range of practical problems that are currently too complex to be solved. Optimisation involving huge data sets is ubiquitous. Sparse optimisation has emerged as a challenging frontier of modern optimisation because it effectively computes an optimal solution with desired low complexity structure so that a resulting solution can be efficiently stored, implemented and utilised, and is robust to the data inexactness. This project aims at developing innovative mathematical techniques and efficient numerical schemes for solving sparse optimisation problems. The intended outcomes will have significant impact on many areas of science, medicine and engineering, where sparse optimisation is used, including cancer radiotherapy optimal planning.Read moreRead less
Flow structures and transport: predictability and control. Moving flow structures (the boundary of an eddy, the flow interface between two fluids) are crucial in fluid mixing and in the transport of heat, pollutants and nutrients. This project will analyse their roles in improving predictions of spreading extents and rates for geophysical-scale problems, and in controlling transport at the micro-scale. Inaccuracies in currently available numerical diagnostics for transport prediction will be com ....Flow structures and transport: predictability and control. Moving flow structures (the boundary of an eddy, the flow interface between two fluids) are crucial in fluid mixing and in the transport of heat, pollutants and nutrients. This project will analyse their roles in improving predictions of spreading extents and rates for geophysical-scale problems, and in controlling transport at the micro-scale. Inaccuracies in currently available numerical diagnostics for transport prediction will be comprehensively evaluated via comparison with recent exact models. Analytical methods for quantifying transport under unsteady flow protocols will be developed, and used to answer questions on controlling transport in microfluidic applications in conjunction with experimentalists.Read moreRead less