Learning the meso-scale organization of complex networks. This project aims to model and learn the organization of online social networks. We will combine mathematical models, inference, and domain knowledge from computational social sciences to obtain interpretable descriptions of the role groups of users play in the network. The expected outcomes are new mathematical models and computational methods that learn from data how to best decompose a complex network into building blocks and their int ....Learning the meso-scale organization of complex networks. This project aims to model and learn the organization of online social networks. We will combine mathematical models, inference, and domain knowledge from computational social sciences to obtain interpretable descriptions of the role groups of users play in the network. The expected outcomes are new mathematical models and computational methods that learn from data how to best decompose a complex network into building blocks and their interactions, linking connectivity to function. This should provide benefits to industries and policy makers interested in how information spreads in social media, including the critical questions of understanding the mechanisms contributing to political polarization and fragmentation.Read moreRead less
Creating Hybrid Exponential Asymptotics for use with Computational Data. Asymptotic analysis is a vital tool for studying small influences with critical effects. This project aims to create an innovative fully-automated asymptotic framework for studying phenomena which are invisible to classical approximation methods, using new ideas from asymptotics and numerical complex analysis. The outcome will be the first framework that can be used on data from numerical simulations or real-life measuremen ....Creating Hybrid Exponential Asymptotics for use with Computational Data. Asymptotic analysis is a vital tool for studying small influences with critical effects. This project aims to create an innovative fully-automated asymptotic framework for studying phenomena which are invisible to classical approximation methods, using new ideas from asymptotics and numerical complex analysis. The outcome will be the first framework that can be used on data from numerical simulations or real-life measurements, and which can be applied automatically without hands-on expert input. It will be used to design submerged structures and efficient vessels with minimal energy loss from surface waves. Expected benefits include making powerful methods accessible to scientists, and new paths for energy-efficient industrial design.Read moreRead less
Optimising disease surveillance to support decision-making. COVID-19 has demonstrated the critical role of epidemic data and analytics in guiding government response to pandemic threats, reducing disease and saving lives. The demand for epidemic analytics for response to threats of national significance will only grow. The goals of this project are to 1) determine the combination(s) of surveillance methods that provide the most useful data for epidemic analysis and 2) translate these findings in ....Optimising disease surveillance to support decision-making. COVID-19 has demonstrated the critical role of epidemic data and analytics in guiding government response to pandemic threats, reducing disease and saving lives. The demand for epidemic analytics for response to threats of national significance will only grow. The goals of this project are to 1) determine the combination(s) of surveillance methods that provide the most useful data for epidemic analysis and 2) translate these findings into the blueprint for a next-generation infectious disease surveillance system for Australia. We will use a simulation-evaluation approach, coupling methods from infectious disease modelling with those from information theory optimal design. Outcomes will enable more tailored and effective pandemic response.Read moreRead less
Development of a novel best approximation theory with applications . The aim of this project is to develop an innovative best approximation theory for complex fractional boundary value problems with discontinuities and with no compactness, and then apply the theory to study two classes of complex partial differential equation boundary value problems with industrial applications. The work will lead to the development of a new theory and a suite of innovative analytical and computational methods f ....Development of a novel best approximation theory with applications . The aim of this project is to develop an innovative best approximation theory for complex fractional boundary value problems with discontinuities and with no compactness, and then apply the theory to study two classes of complex partial differential equation boundary value problems with industrial applications. The work will lead to the development of a new theory and a suite of innovative analytical and computational methods for solving a wide range of nonlinear problems with singularities and non-local properties. The expected outcomes of the project will significantly advance our methods for the modelling and control of many industrial systems and processes.
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Indigenous mathematical transforms. A class of mathematical transforms, or systematic conversions between related spaces or objects, was practised by some Aboriginal and Torres Strait Islander groups. Such transforms from ground to night sky were used in long-distance route-recording and wayfinding techniques. This project aims to elucidate these transforms, and to use this knowledge to extend the mathematical framework and applications of Fourier analysis. There is significant potential for new ....Indigenous mathematical transforms. A class of mathematical transforms, or systematic conversions between related spaces or objects, was practised by some Aboriginal and Torres Strait Islander groups. Such transforms from ground to night sky were used in long-distance route-recording and wayfinding techniques. This project aims to elucidate these transforms, and to use this knowledge to extend the mathematical framework and applications of Fourier analysis. There is significant potential for new mathematics to emerge at this exciting interface of Indigenous/non-Indigenous knowledge. Expected outcomes are interdisciplinary research training for Indigenous students and new understanding of Indigenous sciences. Emerging big data technologies such as holography may benefit. Read moreRead less