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
A dynamical systems theory approach to machine learning. Forecasting the future state of a high-dimensional complex multi-scale system is a challenge we face in areas ranging from climate science to epidemiology. Even when basic physical mechanisms have been identified, the actual evolution equations are often unknown. This project will develop a computationally cheap machine learning framework for forecasting. The proposed mathematical framework provides a forecast together with a quantificati ....A dynamical systems theory approach to machine learning. Forecasting the future state of a high-dimensional complex multi-scale system is a challenge we face in areas ranging from climate science to epidemiology. Even when basic physical mechanisms have been identified, the actual evolution equations are often unknown. This project will develop a computationally cheap machine learning framework for forecasting. The proposed mathematical framework provides a forecast together with a quantification of its uncertainty. We will develop sophisticated mathematical theory underpinning the novel methodology, as well as applying it to the perennial problem of subgrid-scale parametrisation of tropical convection, a missing key element in current climate models.Read moreRead less
Approximation theory of structured neural networks . Mathematical theory for deep learning has been desired due to the power applications of deep neural networks to deal with big data in various practical domains. The main difficulty lies in the structures and architectures imposed to networks designed for specific learning tasks. Neither the classical approximation theory nor the recent one for depths of ReLU neural networks can be applied due to the structures imposed for processing large dime ....Approximation theory of structured neural networks . Mathematical theory for deep learning has been desired due to the power applications of deep neural networks to deal with big data in various practical domains. The main difficulty lies in the structures and architectures imposed to networks designed for specific learning tasks. Neither the classical approximation theory nor the recent one for depths of ReLU neural networks can be applied due to the structures imposed for processing large dimensional data such as natural images of tens of thousands of dimensions. This project aims at an approximation theory for structured neural networks. We plan to establish mathematical theories for deconvolution with deep convolutional neural networks, operator learning, and spectral graph networks. Read moreRead less
A Stress-relax Model for Stellar Flares. This project aims to improve our ability to predict solar and stellar flares by developing a theoretical model for the build-up and release of magnetic stress in stellar atmospheres. Solar flares are the most energetic events in the solar system, and together with associated coronal mass ejections can create hazardous conditions in our local space environment. Stellar flares are thousands of times more energetic and produce dangerous space weather for exo ....A Stress-relax Model for Stellar Flares. This project aims to improve our ability to predict solar and stellar flares by developing a theoretical model for the build-up and release of magnetic stress in stellar atmospheres. Solar flares are the most energetic events in the solar system, and together with associated coronal mass ejections can create hazardous conditions in our local space environment. Stellar flares are thousands of times more energetic and produce dangerous space weather for exoplanets orbiting flare stars. Expected outcomes include insight into the flare mechanism, and new approaches to flare prediction. The major potential benefit is improved solar and stellar space weather forecasting to protect human safety and infrastructure.Read moreRead less
New mathematics to improve understanding of anomalously diffusing reactions. Standard mathematical models for particles that diffuse and react are based on assumptions that improving technologies have revealed do not always hold. This project aims to create a mathematical framework that generalises existing approaches, taking into account observations of complicated transport behaviour at many scales, and including the impact of this anomalous transport on reactions. The development of the fram ....New mathematics to improve understanding of anomalously diffusing reactions. Standard mathematical models for particles that diffuse and react are based on assumptions that improving technologies have revealed do not always hold. This project aims to create a mathematical framework that generalises existing approaches, taking into account observations of complicated transport behaviour at many scales, and including the impact of this anomalous transport on reactions. The development of the framework will involve innovative approaches utilising mathematical techniques, including dynamical systems, fractional calculus, and stochastic processes. This project aims to deliver new mathematical models that can be adopted in applications across different discipline areas, and especially in biological systems. Read moreRead less
A complex systems approach to preventing colony failure in honey bees. This project aims to use complex systems science to detect and prevent colony collapse in honey bees while advancing knowledge of tipping points in complex social systems. Understanding the mathematics of colony collapse can help us develop strategies for safeguarding managed bee populations and the valuable pollination services they provide. Expected outcomes include methods for the early detection of stress in colonies, met ....A complex systems approach to preventing colony failure in honey bees. This project aims to use complex systems science to detect and prevent colony collapse in honey bees while advancing knowledge of tipping points in complex social systems. Understanding the mathematics of colony collapse can help us develop strategies for safeguarding managed bee populations and the valuable pollination services they provide. Expected outcomes include methods for the early detection of stress in colonies, methods for reversing declines, and new mathematical techniques for studying tipping points in complex social systems. This will provide significant benefits for Australian agriculture, much of which depends on bee pollination, while building scientific capacity in complex systems science.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL170100032
Funder
Australian Research Council
Funding Amount
$2,837,520.00
Summary
Zero-dimensional symmetry and its ramifications. This project aims to investigate algebraic objects known as 0-dimensional groups, which are a mathematical tool for analysing the symmetry of infinite networks. Group theory has been used to classify possible types of symmetry in various contexts for nearly two centuries now, and 0-dimensional groups are the current frontier of knowledge. The expected outcome of the project is that the understanding of the abstract groups will be substantially adv ....Zero-dimensional symmetry and its ramifications. This project aims to investigate algebraic objects known as 0-dimensional groups, which are a mathematical tool for analysing the symmetry of infinite networks. Group theory has been used to classify possible types of symmetry in various contexts for nearly two centuries now, and 0-dimensional groups are the current frontier of knowledge. The expected outcome of the project is that the understanding of the abstract groups will be substantially advanced, and that this understanding will shed light on structures possessing 0-dimensional symmetry. In addition to being cultural achievements in their own right, advances in group theory such as this also often have significant translational benefits. This will provide benefits such as the creation of tools relevant to information science and researchers trained in the use of these tools.Read moreRead less
ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellu ....ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellular level and enable new ways of combining diverse and heterogenous data. This will allow us to understand the mechanisms underlying cellular behaviour, and to apply rational design engineering methods in order to control the dynamics of biological systems. Read moreRead less
Airborne ultrafine particles in Australian cities. There is an acute deficiency of knowledge in Australia on urban airborne ultrafine particles, originating from transport and other anthropogenic sources, which pose significant health and environmental risks. The aim of this project is to address this deficiency by an extensive multi-city, cross-disciplinary study using state of the art instrumentation and data analytic techniques. The outcome will be an in depth, quantitative insight into the c ....Airborne ultrafine particles in Australian cities. There is an acute deficiency of knowledge in Australia on urban airborne ultrafine particles, originating from transport and other anthropogenic sources, which pose significant health and environmental risks. The aim of this project is to address this deficiency by an extensive multi-city, cross-disciplinary study using state of the art instrumentation and data analytic techniques. The outcome will be an in depth, quantitative insight into the characteristics of the particles, their sources and spatial and temporal variation across different urban areas and time scales. Further, the impacts of changing fuels, vehicle technologies, and climate on future trends of the particles will be elucidated.Read moreRead less
Industrial Transformation Research Hubs - Grant ID: IH210100025
Funder
Australian Research Council
Funding Amount
$4,379,165.00
Summary
ARC Research Hub for Advanced Manufacturing with 2D Materials (AM2D). Australia holds large resources of critical 2D minerals – key enablers of several existing and emerging technologies in Energy Storage, Purification and Printed Electronics. The AM2D hub aims to provide a sophisticated environment for researchers and an industrial translation platform for manufacturers; a hub where leading academics, bright students, and industry partners come together to learn, apply, collaborate, innovate, a ....ARC Research Hub for Advanced Manufacturing with 2D Materials (AM2D). Australia holds large resources of critical 2D minerals – key enablers of several existing and emerging technologies in Energy Storage, Purification and Printed Electronics. The AM2D hub aims to provide a sophisticated environment for researchers and an industrial translation platform for manufacturers; a hub where leading academics, bright students, and industry partners come together to learn, apply, collaborate, innovate, and deliver industry transformation in advanced manufacturing. Anticipated outcomes include the transformation of newly discovered materials into globally traded, high-value 2D products, enabling Australian industries to capture more wealth and jobs from this large and growing market.
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