New Frontiers and Advances in Discrete Integrable Systems. Integrable systems boast a long and venerable history, and have such famous members as the Kepler system, the Korteweg-de Vries equation, and the sine-Gordon equation. More recently, interest in integrable systems has expanded to include systems with discrete time, that is, ordinary difference equations (or maps) and integrable partial difference equations. These discrete integrable systems are arguably more fundamental than the continuo ....New Frontiers and Advances in Discrete Integrable Systems. Integrable systems boast a long and venerable history, and have such famous members as the Kepler system, the Korteweg-de Vries equation, and the sine-Gordon equation. More recently, interest in integrable systems has expanded to include systems with discrete time, that is, ordinary difference equations (or maps) and integrable partial difference equations. These discrete integrable systems are arguably more fundamental than the continuous-time ones. Based upon recent breakthroughs this study will combine analysis, geometry, and computer algebra to expand and systematise this new interdisciplinary field of discrete integrable systems.Read moreRead less
New Applications of Additive Combinatorics in Number Theory and Graph Theory. The project aims to advance significantly the interplay between additive combinatorics, number theory and graph theory. The project will use and advance methods and results of additive combinatorics and give new applications to such fundamental problems on Cayley graphs as connectivity, random walks, colouring and dominating sets. The significance of the project is ensured by its goal of advancing existing results and ....New Applications of Additive Combinatorics in Number Theory and Graph Theory. The project aims to advance significantly the interplay between additive combinatorics, number theory and graph theory. The project will use and advance methods and results of additive combinatorics and give new applications to such fundamental problems on Cayley graphs as connectivity, random walks, colouring and dominating sets. The significance of the project is ensured by its goal of advancing existing results and methods of additive combinatorics and also in finding their new applications that have long-lasting impact on paramount problems for Cayley graphs that underlie the architecture of crucial communication networks. Achieving progress on these problems and developing relevant methods of additive combinatorics will be the main outcomes. Read moreRead less
Spatio-Temporal Statistics and its Application to Remote Sensing. By their very nature, environmental processes involve strong spatial and temporal variability. Inferring cause-effect relationships requires the incorporation of spatial and temporal dependence in the statistical models. The aims of this project are to develop mass-balanced hierarchical spatio-temporal statistical models, new loss functions that are relevant to multivariate processes, and optimal estimators obtained from the hiera ....Spatio-Temporal Statistics and its Application to Remote Sensing. By their very nature, environmental processes involve strong spatial and temporal variability. Inferring cause-effect relationships requires the incorporation of spatial and temporal dependence in the statistical models. The aims of this project are to develop mass-balanced hierarchical spatio-temporal statistical models, new loss functions that are relevant to multivariate processes, and optimal estimators obtained from the hierarchical model's predictive distribution. These methodologies are intended to be applied to the estimation of near-surface fluxes of atmospheric carbon dioxide, using massive remote sensing datasets from satellites and other data sources.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE210101808
Funder
Australian Research Council
Funding Amount
$395,775.00
Summary
Genetic Programming for Big Data Analytics. The project aims to extend a powerful machine learning method, called genetic programming and also developing a new concept called Alpha program, for big data analytics. This project expects to generate a new approach by finding a systematic approach to develop gene structures using information theory. By borrowing the best genes from the population of programs, the Alpha program concept will be developed for the first time. The proposed approach aims ....Genetic Programming for Big Data Analytics. The project aims to extend a powerful machine learning method, called genetic programming and also developing a new concept called Alpha program, for big data analytics. This project expects to generate a new approach by finding a systematic approach to develop gene structures using information theory. By borrowing the best genes from the population of programs, the Alpha program concept will be developed for the first time. The proposed approach aims to enhance genetic programming for many practical problems. I contend that not only finding better tools for big data analytics is in the best interest of machine learning and big data communities, it also provides significant benefits for other communities and industries in Australia.Read moreRead less
Geodetic groups: foundational problems in algebra and computer science. The project aims to resolve important and longstanding open problems in Geometric Group Theory and Theoretical Computer Science. Since the 1980s researchers have conjectured that the geometric property of being geodetic is equivalent to several purely algebraic, algorithmic, and language-theoretic characterisations.
The project team's expertise in geodesic properties of groups, the interaction between formal languages and g ....Geodetic groups: foundational problems in algebra and computer science. The project aims to resolve important and longstanding open problems in Geometric Group Theory and Theoretical Computer Science. Since the 1980s researchers have conjectured that the geometric property of being geodetic is equivalent to several purely algebraic, algorithmic, and language-theoretic characterisations.
The project team's expertise in geodesic properties of groups, the interaction between formal languages and groups, and the theory of rewriting systems, together with recent breakthroughs by the team ensures that significant results can be expected.
Benefits include training research students and postdoctoral researchers in cutting-edge techniques, and advancing fundamental knowledge in mathematics and computer science.Read moreRead less
ARC Centre of Excellence for Plant Success in Nature and Agriculture. The ARC CoE for Plant Success in Nature and Agriculture will discover the adaptive strategies underpinning productivity and resilience in diverse plants and deepen knowledge of the genetic and physiological networks driving key traits. Using novel quantitative and computational approaches, the Centre will link gene networks with traits across biological levels, giving breeders an unparalleled predictive capacity. The Centre wi ....ARC Centre of Excellence for Plant Success in Nature and Agriculture. The ARC CoE for Plant Success in Nature and Agriculture will discover the adaptive strategies underpinning productivity and resilience in diverse plants and deepen knowledge of the genetic and physiological networks driving key traits. Using novel quantitative and computational approaches, the Centre will link gene networks with traits across biological levels, giving breeders an unparalleled predictive capacity. The Centre will accelerate technologies to transfer successful networks into crops and build legal frameworks to secure this knowledge. With a uniquely multidisciplinary team, the Centre will deliver new strategies to address the problems of food security and climate change, establishing Australia as a global leader in these areas.Read moreRead less
ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights. In today's world, massive amounts of data in a variety of forms are collected daily from a multitude of sources. Many of the resulting data sets have the potential to make vital contributions to society, business and government, as well as impact on international developments, but are so large or complex that they are difficult to process and analyse using traditional tools. The aim of this ....ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights. In today's world, massive amounts of data in a variety of forms are collected daily from a multitude of sources. Many of the resulting data sets have the potential to make vital contributions to society, business and government, as well as impact on international developments, but are so large or complex that they are difficult to process and analyse using traditional tools. The aim of this Centre is to create innovative mathematical and statistical models that can uncover the knowledge concealed within the size and complexity of these big data sets, with a focus on using the models to deliver insight into problems vital to the Centre's Collaborative Domains: Healthy People, Sustainable Environments and Prosperous Societies.Read moreRead less
The mathematics of novel magnetic memory materials. Magnetic memories are the world’s principal device for storing information. The next generation will have greatly increased access speed and data-storage capacity. This project will develop the mathematical theory of these new magnetic memory materials, a crucial first step in understanding and being able to fine-tune their properties.
Discovery Early Career Researcher Award - Grant ID: DE130101670
Funder
Australian Research Council
Funding Amount
$370,410.00
Summary
Scalable Bayesian model selection for massive data sets. This project will develop highly innovative, efficient and ultimately effective methodology for Bayesian model selection for large-scale problems which commonly arise in biostatistics and bioinformatics. The resulting methodology will dramatically reduce the duration of analyses in these areas from days or weeks to minutes or hours.
Discovery Early Career Researcher Award - Grant ID: DE120101113
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Mathematical modelling of breast cancer immunity: guiding the development of preventative breast cancer vaccines. The project will apply various methods from mathematical modelling to simulate anti-breast cancer immune responses to incipient tumours. Results from simulation and analysis will help develop, assess, and optimise preventative breast cancer vaccines for further testing in future experimental studies.