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
Discovery Early Career Researcher Award - Grant ID: DE180100911
Funder
Australian Research Council
Funding Amount
$365,058.00
Summary
The mechanisms driving microbial navigation in marine systems. This project aims to apply advanced video-microscopy to characterise microbial motion at the single cell level, interrogating their navigational responses in precisely controlled physical and chemical conditions. Ocean carbon cycling is driven by the concerted action of marine microbes, but the fine-scale interactions between these microbes and their physical and chemical environments remains elusive. The project findings will unrave ....The mechanisms driving microbial navigation in marine systems. This project aims to apply advanced video-microscopy to characterise microbial motion at the single cell level, interrogating their navigational responses in precisely controlled physical and chemical conditions. Ocean carbon cycling is driven by the concerted action of marine microbes, but the fine-scale interactions between these microbes and their physical and chemical environments remains elusive. The project findings will unravel the fundamental processes governing microbial motion in real environments, and develop the mechanistic modelling tools required to make quantitative ecosystem-level predictions of how soil-atmosphere-water-marine systems respond in the face of environmental change.Read moreRead less
Novel methodology advancing applied Bayesian statistics and applications. Bayesian statistical inference has become the dominant statistical method in significant areas of application. The project aims to develop and apply novel Bayesian computational algorithms. Outcomes will advance scientific understanding in significant multi-disciplinary areas such as infectious diseases, neurological disease and human behaviour.
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
Energy efficient sensing, computing and communication. This research will study trade-offs in resource use: bandwidth, power, and computational capacity of systems of sensors such as cameras, radars, and distributed sensor networks based on a statistical mechanical theory of information processing, leading to practical algorithms to optimize resource use in the design of such systems.
Suspension flows and particle focusing in curved geometries. The project aims to develop fast predictive tools to investigate suspension flows in curved channels and thin ducts and the effect of channel geometry on the focusing of particles by weight to different regions of the channel. Interaction between particles and fluid in suspension flows is a fundamental problem that is little understood but which is important in a wide range of problems in nature and industry (eg for design of microscal ....Suspension flows and particle focusing in curved geometries. The project aims to develop fast predictive tools to investigate suspension flows in curved channels and thin ducts and the effect of channel geometry on the focusing of particles by weight to different regions of the channel. Interaction between particles and fluid in suspension flows is a fundamental problem that is little understood but which is important in a wide range of problems in nature and industry (eg for design of microscale segregation devices for separation of different cells in a blood sample, and of macroscale devices for separation of mineral particles from crushed ore). At present, the description of these processes is qualitative, with quantitative understanding seen as a challenge without intensive computation. The project plans to develop, solve and validate mathematical models to give a quantitative understanding of these processes.Read moreRead less
Advanced numerical and analytical techniques for exact studies in combinatorics and statistical mechanics. Exactly solved models are of immense importance in all areas of the theoretical sciences and play important roles in our understanding of complex natural and social phenomena. This project aims to develop powerful new methods that will enable mathematicians and physicists to greatly expand the types of models for which we can find a solution.
Holonomy groups in Lorentzian geometry. The project studies mathematical models used in physical theories, such as general relativity and string theory, to create a global picture of the universe. The outcomes will enhance the role Australia plays in these developments and contribute to the mathematical knowledge which lies at the foundations of modern technologies.
Discovery Early Career Researcher Award - Grant ID: DE140101268
Funder
Australian Research Council
Funding Amount
$386,820.00
Summary
Stochastic mathematical modelling of the Wnt signalling pathway. The Wnt signalling pathway is pivotal in multicellular organisms, regulating cellular processes such as proliferation, apoptosis and migration. Faulty Wnt signalling is associated with degenerative diseases, developmental disorders and cancers and is therefore a potential target for therapeutic drugs. This project will perform a stochastic spatial simulation of the Wnt signalling pathway which will be matched to experimental data. ....Stochastic mathematical modelling of the Wnt signalling pathway. The Wnt signalling pathway is pivotal in multicellular organisms, regulating cellular processes such as proliferation, apoptosis and migration. Faulty Wnt signalling is associated with degenerative diseases, developmental disorders and cancers and is therefore a potential target for therapeutic drugs. This project will perform a stochastic spatial simulation of the Wnt signalling pathway which will be matched to experimental data. The model will be extended to integrate with the cell cycle. Increased proliferation in tumours has been linked to mutations in Wnt components. Using the extended model, the effect of Wnt-targeting therapeutic cancer drugs on cancer cell proliferation rates will be predicted and compared to experiments.Read moreRead less