Communication and information storage mechanisms in complex dynamical brain networks. Recordings of electrical activity in the brain often cycle repetitively. The aim of this research is to explain how these brain rhythms assist the brain to coordinate simultaneous activity in several regions. Australian socioeconomic benefits include: (i) contributions to the knowledge base of theoretical neuroscience, enhancing Australia's reputation for cutting-edge research; (ii) strengthening of internation ....Communication and information storage mechanisms in complex dynamical brain networks. Recordings of electrical activity in the brain often cycle repetitively. The aim of this research is to explain how these brain rhythms assist the brain to coordinate simultaneous activity in several regions. Australian socioeconomic benefits include: (i) contributions to the knowledge base of theoretical neuroscience, enhancing Australia's reputation for cutting-edge research; (ii) strengthening of international collaborations with Europe and Japan; (iii) outcomes will ultimately impact on improved medical bionics and future interfaces between brain activity and machines or computers; and (iv) commercialization and technology transfer opportunities, via the transfer of results to biologically inspired engineering.Read moreRead less
Dynamic risk measures. Exposure to risk is a pervasive problem. The results will be of importance for financial institutions when they estimate their exposure to risk. Other applications will be to determine the level of risk from a terrorist attack or regional instability. Companies wish to allocate resources to minimize their exposure to adverse events.
Mathematical modelling of information flow in social networks. This proposal aims to develop new mathematical and statistical methods to understand information flow in social networks. By using novel information theoretic techniques, it will create new methods to characterise social information flow in social networks. These tools will allow derivation of fundamental limits of predictability for AI methods applied to digital data. New mathematics of information flow will produce insights into so ....Mathematical modelling of information flow in social networks. This proposal aims to develop new mathematical and statistical methods to understand information flow in social networks. By using novel information theoretic techniques, it will create new methods to characterise social information flow in social networks. These tools will allow derivation of fundamental limits of predictability for AI methods applied to digital data. New mathematics of information flow will produce insights into social influence in online social networks. Benefits include: better understanding of how echo chambers may form in social networks, predictive models for how misinformation can spread online such as during an emergency, and a framework for intercomparison of AI methods applied to digital data on individuals. Read moreRead less
The fundamental equations for inversion of operator pencils. This project seeks to deepen understanding of how complex systems may be significantly changed by incremental changes to ambient conditions. Mathematical models of complex systems (climate change processes, optimal driving strategies, efficient distribution policies, effective search routines) often depend on key parameters. If small perturbations to the parameters cause large changes to the solution, then the perturbations are said to ....The fundamental equations for inversion of operator pencils. This project seeks to deepen understanding of how complex systems may be significantly changed by incremental changes to ambient conditions. Mathematical models of complex systems (climate change processes, optimal driving strategies, efficient distribution policies, effective search routines) often depend on key parameters. If small perturbations to the parameters cause large changes to the solution, then the perturbations are said to be singular. This project aims to reveal the underlying mathematical structures and develop new computational algorithms to analyse a general class of perturbed systems both locally near an isolated singularity and globally. It plans to use these algorithms to solve systems of equations, calculate generalised inverse operators, examine perturbed Markov processes, and estimate exit times from meta-stable states in stochastic population dynamics.Read moreRead less
Occupational measures, perturbations and complex deterministic systems. When tackling complex problems, scientists and engineers seek methods that judiciously exploit stochasticity and perturbations as antidotes to unpredictability of outputs that the latter can induce if they inadvertently influence their models. The project proposes for this study vaccine-like perspective of stochasticity and singular perturbations.
Two-price quantitative finance. This project aims to establish a novel field, namely two-price quantitative finance, and explore its applications. The new field will integrate two major schools for modelling and explain the presence of two prices, the buying and selling prices, widely observed in the real-world markets, and the equilibrium approach from the fundamental law of one price. The outcomes would deepen our understanding of the fundamental relationship among liquidity, prices, risk and ....Two-price quantitative finance. This project aims to establish a novel field, namely two-price quantitative finance, and explore its applications. The new field will integrate two major schools for modelling and explain the presence of two prices, the buying and selling prices, widely observed in the real-world markets, and the equilibrium approach from the fundamental law of one price. The outcomes would deepen our understanding of the fundamental relationship among liquidity, prices, risk and the economy. This project expects to bring about long-term impact on quantitative finance and related applications through providing a deep understanding of, and a new perspective for, the design, risk and fairness of the finance, property and insurance markets.Read moreRead less
G-expectation and its applications to nonlinear risk management. This project will develop novel theories and methods for nonlinear risk management based on nonlinear expectations and Backward Stochastic Differential Equations. The expected outcomes of the project will place Australia in the forefront and the leading position of these fields.
Uncertainties in coherent transport of particles and intrinsic properties. This Project aims to quantify the uncertainty of a model output in terms of uncertainties in modelling assumptions, by developing new mathematical techniques and applying them to real-world data. This will be in the context of assessing the accuracy of tracking coherently moving structures (e.g., hurricanes, oceanic biodiversity hotspots, pollutant patches, insect swarms) from experimental/observational data sets. Novel, ....Uncertainties in coherent transport of particles and intrinsic properties. This Project aims to quantify the uncertainty of a model output in terms of uncertainties in modelling assumptions, by developing new mathematical techniques and applying them to real-world data. This will be in the context of assessing the accuracy of tracking coherently moving structures (e.g., hurricanes, oceanic biodiversity hotspots, pollutant patches, insect swarms) from experimental/observational data sets. Novel, data-tested, mathematical methods for uncertainty quantification of coherent structures will be developed as Project outcomes. Project benefits include new insights into protecting the environment, improved uncertainty quantification in climate modelling, and the generation of interdisciplinary knowledge and training.Read moreRead less
Paving the way: an experimental approach to the mathematical modelling and design of permeable pavements. The intelligent use of permeable pavements will enable restoration of degraded land corridors. Collection and treatment of stormwater via filtration through porous media will improve water quality in urban environments and will also control flooding. The integration of ecology and urban living will present a revolutionary way to revitalize cities.