New methods for integrating population structure and stochasticity into models of disease dynamics. Epidemics, such as the 2007 equine 'flu outbreak and 2009 swine 'flu pandemic, highlight the need to make informed decisive responses. This project will develop new methods that incorporate two important aspects of disease dynamics---host structure and chance---into mathematical models, and determine their impact in terms of controlling infections.
Epidemics in large populations: long-term and near-critical behaviour. The project aims to prove qualitative and quantitative results concerning aspects of the long-term behaviour of near-critical epidemics, including the probability and duration of a large outbreak, and the total number of people infected. This project is a theoretical study of stochastic models of epidemics in large populations. The project will focus on emerging epidemics, where the average number of contacts, infection and r ....Epidemics in large populations: long-term and near-critical behaviour. The project aims to prove qualitative and quantitative results concerning aspects of the long-term behaviour of near-critical epidemics, including the probability and duration of a large outbreak, and the total number of people infected. This project is a theoretical study of stochastic models of epidemics in large populations. The project will focus on emerging epidemics, where the average number of contacts, infection and recovery rates are such that the basic reproduction number of the disease is near the critical value 1. The project will plan to both analyse particular epidemic models and develop new methodologies applicable in broader contexts. The mathematical predictions will be tested through simulations and comparison to real-world data. The significant outcome of the project should be the advancement in mathematical understanding of infectious disease spread, eventually leading to improved epidemic surveillance and control, and resulting in more effective protection of public health, improved quality of life, and obvious economic benefits.Read moreRead less
Advanced matrix-analytic methods with applications. Over the last twenty-five years, matrix-analytic methods have proved to be very successful in formulating and analysing certain classes of stochastic models. Motivated by applications, this project will investigate more advanced matrix-analytic methods than have hitherto been studied.
Discovery Early Career Researcher Award - Grant ID: DE160100999
Funder
Australian Research Council
Funding Amount
$295,020.00
Summary
Applying forward-backward stochastic differential equations to optimisation. This project intends to develop new ways to solve optimisation problems that are currently difficult to solve because of their complexity and size. In particular, forward–backward stochastic differential equations (FBSDEs) are a new technique that is showing ways to solve problems for which there is yet to be a solution. This project's focus will be on problems that cannot use existing software because the decision-maki ....Applying forward-backward stochastic differential equations to optimisation. This project intends to develop new ways to solve optimisation problems that are currently difficult to solve because of their complexity and size. In particular, forward–backward stochastic differential equations (FBSDEs) are a new technique that is showing ways to solve problems for which there is yet to be a solution. This project's focus will be on problems that cannot use existing software because the decision-making processes require intensive consideration of all possible outcomes in the modelled environment. In comparison to previous optimisation methods, the FBSDE approach is easier to work with and much more informative. The project's main potential applications are multiplayer games with mean-field interaction and financial markets with partial information.Read moreRead less
Advanced Monte Carlo Methods for Spatial Processes. The modeling and analysis of spatial data relies more and more on sophisticated Monte Carlo simulation methods. However, with the growing complexity of today's spatial data, traditional Monte Carlo methods increasingly face difficulties in terms of speed and accuracy. The aim of this project is to develop new theory and applications at the interface of Monte Carlo methods and spatial statistics, building upon exciting theoretical and computatio ....Advanced Monte Carlo Methods for Spatial Processes. The modeling and analysis of spatial data relies more and more on sophisticated Monte Carlo simulation methods. However, with the growing complexity of today's spatial data, traditional Monte Carlo methods increasingly face difficulties in terms of speed and accuracy. The aim of this project is to develop new theory and applications at the interface of Monte Carlo methods and spatial statistics, building upon exciting theoretical and computational advances in both areas in recent years. The research will stimulate the design of microscopic and macroscopic complex spatial structures with superior properties, such as composite materials, solar cells, telecommunication networks, mining operations, and road systems.Read moreRead less
Random walks with long memory. This project aims to study novel random walk models with long memory, including systems of multiple random walkers that interact through their environment. This would provide a mathematical understanding of phenomena such as aggregation in colonies of bacteria, and ant colony optimisation algorithms. The project aims to produce highly cited publications, and to train future researchers.
Discovery Early Career Researcher Award - Grant ID: DE200101467
Funder
Australian Research Council
Funding Amount
$419,778.00
Summary
The geometric structure of spatial noise. Spatial noise is ubiquitous in nature and science: as interference in medical imaging, in oceanography, in the modelling of telecommunication networks etc. Despite this diversity of sources, spatial noise can be studied in a unified way by considering mathematical models that capture its essential features. This project aims to study spatial noise by analysing its geometric structure, for instance by considering the number of contour lines of the noise, ....The geometric structure of spatial noise. Spatial noise is ubiquitous in nature and science: as interference in medical imaging, in oceanography, in the modelling of telecommunication networks etc. Despite this diversity of sources, spatial noise can be studied in a unified way by considering mathematical models that capture its essential features. This project aims to study spatial noise by analysing its geometric structure, for instance by considering the number of contour lines of the noise, and the way these lines connect different regions of space. The project further aims to apply this analysis to construct statistical tests that can distinguish different classes of spatial noise, with potential applications across all of the disciplines mentioned above.Read moreRead less
Overseeing the internet: new paradigms of network measurement. Like the electricity network, the internet is a core infrastructure, and so must be reliable and efficient. A gap in bandwidth supply is like a blackout in terms of lost business and productivity. This project will provide the measurement breakthroughs to ensure that network behaviour can be accurately and comprehensively monitored.
Discovery Early Career Researcher Award - Grant ID: DE140100993
Funder
Australian Research Council
Funding Amount
$293,520.00
Summary
Mathematics of importance: The optimal importance sampling algorithm for estimating the probability of a black swan event. Rare event simulation and modelling is critical to our understanding of high-cost hard-to-predict events such as nuclear accidents, natural disasters, and financial crises. Quantitative analysis of such high-impact events demands the accurate estimation of the probability of occurrence of such rare events. In realistic models this probability is very difficult to estimate, ....Mathematics of importance: The optimal importance sampling algorithm for estimating the probability of a black swan event. Rare event simulation and modelling is critical to our understanding of high-cost hard-to-predict events such as nuclear accidents, natural disasters, and financial crises. Quantitative analysis of such high-impact events demands the accurate estimation of the probability of occurrence of such rare events. In realistic models this probability is very difficult to estimate, because exact simple analytical formulas are not available and the existing estimation methods fail spectacularly. There is an urgent need for new efficient methodology. This project develops a new Monte Carlo method that will be able to estimate reliably and accurately rare-event probabilities. Read moreRead less
Time consistency, risk-mitigation and partially observable systems. This project aims to find optimal decision rules that mitigate risk in a time consistent manner for partially observable systems. Many problems in conservation management and engineering systems are dependent on random environments and entail risk of failure. The challenge of consistently minimising such a risk while achieving satisfactory and sustainable resource consumption is considerable. This project aims to develop analyti ....Time consistency, risk-mitigation and partially observable systems. This project aims to find optimal decision rules that mitigate risk in a time consistent manner for partially observable systems. Many problems in conservation management and engineering systems are dependent on random environments and entail risk of failure. The challenge of consistently minimising such a risk while achieving satisfactory and sustainable resource consumption is considerable. This project aims to develop analytical and numerical methods for optimal control in such scenarios. These methods will have application to fishery management, communication networks, power systems and social resource allocation scenarios.Read moreRead less