Interrogation and estimation of differential equation networks. Complex networks occur in many physical processes, in bridges and buildings and in small nanoscale systems like carbon nanotubes. Similar systems arise in electronics, photonics, and social networks. This project aims to determine optimal measurement regimes to estimate their dynamical states, and to find the limits of that estimation process.
Modelling patient flows through hospitals: optimizing effective use of resources. Hospitals are complex, dynamic systems confronted by increased demand in the face of shrinking real capacity. Managing such systems is currently undertaken with sub-optimal analytical support, particularly when demand and capacity are changing and resources must be manipulated to respond to such changes. In this project, the investigators will apply a mathematical modelling approach to the analysis of hospital pati ....Modelling patient flows through hospitals: optimizing effective use of resources. Hospitals are complex, dynamic systems confronted by increased demand in the face of shrinking real capacity. Managing such systems is currently undertaken with sub-optimal analytical support, particularly when demand and capacity are changing and resources must be manipulated to respond to such changes. In this project, the investigators will apply a mathematical modelling approach to the analysis of hospital patient flows. Furthermore, they will employ statistical process control methodologies to the problem of recognising and responding to changes in the flows, so that performance objectives are met. In doing this, they will give health service managers and clinicians a significant advantage in deciding how best to manage a constrained resource to maximize access, throughput and patient outcomes.Read moreRead less
Models for Australian Electricity Derivatives. Electricity derivatives, such as electricity futures and options are used to manage the risk associated with volatility in prices of electricity. This project aims to develop models for pricing electricity derivatives specifically suited for Australia. Because of the non-storable nature of electricity the standard option pricing principle of "no-arbitrage" does not apply to electricity options, such as caps and floors, but applies to options on elec ....Models for Australian Electricity Derivatives. Electricity derivatives, such as electricity futures and options are used to manage the risk associated with volatility in prices of electricity. This project aims to develop models for pricing electricity derivatives specifically suited for Australia. Because of the non-storable nature of electricity the standard option pricing principle of "no-arbitrage" does not apply to electricity options, such as caps and floors, but applies to options on electricity futures. Therefore a specific model is needed that takes into account the pricing principle of "no-arbitrage" and combines it with other factors that drive electricity prices. The novel element in this proposal is incorporation of the weather forecasts into the models for electricity options. As a result of this study appropriate models for electricity derivatives for various geographical regions in Australia will be developed.Read moreRead less
Increasing internet energy and cost efficiency by improving higher-layer protocols. Australians rely heavily on our telecommunications infrastructure due to our geographic dispersion. We are also very susceptible to climate change, given our reliance on agriculture. Information technology is consuming a rapidly increasing fraction of our power and our budget. This research will help to reverse both those trends, by finding novel and practical ways to use our infrastructure more efficiently, and ....Increasing internet energy and cost efficiency by improving higher-layer protocols. Australians rely heavily on our telecommunications infrastructure due to our geographic dispersion. We are also very susceptible to climate change, given our reliance on agriculture. Information technology is consuming a rapidly increasing fraction of our power and our budget. This research will help to reverse both those trends, by finding novel and practical ways to use our infrastructure more efficiently, and to minimise its energy use. This will enable the Australian telecommunications industry to provide better service (including to Australian industries and rural communities) at lower economic and environmental cost. This project will put Australia on the international stage as a leading contributor to energy-efficient internet technology.Read moreRead less
Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions ....Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions and estimate the errors involved. Applications include analysis of data in insurance, finance, flood prediction in hydrology.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE210101352
Funder
Australian Research Council
Funding Amount
$330,000.00
Summary
Inverting the Signature Transform for Rough Paths and Random Processes. The signature transform provides an effective summary of the essential information encoded in multidimensional paths that are highly oscillatory and involve complicated randomness. The main goal of this project is to develop new algorithmic methods to reconstruct rough paths and random processes from the signature transform at various quantitative levels. This project expects to make theoretical breakthrough on the significa ....Inverting the Signature Transform for Rough Paths and Random Processes. The signature transform provides an effective summary of the essential information encoded in multidimensional paths that are highly oscillatory and involve complicated randomness. The main goal of this project is to develop new algorithmic methods to reconstruct rough paths and random processes from the signature transform at various quantitative levels. This project expects to make theoretical breakthrough on the significant open problem of signature inversion, thereby advancing knowledge in the areas of rough path theory and stochastic analysis. The newly developed methods will be utilised in combination with the emerging signature-based approach to study important problems in financial data analysis and visual speech recognition.
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Self-Interacting Random Walks. This project aims to study the growth properties of a class of self-interacting processes defined on Euclidean lattices. This project expects to determine whether a shape theorem holds for once-reinforced random walks, and establish conditions for their recurrence/transience. It also expects to obtain new and very precise estimates for the local time of simple random walks. Expected outcomes of this project include solving long-standing open problems in the field o ....Self-Interacting Random Walks. This project aims to study the growth properties of a class of self-interacting processes defined on Euclidean lattices. This project expects to determine whether a shape theorem holds for once-reinforced random walks, and establish conditions for their recurrence/transience. It also expects to obtain new and very precise estimates for the local time of simple random walks. Expected outcomes of this project include solving long-standing open problems in the field of reinforced random walks, and the development of novel methods for their study. This should provide significant benefits not only to the field of mathematics, but also to the myriad of applied disciplines where self-interacting processes are utilised.Read moreRead less
The estimation of genotype-phenotype relationships from family data and of animal abundance from capture-recapture data with frequent capture occasions: A semiparametric approach. Semiparametric statistical methods allow researchers to only model those features of their data that are of interest, but still allow standard statistical inferences to be made about these features. The aim here is to develop non standard applications of semiparametric statistical methods in the estimation of genotype ....The estimation of genotype-phenotype relationships from family data and of animal abundance from capture-recapture data with frequent capture occasions: A semiparametric approach. Semiparametric statistical methods allow researchers to only model those features of their data that are of interest, but still allow standard statistical inferences to be made about these features. The aim here is to develop non standard applications of semiparametric statistical methods in the estimation of genotype-phenotype relationships from family data and the estimation of animal abundance from capture-recapture data. The methods will be applied to real data and their theoretical properties developed. The practical significance of the project is the flexible new statistical methods that will become available to researchers. The theoretical significance will be the insights into semiparametric methods gained by developing these nonstandard applications. The expected outcomes are the new statistical procedures and the resulting theoretical insights into semiparametric statistics.Read moreRead less
Mathematical studies on the statistical properties of complex systems. Introduced in the late `50's to model nuclear spectra, random matrices are now standard in the theory of quantum chaos, mesoscopic phenomena and disordered systems. These are all examples of physical complex systems, characterized by unknown interactions leading to predictable behaviour due to symmetries. Vast mathematical structures result from the symmetries - integrable systems, Painleve equations, Macdonald polynomial the ....Mathematical studies on the statistical properties of complex systems. Introduced in the late `50's to model nuclear spectra, random matrices are now standard in the theory of quantum chaos, mesoscopic phenomena and disordered systems. These are all examples of physical complex systems, characterized by unknown interactions leading to predictable behaviour due to symmetries. Vast mathematical structures result from the symmetries - integrable systems, Painleve equations, Macdonald polynomial theory to name a few. These structures will be further developed, leading to the analytic form of distribution functions quantifying classes of complex systems. Analogous statistical quantification is the essence of recently proposed methods to analyze artificial complex systems such as the stock market.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL150100150
Funder
Australian Research Council
Funding Amount
$2,413,112.00
Summary
Bayesian learning for decision making in the big data era. Bayesian learning for decision making in the big data era: This fellowship project aims to develop new techniques in evidence-based learning and decision-making in the big data era. Big data has arrived, and with it a huge global demand for statistical knowledge and skills to analyse these data for improved learning and decision-making. This project will seek to address this need by creating a step-change in knowledge in Bayesian statist ....Bayesian learning for decision making in the big data era. Bayesian learning for decision making in the big data era: This fellowship project aims to develop new techniques in evidence-based learning and decision-making in the big data era. Big data has arrived, and with it a huge global demand for statistical knowledge and skills to analyse these data for improved learning and decision-making. This project will seek to address this need by creating a step-change in knowledge in Bayesian statistics and translating this knowledge to real-world challenges in industry, environment and health. The new big data statistical analysts trained through the project could also create much needed capacity at national and international levels.Read moreRead less