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
Quantum Spectra. Fundamental quantum processes will play a key role in emerging technologies in the twenty-first century across diverse industries including quantum information technology, quantum computers and electronics, quantum optics, nanoscale quantum microscopes and superconductor technology. Australia has a strong base of expertise in the underpinning quantum disciplines. This project in strategic basic research within mathematical physics will develop a comprehensive and consistent math ....Quantum Spectra. Fundamental quantum processes will play a key role in emerging technologies in the twenty-first century across diverse industries including quantum information technology, quantum computers and electronics, quantum optics, nanoscale quantum microscopes and superconductor technology. Australia has a strong base of expertise in the underpinning quantum disciplines. This project in strategic basic research within mathematical physics will develop a comprehensive and consistent mathematical description of quantum processes. This research will lead to a deeper understanding of quantum processes, keep Australia at the leading edge of international developments and increase Australia's capacity to develop and implement these new technologies.Read moreRead less
Centre for Mathematical and Statistical Modelling of Complex Systems. This Centre, formed by a group of high-profile researchers, brings expertise from linked but hitherto disparate areas together. It will place Australia at the forefront of research into complex systems.
The mission of the Centre is to stimulate research in mathematical and statistical modelling of complex systems and to encourage cross-fertilisation of ideas and techniques. The specific objectives are
- to formulate and ana ....Centre for Mathematical and Statistical Modelling of Complex Systems. This Centre, formed by a group of high-profile researchers, brings expertise from linked but hitherto disparate areas together. It will place Australia at the forefront of research into complex systems.
The mission of the Centre is to stimulate research in mathematical and statistical modelling of complex systems and to encourage cross-fertilisation of ideas and techniques. The specific objectives are
- to formulate and analyse mathematical and statistical models for natural and artificial complex systems,
- to use these models to develop an understanding of the behaviour of these systems
- to incorporate this understanding into strategies for management and control.Read moreRead less
Linkage Infrastructure, Equipment And Facilities - Grant ID: LE0346878
Funder
Australian Research Council
Funding Amount
$190,000.00
Summary
GeoWulf: An Inference Engine for Complex Earth Systems. The project is to build a `Beowulf' cluster as a platform for solving
complex data inference problems in the Earth sciences, and in
particular the fields of thermochronology, seismology, crustal and
mantle dynamics, and landform evolution. A Beowulf cluster is a
network-linked set of commonly available `off-the-shelf' PC-computers
configured to give unprecedented performance/cost ratio. Projects
using the Beowulf facility will combine ....GeoWulf: An Inference Engine for Complex Earth Systems. The project is to build a `Beowulf' cluster as a platform for solving
complex data inference problems in the Earth sciences, and in
particular the fields of thermochronology, seismology, crustal and
mantle dynamics, and landform evolution. A Beowulf cluster is a
network-linked set of commonly available `off-the-shelf' PC-computers
configured to give unprecedented performance/cost ratio. Projects
using the Beowulf facility will combine state-of-the-art computational
techniques recently developed at ANU, and high quality data sets
collected over the past decade to address fundamental questions in
the Geosciences.Read moreRead less
Virtual Star Clusters: The Dynamics and Evolution of Stars and Planets. Most stars are born in star clusters. When stars age
they swell and contract, change composition,
lose mass, and in dense regions they may collide.
Further, about 50% of stars are binary pairs,
and when these swell they can merge or
transfer mass. These effects dramatically
alter the lives of stars and their chemical makeup.
By combining special
purpose computers with newly developed simulation techniques,
we will ....Virtual Star Clusters: The Dynamics and Evolution of Stars and Planets. Most stars are born in star clusters. When stars age
they swell and contract, change composition,
lose mass, and in dense regions they may collide.
Further, about 50% of stars are binary pairs,
and when these swell they can merge or
transfer mass. These effects dramatically
alter the lives of stars and their chemical makeup.
By combining special
purpose computers with newly developed simulation techniques,
we will include all these effects to answer timely
and important astronomical
questions such as: can planets survive life in
a cluster? how do interactions between stars
affect the chemical enrichment of
clusters and galaxies?Read moreRead less
The Sakai scheme-Askey table correspondence, analogues of isomonodromy and determinantal point processes. The Australian mathematical sciences enjoys two research groups with active interests on Painleve equations in applied mathematics which are able to address difficult problems. Such a problem is to give a formulation of Sakai's 2001 classification of the Painleve equations in a form most suitable for applications. For this links will be made with a seemingly distinct area of mathematics - t ....The Sakai scheme-Askey table correspondence, analogues of isomonodromy and determinantal point processes. The Australian mathematical sciences enjoys two research groups with active interests on Painleve equations in applied mathematics which are able to address difficult problems. Such a problem is to give a formulation of Sakai's 2001 classification of the Painleve equations in a form most suitable for applications. For this links will be made with a seemingly distinct area of mathematics - the Askey table from the theory of hypergeometric orthogonal polynomials. A number of tractable PhD projects are suggested by this proposal.Read moreRead less
Forecasting with single source of randomness state space models. The framework developed in this project, for identifying and
extrapolating trends, seasonal patterns and economic cycles in time
series, has a large and diverse range of useful applications in
Australia. Some examples include its potential use in the
development of appropriate monetary policy, its use to better inform
finance markets of risk levels associated with shares, its use to
forecast demand in supply chains to provide ....Forecasting with single source of randomness state space models. The framework developed in this project, for identifying and
extrapolating trends, seasonal patterns and economic cycles in time
series, has a large and diverse range of useful applications in
Australia. Some examples include its potential use in the
development of appropriate monetary policy, its use to better inform
finance markets of risk levels associated with shares, its use to
forecast demand in supply chains to provide a better service to
customers, and its use in call centres to better tailor staff
schedules to meet customer calls.Read moreRead less
Integrating dynamic and optimization models for efficient pipeline system operations in an evolving water and energy market. Developing an integrated dynamical and optimisation model for a piped water distribution system will advance Australia's capacity to deploy the most recent optimisation approaches to achieve the high level of efficiency required in the delivery of water to dryland regions. The outcomes of this project will be readily transferable to other regions and indeed other water d ....Integrating dynamic and optimization models for efficient pipeline system operations in an evolving water and energy market. Developing an integrated dynamical and optimisation model for a piped water distribution system will advance Australia's capacity to deploy the most recent optimisation approaches to achieve the high level of efficiency required in the delivery of water to dryland regions. The outcomes of this project will be readily transferable to other regions and indeed other water distribution systems. This will provide capability in securing Australia's water supplies and delivery systems. There may also be associated benefits to other pipeline operators in the oil and gas industries.Read moreRead less
GEOMETRIC NUMERICAL INTEGRATION. Many scientific phenomena in physics, astronomy, and chemistry, are modelled by ordinary differential equations (ODEs). Often these equations have no solution in closed form, and one relies on numerical integration. Traditionally this is done using Runge-Kutta methods or linear multistep methods. In the last decade, however, we (and others) have discovered novel classes of so-called "geometric" numerical integration methods that preserve qualititative featur ....GEOMETRIC NUMERICAL INTEGRATION. Many scientific phenomena in physics, astronomy, and chemistry, are modelled by ordinary differential equations (ODEs). Often these equations have no solution in closed form, and one relies on numerical integration. Traditionally this is done using Runge-Kutta methods or linear multistep methods. In the last decade, however, we (and others) have discovered novel classes of so-called "geometric" numerical integration methods that preserve qualititative features of certain ODE's exactly (in contrast to traditional methods), leading to crucial stability improvements. Extending concepts from dynamical systems theory and traditional numerical ODEs, this project will improve, extend and systematize this new field of geometric integration.Read moreRead less
Green functions, correlation functions and differential equations. Classical and quantum exact solutions are established cornerstones in Australian applied mathematical research. In this project, we will:- 1). Address long standing open problems, whose resolution will add to mathematical knowledge and enhance Australia's reputation as a leading contributor to these topics; 2). List concrete and tractable sub-projects that will engage young scientists, whose training we are particularly keen on, ....Green functions, correlation functions and differential equations. Classical and quantum exact solutions are established cornerstones in Australian applied mathematical research. In this project, we will:- 1). Address long standing open problems, whose resolution will add to mathematical knowledge and enhance Australia's reputation as a leading contributor to these topics; 2). List concrete and tractable sub-projects that will engage young scientists, whose training we are particularly keen on, in vigorous and internationally competitive research; 3). Facilitate collaborations between various Australian research groups, all of whom are very well positioned to contribute to it; 4). Bring leading scientists to visit Australia to the benefit of the entire Australian mathematical community.Read moreRead less