Graph isomorphism and quantisation of longest cycles by means of determinants and spectra. A characterisation of the difficulty of the Hamiltonian cycle problem and the graphs isomorphism problem will be a significant conceptual advancement with repercussions in a number of fields including combinatorial optimisation and theoretical computer science, in particular, the Google PageRank. Applications of tensor networks technique will lead to a design of a quantum computer that enumerates all Hamil ....Graph isomorphism and quantisation of longest cycles by means of determinants and spectra. A characterisation of the difficulty of the Hamiltonian cycle problem and the graphs isomorphism problem will be a significant conceptual advancement with repercussions in a number of fields including combinatorial optimisation and theoretical computer science, in particular, the Google PageRank. Applications of tensor networks technique will lead to a design of a quantum computer that enumerates all Hamiltonian cycles in a graph. Analysis of the determinant objective function in terms of the eigenvalues may lead to new spectral properties of stochastic matrices. Algorithmic advances exploiting such a characterisation will significantly contribute to existing technologies for solving problems in a wide range of applications.Read moreRead less
Doubly Stochastic Matrices & The Hamiltonian Cycle Problem. The classical hard problem of determining whether a given graph possesses a Hamiltonian cycle contains the essential difficulty of the famous 'Travelling Salesman Problem'. A characterisation of this difficulty in terms of variability of returns (to the initial state) in a controlled stochastic process will be a significant conceptual advance with repercussions in a number of fields including optimisation and theoretical computer scien ....Doubly Stochastic Matrices & The Hamiltonian Cycle Problem. The classical hard problem of determining whether a given graph possesses a Hamiltonian cycle contains the essential difficulty of the famous 'Travelling Salesman Problem'. A characterisation of this difficulty in terms of variability of returns (to the initial state) in a controlled stochastic process will be a significant conceptual advance with repercussions in a number of fields including optimisation and theoretical computer science. Algorithmic advances exploiting such a characterisation will significantly contribute to existing technologies for solving problems in applications ranging from logistics to cryptography. Since TSP describes certain efficient ways of routing its applicability to information networks is clear.Read moreRead less
Cross-Entropy Methods in Complex Biological Systems. The Cross-Entropy method provides a powerful new way to find superior solutions to complicated optimisation problems in biology, ranging from better design and implementation of medical treatments to an increased understanding of complex ecosystems.
Perturbation and approximation methods for linear operators with applications to train control, water resource management and evolution of physical systems. Linear equations are used to solve practical problems. In realistic problems the equations and their solutions depend on parameters obtained by measurement of physical quantities and on data derived from observations and experiments. Changes to the values of the key parameters will lead to changes in the solutions. This project will devel ....Perturbation and approximation methods for linear operators with applications to train control, water resource management and evolution of physical systems. Linear equations are used to solve practical problems. In realistic problems the equations and their solutions depend on parameters obtained by measurement of physical quantities and on data derived from observations and experiments. Changes to the values of the key parameters will lead to changes in the solutions. This project will develop methods to better understand the relationships between the key parameters and the solutions and will apply the new insights to practical problems such as the minimization of fuel consumption in trains, optimal resource management in water supply systems and the evolution of physical systems.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
Control of Markov jumping processes with constraints. The project outcomes will constitute the set of tools for modelling and optimisation of complex stochastic systems and will lead to new and more precise characterisations of optimal behaviour of complex controllable systems arising in Resource Management, Engineering and Telecommunications. Therefore, the project fits to the research priority areas Breakthrough Science and Frontier Technologies in the topic of mathematical modelling and optim ....Control of Markov jumping processes with constraints. The project outcomes will constitute the set of tools for modelling and optimisation of complex stochastic systems and will lead to new and more precise characterisations of optimal behaviour of complex controllable systems arising in Resource Management, Engineering and Telecommunications. Therefore, the project fits to the research priority areas Breakthrough Science and Frontier Technologies in the topic of mathematical modelling and optimisation of Complex Systems.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
Frontiers in inference about risk. The project aims to develop new methods for robust risk evaluation and minimisation under various constraints and scenarios. Risk evaluation, estimation and prediction using past data is a central activity in diverse areas such as finance, insurance, superannuation and environmental regulation. The project aims to propose and solve innovatively robust risk optimisation problems under constraints, taking into account the time dynamics. Applications include risk ....Frontiers in inference about risk. The project aims to develop new methods for robust risk evaluation and minimisation under various constraints and scenarios. Risk evaluation, estimation and prediction using past data is a central activity in diverse areas such as finance, insurance, superannuation and environmental regulation. The project aims to propose and solve innovatively robust risk optimisation problems under constraints, taking into account the time dynamics. Applications include risk management around natural catastrophes and long-term asset investment of pension funds. The solutions and outcomes are expected to deliver optimal resource allocation proposals and better management of risk exposure in practice.Read moreRead less
Special Research Initiatives - Grant ID: SR0354727
Funder
Australian Research Council
Funding Amount
$20,000.00
Summary
Mathematics for Government, Industry and Community -- The *Magic* Network. The *Magic* network will promote the use of mathematics by government, industry and community to analyse real problems and implement practical solutions. It will connect the most promising young Australian mathematicians to experienced researchers with strong research teams linked directly to the broader community. Our program will demand research excellence, emphasise a sustainable society, support outstanding young mat ....Mathematics for Government, Industry and Community -- The *Magic* Network. The *Magic* network will promote the use of mathematics by government, industry and community to analyse real problems and implement practical solutions. It will connect the most promising young Australian mathematicians to experienced researchers with strong research teams linked directly to the broader community. Our program will demand research excellence, emphasise a sustainable society, support outstanding young mathematicians and create opportunities for promising postgraduate students. We will offer scholarships for professional development and fund research visits and exchanges. *Magic* will provide tangible incentives for young Australian mathematicians and a new generation of researchers and research leaders.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE240100006
Funder
Australian Research Council
Funding Amount
$444,847.00
Summary
Robust Derivative-Free Algorithms for Complex Optimisation Problems. Mathematical optimisation gives a systematic way for optimal decision-making. This project aims to develop new mathematical tools for complex optimisation problems where limited problem information is available. It will generate new foundational theories for alternative optimisation tools, introducing substantial new capability and rigour to the discipline. The project will create significant new mathematical optimisation techn ....Robust Derivative-Free Algorithms for Complex Optimisation Problems. Mathematical optimisation gives a systematic way for optimal decision-making. This project aims to develop new mathematical tools for complex optimisation problems where limited problem information is available. It will generate new foundational theories for alternative optimisation tools, introducing substantial new capability and rigour to the discipline. The project will create significant new mathematical optimisation techniques and create world-leading and publicly available software. These new techniques and software may ultimately be able to solve some of the most complex optimisation problems in research and industry, such as improving long-term climate predictions and designing 3D-printed medical implants.Read moreRead less