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
Mathematical models for water management systems. The Australian community is currently talking about schemes to return water to the Murray-Darling river system to combat increased salinity and dramatically reduced river flow. Many believe that vastly improved water management policies are essential to maintain agricultural well-being in Australia. Salinity and water quality depend directly on flow rates and are also important in smaller catchments. In this study we will use statistical rainf ....Mathematical models for water management systems. The Australian community is currently talking about schemes to return water to the Murray-Darling river system to combat increased salinity and dramatically reduced river flow. Many believe that vastly improved water management policies are essential to maintain agricultural well-being in Australia. Salinity and water quality depend directly on flow rates and are also important in smaller catchments. In this study we will use statistical rainfall models and stochastic dynamic programming to find practical water management policies that minimise the risk to water supply. We will develop an interactive simulation and management tool using a modern computer graphics package.Read moreRead less
A graphical simulation package for optimal management and risk assessment in urban stormwater harvesting systems. We will develop a Scalar Vector Graphics (SVG) simulation tool for optimal management and risk assessment in urban stormwater harvesting and utilisation schemes. The generic model will be applied to existing and proposed schemes within the City of Salisbury (CoS) and will include a capture dam, one or more storage dams and an aquifer storage and recovery (ASR) facility. The discret ....A graphical simulation package for optimal management and risk assessment in urban stormwater harvesting systems. We will develop a Scalar Vector Graphics (SVG) simulation tool for optimal management and risk assessment in urban stormwater harvesting and utilisation schemes. The generic model will be applied to existing and proposed schemes within the City of Salisbury (CoS) and will include a capture dam, one or more storage dams and an aquifer storage and recovery (ASR) facility. The discrete state vector will be the content of each storage unit and the daily transition will be driven by a new stochastic rainfall model (SRM). The objective will be to find a practical management policy that minimises Conditional Value-at-Risk (CVaR).Read moreRead less
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
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.
Stochastic Scheduling for Production and Delivery of Perishable Products with Imperfect Information. Australia has a wide range of industries producing perishable goods such as wheat, fruit, vegetables, meat, milk, seafood and health products, as well as fashion and entertainment goods. These industries play a critical role in the Australian economy, as well as impacting on national health and the environment. This project will provide new strategies, models and techniques to increase efficiency ....Stochastic Scheduling for Production and Delivery of Perishable Products with Imperfect Information. Australia has a wide range of industries producing perishable goods such as wheat, fruit, vegetables, meat, milk, seafood and health products, as well as fashion and entertainment goods. These industries play a critical role in the Australian economy, as well as impacting on national health and the environment. This project will provide new strategies, models and techniques to increase efficiency in both the production and delivery of perishable products. The outcomes of the project will enable decision makers in industries handling perishable products to optimise the use of resources, reduce costs and waste, raise productivity and improve services. The nation will benefit with higher export income and better quality of consumer products.Read moreRead less
Stochastic majorization--minimization algorithms for data science. The changing nature of acquisition and storage data has made the process of drawing inference infeasible with traditional statistical and machine learning methods. Modern data are often acquired in real time, in an incremental nature, and are often available in too large a volume to process on conventional machinery. The project proposes to study the family of stochastic majorisation-minimisation algorithms for computation of inf ....Stochastic majorization--minimization algorithms for data science. The changing nature of acquisition and storage data has made the process of drawing inference infeasible with traditional statistical and machine learning methods. Modern data are often acquired in real time, in an incremental nature, and are often available in too large a volume to process on conventional machinery. The project proposes to study the family of stochastic majorisation-minimisation algorithms for computation of inferential quantities in an incremental manner. The proposed stochastic algorithms encompass and extend upon a wide variety of current algorithmic frameworks for fitting statistical and machine learning models, and can be used to produce feasible and practical algorithms for complex models, both current and future.
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
Strategic integration of renewable energy systems into the electricity grid. The Intergovernmental Panel on Climate Change states that 'warming of the climate system is unequivocal' and there is high probability it is anthropogenic. In response to the growing awareness of climate change, there is an expansion in Australia in the use of renewable energy resources in electricity generation, albeit from a low base. The various renewable energy systems have differing patterns of availability and vol ....Strategic integration of renewable energy systems into the electricity grid. The Intergovernmental Panel on Climate Change states that 'warming of the climate system is unequivocal' and there is high probability it is anthropogenic. In response to the growing awareness of climate change, there is an expansion in Australia in the use of renewable energy resources in electricity generation, albeit from a low base. The various renewable energy systems have differing patterns of availability and volatility, and it is difficult to determine the right mixture to best match the demand. It is imperative that future growth be structured so that both maximum grid penetration, and required greenhouse gas reductions be attained. Read moreRead less