Construction of near optimal oscillatory regimes in singularly perturbed control systems via solutions of Hamilton-Jacobi-Bellman inequalities. Problems of optimal control of systems evolving in multiple time scales arise in a great variety of applications (from diet to environmental modelling). This project addresses the challenge of analytically and numerically constructing rapidly oscillating controls that would 'near optimally coordinate' the slow and fast dynamics.
Decomposition and Duality: New Approaches to Integer and Stochastic Integer Programming. Because of their rich modelling capabilities, integer programs are widely used in industry for decision making and planning. However their solution algorithms do not have the maturity of their cousins in convex optimisation, where the theory of strong duality is ubiquitous. Efficient methods for convex optimisation under uncertainty do not apply to the integer case, which is highly non-convex. Furthermore, i ....Decomposition and Duality: New Approaches to Integer and Stochastic Integer Programming. Because of their rich modelling capabilities, integer programs are widely used in industry for decision making and planning. However their solution algorithms do not have the maturity of their cousins in convex optimisation, where the theory of strong duality is ubiquitous. Efficient methods for convex optimisation under uncertainty do not apply to the integer case, which is highly non-convex. Furthermore, integer models usually assume the data is known with certainty, which is often not the case in the real world. This project will develop new theory and algorithms to enhance the analysis of integer models, including those that incorporating uncertainty, while also enabling the use of parallel computing paradigms. Read moreRead less
Occupational measures, perturbations and complex deterministic systems. When tackling complex problems, scientists and engineers seek methods that judiciously exploit stochasticity and perturbations as antidotes to unpredictability of outputs that the latter can induce if they inadvertently influence their models. The project proposes for this study vaccine-like perspective of stochasticity and singular perturbations.
Improving Choice Models: Multiple Goal Pursuit and Multi-Stage Decision Processes. This project aims to develop new econometric models of choice behaviour that recognise individuals adopt “how to decide” strategies when choosing between alternatives. Existing models simplistically assume that people evaluate all goods and choose the best of them, when in fact they ignore some goods, select what information is relevant, pursue multiple goals, and otherwise deviate from the assumptions commonly ma ....Improving Choice Models: Multiple Goal Pursuit and Multi-Stage Decision Processes. This project aims to develop new econometric models of choice behaviour that recognise individuals adopt “how to decide” strategies when choosing between alternatives. Existing models simplistically assume that people evaluate all goods and choose the best of them, when in fact they ignore some goods, select what information is relevant, pursue multiple goals, and otherwise deviate from the assumptions commonly made in econometric models. Filling in this significant gap in the choice modelling literature constitutes a significant contribution to improving our understanding of human decision making and policy analysis in every area of human endeavour.Read moreRead less
Accounting for preference seperability in stated choice experiments. This project aims to unite three separate streams of applied economic research into a single framework in order to develop a micro-economically consistent framework for demand forecasting and analysis. Forecasting demand to improve product performance or policy impacts requires realistic representations of how humans actually make choices. Combining theories of preference separability with recent developments in both activity a ....Accounting for preference seperability in stated choice experiments. This project aims to unite three separate streams of applied economic research into a single framework in order to develop a micro-economically consistent framework for demand forecasting and analysis. Forecasting demand to improve product performance or policy impacts requires realistic representations of how humans actually make choices. Combining theories of preference separability with recent developments in both activity and time use modelling and stated choice techniques, the project plans to develop new insights into consumer equilibrium as well as new econometric methods to test for the assumption of preference separability. Project outcomes would lead to an improved understanding of consumer behaviour as well as demand forecasting, with benefits to studies involving the need for benefit cost comparisons.Read moreRead less
Optimal electromaterial structures for energy applications. This project aims to develop new mathematical and modelling approaches to determine optimal configurations and parameters for material structures created from three-dimensional printing of combined metals and electromaterials. Electromaterials are needed for sustainable energy, but solving coupled-systems of highly nonlinear governing equations is needed for optimal control of spatial arrangement and composition in nano and micro-struct ....Optimal electromaterial structures for energy applications. This project aims to develop new mathematical and modelling approaches to determine optimal configurations and parameters for material structures created from three-dimensional printing of combined metals and electromaterials. Electromaterials are needed for sustainable energy, but solving coupled-systems of highly nonlinear governing equations is needed for optimal control of spatial arrangement and composition in nano and micro-structural domains. Dealing with this mathematical complexity is critical to developing high efficiency energy generation and gas storage systems. This is expected to enhance transport mechanisms within electrochemical devices and create opportunities for industry to use electrofunctional materials.Read moreRead less
Suspension flows and particle focusing in curved geometries. The project aims to develop fast predictive tools to investigate suspension flows in curved channels and thin ducts and the effect of channel geometry on the focusing of particles by weight to different regions of the channel. Interaction between particles and fluid in suspension flows is a fundamental problem that is little understood but which is important in a wide range of problems in nature and industry (eg for design of microscal ....Suspension flows and particle focusing in curved geometries. The project aims to develop fast predictive tools to investigate suspension flows in curved channels and thin ducts and the effect of channel geometry on the focusing of particles by weight to different regions of the channel. Interaction between particles and fluid in suspension flows is a fundamental problem that is little understood but which is important in a wide range of problems in nature and industry (eg for design of microscale segregation devices for separation of different cells in a blood sample, and of macroscale devices for separation of mineral particles from crushed ore). At present, the description of these processes is qualitative, with quantitative understanding seen as a challenge without intensive computation. The project plans to develop, solve and validate mathematical models to give a quantitative understanding of these processes.Read moreRead less
Prediction of inertial particle focusing in curved microfluidic ducts. This project aims to develop mathematical models to predict migration of particles suspended in flow through curved microfluidic ducts and their focusing by size to different regions in the cross-section of the duct. New knowledge in mathematics and engineering will be generated through models that capture the two-way force balance between fluid and particles and by a novel use of asymptotics for computational efficiency. Exp ....Prediction of inertial particle focusing in curved microfluidic ducts. This project aims to develop mathematical models to predict migration of particles suspended in flow through curved microfluidic ducts and their focusing by size to different regions in the cross-section of the duct. New knowledge in mathematics and engineering will be generated through models that capture the two-way force balance between fluid and particles and by a novel use of asymptotics for computational efficiency. Expected outcomes are understanding of the physics that drives particle migration and the parameters that may be used to control particle focusing. This will benefit design and operation of microfluidic devices for particle sorting as required for "liquid biopsy", the isolation of cancer cells in a routine blood sample.Read moreRead less
Mathematical modelling of information flow in social networks. This proposal aims to develop new mathematical and statistical methods to understand information flow in social networks. By using novel information theoretic techniques, it will create new methods to characterise social information flow in social networks. These tools will allow derivation of fundamental limits of predictability for AI methods applied to digital data. New mathematics of information flow will produce insights into so ....Mathematical modelling of information flow in social networks. This proposal aims to develop new mathematical and statistical methods to understand information flow in social networks. By using novel information theoretic techniques, it will create new methods to characterise social information flow in social networks. These tools will allow derivation of fundamental limits of predictability for AI methods applied to digital data. New mathematics of information flow will produce insights into social influence in online social networks. Benefits include: better understanding of how echo chambers may form in social networks, predictive models for how misinformation can spread online such as during an emergency, and a framework for intercomparison of AI methods applied to digital data on individuals. Read moreRead less
Modelling mean and dispersion using fixed and random effects. The aims of the project are to develop methods for joint mean and dispersion modelling using fixed and random effects, in the generalized linear models context and for Gaussian longitudinal data. The significance is the more efficient, precise and appropriate analysis of data arising from many areas of application. The expected outcomes are therefore better methods of analysis, software to carry the analyses out, and potentially impor ....Modelling mean and dispersion using fixed and random effects. The aims of the project are to develop methods for joint mean and dispersion modelling using fixed and random effects, in the generalized linear models context and for Gaussian longitudinal data. The significance is the more efficient, precise and appropriate analysis of data arising from many areas of application. The expected outcomes are therefore better methods of analysis, software to carry the analyses out, and potentially important results in applications.Read moreRead less