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.
Security and Privacy of Individual Data Used to Extract Public Information. The project aims to contribute to the development of techniques to allow the harvesting of useful information without compromising personal privacy. Intelligent analysis of personal data can reveal valuable knowledge about a population but at a risk of invading an individual's privacy. This project aims to provide at least partial solutions to some of the problems associated with the protection of private data. In partic ....Security and Privacy of Individual Data Used to Extract Public Information. The project aims to contribute to the development of techniques to allow the harvesting of useful information without compromising personal privacy. Intelligent analysis of personal data can reveal valuable knowledge about a population but at a risk of invading an individual's privacy. This project aims to provide at least partial solutions to some of the problems associated with the protection of private data. In particular, it plans to work on the problem of security of statistical databases and privacy of streaming data. This would be underpinned by a study of anonymisation and homomorphic encryption. The expected outcomes are new theoretical results, new algorithms and protocols applicable to at least some of the current significant problems in information security.Read moreRead less
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
Elliptic curves: number theoretic and cryptographic aspects. Smart information use is of fundamental nature and has a great number of applications. First-generation security solutions are unable to support the modern requirements and new security infrastructures are emerging that must be carefully, but rapidly, defined. This urgently needs new mathematical tools, which is the main goal of this project.
Search strategy optimisation by theory, functional analysis and simulation. This project aims to develop a novel computational platform, based on mathematical, statistical and physical theory, as well as advanced simulations, enabling the quantitative prediction of the optimal search strategy to be adopted by populations of agents searching for scarce targets in any given environment. This could lead to significant impacts on breakthrough developments in cancer immunotherapy, search and rescue r ....Search strategy optimisation by theory, functional analysis and simulation. This project aims to develop a novel computational platform, based on mathematical, statistical and physical theory, as well as advanced simulations, enabling the quantitative prediction of the optimal search strategy to be adopted by populations of agents searching for scarce targets in any given environment. This could lead to significant impacts on breakthrough developments in cancer immunotherapy, search and rescue robotics, ecological and environmental management, and developmental biology.Read moreRead less
More information for better utility; less information for better privacy. More information for better utility; less information for better privacy. The contradiction is everywhere in contemporary IT: doctors need accurate information for diagnosis, but insurance companies' access should be limited; on-line retailers use your postcode to present interesting products, but they also deduce from it how much you will pay. One way to manage this contradiction is to tolerate "small" information flows p ....More information for better utility; less information for better privacy. More information for better utility; less information for better privacy. The contradiction is everywhere in contemporary IT: doctors need accurate information for diagnosis, but insurance companies' access should be limited; on-line retailers use your postcode to present interesting products, but they also deduce from it how much you will pay. One way to manage this contradiction is to tolerate "small" information flows providing the risks involved can be accurately gauged. This project will build on recent advances in information measuring to develop new techniques for measuring the extent to which computer systems can defend against threats to privacy. Success in this project will lead to completely novel methods for security analysis of on-line applications where privacy is a critical issue.Read moreRead less
Exploratory Experimentation and Computation in the Mathematical Sciences: Theory and Practice. Seemingly disparate mathematical research projects rely on subtle experimental mathematics methods, and have unveiled weaknesses in current computer algebra systems and symbolic-numeric-graphic tools. The project attacks issues of efficiency, effectiveness, reliability, and certifiability in high-precision mathematical and scientific computation. This will be done by developing enhanced tools for advan ....Exploratory Experimentation and Computation in the Mathematical Sciences: Theory and Practice. Seemingly disparate mathematical research projects rely on subtle experimental mathematics methods, and have unveiled weaknesses in current computer algebra systems and symbolic-numeric-graphic tools. The project attacks issues of efficiency, effectiveness, reliability, and certifiability in high-precision mathematical and scientific computation. This will be done by developing enhanced tools for advanced computation of special functions driven by pursuit of challenging research problems. The focus is on tractable components that arose in prior research on effective high-precision algorithms for multiple integrals, such as arise throughout mathematical physics, number theory and elsewhere.Read moreRead less
Beyond Planarity: Algorithms for Visualisation of Sparse Non-Planar Graphs. This project aims to develop new efficient algorithms to enable analysts to visually understand complex data and detect anomalies or patterns. It aims to develop visualisation algorithms for sparse non-planar graphs arising from real-world networks. Specifically, the project plans to investigate structural properties of sparse non-planar topological graphs such as k-planar graphs, k-skew graphs, and k-quasi-planar graphs ....Beyond Planarity: Algorithms for Visualisation of Sparse Non-Planar Graphs. This project aims to develop new efficient algorithms to enable analysts to visually understand complex data and detect anomalies or patterns. It aims to develop visualisation algorithms for sparse non-planar graphs arising from real-world networks. Specifically, the project plans to investigate structural properties of sparse non-planar topological graphs such as k-planar graphs, k-skew graphs, and k-quasi-planar graphs, and design efficient testing algorithms, embedding algorithms, and drawing algorithms. These algorithms will be evaluated with real-world social networks and biological networks. New insights into the mathematical interplay between combinatorial and geometric structures would provide a theoretical foundation for a new generation of complex network visualisation methods with potential applications in social networks, systems biology, health informatics, finance and security.Read moreRead less
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