Regularisation methods of inverse problems: theory and computation. This project aims to investigate regularisation methods for inverse problems which are ill-posed in the sense that their solutions depend discontinuously on the data. When only noisy data is available, regularisation methods define stable approximate solutions by replacing the original inverse problem with a family of well-posed neighbouring problems monitored by a so-called regularisation parameter. The project expects to devel ....Regularisation methods of inverse problems: theory and computation. This project aims to investigate regularisation methods for inverse problems which are ill-posed in the sense that their solutions depend discontinuously on the data. When only noisy data is available, regularisation methods define stable approximate solutions by replacing the original inverse problem with a family of well-posed neighbouring problems monitored by a so-called regularisation parameter. The project expects to develop purely data-driven rules to choose the regularisation parameter and show how they work in theory, and in practice. It will also develop convex framework, acceleration strategies as well as preconditioning and splitting ideas to design efficient regularisation solvers.Read moreRead less
Solving and estimating dynamic models of strategic interaction. This project aims to investigate how firms interact with each other through time and how these interactions drive both the operation of, and value created in, economic markets. While recent theoretical models predominantly capture the complexity of these dynamic interactions, the methods for testing these models’ predictions against observed data do not. Instead, they are based on a range of simplifying assumptions that undermine th ....Solving and estimating dynamic models of strategic interaction. This project aims to investigate how firms interact with each other through time and how these interactions drive both the operation of, and value created in, economic markets. While recent theoretical models predominantly capture the complexity of these dynamic interactions, the methods for testing these models’ predictions against observed data do not. Instead, they are based on a range of simplifying assumptions that undermine the reliability of their analysis. This project will develop statistical and computational methods to better understand observed economic behaviour. By allowing the effects of proposed economic interventions and regulations ex ante, this project will support the development of more efficient and better-targeted policies in every area of the economy.Read moreRead less
Single spin molecular microscope. This project aims to create a new tool for imaging and analysing material at the atomic level. The tool is based on individual quantum coherent spins in diamond which can be manipulated and optically read. The project expects to generate knowledge in quantum metrology and an understanding of molecular dynamics at the nanoscale. The expected outcome is a new type of device capable of imaging complex physical systems at the level of their individual constituent co ....Single spin molecular microscope. This project aims to create a new tool for imaging and analysing material at the atomic level. The tool is based on individual quantum coherent spins in diamond which can be manipulated and optically read. The project expects to generate knowledge in quantum metrology and an understanding of molecular dynamics at the nanoscale. The expected outcome is a new type of device capable of imaging complex physical systems at the level of their individual constituent components. This has significant benefits in improving designer materials, energy production, information storage, and drug design.Read moreRead less