New Frontiers and Advances in Discrete Integrable Systems. Integrable systems boast a long and venerable history, and have such famous members as the Kepler system, the Korteweg-de Vries equation, and the sine-Gordon equation. More recently, interest in integrable systems has expanded to include systems with discrete time, that is, ordinary difference equations (or maps) and integrable partial difference equations. These discrete integrable systems are arguably more fundamental than the continuo ....New Frontiers and Advances in Discrete Integrable Systems. Integrable systems boast a long and venerable history, and have such famous members as the Kepler system, the Korteweg-de Vries equation, and the sine-Gordon equation. More recently, interest in integrable systems has expanded to include systems with discrete time, that is, ordinary difference equations (or maps) and integrable partial difference equations. These discrete integrable systems are arguably more fundamental than the continuous-time ones. Based upon recent breakthroughs this study will combine analysis, geometry, and computer algebra to expand and systematise this new interdisciplinary field of discrete integrable systems.Read moreRead less
Estimating the Topology of Low-Dimensional Data Using Deep Neural Networks. This project will expand on the superhuman visual capabilities of deep neural networks to allow us to analyse the topology of 3- and 4-dimensional manifolds. While these spaces still count as low-dimensional, 4-dimensional manifolds typically are beyond human visual comprehension. The topology of a manifold describes its essential properties such as the number of connected components, holes, tunnels and cavities of vario ....Estimating the Topology of Low-Dimensional Data Using Deep Neural Networks. This project will expand on the superhuman visual capabilities of deep neural networks to allow us to analyse the topology of 3- and 4-dimensional manifolds. While these spaces still count as low-dimensional, 4-dimensional manifolds typically are beyond human visual comprehension. The topology of a manifold describes its essential properties such as the number of connected components, holes, tunnels and cavities of various dimensions. Traditional methods from computational topology fail in large practical applications due to computational restrictions. We propose an approximation that overcomes previous limitations and can open new doors to data analysis in material science, medical imaging, dynamical systems and other applications.
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Topological data analysis for enhanced modelling of the physical properties of complex micro-structured materials. The way water flows through sandstone depends on the connectivity of its pores, the balance of forces in a grain silo on the contacts between individual grains, and the impact resistance of metal foam in a car door on the arrangement of its cells. These structural properties are described mathematically by topology. Advanced three-dimensional X-ray imaging can now reveal the interna ....Topological data analysis for enhanced modelling of the physical properties of complex micro-structured materials. The way water flows through sandstone depends on the connectivity of its pores, the balance of forces in a grain silo on the contacts between individual grains, and the impact resistance of metal foam in a car door on the arrangement of its cells. These structural properties are described mathematically by topology. Advanced three-dimensional X-ray imaging can now reveal the internal detail of micro-structured materials. Recent developments in image analysis mean it is possible to compute accurate topological information from such images. This project aims to investigate how fundamental measures of shape influence the physical properties of complex materials and clarifies the mathematics that underpins these relationships.Read moreRead less
Hybrid methods with decomposition for large scale optimization. This project aims to develop advanced approaches for solving large scale real-world optimisation problems that are expensive to evaluate, and difficult to formulate, involving thousands of variables and constraints. The project will make novel contributions to improving state-of-the-art large scale optimisation algorithms in terms of scalability, effectiveness, and efficiency for real-world problem solving. The outcomes of this proj ....Hybrid methods with decomposition for large scale optimization. This project aims to develop advanced approaches for solving large scale real-world optimisation problems that are expensive to evaluate, and difficult to formulate, involving thousands of variables and constraints. The project will make novel contributions to improving state-of-the-art large scale optimisation algorithms in terms of scalability, effectiveness, and efficiency for real-world problem solving. The outcomes of this project will bring about greater understanding of real-world large scale optimisation, and deliver practical solutions to these problems.Read moreRead less
New Methods in Theory and Cosmic Applications of Spherical Random Fields. This project aims to investigate and model spherical random fields which are described as solutions of stochastic differential equations on a sphere or a ball. The project plans to study properties and develop spectral analysis of these solutions. It then plans to use the obtained theoretical results to construct new methods for numerical approximation and statistical estimation of these random fields. In particular, it pl ....New Methods in Theory and Cosmic Applications of Spherical Random Fields. This project aims to investigate and model spherical random fields which are described as solutions of stochastic differential equations on a sphere or a ball. The project plans to study properties and develop spectral analysis of these solutions. It then plans to use the obtained theoretical results to construct new methods for numerical approximation and statistical estimation of these random fields. In particular, it plans to develop novel asymptotic and statistical methodology for tensor random fields. The project will apply the results to model and analyse cosmic microwave background data. Expected outcomes will improve the accuracy in determining cosmological parameters and provide novel tools for better understanding of the universe during its early stages.Read moreRead less
Extreme soil acidification and metal release risks from increasing drought. The project aims to study the effects of drought on pH and metal speciation in soils, and develop tools to assess current and future risks. Social and economic well-being depends on good soil and water quality. Climate change makes droughts more frequent and severe, which could cause soil acidification (pH<4) and metal release in many regions. The project will integrate experimental data on the effects of drought on soil ....Extreme soil acidification and metal release risks from increasing drought. The project aims to study the effects of drought on pH and metal speciation in soils, and develop tools to assess current and future risks. Social and economic well-being depends on good soil and water quality. Climate change makes droughts more frequent and severe, which could cause soil acidification (pH<4) and metal release in many regions. The project will integrate experimental data on the effects of drought on soil geochemistry with hydro-geochemical models, and apply these to national-scale predictions. The intended outcomes are improved management and preparedness for droughts and new research directions for geochemistry.Read moreRead less
Paving the way: an experimental approach to the mathematical modelling and design of permeable pavements. The intelligent use of permeable pavements will enable restoration of degraded land corridors. Collection and treatment of stormwater via filtration through porous media will improve water quality in urban environments and will also control flooding. The integration of ecology and urban living will present a revolutionary way to revitalize cities.
Distributionally robust dynamic optimisation for nonlinear switched system. Biochemical production utilising fermentation processes evidences poor product repeatability. This project aims to control and optimise 1,3-propanediol production via microbial fermentation. 1,3-propanediol is an essential ingredient for many polymeric materials and is present in cosmetics, personal care and cleaning products. New theory and parallel algorithms will be developed for the control and optimisation of the mi ....Distributionally robust dynamic optimisation for nonlinear switched system. Biochemical production utilising fermentation processes evidences poor product repeatability. This project aims to control and optimise 1,3-propanediol production via microbial fermentation. 1,3-propanediol is an essential ingredient for many polymeric materials and is present in cosmetics, personal care and cleaning products. New theory and parallel algorithms will be developed for the control and optimisation of the microbial fermentation of 1,3-propanediol production, where the bacteria kinetic parameters are uncertain without full knowledge of the probability distribution. This theory will also be applicable to other fermentation processes. The project outcomes are expected to significantly improve the productivity of the biochemical engineering industry involving fermentation processes.Read moreRead less
Saving energy on trains - demonstration, evaluation, integration. Reducing energy use from rail transport will significantly contribute to cutting carbon dioxide emissions. This project will develop a toolkit to facilitate the introduction of in-cab technologies that help train drivers save energy and stay on time. The toolkit will make it easier to demonstrate, evaluate and integrate the system in a range of railways.