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.
Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unit ....Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unites geometric techniques with powerful methods from operations research, such as linear and discrete optimisation, to build fast, powerful tools that can for the first time systematically solve large topological problems. Theoretically, this project has significant impact on the famous open problem of detecting knottedness in fast polynomial time.Read moreRead less
Advanced Monte Carlo Methods for Spatial Processes. The modeling and analysis of spatial data relies more and more on sophisticated Monte Carlo simulation methods. However, with the growing complexity of today's spatial data, traditional Monte Carlo methods increasingly face difficulties in terms of speed and accuracy. The aim of this project is to develop new theory and applications at the interface of Monte Carlo methods and spatial statistics, building upon exciting theoretical and computatio ....Advanced Monte Carlo Methods for Spatial Processes. The modeling and analysis of spatial data relies more and more on sophisticated Monte Carlo simulation methods. However, with the growing complexity of today's spatial data, traditional Monte Carlo methods increasingly face difficulties in terms of speed and accuracy. The aim of this project is to develop new theory and applications at the interface of Monte Carlo methods and spatial statistics, building upon exciting theoretical and computational advances in both areas in recent years. The research will stimulate the design of microscopic and macroscopic complex spatial structures with superior properties, such as composite materials, solar cells, telecommunication networks, mining operations, and road systems.Read moreRead less