The so-called lattice approach is a very successful first principle method that allows to solve Gauge Theories. Calculations resort to large scale simulations and are typically run on the largest supercomputers. Lattice simulations are a unique tool to explore non perturbative phenomena in theories which are not well understood. In Nature, non perturbative phenomena
Monte-Carlo methods are widely used in theoretical physics, statistical mechanics and condensed matter. Most of the applications have relied on importance sampling, which allows us to evaluate stochastically with a controllable error multi-dimensional integrals of localised functions. In lattice gauge theories, most quantities of interest can be expressed in the path integral formalism as ensemble
Non-random sample selection is a commonplace amongst many empirical studies and it arises when an output variable of interest is available only for a restricted non-random subsample of data. This often occurs in sociological, medical and economic studies where individuals systematically select themselves into (or out of) the sample based on a combination of observed
Various dynamical systems are described by differential equations. In control theoretic problems (e.g., in robotics), it is essential to determine and utilise the degrees of freedom of a system. The aim of this project is to develop new algorithmic methods for determining integrability conditions for systems of partial differential equations (PDEs). Certain effective techniques in
In twistor theory, the points of Minkowski space-time are picked out by the families of null geodesics through them. In relativity, each such family has the conformal structure of a sphere, interpreted in twistor theory as a Riemann sphere, or in other words a complex projective line. These complex projective lines lie inside the three
This project is concerned with the development and application of statistical methods to combine evidence from clinical trials, to produce more reliable estimates, making informed and evidence-based decision for health. Most health technology assessment requires making use of all available evidence. A meta-analysis is often conducted to obtain an overall effect estimate by combining results
This project will build on recent work that aims to test the security of base problems in lattice-based cryptography. These problems are computational lattice problems (e.g., learning with errors), which are conjectured to be difficult to solve. Such problems are central to the discipline of cryptography, the importance of which is shown by its prevalence
QCD is the basic theory behind nuclear physics . The quarks and gluons combine together to form bound states. Currently the only confirmed type of bound states found in experiments are either mesons (quark and antiquark bound together) or baryons (a collective state of three quarks), but QCD allows other possibilities. One particularly exciting type of bound state is called
This project will build on recent work that developed models that provide clinicians with a better understand of changes in children’s eyes as they get older. The models for visual acuity measurements made on each eye were based on two-dimensional probability density functions called copulas and smooth curves called splines that relate the shape of
This project will build on recent work concerning the extraction of information from Social Media such as Facebook and Twitter. It will develop methodology to provide a dynamic understanding of sentiments expressed on social media, including sentiments represented by emoticons, and to relate these to events such as news stories and stock market fluctuations. It