This project will involve understanding the links between the behaviour of gravity on small scales and on cosmological scales. These will be used to understand how to model inhomogeneities in cosmology in a background independent way, and to construct frameworks for testing relativistic gravity on a wide range of spatial scales.

This project will examine traditionalist nationalism in the 'High Commission Territories' (HCT) states of Lesotho, Botswana and Swaziland during the interwar period. The interwar was vital for traditionalist nationalist movements, whose bases were situated in rural milieu and whose ideas were often rooted in local politics. The nationalism exhibited in these countries during the interwar period confounds assumptions that nationalism was initiated by the experience of WWII and widens the discussion surrounding African nationalism. In Lesotho, Botswana and Swaziland traditionalist nationalism emerged from different sources but each shared some key commonalities. Notably each movement featured a syncretic ideological outlook combined with a presentation of their transformative agenda as rigidly respecting established cultural conventions of law and government. Whether it was Lekhotla La Bafo (LLB) in Lesotho, the activities of Simon Ratshosa in Botswana, or the expansion of the Liqoqo council in Swaziland, all three saw the development of nationalist activism. This study aims to use a variety of private and public transcripts produced from both anti-colonial activists and British officials. These rural anti-colonial groups often left a wide-ranging repertoire of sources due to being closely monitored by the colonial state. We have significant insight into their activities and worldviews. I will make extensive use of the colonial records at the National Archives located in Kew (TNA), the Royal Archives of Lesotho located in the British Library (BL) along with the national archives of Lesotho, Botswana and Swaziland; located within Morija, Gaborone and Mbabane respectively. Through examining these sources my project's primary contributions to the historiography of African history will therefore be threefold. Firstly, it will demonstrate that traditionalist nationalism as its own unique entity, seeming to combines aspects of a 'nativist movement' with modern nationalism. Secondly, it will challenge the assertion made by previous studies that it was only after WWII that diverse forms of African mobilization began. Lastly it will reveal some unique exercises in nation building, which challenge the idea of western style nationalism was the only kind of successful nationalism in the African context.

Over the past ten years there has been a marked reduction in the number of deaths from heart disease. A major factor contributing to this is the wider use of a group of medicines called statins. Large clinical trials including the Heart Protection Study played a key role in demonstrating the important protective actions of statins for patients with symptoms of heart disease, as well as for those who are likely to develop disease because of high cholesterol levels or other risk factors. However, this study was unable to predict those who had the most active disease and likely to suffer from heart attacks or other vascular events such as stroke. If a simple diagnostic test became available to detect people at highest risk of disease at an early stage, this would allow more intensive medical treatment, as well as diet and lifestyle advice to cut their risk of life-threatening vascular events or sudden death. Endothelin is a vasoconstrictor peptide produced by the endothelium (a single layer of cells that line every blood vessel). Research over the past twenty years has strongly implicated endothelin in the underlying processes leading to heart disease. But measuring endothelin in blood samples is too difficult to provide a reliable means of diagnosis. However, when endothelin is produced in cells it is synthesized as part of a large protein called proendothelin. Because fragments of this protein are also secreted with endothelin it is likely that one of these fragments can provide a reliable indicator of the level of endothelin production, and indirectly the presence of active heart disease. The aims of this project are: (1) to identify the best fragment of proendothelin to use as a new diagnostic test, and (2) to evaluate the usefulness of this test to detect people with heart disease. The diagnostic potential of this new test will be evaluated in a two-step process. Firstly, samples from a well-characterised set of 500 diabetic patients who have undergone detailed screening for heart disease, and progression of disease will be used to assess which is the best method of proendothelin measurement for identifying active heart disease. The second stage of validation will be to apply the best method to measurement of the baseline samples from the 20,536 subjects participating in the Heart Protection Study. These investigations are likely to lead to a new diagnostic test for screening for heart disease.

The purpose of this proposal is to test the idea that the puzzling variations in the behaviour of carbon nanotubes under high pressure observed by different research groups around the world are due to Raman resonance effects. The implication is that high-pressure Raman spectroscopy of nanotubes - and indeed the study of nanotubes in different solvents - absolutely requires tunable laser excitation, so the same nanotubes (diameter and chirality) can be picked out as the conditions are changed. This would bring high-pressure Raman to a much higher degree of precision and here enable reliable and definitive high-pressure data to be obtained for single wall carbon nanotubes. As far as we are aware, no laboratory world-wide has the capabilities (tunable Raman plus high pressure) required for this programme, so the apparatus will constitute a novel, indeed unique facility. The results of this programme will have pivotal implications for the entire literature on the subject. The results will provide means of reliable testing of mechanical response of carbon nanotubes to applied stress and will provide decisive insights into interplay (and connection) between mechanical and electronic properties of nanotubes. This will provide vital information to the academic community and to workers in nanotechnology exploiting carbon nanothubes.

This project is at the intersection of stochastic topology and geometry. Phase transitions are common phenomena in probability and statistical models, where the behaviour of a system changes abruptly. Our goal is to study various types of topological phase transitions in stochastic geometry models, generalising well-known lower dimensional phenomena. The phenomena we study are also related to statistical challenges in topological data analysis (TDA). To analyse high-dimensional structures we use the language of homology from algebraic topology. Briefly, in addition to connected components, homology can describe "holes" (closed loops), "cavities" (closed surfaces), and higher dimensional structures known as k-cycles. The first part of this proposal deals with high-dimensional generalisations of connectivity. From a homological perspective, connectivity is the "convergence" of 0-cycles to their ultimate (trivial) limit. Analogously, we can study phase transitions where higher-dimensional k-cycle converge. We plan to study several random models related to both stochastic geometry and TDA. Our goal is to prove sharp transitions for homological connectivity and analyse the obstructions to connectivity in the critical window. Our analysis relies on Morse theory - a mathematical framework linking between topology and differentiable functions. Specifically, we use critical points of the distance function to analyse changes in homology. In terms of TDA, the outcomes will be useful to prove consistency for topological inference methods, and to reduce their computational costs. The second part addresses the well-established area of coverage theory. Problems in this field are concerned with the ability of random small sets to cover a bigger region. We propose a novel topological approach linking Morse theory to coverage. This allows us to translate questions about m-coverage (where each point is covered by m or more small sets) into questions about the critical points of a new type of distance functions. Our new approach enables us to provide new and simpler proofs for well-known results, extend these results to more generic settings, and provide functional limit theorems for the vacant regions. In addition, we can go beyond coverage, and study homological connectivity for m-coverage objects. The third part deals with the formation of large-scale topological structures. This is a high-dimensional generalisation for percolation theory - the study of large connected components in random media. Our goal is to extend this study from components to large k-cycles, i.e. large "loops" or "closed sheets". We refer to this study as homological percolation. The main challenge is that the techniques used in percolation theory do not naturally extend to higher dimensions. As a first step, we will study homological percolation in compact spaces and the formation of "giant" k-cycles. Once the theory matures, we will shift our focus to infinite spaces, which is the most well-studied setting in classical percolation. This will present a new line of challenges, as topological definitions and dualities do not extend naturally to non-compact spaces. Finally, we plan to study the link between homological percolation and the Euler characteristic (EC). The connection we seek is highly non-obvious, as the EC is dominated by many small local objects, and a-priori should not be related to the appearance of a few large global structures. Nevertheless, recent experimental work suggests a strong link between the critical values for homological percolation and the zeros of the EC curve. The contribution of this study is twofold. In TDA, it will provide important insights into the detectability of meaningful topological features in data. In percolation theory, it represents new high-dimensional generalisations for the theory and methods used. Ultimately, this generalised theory will provide significant novel insight into classical special cases.