There are certain kinds of computer systems and devices from which we demand impeccable performance: medical devices; air traffic control systems; railway signalling; self-driving cars. In such mission-critical systems anything less than perfect performance could amount to unimaginable losses. One way to certify a mission-critical system's behaviour is to produce a mathematical proof that it will function as expected. However, this approach merely replaces one problem with another: how can we then be sure that the proof is correct, especially when it may run to hundreds of pages of detailed technical arguments? To solve this problem we have developed proof assistants. These are remarkable pieces of software: not only can they help us build large proofs, but they can also check the correctness of a proof on our behalf. Thus, as long as we trust the kernel of the proof assistant, we have some assurance that our proof is correct (and hence that our system/hardware/software is bug-free). However, this solution is not perfect. Developing proofs is a challenging task, perhaps an order of magnitude more difficult than software development. This has led in the last 10 years to the creation of proof engineering, a new field of Computer Science which is concerned with the development of large mathematical proofs. In this project we aim to make foundational contributions to one popular aspect of proof engineering, namely the formulation of Domain Specific Languages (DSLs). We aim to show that practical DSLs developed and used by proof engineers can be given a solid footing using a field of mathematical logic known as type theory. Our results will lead to better, simpler, reusable, and more transparent ways to design DSLs. This will offer substantial benefits to proof engineers, who will then be able to employ our techniques in order to verify the safety of even larger mission-critical systems in a systematic fashion, and with less effort. The project will be carried out by combining the theoretical background of the PI in the semantics of type theory with the practical expertise of the international collaborator, who has previously crafted development tools for testing within a popular proof assistant, Coq

In the past a few year, we have seen a dramatic increase in the scale and financial damage caused by cyber attacks. A survey commissioned by the government's Department for Business, Innovations and Skills (BIS) found that 93% of large businesses and 87% of smaller businesses suffered security breaches during 2013. An estimation from IDC says that companies around the world will spend $364 billion for dealing with data breaches in 2014. Data security is of paramount importance for most organisations. Compounding the problem, changes in computing -- particularly the booming of Cloud computing and collaborative data analysis -- has added another layer of complexity to the security landscape. Secure computation has the potential to completely reshape the cybersecruity landscape, but this will happen only if we can make it practical. Despite significant improvements recently, secure computation is still orders of magnitude slower than computation in the clear. Even with the latest technology, running the killer apps, which are often data-intensive, in secure computation is still a mission impossible. To make secure computation practical, we propose this groundbreaking data structural approach. In computer science, there are two fundamental approaches to improve performance of computation: by using a better algorithm, or by using a proper data structure. In secure computation, we have seen many improvements through the algorithmic approach. But surprisingly, data structures have been largely overlooked in the past. Recently, we have found ample evidence in our own and also others' research that data structures can be a key efficiency and scalability booster of secure computation. Based on the evidence, we believe the situation is sure to change: with data playing the central role and driving the computation, data structural design will become an indispensable part of secure computation. It is time to systematically investigate the design of data structures and accompanied protocols in the context of secure computation. Our proposed research will make scientific advances by investigating both data structures and cryptography. The starting point will be comprehensive case-by-case studies. Then the focus will be solving more complex problems by composition and to make data structures generic across multiple secure computation frameworks. Eventually we will draw design principles to guide future design practice.

When a disease epidemic sweeps through a population of plants, animals, or humans, the youngest individuals in the population are often hardest hit. This is because juveniles are typically more susceptible to infectious disease than adults. Indeed, the spread of many human diseases such as measles and chicken pox is largely driven by children. Likewise in many wildlife species, the spring 'pulse' of new highly susceptible young can drive epidemics, including diseases that risk spilling over into human or livestock populations. However, while the importance of juvenile susceptible to disease control has long been recognised, we lack a basic understanding of why juveniles are inherently so susceptible, even after accounting for prior exposure to disease. This research will use mathematical models and experiments with a model plant system to investigate the fundamental ecological and evolutionary processes driving the evolution of age-specific susceptibility. The results will substantially increase our understanding of the feedbacks between resistance evolution and disease spread, which will improve management strategies for wildlife disease, and inform crop breeding for disease resistance. The research will also increase public understanding of science and enrich local biodiversity records and museum collections through new citizen science outreach activities that are integrated with the basic research. The question of why juveniles are so susceptible is puzzling from an evolutionary perspective because infection prior to reproduction would seem to have a much greater negative impact on a host than infection later in life (after the host has had a chance to reproduce). Natural selection should therefore favour individuals that are less susceptible to disease when they are young. This project will test the novel hypothesis that juvenile susceptibility is maintained by feedbacks between evolutionary change in host resistance and ecological change in disease abundance. These "eco-evolutionary" feedbacks occur because the evolution of disease resistance at any age in the host population can in turn reduce the intensity of disease epidemics. Critically, lower disease-levels make it less likely that a host will encounter disease as a juvenile, thereby allowing the maintenance of juvenile susceptibility. The researchers will build on this novel eco-evolutionary framework to develop a predictive mathematical theory for understanding key host and pathogen traits, and the feedbacks driving the evolution of age-specific disease susceptibility. Then to establish how these age-specific selection pressures are instantiated in a real-world system and to test key predictions from the model, the research team will utilise the model plant-disease system, anther-smut disease (Microbotryum) on white campion (Silene latifolia) to quantify the fitness costs, benefits, and evolutionary potential of age-specific resistance under a range of disease frequencies. To increase the broader impacts and societal benefits of the proposed work they will engage local natural history societies in original scientific research on the distribution and diversity of 'micro-fungi', and provide meaningful research opportunities for undergraduates.

Research context:\nRobert Southey (1774-1843), poet, essayist, historian, biographer, translator and polemicist, was one of the most controversial of all Romantic period writers. He was a central figure in late C18th and early C19th British culture, a time of imperial expansion that saw Britain beset by war abroad and political, social and industrial change at home. Although Southey was a prolific correspondent, his letters have never been published in full. At present, the published letters are available only in out-of-print C19th and C20th selections, the former edited according to C19th conventions, with texts censored and cut. In addition, c.1500 letters have never been published at all. \n\nAims and objectives:\nThe Collected Letters will revolutionize this situation, making these important documents available in one place, many for the first time. \nThe 3200+ letters will be transcribed from original manuscripts, freshly edited and annotated to the very highest standards. c.1500 will be published for the first time, thus providing readers with a vast amount of new information about Southey's life, works and relationships with contemporaries. \n\nThe edition will thus fill a huge gap in Southey's writings. It will, furthermore, provide its intended audience of literary scholars and historians with the textual resources essential to future work on his life, works and intersections with his peers - writers, politicians, campaigners and scientists.\n\nEdited by a team of experienced, interdisciplinary scholars, the Collected Letters is an electronic edition and will be published from 2008-12 by the long-established, peer-reviewed specialists Romantic Circles [http://www.rc.umd.edu]. Romantic Circles' involvement is testimony to the project's internationally recognized significance. The technical expertise and financial support provided by Romantic Circles will ensure that the Collected Letters will incorporate the very highest electronic production values and be made available to the widest possible audience on a free-access web-site. \n \nThe co-applicants have already carried out a great deal of preliminary research. This application is for funding to allow them to complete the first half of the Collected Letters (Parts 1-4, scheduled for publication 2007-9) and to lay the foundations for the second half. In addition, the project RA will produce supplementary bibliographical databases, making these available on a free-access web-site. They will thus provide a set of unique research tools essential for completion of the Collected Letters and of great value to scholars working on Southey and British Romanticism.\n\nApplications and benefits:\nThe Collected Letters appears at a time when interest in Southey is increasing rapidly, a situation testified to by the appearance in 2004 of the first major critical edition of his early-mid career poetry (Robert Southey: Poetical Works 1793-1810, eds. Pratt, Fulford and Roberts, 5 vols: Pickering and Chatto) and in 2006 by the publication of a new biography (W. A. Speck, Robert Southey: Man of Letters, Yale UP) and the first ever collection of essays devoted to his impact upon Romantic-period culture (Robert Southey and the Contexts of English Romanticism, ed. Lynda Pratt, Ashgate). The Collected Letters will build upon these achievements, advancing critical understanding of Southey as a major writer central to a re-historicised, public Romanticism. \n\nThe edition will be published serially (2007-2012) and at all stages will fill acknowledged gaps both in knowledge of Southey's life and works and in understanding of his relationships with his contemporaries. It will be consulted by scholars from a range of disciplines: literary critics and historians. It will also become the standard scholarly resource for generations of researchers to come, taking its place alongside the collected editions of the correspondence of his peers, Coleridge and Wordsworth.

Although the terrestrial mantle comprises ~80 vol.% of our planet, its compositional architecture is not well understood despite the importance such knowledge holds for constraining Earth's thermal and chemical evolution over ~4.5 billion years of geological time. Our lack of detailed insight into the mantle stems in part from the fact that it is rarely exposed at our planets surface, making direct observation and study difficult. It is clear from recent study, however, that the mantle cannot be assumed to be compositionally homogenous or static over geological time. Peridotites from the ocean basins (abyssal peridotites) and from ophiolites preserve evidence for a convecting upper mantle that is chemically and isotopically heterogeneous at regional (100's km) and small (cm-to-m) scales. Complex formation and alteration upper mantle histories involving processes of melt-depletion, refertilisation (whereby originally refractory residues such as harzburgites become lherzolites again via melt addition) and melt-rock reaction have been held responsible, but the causes, timing and distribution of such processes are poorly resolved. Ophiolites, which represent partially-to-wholly preserved slivers of obducted oceanic mantle, are particularly valuable resources for assessing the timing, causes and extent of mantle heterogeneity, as they allow field-based observation to be coupled with geochemical investigation on otherwise inaccessible mantle material. Furthermore, ophiolites preserve a range of oceanic mantle lithologies (e.g., harzburgites, lherzolite and dunite) and such variation allows detailed assessment of the distribution and relative timing of events acting upon the mantle that is preserved. A distinctive attribute of some ophiolites, which contrasts with abyssal peridotites, is the presence of podiform chromitite seams, typically in the region of the petrological Moho, which are often associated with Platinum-group element mineralization. The timing and genesis of ophiolite podiform chromitites is controversial, but it has been suggested that they represent zones of focused melt channeling in supra-subduction zone settings. The Shetland (UK) and Leka (Norway) supra-subduction zone ophiolites comprise oceanic lithosphere separated at ~620 Ma on either side of a mid-ocean ridge and subsequently obducted over continental crust ~130 Ma later, each on opposite sides of the northern Iapetus Ocean. A pilot study already carried out on the Shetland ophiolite by the PI and Project Partner reveals that it preserves evidence for a complex sequence of melt depletion, percolation and refertilisation events that occurred over the lifetime of the Iapetus mantle. The critical observation made from the pilot dataset is that later mantle events only partially overprint the compositional heterogeneities developed from earlier mantle processes and that the relatively high degrees of partial melting associated with the supra-subduction zone are very effective at generating such heterogeneity. This important observation will be tested in the proposed research by 1) extending the Shetland study to greater levels of detail; 2) inclusion of a comparative study of carefully selected samples from the well-preserved Leka ophiolite; 3) drawing comparisons with existing geochemical and isotopic datasets from ophiolites that formed in other (e.g., mid-ocean ridge) tectonic settings. In order to achieve this, the powerful combination of the Re-Os isotopic system and highly-siderophile element (Os, Ir, Ru, Rh, Pt, Pd, Re, Au) abundance measurements will be utilised to discriminate between the processes responsible for generating mantle heterogeneities such as melt depletion, refertilisation and melt-rock reaction. Thus, profound insight will be gained into the chemical evolution of a piece of oceanic mantle and the development of compositional heterogeneity therein, from outcrop to oceanic plate scales, over much of the lifetime of the Iapetus Ocean.