EPSRC's EngD was successfully modernised by WMG in 2011 with radical ideas on how high-level skills should be implemented to address the future needs of manufacturing companies within the UK and globally. In a continual rise to the challenge of a low environmental impact future, our new proposed Centre goes a step further, delivering a future generation of manufacturing business leaders with high level know-how and research experience that is essential to compete in a global environment defined by high impact and low carbon. Our proposed Centre spans the area of Sustainable Materials and Manufacturing. It will cover a wide remit of activity necessary to bring about long term real world manufacturing impacts in critical UK industries. We will focus upon novel research areas including the harnessing of biotechnology in manufacturing, sustainable chemistry, resource efficient manufacturing and high tech, low resource approaches to manufacturing. We will also develop innovative production processes that allow new feedstocks to be utilised, facilitate dematerialisation and light weighting of existing approaches or enable new products to be made. Research will be carried into areas including novel production technologies, additive layer manufacturing, net shape and near-net shape manufacturing. We will further deliver materials technologies that allow the substitution of traditional materials with novel and sustainable alternatives or enable the utilisation of materials with greater efficiency in current systems. We will also focus upon reducing the inputs (e.g. energy and water) and impacting outputs (e.g. CO2 and effluents) through innovative process and product design and value recovery from wastes. Industry recognises there is an increasing and time-critical need to turn away from using non-sustainable manufacturing feed-stocks and soon we will need to move from using processes that are perceived publically, and known scientifically, to be environmentally detrimental if we are to sustain land/water resources and reduce our carbon footprint. To achieve this, UK PLC needs to be more efficient with its resources, developing a more closed-loop approach to resource use in manufacturing whilst reducing the environmental impact of associated manufacturing processes. We will need to train a whole new generation of doctoral level students capable of working across discipline and cultural boundaries who, whilst working with industry on relevant TRL 1-5 research, can bring about these long term changes. Our Centre will address industrially challenging issues that enable individuals and their sponsoring companies to develop and implement effective low environmental impact solutions that benefit the 'bottom line'. Research achievements and enhanced skills capabilities in Sustainable Materials and Manufacturing will help insure businesses against uncertainty in the supply of materials and price volatility in global markets and enable them to use their commitment to competitively differentiate themselves.

Quantum technologies have seen considerable development over the last decade and there are now several material platforms available in which a small number of qubits can be operated; such as those based on trapped ions, superconducting, or semiconductor materials. Of these, one of the most promising current qubit implementations are dopant spins in silicon. The coherent times of electron and nuclear spins in silicon routinely exceeds milliseconds and seconds, respectively. At the same time, the silicon platform benefits from being able to build on the expertise and fabrication facilities of the semiconductor industry. Nevertheless, using semiconductor materials as a platform for solid-state qubits comes with its own unique challenges that are different from even state-of-the art-classical silicon technology. For example, unlike semiconductor chips found in classical electronics, spin qubits are susceptible to even the smallest magnetic field fluctuations, are sensitive to charge fluctuations via spin-to-charge coupling pathways such as spin-orbit or exchange coupling, and typically require operation at cryogenic temperatures. To develop dopant spins in silicon into a viable and scalable technology that would benefit society still requires a number of step changes and sustained investment from academic and industry partners. Here, we will therefore bring together a network of people from both UK and overseas universities, as well as many industry collaborators, which are uniquely suited to address these challenges. Of the key capabilities that our network of people brings, the first is the ability to fabricate dopant devices with atomic precision (UCL). Internationally there are very few groups with this expertise, and in some aspects, such as the incorporation of As dopants in silicon, our expertise is truly unique. To assess the devices requires mK transport measurements to establish key metrics such as quantum coherence and gate fidelities. Here we bring together several groups (UCL, Sydney) which have a long track record in this regard, as well as the required theoretical underpinning in terms of benchmarking and quantum error correction (Sydney, McGill). Still, for a full understanding of the device performance it is essential to understand and, quite literally, map out the performance of the quantum devices with energy and spatial resolution not possible with any conventional technology. In our network, we have the capability to combine the transport measurements with mK scanning gate mapping of the device (Cambridge) and single-electron sensitivity on the nm scale (McGill). The work will be brought together in two work packages, the first focussing on building the required qubit fabrication and device structures, whereas the second work package will focus on creating entanglement between physically separated qubit. Combining these key capabilities and research efforts into a single network allows us to go significantly beyond the current state of the art in terms of quantum device development and characterisation such that reliable and viable prototypes can be built. Looking beyond the first prototypes the network will also be working on the scalability of the platform, both in terms of device fabrication (UCL) and the required - classical cryogenic - control electronics (Sydney). An additional benefit is that the research group is strongly integrated with industrial leaders, in terms of data acquisition, materials characterisation and hardware and software development. To ensure our research will reach a wide audience and be available to all relevant stakeholders we will have a dedicated outreach programme (Sydney lead).

Correct-by-construction program development uses advanced type systems to describe both the data manipulated by computation, and the correctness of those computations. Embedding correctness within software has many advantages, as certified by several decades of pioneering work in the UK and elsewhere, which have culminated in systems such as Agda, Idris, Coq, Lean, HOL, Isabelle, etc., which are powerful enough to implement this vision and which are now having significant impact in both academia and industry. The main question that motivates this research is: can correct-by-construction programming be extended to computation with approximate values, e.g. in: i) stochastic systems where one needs to handle inherent/simulated randomness; ii) resource limited environments, where exact computation is prohibitively expensive; iii) systems with imperfect/partial recall, where one only has limited information about what has happened or the intentions/trustworthiness of each agent; and iv) non-exact computation where primitive data (e.g. from sensors) is inexact and supplied with error bars. These scenarios arise in e.g. cyber-physical systems, machine learning, robotics, automotive engineering, aerospace, and energy systems. Measuring how close measurements might be from their true values naturally leads to the use of metrics but, despite some successes, their use suffers from a number of drawbacks, e.g. i) metrics defined in one problem domain often do not carry over to others; ii) metrics based upon system structure often do not reflect behavioural similarity and vice-versa; and iii) increasingly accurate models of a system's structure are not guaranteed to have increasingly accurate behaviours to that of the modelled system. We conjecture that these problems are manifestations of the deeper problem that all of the mathematics underpinning computation takes exact equality as primitive, so approximation is built over an exact meta-theory. However, in a recent breakthrough, Mardare and his collaborators introduced Quantitative Algebra (QA) which generalises one of the central pillars of modern mathematics, namely universal algebra (UA), to allow approximate equations in formal reasoning. The generality of this new idea - replacing classical reasoning with a more refined approximate reasoning in the very fabric of mathematics - gives us a new paradigm which supports a rigorous logical framework for a proper approximation theory, where bounds can be handled, convergences proven and limits approximated. This project will transform the theory and applications of approximate computation by designing, implementing and deploying a new language for trusted approximate computation. It involves: i) Mathematical Research: We replicate the shift from UA to QA with a similarly revolutionary one from exact computation to approximate computation by developing new quantitative generalisations of the common mathematical structures underpinning exact computation. Approximate computation will then be driven by these new approximate versions of the key structures that drive exact computation. ii) Type Theory & Programming Languages Research: We develop a core dependent type theory incorporating equality-up-to-approximation and type checking to ensure approximation bounds are adhered to; and we convert our type theory into a usable programming language by developing high level features. iii) Applications and Impact Generation: We create case studies in systems biology and digital twins to validate our research and create impact with academic/industrial collaborators who have co-created this proposal. This involves the development of approximate game theory as both these case studies involve autonomous agents that need to make optimal decisions in the presence of uncertainty.

EPSRC : Jakub Deja : EP/V519509/1 The pollution from aircraft is expected to be seven to ten times higher in 2050 compared to 1990 level. To address the issue, a kinetic energy recovery system fitted onboard commercial aircraft is proposed. The system is widely used in automotive industry but has never been proposed for aerospace applications. Electric machines are a limiting factor because they have low power output relative to weight. This research project will be a part of the wider study and will focus on development of electric machine beyond current technological limits and therefore will allow to meet the aerospace application requirements at a minimum weight penalty. The expected exchange outcome is a finalized electric machine topology selection and optimization. In addition, the network developed throughout the exchange would be a beginning of long-term collaboration focused on electric machines for aerospace applications, which would benefit both the UK and Canada.

Saints were the heroes of medieval culture, the centre of lively cults which presented them as active intercessors and examples for their fellow Christians. We will explore how devotion to medieval saints was constructed through the combination of liturgical, musical and material elements, in an area that has received little scholarly attention despite its rich culture: early medieval Iberia. Our study of the development and transmission of Iberian saints' cults from the Visigothic period to the 14th century will integrate hagiography, liturgical texts, chant, and material culture for the first time. This will offer a new perspective on how saints were constructed by and experienced by the communities that venerated them. We will publish a series of peer-reviewed journal articles and a team-authored monograph, as well as inviting an international general public to gain a new appreciation of this unique heritage via an interactive, multilingual and multimedia exhibition. We know that saints were proudly defended elsewhere in Western Europe as local patrons and community figureheads, and that veneration of saints was gendered: women were commemorated for virginity; and men were celebrated for leadership. Iberian saints, however, have not been analysed for their socio-cultural significance and integrated into wider European paradigms. This is the result of inaccessible manuscript sources, and lack of scholarly familiarity with the distinctive Old Hispanic rite. 'Iberian saints' brings together an interdisciplinary team to address these gaps in the research agenda, and to produce the first holistic study of saints' cults in early medieval Iberia, straddling multiple disciplinary specialisms, and engaging with how the veneration of Iberian saints shifted over the centuries, in particular during and after the 11th-century imposition of the Roman liturgy across much of Iberia. Our work will open up new research avenues for scholars in multiple disciplines, modelling an interdisciplinary approach that can shed new light on historical moments about which only fragmentary evidence survives. By adding a significant body of Old Hispanic material to www.musicahispanica.eu and www.cantusindex.org, we will facilitate integration of Old Hispanic liturgical evidence into the wider European context. Further, this data sharing will make the Old Hispanic materials widely accessible, with the (intricate and unfamiliar) liturgical structure ready parsed. We will undertake innovative transcription work in our web-based Chant Editing and Analysis Program (neumes.org.uk). Old Hispanic notation is unpitched, which poses significant challenges to scholars engaging with the melodies. In Iberian Saints, we will continue to develop analytical tools and methods that break new ground in our understanding of medieval monophonic melodic languages, available to all through our software and exemplified in our publications. Beyond academic discourse, our interactive digital exhibition will significantly increase the cultural value of our research findings. The exhibition will reconnect locals who visit archives and museums in Lamego, Coimbra, Salamanca and Toledo with this almost-forgotten aspect of their cultural heritage, as well as reaching out to tourists, and being available online. It will raise consciousness of Old Hispanic liturgy and its manuscripts, while communicating our new findings to the general public. The exhibition will engage audiences in ways that go far beyond superficial appreciation of the beauty and antiquity of the materials: they will be taught to navigate the texts, melodies and liturgical context, performing basic forms of analysis through interactive games, and navigating the GIS maps of each saint's cult. For some, there will be devotional and spiritual benefits as well; they will re-examine their own religious practices in the light of the thousand-year old culture to which we are drawing their attention.