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The theory of operator algebras goes back to Murray, von Neumann, Gelfand and Naimark. The original motivation was to provide a mathematical foundation for quantum mechanics. At the same time, from the very beginning of the subject, it was anticipated that operator algebras form very interesting structures on their own right and will have applications to unitary representations of groups and operator theory in Hilbert space. Actually, much more turned out to be true. After some dramatic and unexpected developments, the theory of operator algebras has established itself as a very active and highly interdisciplinary research area. Not only do there exist - as initially envisioned - strong connections to quantum physics as well as representation theory and operator theory, operator algebras nowadays have far reaching applications in various mathematical disciplines like functional analysis, algebra, geometric group theory, geometry, topology or dynamical systems. One of the most important classes of operator algebras is given by C*-algebras, which are defined as norm-closed, self-adjoint algebras of bounded linear operators on a Hilbert space. As in many areas in mathematics, advances in the theory of C*-algebras went hand in hand with the discovery of interesting and illuminating examples, the most prominent ones being group C*-algebras and C*-algebras attached to dynamical systems, so-called crossed products. The main objects of study in this research project are given by semigroup C*-algebras, which are natural generalizations of group C*-algebras. Our goal is to analyse the structure of semigroup C*-algebras and to use this construction as a tool to study groups and their subsemigroups from the point of view of geometric group theory. Closely related to this, this project also aims at a better understanding of the interplay between C*-algebras and dynamical systems. Our project lies at the frontier of current research. We take up recent advances in semigroup C*-algebras, classification of C*-algebras, the interplay between C*-algebras and symbolic dynamics, as well as the discovery of rigidity phenomena in operator algebras and dynamical systems. One of the key characteristics of our research project is its high interdisciplinary character. It lies at the interface of several research areas in mathematics and brings together expertise from different fields. This takes up the trend in mathematics that interactions between different branches are becoming more and more important. Therefore, the mathematical community as a whole benefits through an active and inspiring exchange of ideas.

The demand for future conversational speech technologies is estimated to reach a market value of $3 billion by 2020 (Grand View Research, 2014). Our proposed technology will provide vital foundations and impetus for the rapid development of a next-generation of naturally interactive conversational interfaces with deep language understanding, in areas as diverse as healthcare, human-robot interaction, wearables, home automation, education, games, and assistive technologies. Future conversational speech interfaces should allow users to interact with machines using everyday spontaneous language to achieve everyday needs. A commercial example with quite basic capabilities is Apple's Siri. However, even today's limited speech interfaces are very difficult and time-consuming to develop for new applications: their key components currently need to be tailor-made by experts for specific application domains, relying either on hand-written rules or statistical methods that depend on large amounts of expensive, domain-specific, human-annotated dialogue data. The components thus produced are of little or no use for any new application domain, resulting in expensive and time-consuming development cycles. One key underlying reason for this status quo is that for spoken dialogue, general, scalable methods for natural language understanding (NLU), dialogue management (DM), and language generation (NLG) are not yet available. Current domain-general methods for language processing are sentence-based and so perform fairly well for processing written text, but they quickly run into difficulties in the case of spoken dialogue, because ordinary conversation is highly fragmentary and incremental: it naturally happens word-by-word, rather than sentence-by-sentence. Real conversation happens bit by bit, using half-starts, suggested add-ons, pauses, interruptions, and corrections -- without respecting the boundaries of sentences. And it is precisely these properties that contribute to the feeling of being engaged in a normal, natural conversation, which current state-of-the-art speech interfaces fail to produce. We propose to solve these two problems together, by for the first time: (1) combining domain-general, incremental, and scalable approaches to NLU, DM, and NLG; (2) developing machine learning algorithms to automatically create working speech interfaces from data, using (1). We propose a new method "BABBLE" in which speech systems can be trained to interact naturally with humans, much like a child who experiments with new combinations of words to discover their usefulness (though doing this offline to avoid annoying real users while doing so!). BABBLE will be deployed as a developer kit and as mobile speech Apps for public use and engagement, and will also generate large dialogue data sets for scientific and industry use. This new method will not require expensive data annotation or expert developers, leading to easy creation of new speech interfaces that advance the state-of-the-art in interacting more naturally, and therefore more successfully and engagingly with users. New advances have been made in key areas relevant to this proposal: incremental grammars, formal semantic models of dialogue, and sample-efficient machine learning methods. The opportunity to combine and develop these approaches has arisen only recently, and now makes major advances in spoken dialogue technology possible.

Advances in fit for use manufacturing of biopharmaceutical drug delivery and pharmaceutical systems are now required to fit Quality by Design (QbD) models. These current regulations require excellence to be built into the preparation of emerging products (both material and process) thereby leading to product robustness and quality. In addition, industrial needs (economical and reproducible quality enhancement) are driving manufacturing towards continuous processes over batch type processes which also rely on QbD (for integrity and quality). EHDA technology is a robust process that has been utilised in various formats (e.g. electrospinning, electrospraying, bubbling and even 3D printing) and is favourable due to applicability with the development of stable nanomedicines and biopharmaceuticals, the emergence of this technology is clearly evident in the UK and on the global scale. Attempts in scaling up (for suitable pharmaceutical scale) and in tandem with continuous processes (including controlled manufacturing) have been very limited. There also, now, remains a huge void in the adaptation of sensible QbD (multi-variate) for the current methods developed and also those required by industry. While lab scale research continues with the ongoing development of such processes (e.g. nanomedicines, smart and controlled delivery), the transition to industry or the clinic will have to meet these regulations (and scales) for there to be a real impact, which is now, also, an important aspect of grass root research in the UK. The EHDA network brings together specialists from academia and industry to advance this technology through several means. Firstly, initiating developments towards a real-viable scale for Pharmaceutical production. Secondly, to incorporate developments in lean manufacturing and legislation (e.g. continuous manufacturing, online diagnostics, QbD and adaptable scale). Thirdly, to marry optimised lean technologies with novel and emerging macromolecular therapies and actives. The network has a wide range of activities and initiatives which will lead to significant developments (and collaborations) in an area of increasing global interest (EHDA processes) - but currently only on a viable lab scale to date. This network will be the first of its kind and will serve as the central and pioneering hub in this remit.

The present project proposes a new approach to replace fossil fuels by man-made ones using ultra-small metal particles. Our current energy needs are met by fossil fuels. This approach however is unsustainable owing to the different timescales of fuel production and combustion, the latter of which also generates greenhouse gases, changing the climate globally. On the other hand, uneven occurrence and distribution of sustainable energy sources, such as solar or wind power, warrants energy storage. Nature stores the Sun's energy as reduced carbon, e.g. coal, oil and gas. The present proposal will also employ this approach. Context Heterogeneous catalyst activity is dependent on the catalyst's surface area. With decreasing catalyst size, the surface-to-volume ratio increases, leading to improved activities. This could lead to the assumption that single atoms have the highest catalytic activity. However, size reduction may also alter the materials' physical and chemical properties related to the delocalisation of free electrons. Chemical reactivity of transition-metals is not only dependent on the atom numbers in a cluster but also on their arrangement, i.e. shape, owing to the spatial properties of d orbitals. In order to design transition-metal catalysts with selective and enhanced catalytic activity, it is thus crucial to establish the relationship between particle geometry and reactivity. Aims and Objectives The proposed project, will focus on ultra-small transition-metal particles, in the 1-50 atom range, supported on highly porous metal-organic frameworks. The particles' geometry-catalytic activity relationship will be explored for the conversion of feedstock harvested from air (CH4 and CO2) and water (H2) into synthetic fuels. The proposed project will first develop methods to synthesise shape- and size-controlled ultra-small metal particles using metal-organic frameworks as templates. The greatest challenge is identified as increased surface energy, a consequence of the increased surface-to-volume ratio. High surface energy in turn compromises the thermodynamic stability of particles and renders their size control difficult. Geometry control of the ultra-small transition-metal particles will be achieved by establishing strong metal-support interactions by i) preliminary computational calculations in collaboration with Prof Thomas Heine and ii) the application of metal-organic frameworks with chemical functionalities capable of selective host-guest interactions, which is herein proposed for the first time. Subsequently, the activity of the stable ultra-small transition-metal catalysts will be explored for the conversion of methane into longer chain hydrocarbons, the conversion of carbon dioxide through reduction with H2 (or CH4) and the activation and storage of hydrogen under mild conditions. Thanks to the PI's experience in both the functionalisation of metal-organic frameworks and their application as support for metal nanoparticles, together with her unique skillset in coordination and physical chemistry, and gas technologies, she is ideally placed to carry out this interdisciplinary and ambitious research. Applications and Benefits The particles will have various properties depending on their size and shape and will be exploited for ambient-temperature hydrogen storage, and the catalytic conversion of carbon dioxide, methane and hydrogen. Synthesis of fuels from pollutants such as CO2 and CH4 will reduce atmospheric pollution and convert them into more valuable chemicals while making use of already existing distribution infrastructures. The development of renewable, low-carbon energy carriers will benefit our society for energy security and the reduction of atmospheric pollutant levels. The proposed project will also accrue technology for gas sensing, drug delivery, electronics, water purification, gas separation, and in fuel cell and battery research.

With rapid increases in data volume in all areas of life, the meaningful analysis of these data is becoming a crucial bottleneck. Whether data are generated by customer transactions, through communications on social media, or as a by-product of manufacturing processes, data are meaningless unless suitable techniques are available to select the most relevant data, analyze these data and turn raw data into tangible information and insight. To some extent, "big data" reverses traditional approaches in data-mining, as data collection now frequently precedes the definition of an actual question or hypothesis. The purported advantage of this approach is that novel, unexpected findings may materialize - a premise that relies, however, on the expert use of suitable approaches for exploratory data analysis. The prominence of "big data" therefore fuels the need and use of scalable and powerful approaches to exploratory data analysis. Data clustering techniques present one of the most fundamental tools in exploratory data analysis, and this project aims to deliver novel techniques that are accurate, flexible and scalable to large data sets. Data clustering techniques present one of the most fundamental tools in exploratory data analysis. Conceptually, data clustering refers to the identification of sub-groups within a data set so that items within the same group are similar and those in different groups are dissimilar; e.g., in the context of insurance data, a "cluster" of people may relate to customers who show similar behaviour in their claim patterns over time, while those in different clusters behave differently. Mathematically, data clustering can be seen as an example of a problem where good solutions are best described using a set of different criteria that account for conflicting properties such as the compactness of clusters and the separation between clusters. The above observation has recently led to the development of multi-criterion approaches to data clustering, which explicitly consider a number of clustering criteria. This approach has shown a lot of promise, in terms of the accuracy and the robustness of the solutions obtained. However, current techniques for multi-criterion clustering are limited regarding their scalability to very large data sets and also their flexibility with respect to their consideration of different sources of dissimilarity data. This project proposes a novel technique for multi-criterion clustering: the algorithm will combine complementary ideas from two sub-fields of computer science, leading to improved scalability and flexibility of the technique developed. The work will include the development of an interactive user-interface and the application of multi-criterion clustering to problems in finance and marketing. All software produced will be released publicly.

The world's manufacturing economy has been transformed by the phenomenon of globalisation, with benefits for economies of scale, operational flexibility, risk sharing and access to new markets. It has been at the cost of a loss of manufacturing and other jobs in western economies, loss of core capabilities and increased risks of disruption in the highly interconnected and interdependent global systems. The resource demands and environmental impacts of globalisation have also led to a loss of sustainability. New highly adaptable manufacturing processes and techniques capable of operating at small scales may allow a rebalancing of the manufacturing economy. They offer the possibility of a new understanding of where and how design, manufacture and services should be carried out to achieve the most appropriate mix of capability and employment possibilities in our economies but also to minimise environmental costs, to improve product specialisation to markets and to ensure resilience of provision under natural and socio-political disruption. This proposal brings together an interdisciplinary academic team to work with industry and local communities to explore the impact of this re-distribution of manufacturing (RDM) at the scale of the city and its hinterland, using Bristol as an example in its European Green Capital year, and concentrating on the issues of resilience and sustainability. The aim of this exploration will be to develop a vision, roadmap and research agenda for the implications of RDM for the city, and at the same time develop a methodology for networked collaboration between the many stakeholders that will allow deep understanding of the issues to be achieved and new approaches to their resolution explored. The network will study the issues from a number of disciplinary perspectives, bringing together experts in manufacturing, design, logistics, operations management, infrastructure, resilience, sustainability, engineering systems, geographical sciences, mathematical modelling and beyond. They will consider how RDM may contribute to the resilience and sustainability of a city in a number of ways: firstly, how can we characterise the economic, social and environmental challenges that we face in the city for which RDM may contribute to a solution? Secondly, what are the technical developments, for example in manufacturing equipment and digital technologies, that are enablers for RDM, and what are their implications for a range of manufacturing applications and for the design of products and systems? Thirdly, what are the social and political developments, for example in public policy, in regulation, in the rise of social enterprise or environmentalism that impact on RDM and what are their implications? Fourthly, what are the business implications, on supply networks and logistics arrangements, of the re-distribution? Finally, what are the implications for the physical and digital infrastructure of the city? In addition, the network will, through the way in which it carries out embedded focused studies, explore mechanisms by which interdisciplinary teams may come together to address societal grand challenges and develop research agendas for their solution. These will be based on working together using a combination of a Collaboratory - a centre without walls - and a Living Lab - a gathering of public-private partnerships in which businesses, researchers, authorities, and citizens work together for the creation of new services, business ideas, markets, and technologies.

This programme is proposed to answer the EPSRC call on "Carbon capture and storage for natural gas power stations" by forming a close partnership between the University of Southampton and E.ON. The proposed research has a strong focus on industrial needs by integrating with the industrial partner's existing activities for developing CCS technologies suitable for commercial gas power plants. E.ON is generating around 10% of the UK's electricity and is committed to reducing its CO2 emission by 50% by 2030 (1990 baseline). E.ON has setup a dedicated CCS unit to address the technical challenges while one of the priorities is to develop CCS technologies suitable for natural gas power stations. This research specifically targets at natural gas power plants, which has a lower concentration of CO2 approx. 4% compared to 13% from coal-fired plants, and harder to extract, representing the most challenging case for CCS. Carbon capture and storage involves separating the CO2 from emissions so it can be transported and stored away from the atmosphere. The most commercially viable approach to be fitted in natural gas power plants is the post-combustion capture which absorbs CO2 from the flue gas using a chemical reaction - also known as scrubbing, which E.ON has been actively pursuing and will be the focus of this research. Whilst research on the chemical processes has been taking place for several decades, CFD modelling of the reactor is a recent development. E.ON has recognised that CFD plays a vital role in the optimisation of current CCS reactors by including more CFD research in their future research strategy. University of Southampton is a prime place for CFD based research while the School of Engineering Sciences currently holds £5M CFD focused EPSRC projects. The combined expertise forms a strong academic and industrial partnership to tackle current barriers of reactor scale-up in carbon capture using advanced CFD models. By addressing all the challenges outlined in the EPSRC call, this research aims to design an optimised reactor using a novel CFD modelling approach that is capable of achieving in excess of 90% CO2 absorption whilst ensuring the cost of service energy is minimised to below 35%. The new concept idea will incorporate improved mixing designs and improved heat transfer whilst reducing reactor size. It is planned through the enhancement of current CFD multiphase models to incorporate reaction and the inclusion of flow control devices that an optimal structured packing arrangement, which promotes the reaction process whilst reducing pressure drop, can be found. This project will not only produce conceptual ideas developed through enhance CFD methods but will also perform tests, in a lab-scale reactor, to determine its validity with respect to its flow dynamics and would potentially lead to the production of intellectual property.

The project concerns how groups of partially informed and self-interested agents (e.g., humans, robots), which are faced with a common problem, take a collective decision by exchanging their individual opinions to, possibly, reach a consensus. It aims at understanding how processes of opinion formation in groups behave and how they can be engineered in groups of artificial agents, like robots. The project capitalizes on techniques developed in the social and economic sciences, applying them to the artificial intelligence setting. It extends the state-of-the-art in the application of voting theory to artificial intelligence, addressing the process of opinion formation, and lays the theoretical groundwork for the development of collective decision-making techniques in autonomous systems.

Scattering problems (or diffraction problems) consist in studying the field resulting from a wave incident upon an obstacle. This can for example be an acoustic or an electromagnetic wave. In general, these are complicated time-dependent problems, but often a justified hypothesis can be made, which allows time considerations to be dismissed. As a consequence, the wave fields encountered in such problems all satisfy the same equation called the Helmholtz equation. The adjective "canonical" in the title of the project derives from studying simple obstacles, generally of infinite size, with particular characteristics such as sharp edges or corners. Although "simple", these canonical geometries can be used to evaluate the scattered field of more complicated finite obstacles subject to high frequency incident waves. The first such canonical problem to be considered was the problem of diffraction by a semi-infinite half-plane, and it was solved very elegantly by Arnold Sommerfeld in 1896. This was the start of the mathematical theory of diffraction. Since then, some very ingenious mathematical methods have been developed to tackle such problems, the most famous being the Wiener-Hopf and the Sommerfeld-Malyuzhinets techniques. However, despite tremendous efforts in this field, some canonical problems remain open mathematically, in the sense that no clear analytical solution is available for them. In particular, this is the case for two such problems, the three-dimensional problem of diffraction by a quarter-plane and the two-dimensional problem of diffraction by a penetrable wedge. The word penetrable means that waves can propagate inside the wedge region as well as outside, but with dissimilar wave speeds in the two regions. The aim of this project is to find a mathematical solution to these two problems, and to use these in concrete applications. It is motivated by a need to address environmental and economical issues linked to both climate change and the near future extinction of fossil fuels. In particular, results on the quarter-plane will be used to understand noise generation within a new type of aeroengine (predicted to drastically reduce the fuel consumption of civil aircraft) and underwater propulsors. This will have a significant impact in these fields of engineering, and will help to cement the UK's position as one of the leading countries for aero and underwater propulsor design. Results on the penetrable wedge will be used in collaboration with climate scientists at the University of Manchester to improve current models for quantifying the effect of light diffraction by ice crystals in clouds. This is a particularly important application since, due to the complex shapes of ice crystals, this problem currently represents one of the biggest uncertainties in predicting climate change. Furthermore, both aspects of the project will enhance the UK's reputation for high quality interdisciplinary applied mathematics research.

To reduce whole-life costs of the railway system (through increased asset life, reduced maintenance) and generate performance improvements (such as increased service availability and reliability), it is important to select the optimum material composition for railway components. Selecting the optimum materials for wheels and rails is a complex task with many conflicting requirements, including: a range of failures mechanisms, variety of operating and loading conditions and the associated financial implications. This research will establish a comprehensive scientific understanding of the metallurgical characteristics of rail and wheel steels to enable scientifically-informed choices. It will take account of both the specific requirements arising from the peculiarities of railway wheel-rail contact and the economic trade-offs at a system-wide level. Recent development of 'High Performance' (HPRail) rail steel by Tata Steel has shown that improvements in the resistance to both wear and rolling contact fatigue (RCF) can be achieved through judicious choice of alloying elements to alter the microstructural characteristic of the steel. However, the understanding of reasons for the success of such steels requires further fundamental research to establish how the different constituents of steel microstructures react to the forces imposed at the wheel-rail interface. The results of such research will help establish the design rules to engineer steel microstructures that provide a step change in the resistance to key degradation mechanisms with greater predictability of the deterioration rates. The project combines the skills of an interdisciplinary team from four Universities (based at the Universities of Huddersfield, Cambridge, Leeds and Cranfield), necessary to deal with the complexity of the phenomena,