The work our groups have carried out on alloys exposed to recently developed processes for low-temperature carburising and nitriding revealed that extraordinarily high concentrations of carbon and nitrogen can be dissolved in Fe-Cr-Ni alloys (austenitic stainless steel). In this process, carbon or nitrogen diffuses into the alloy from the surface at a temperature sufficiently low to suppress the precipitation of carbides or nitrides. This enables the formation of a homogeneous, precipitate-free, superhard " S-phase" consisting with carbon or nitrogen concentrations that exceed the equilibrium solubility limit by about one-hundred-thousand times! To date, our work has focused on the underlying physical principles of this "colossal supersaturation" (CSS) and the mechanical properties and corrosion resistance of the as-processed 25-50 micron -thick hardened layer provided by the interstitial solute ("case") below the surface. The work we propose here constitutes a first effort to investigate the reliability and lifetime of this unusual material at elevated temperature and under applied mechanical stress and to further process it by tempering - i. e. exposure to heat treatments. Moreover, we propose to extend the research to Ni-Cr and Co-Cr alloys, for which hardening by colossal supersaturation has great technological importance. Alloys with a colossal supersaturation of interstitial solute (carbon, nitrogen) constitute unique model systems for fundamental studies of decomposition and precipitation phenomena in metals under unusual conditions. In particular, it will enable understanding the physical principles of carbide and nitride nucleation, growth, and ripening under extremely high supersaturation and how the decomposition affects the remarkable mechanical properties and outstanding corrosion resistance initially provided by CSS. This provides a high potential for "transformative" discoveries. The largely complementary expertise, experience, and instrumentation of the two involved research group will enable significant progress in this important field of surface engineering. This project will lay the foundation for long-term cooperation of two leading groups in the field of surface engineering. The physical understanding of the decomposition of CSS-hardened alloys under applied temperature and stress we intend to obtain is of great importance for many applications of structural alloys, e. g. bearings, food processing blades, valves, bushings, dies, nuclear reactor components, medical implants and surgical and dental instruments. The increase of reliability and lifetime we hope to enable by understanding their physical foundations will lead to major savings of primary energy resources and conservation of strategic raw materials by avoiding unnecessary production and recycling of alloy parts. The availability of super-hard wear-and corrosion-resistant alloys will strengthen US and UK industry by enabling the design of new products, which can contribute to the creation of new jobs. The long-life body implants can improve the quality of life of patients and reduce UK/US health service costs. The results of the proposed research are highly likely to generate new intellectual property. The project will have significant impact on student education and training at CWRU and UoB. The results will directly impact the theoretical and practical parts of materials science courses at both universities. Further, the project will enable significant practical participation of undergraduate students and will therefore help to attract excellent undergraduate students to our institutions. The PIs have a record in engaging undergraduate students and women students and in exchanging research students and postdoctoral research associates in their research activities.

Computational models are being used increasingly to offer answers to important questions that affect us all. Scientists are increasingly resorting to computational models to simulate phenomena as diverse as the effects of drugs on a physiology, transmissions of diseases in a society, or the flow of blood through an artery. Within the public sector, computational models are fundamental to enabling the prediction of weather patterns, both in the short term and also to predict the impact of global warming in the longer term. They are also increasingly vital for supporting decisions on infrastructure spend; our project partners in the DAFNI project are developing computational modelling infrastructure to support the investment of £460bn over the course of the coming decade. Given the high-stakes decisions that are usually involved, mistakes or "bugs" in a model can lead (and have led) to disastrous consequences. It is critical that these systems are rigorously tested to minimise this risk. Computational models are however not amenable to traditional software testing and debugging techniques. They can include large numbers of parameters and configuration options. They can take a very long time (and require a lot of computational resources) to execute a single test run, which makes it infeasible to run large numbers of test executions. The data structures that they operate on can be particularly complex (e.g. 3D models of cities or coronary arteries), which means that these can be difficult to synthesise and inspect. Finally, if a test run is found to produce an incorrect result, these factors can make it very difficult to identify where the bug is in the source code of the model. CITCoM is based on the observation that the challenge is in many ways rooted in data-analysis. In the presence of large numbers of input variables, there is the challenge of analysing the tested behaviour and ensuring that the observed behaviour is caused by the parameters that are the focus of the test (and not accidentally caused by other incidental parameters). There is the converse challenge of selecting which inputs need to be varied and which ones need to be controlled to demonstrate that a given combination of inputs causes a particular behaviour whilst keeping the number of test cases this requires to a minimum. If a fault occurs, there is the challenge of interrogating the data to locate the fault in the code. Similar problems arise in a wide range of disciplines, and especially in the field of Epidemiology - where population data are scrutinised to determine the effects of drug treatments or medical interventions. Again, there are many variables at play (lifestyle, cultural background, genetic traits, habits). Collecting data can be expensive and time-consuming. Outcomes can be difficult to measure and complex to scrutinise. For such situations, the last decade has seen the rapid rise of a family of statistical analysis approaches called Causal Inference. This has enabled statisticians to design and reason about epidemiological trials and data in new and powerful ways to efficiently sample data, handle missing data-attributes, and use existing data to answer "what-if" questions, even if the data in question has not been collected yet. CITCoM will use these powerful Causal Inference analysis capabilities to address the problems that arise when testing computational models. We will generate Causal Inference-driven automated test-generation techniques, test oracles, and debugging techniques. These will be trialled and honed on a set of large case-study models in collaboration with our partners on the DAFNI project at STFC, at DSTL, and within The University of Sheffield. Ultimately, CITCoM will enable us to generate, collect, and analyse evidence from computational models to ensure that they do not contain faults, so that any decisions that they feed into are well-founded and trustworthy.

When we begin to study mathematics, we learn that the operation of multiplication on numbers satisfies some basic rules. One of these rules, known as associativity, says that for any three numbers a, b and c, we get the same result if we multiply a and b and then multiply the result by c or if we multiply a by the result of multiplying b and c. This leads to the abstract algebraic notion of a monoid, which is a set (in this case the set of natural numbers) equipped with a binary operation (in this case multiplication) that is associative and has a unit (in this case the number 1). If we continue to study mathematics, we encounter a new kind of multiplication, no longer on numbers but on sets, which is known as Cartesian product. Given two sets A and B, their Cartesian product is the set A x B whose elements are the ordered pairs (a, b), where a is an element of A and b is an element of B. Pictorially, the Cartesian product of two sets is a grid with coordinates given by the elements of the two sets. This operation satisfies some rules, analogous to those for the multiplication of numbers, but a little more subtle. For example, if we are given three sets A, B and C, then the set A x (B x C) is isomorphic (rather than equal) to the set (A x B) x C. Here, being isomorphic means that we they are essentially the same by means of a one-to-one correspondence between the elements A x (B x C) and those of (A x B) x C. This construction leads to the notion of a monoidal category, which amounts to a collection of objects and maps between them (in this case the collection of all sets and functions between them) equipped with a multiplication (in this case the Cartesian product) that is associative and has a unit (in this case the one-element set) up to isomorphism. Monoidal categories, introduced in the '60s, have been extremely important in several areas of mathematics (including logic, algebra, and topology) and theoretical computer science. In logic and theoretical computer science, they connect to linear logic, in which one keeps track of the resources necessary to prove a statement. This project is about the next step in this sequence of abstract notions of multiplication, which is given by the notion of a monoidal bicategory. In a bicategory, we have not only objects and maps but also 2-maps, which can be thought of as "maps between maps" and allow us to capture how different maps relate to each other. In a monoidal bicategory, we have a way of multiplying their objects, maps and 2-maps, subject to complex axioms. Monoidal bicategories, introduced in the '90s, have potential for applications even greater than that of monoidal categories, as they allow us to keep track of even more information. We seek to realise this potential by advancing the theory of monoidal bicategories. We will prove fundamental theorems about them, develop new connections to linear logic and theoretical computer science and investigate examples that are of interest in algebra and topology. Our work connects to algebra via an important research programme known as "categorification", which is concerned with replacing set-based structures (like monoids) with category-based structures (like monoidal categories) in order to obtain more subtle invariants. Our work links to topology via the notion of an operad, which is a flexible tool used to describe algebraic structures in which axioms do not hold as equalities, but rather up to weak forms of isomorphism. Overall, this project will bring the theory of monoidal bicategories to a new level and promote interdisciplinary research within mathematics and with theoretical computer science.

When we begin to study mathematics, we learn that the operation of multiplication on numbers satisfies some basic rules. One of these rules, known as associativity, says that for any three numbers a, b and c, we get the same result if we multiply a and b and then multiply the result by c or if we multiply a by the result of multiplying b and c. This leads to the abstract algebraic notion of a monoid, which is a set (in this case the set of natural numbers) equipped with a binary operation (in this case multiplication) that is associative and has a unit (in this case the number 1). If we continue to study mathematics, we encounter a new kind of multiplication, no longer on numbers but on sets, which is known as Cartesian product. Given two sets A and B, their Cartesian product is the set A x B whose elements are the ordered pairs (a, b), where a is an element of A and b is an element of B. Pictorially, the Cartesian product of two sets is a grid with coordinates given by the elements of the two sets. This operation satisfies some rules, analogous to those for the multiplication of numbers, but a little more subtle. For example, if we are given three sets A, B and C, then the set A x (B x C) is isomorphic (rather than equal) to the set (A x B) x C. Here, being isomorphic means that we they are essentially the same by means of a one-to-one correspondence between the elements A x (B x C) and those of (A x B) x C. This construction leads to the notion of a monoidal category, which amounts to a collection of objects and maps between them (in this case the collection of all sets and functions between them) equipped with a multiplication (in this case the Cartesian product) that is associative and has a unit (in this case the one-element set) up to isomorphism. Monoidal categories, introduced in the '60s, have been extremely important in several areas of mathematics (including logic, algebra, and topology) and theoretical computer science. In logic and theoretical computer science, they connect to linear logic, in which one keeps track of the resources necessary to prove a statement. This project is about the next step in this sequence of abstract notions of multiplication, which is given by the notion of a monoidal bicategory. In a bicategory, we have not only objects and maps but also 2-maps, which can be thought of as "maps between maps" and allow us to capture how different maps relate to each other. In a monoidal bicategory, we have a way of multiplying their objects, maps and 2-maps, subject to complex axioms. Monoidal bicategories, introduced in the '90s, have potential for applications even greater than that of monoidal categories, as they allow us to keep track of even more information. We seek to realise this potential by advancing the theory of monoidal bicategories. We will prove fundamental theorems about them, develop new connections to linear logic and theoretical computer science and investigate examples that are of interest in algebra and topology. Our work connects to algebra via an important research programme known as "categorification", which is concerned with replacing set-based structures (like monoids) with category-based structures (like monoidal categories) in order to obtain more subtle invariants. Our work links to topology via the notion of an operad, which is a flexible tool used to describe algebraic structures in which axioms do not hold as equalities, but rather up to weak forms of isomorphism. Overall, this project will bring the theory of monoidal bicategories to a new level and promote interdisciplinary research within mathematics and with theoretical computer science.

The World Health Organization (WHO) model of 'age-friendly cities' emphasizes the theme of supportive urban environments for older citizens. These defined as encouraging 'active ageing' by 'optimizing opportunities for health, participation and security in order to enhance quality of life as people age' (WHO, Global Age-friendly Cities, 2007). The goal of establishing age-friendly cities should be seen in the context of pressures arising from population ageing and urbanisation. By 2030, two-thirds of the world's population will reside in cities, with - for urban areas in high-income countries - at least one-quarter of their populations aged 60 and over. This development raises important issues for older people: To what extent will cities develop as age-friendly communities? Will so-called global cities integrate or segregate their ageing populations? What kind of variations might occur across different types of urban areas? How are different groups of older people affected by urban change? The 'age-friendly' city perspective has been influential in raising awareness about the impact of population ageing. Against this, the value of this approach has yet to be assessed in the context of modern cities influenced by pressures associated with global social and economic change. The IPNS has four main objectives: first, to build a collaborative research-based network focused on understanding population ageing in the context of urban environments; second to develop a research proposal for a cross-national study examining different approaches to building age-friendly cities; third to provide a systematic review of data sets and other resources of relevance to developing a research proposal on age-friendly cities; fourth, to develop training for early career resarchers working on ageing and urban issues. The network represents the first attempt to facilitate comparative research on the issue of age-friendly cities. It builds upon two meetings held at the Universities of Keele and Manchester in 2011 that sought to establish the basis for cross-national work around the 'age-friendly' theme. The IPNS represents brings together world class research groups in Europe, Hong Kong and North America, professionals concerned with urban design and architecture, and leading NGOs working in the field of ageing. A range of activities have been identified over the two-year funding period: (1) Preparation of research proposals for a cross-national study of approaches to developing age-friendly urban environments. (2) Two workshops to specify theoretical and methodological issues raised by demographic change and urbanisation. (3) A Summer School exploring links between data resources of potential relevance to the ageing and urbanisation theme and which might underpin research proposals. (4) Master classes for network members from key researchers in the field of urbanisation and ageing. (5) A workshop with a user-based theme developing older people's participation in research on building age-friendly communities. (6) Themed workshops (face-to-face and via video-link) to identify research and policy gaps drawing on inter-disciplinary perspectives The IPNS will be sustained in a variety of ways at the end of the funding period. A collaborative research proposal as well as one to maintain the network will be major outputs from the project and work with potential funding bodies will continue after 2014. Dissemination activities will continue through professional networks, symposia at major international conferences, and involvement in expert meetings. The project will continue to be advertised through the maintenance of a website maintained by the host UK HEI. The project will continue to make a contribution to policy development around the theme of age-friendly cities, notably with the main NGOs working in the field.