In 1872, Felix Klein published his now famous Erlangen Programme, in which he treated geometry as the study of invariants, formalised using group theory. This radically new approach allowed tying together different types of non-Euclidean geometries that had emerged in the nineteenth century and has had a profound methodological and cultural impact on geometry in particular and mathematics in general. New fields of mathematics such as exterior calculus, algebraic topology, the theory of fibre bundles and sheaves, and category theory emerged as a continuation of Klein's blueprint. The Erlangen Programme was also fundamental for the development of physics in the first half of the twentieth century, with Noether's theorem and the notion of gauge invariance successfully providing a unification framework for electromagnetic, weak, and strong interactions, culminating in the Standard Model in the 1970s. Now is the time for an "Erlangen Programme" for AI, based on rigorous mathematical principles that would bring better understanding of existing AI methods as well as a new generation of methods that have guaranteed expressive and generalisation power, better interpretability, scalability, and data- and computational-efficiency. Just as the ideas of Klein's Erlangen Programme spilled into other disciplines and produced new theories in mathematics, physics, and beyond, we will draw inspiration from these analogies in our AI research programme. By resorting to powerful tools from the mathematical and algorithmic fields sometimes considered "exotic" in applied domains, new theoretical insights and computational models can be derived. Our "Erlangen Programme of AI" will study four fundamental questions that underlie modern AI/ML systems, striving to provide rigorous mathematical answers. How can hidden structures in data be discovered and expressed in the language of geometry and topology in order to be exploited by ML models? Can we use geometric and topological tools to characterise ML models in order to understand when and how they work and fail? How can we guarantee learning to benefit from these structures, and use these insights to develop better, more efficient, and safer new models? Finally, how can we use such models in future AI systems that make decisions potentially affecting billions of people? With a centre at Oxford, and broad geographic coverage of the UK, the Hub will bring together leading experts in mathematical, algorithmic, and computational fields underpinning AI/ML systems as well as their applications in scientific and industrial settings. Some of the Hub participants have a track record of previous successful work together, while other collaborations are new. The research programme in the proposed Hub is intended to break barriers between different fields and bring a diverse and geographically-distributed cohort of leading UK experts rarely seen together with the purpose of strong cross-fertilisation. In the fields of AI/ML, our work will contribute to the exploitation of tools from currently underexplored mathematical fields. Conversely, our programme will help attract the attention of theoreticians to new problems and applications.

Our current approach to packaging food and other products is not sustainable; being primarily based on single-use plastics that, when disposed of incorrectly, cause significant harm to the environment. Recycling, while clearly a better option than landfill, also has its limitations - e.g., the functional properties of plastics degrade as a result of the recycling process. And reducing consumption is only possible to a certain degree. It is therefore clear that we - that is science, industry, government, and society - need to find ways to enable people to reuse packaging, such that it stays in circulation longer before ending up in the waste stream. The proposed research, led by a multidisciplinary team of scientists working in partnership with key stakeholders, will explore models of reuse and provide the insights needed to enable a wholesale shift toward reuse. Our research will be structured around five work packages (WPs). WP1 will examine the language that people use to describe different types of plastic and actions associated with their reuse / disposal. We will study the extent to which public understanding of plastic and actions is aligned with that of stakeholders (e.g., local authorities, manufacturers), and how language can be used as a tool to promote changes in thinking and behaviour (e.g., by describing materials and actions in different ways). WP2 will look at both historical (e.g., doorstep delivery of milk) and contemporary (e.g., supermarket refill stations) models of reuse, as well as standardised models of packaging (e.g., tin cans) to identify what role reuse might play in the future and what factors might facilitate and/or impede this. WP3 will identify what people might be willing to reuse, when, and why. We will also consider the point at which deterioration in materials and / or potential contamination makes reuse unacceptable; and, critically, how such decisions might be shifted in an effort to promote (appropriate) reuse. WP4 will use life cycle assessment to identify the environmental impacts of a range of different reuse models in a range of different contexts; thereby providing the data needed to accurately determine which model of reuse is "best". Finally, WP5 will investigate the suitability of current and emerging polymers, and other materials for reusable packaging by simulating repeated washing and potential contamination by ingredients in food, personal care, and household products. Together, the outputs of the proposed research will be an understanding, based on robust scientific data, of when and how reuse models for plastic packaging make good sense. For example, our research may lay the groundwork for promoting a societal-shift in thinking toward buying the product, but renting the packaging. Our approach recognises that a new system that prioritises reuse, and then recycling, of durable materials requires a step change in behaviour and that truly creative and novel ideas occur at the interfaces between disciplines, when different perspectives are brought together in an open and 'safe' environment. The applicants have demonstrated their ability to work together as a multidisciplinary team alongside key stakeholders as in an on-going single use plastics project. The present proposal describes the research needed to translate this expertise and initial ideas into scientifically rigorous and joined up data that can provide the basis for delivering reuse as a national (and potentially international) vision; thereby, preventing plastic from entering the environment and stimulating more sustainable business, supply chain, and economic models.

Campylobacter spp. are extremely important food borne enteropathogenic bacteria, estimated to cause over 600,000 cases of infection in the UK each year with around 100 deaths. It is estimated that Campylobacter infections cost the UK economy around £1 billion per year. Infection is characterised by acute and sometimes bloody diarrhoea, particularly in children. The last few years have seen a marked rise in cases in compromised elderly populations and in such people, particularly those with bowel cancer, infection can be fatal. Chicken meat is the most important source and vehicle for human Campylobacter infections and around 80% of chickens on sale in the UK are Campylobacter-positive. Campylobacter are natural inhabitants of the intestinal tract of chickens and other food animals. Contamination of chicken meat takes two forms. Carcass surfaces can carry high levels of Campylobacter and this can lead to cross-contamination in both domestic and commercial catering. This is an important risk factor for infection. However, and perhaps more importantly, Campylobacter have been recovered from deep muscle tissues of up to 27% of chickens tested. Furthermore, liver tissues are also commonly contaminated. In these tissues the bacteria will be better protected from the effects of cooking. Undercooked chicken meat and chicken liver pate are internationally important vehicles of Campylobacter infection. To improve public health in the UK it is essential that the number of contaminated chickens on sale is reduced. The proposed research will examine the different systems in which UK chickens are grown to identify cost-effective farm-based control options. Our work will focus on chickens reared intensively in housed systems as these comprise ~90% of the UK market. The work will be in collaboration with the three biggest poultry producers in the UK and all the major UK food retailers are giving financial support. The proposed research builds on past studies which showed that chickens (broilers) reared under higher welfare systems are less likely to have Campylobacter than birds reared more intensively. The higher welfare systems generally use slower-growing birds and stock houses with fewer birds than the more intensive systems. Our work showed that birds reared in the more intensive system had poorer welfare, as shown by high rates of endemic disease and general health and leg problems. This might explain why these birds were more likely to be Campylobacter-positive, as birds compromised by poor health and/or welfare are more susceptible to these bacteria. These differences might be due to the birds used and/or the in-house environment and we will determine this. Our field work might also indicate that the slower-growing bird types may be inherently more Campylobacter-resistant. We will conduct longitudinal studies on flocks reared under different systems and determine when birds first become Campylobacter-positive and relate this to changes in bird health and welfare. We will also determine whether the spread of Campylobacter from the intestine of the birds to edible tissues like liver occurs on farm and if it is linked to poor welfare for endemic disease. Our aim is to provide the UK poultry industry with science-based and cost-effective control options, which will help it meet customer demands and comply with forth-coming EU legislation aimed at reducing the number of chickens that are Campylobacter-positive.