The literature on social networks in economics, both empirical and theoretical has been growing substantially in the last few decades. Much of this growth can be attributed to the proliferation of online social networks. Theory papers have provided important models for the process of network formation and the spread of influence within networks (Jackson and Wolinsky, 1996; Mutuswami and Winter, 2002; Kempe et al., 2003; Ballester et al., 2006; Jackson, 2011). Empirical papers used existing data as well as field experiments to study how behavior diffuses within a network (Ichino and Maggi, 2000; Sacerdote, 2001; Mas and Moretti, 2009; Banerjee et al., 2013). There is also emerging literature on social media platforms (Ghosh and McAfee, 2011; Ashish, and Ronaghi, 2012; Ghosh and Hummel, 2014). Most of the Graph/Game theory literature of social media treats the network structure as given and fixed and focuses on the flow of information through the network and on users' strategic considerations. The role of the platform itself is typically left un-modeled. Our objective in this project is to develop and analyze models of social media using primarily tools in Game Theory and Graph Theory. Our approach is different from much of the existing literature in that we treat the platform's owners/managers as a major player in the social media game - one that has an enormous influence on the activity that takes place in the network. This influence arises through a certain degree of control over the structure of the social network and almost full control over users' available actions. Our modeling efforts will not only focus on users' motives and preferences. The motives and preferences of the platform itself are equally important. These preferences critically depend on the platform's business model. They can be aligned with users' preferences in some business models and conflicting with users' preferences in others. We note here that platforms' preferences and interests are key elements in models that aspire to provide policy implications. If platforms and users have identical interests there is little need for intervention. It is when these interests are conflicting that intervention by governments or international organizations in certain circumstances might be required. Our first objective will be to identify areas in which the interests of the platform and its users are conflicting and areas in which they coincide. We will also study mechanisms and rules for social media that can bring about Pareto improvements in SM content quality or substantial improvement to users' welfare with no major revenue losses to the platform. More specific questions we plan to address are: What are the optimal network structures from the point of view of the platform and what sort of implications such structure might have on the distribution of users' right to express themselves and their overall welfare? How do social media platforms based on undirected graphs (e.g. Facebook and LinkedIn) differ from those based on directed graphs (Twitter and Instagram) in terms of users' welfare? What is the optimal policy for the flow of content in the network (e.g., feed news policy) from the point of view of both the platform and users? What are the incentives behind users' spreading abusive content and fake news through the network, and how can such ill incentives be mitigated? Our project is designed to have a substantial policy impact through collaboration with organizations such as Ofcom, FCC. Promisingly enough the initiative for such collaboration came from Ofcom following the appearance of our discussion paper on the topic. We were invited to present our work at Ofcom and we are now collaborating with Ofcom in organizing a conference on this subject where key policy people from Ofcom, the FCC, Facebook and Google have confirmed their participation. We plan to hold regular meetings with people at Ofcom during the implementation of the project.

We have yet to experience a complete lifespan in the Digital Age, from conception to death in old age. Those who have grown up interacting with digital technology from a very early age are still young, whilst older technology adopters have identities that pre-date the Digital Age, populated with paper trails of memories. Many citizens have only a limited awareness of the permanency and consequence of posting in public and extended social circles. Digital posts from student or teenage years reflecting opinions or behaviour that seemed socially appropriate at that time may not reflect well in future professional life. Digitally mediated interactions produced in life may develop an undesirable perspective if they linger after physical death. The lifelong digital trails generated through our digitally mediated interactions, including online, echo our 'offline' lives, but unlike a physical life, the Digital Lifespan can persist indefinitely, and the rich personal context it provides can be harnessed in ways an individual might not expect or desire. In this EPSRC-funded research, we will produce unique insights into the digital lifespan of UK citizens both now and in a future where our young Digital Natives approach adulthood, become parents, retire, and pass away. To help generate these insights, we will first chart the unmapped territory of the "Digital Lifespan" as it is now in the UK, exploring the ways in which virtual and physical aspects of our lives converge, diverge and clash. This chart will be grounded in a series of in-depth studies with UK citizens at four transition points in their lives: approaching adulthood, becoming parents, retiring, and bereavement. The chart that we create will guide us as we look into a future where citizens increasingly live out their lives through digitally mediated interactions. We will explore the implications of this future with individuals, policymakers, legislators and industry representatives. The knowledge and insight developed into issues surrounding ownership and management of citizens' Digital Lifespans will be used to raise digital literacy. New technologies will be designed and developed, bringing personal digital content together in one place to create a far richer picture than that afforded by currently available tools. Our new technologies will automatically draw out the personal context of such content, making inferential links and distilling the impressions that citizens present of themselves through digital media. These distilled impressions will be reflected back to individuals, raising digital literacy by promoting awareness of how individuals' digital identities are (or will in future be) represented online over their entire lifespan. Further these novel technologies will equip citizens with ways to manage the impression that they give. Beyond individual citizens, our work will inform educators, policymakers and legislators providing a deeper understanding of what it means to live as a UK citizen in a Digital Age.

The increasing popularity of smartphones and other mobile devices, where the end user has access to a host of rich multimedia functionality, means that the current mobile network architecture is struggling to meet surging data demands. Smartphone ownership in the UK alone has risen from 38% of the population in early 2010 to 60% in 2013 with the ONS reporting that over 32% of adults now access the Internet using their smartphone every day. This figure is expected to grow significantly in the coming years with Cisco predicting that worldwide demand for mobile data traffic will outstrip fixed data, reaching 11.2 Exabytes per month by 2017. Although the global rollout of 4G networks is well underway, it is unlikely that that 4G alone will be able to service the growing data requirements of mobile users. Furthermore, while voice, data, and compressed streaming media are now the norm, it is future social networking applications which will undoubtedly present mobile network designers and operators with their greatest challenge. Both Google and Samsung, through their Glass and Galaxy Gear based concepts respectively, have given us a glimpse of some of the exciting new pervasive technologies that will push the boundaries on the maximum rate at which data can be communicated over mobile networks. For example, using Google Glass, users will no longer just shop and download compressed audio and video, instead they will be immersed into a completely new augmented reality in which they can share their immediate perception and senses with friends and colleagues in the cloud. While this technology will revolutionise social networking it will add further stress to already overburdened mobile networks. To avoid future congestion caused by this huge influx of data, a major change in the way mobile networks are setup and operated is required. However, considerable academic, industrial and regulatory challenges remain and this is the focus of the proposed research programme. To help overcome the future "communications bottleneck" in mobile systems, this project proposes a new paradigm for ultra-high capacity mobile networks by simultaneously and jointly addressing the bandwidth problem and the dynamic network management issues associated with device-to-device communications. Combining the complementary expertise of research teams in Queens University Belfast and Cardiff University, this project will focus on understanding and exploiting incentivised, multimode user equipment operating as an ultra-high capacity underlay network featuring real-time opportunistic adaptive routing all overseen by a context aware mobile network infrastructure.

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.

Understanding human behaviour and how it shapes organisations, communities and societies is needed to address global challenges such as the environmental, economic and health crises that we face now and in the future. Currently, behavioural research is not well coordinated in the UK. It also doesn't always ask the right research questions, involve people with the best skills, make good use of existing data, take advantage of innovative research methods or produce findings that can be used to make positive changes. The Behavioural Research UK Leadership Hub (BR-UK) will change this. BR-UK brings together a team from England, Scotland, Wales and Northern Ireland that includes experienced researchers from many different backgrounds and partners from government, the wider public sector, charities and businesses. We will work with communities to better understand behaviour and conduct research to improve lives and livelihoods. BR-UK will deliver a detailed work programme for the first 18 months. At the same time, we will expand our initial plans for the longer term to be reviewed by the funder, the Economic and Social Research Council (ESRC). In the first 18 months, we will: - Carry out a scoping study to look at needs, priorities and opportunities for behavioural research and set up a national network of researchers and research users - Determine how behavioural research can be more sustainable to make the best use of available funding - Identify (with our international advisory board) under-used global evidence as well as methods and theories to improve behavioural research excellence - Conduct 'demonstration projects' to show how the team can work together to use existing data and speed up the application of models and frameworks to provide rapid results. Topics include how behavioural advice was used during the Covid-19 pandemic, how we address some current issues like speeding on our roads, how to combine large amounts of data more efficiently and how well public support for different policies to help tackle climate change can be transferred between countries - Set up & test a responsive-mode consultancy service where organisations can ask questions about how behavioural research could help them with their policies or practices, and be matched to team members with relevant expertise. Looking ahead, BR-UK will organise our work around four Work Packages (WPs) and Themes (T). Work Packages are about HOW we will do things, and our Themes are about WHAT we will focus on. These are: WP1: Capability Building; WP2: Data and Technology; WP3: Methods and Evidence Synthesis; WP4: Engagement and Involvement; T1: Environment and Sustainability; T2: Health and Wellbeing; T3: Resilient Communities: and T4: Organisations, Markets and the Economy. We will conduct new studies across WPs and Themes. Examples of research questions to illustrate the range are: how to better use mobile phone technologies to engage people long-term to stop smoking or reduce their alcohol consumption; how to help regulators and the police keep children safer online and tackle internet crime; how to help people and organisations shift to transport that is better for the environment; how best to work with local and national governments to better understand the needs of their local communities when making policy decisions. As a Leadership 'Hub', BR-UK will work with other parts of the programme ('spokes' including a centre to train students and early career researchers as they develop. We will be flexible, and reserve part of the funding that could lead to new studies when sudden events like a new threat, emergency or event occur. We are well positioned to carry out rapid reviews of existing research to help governments and organisations know what behavioural evidence exists to inform decisions, and to identify evidence gaps. We will be ready to adapt and bring in new members with skills and experience that are most needed as BR-UK evolves.