Artificial intelligence (AI) is on the verge of widespread deployment in ways that will impact our everyday lives. It might do so in the form of self-driving cars or of navigation systems optimising routes on the basis of real-time traffic information. It might do so through smart homes, in which usage of high-power devices is timed intelligently based on real- time forecasts of renewable generation. It might do so by automatically coordinating emergency vehicles in the event of a major incident, natural or man-made, or by coordinating swarms of small robots collectively engaged in some task, such as search-and-rescue. Much of the research on AI to date has focused on optimising the performance of a single agent carrying out a single well-specified task. There has been little work so far on emergent properties of systems in which large numbers of such agents are deployed, and the resulting interactions. Such interactions could end up disturbing the environments for which the agents have been optimised. For instance, if a large number of self-driving cars simultaneously choose the same route based on real-time information, it could overload roads on that route. If a large number of smart homes simultaneously switch devices on in response to an increase in wind energy generation, it could destabilise the power grid. If a large number of stock-trading algorithmic agents respond similarly to new information, it could destabilise financial markets. Thus, the emergent effects of interactions between autonomous agents inevitably modify their operating environment, raising significant concerns about the predictability and robustness of critical infrastructure networks. At the same time, they offer the prospect of optimising distributed AI systems to take advantage of cooperation, information sharing, and collective learning. The key future challenge is therefore to design distributed systems of interacting AIs that can exploit synergies in collective behaviour, while being resilient to unwanted emergent effects. Biological evolution has addressed many such challenges, with social insects such as ants and bees being an example of highly complex and well-adapted responses emerging at the colony level from the actions of very simple individual agents! The goal of this project is to develop the mathematical foundations for understanding and exploiting the emergent features of complex systems composed of relatively simple agents. While there has already been considerable research on such problems, the novelty of this project is in the use of information theory to study fundamental mathematical limits on learning and optimisation in such systems. Information theory is a branch of mathematics that is ideally suited to address such questions. Insights from this study will be used to inform the development of new algorithms for artificial agents operating in environments composed of large numbers of interacting agents. The project will bring together mathematicians working in information theory, network science and complex systems with engineers and computer scientists working on machine learning, AI and robotics. The aim goal is to translate theoretical insights into algorithms that are deployed onreal world applications real systems; lessons learned from deploying and testing the algorithms in interacting systems will be used to refine models and algorithms in a virtuous circle.

AI/ML systems are becoming an integral part of user products and applications as well as the main revenue driver for most organizations. This resulted in shifting the focus toward the Edge AI paradigm as edge devices possess the data necessary for training the models. Main Edge AI approaches either coordinate the training rounds and exchange model updates via a central server (i.e., Federated Learning), split the model training task between edge devices and a server (i.e., split Learning), or coordinate the model exchange among the edge devices via gossip protocols (i.e., decentralized training). Due to the highly heterogeneous learners, configurations, environment as well as significant synchronization challenges, these approaches are ill-suited for distributed edge learning at scale. They fail to scale with a large number of learners and produce models with low qualities at prolonged training times. It is imperative for modern applications to rely on a system providing timely and accurate models. This project addresses this gap by proposing a ground-up transformation to decentralized learning methods. Similar to Uber's delivery services, the goal of KUber is to build a novel distributed architecture to facilitate the exchange and delivery of acquired knowledge among the learning entities. In particular, we seize an opportunity to decouple the training task of a common model from the sharing task of learned knowledge. This is made possible by the advances in the AI/ML accelerators embedded in edge devices and the high-throughput and low-latency 5G/6G technologies. KUber will revolutionize the use of AI/ML methods in daily-life applications and open the door for flexible, scalable, and efficient collaborative learning between users, organizations, and governments.

Respiratory Tract Infections (RTIs) are the most common cause of illness. This was true even before the COVID-19 pandemic. They are most often the reason patients consult a GP. The illness they cause is usually mild, but in some cases can become severe, and occasionally can lead to death. Around half of all antibiotic prescriptions are for RTIs. Most people with an RTI get better without needing treatment. However, we need to notice quickly when people are getting seriously ill. If we do not, the effect on them and on healthcare services can be large. Doctors have rules and tests that help them identify patients who are more likely to need treatment, but these do not work well for every patient. Also, they are not useful for helping patients manage their own illness. Using machine learning (AI systems) to analyse breathing and speech sounds automatically could be a game-changer. Firstly, it could reassure many patients that they do not need to see a doctor. Secondly, it could reduce prescriptions for antibiotics by identifying patients who will get better on their own. Identifying patients at higher risk could also reduce hospital admissions, cases of severe illness and the number who die. All these effects would reduce pressure on the NHS. We already know that some signs, such as breathing faster, can tell us whether an RTI is getting worse, and we know we can measure these signs by recording the sound of the breath. We know that RTIs also affect breathing pattern, the sound of speech and trying to breathe when speaking. We believe that other breathing sounds and patterns are also likely to change when you get an RTI and this is something we want to explore in this project. We aim to find information in sound recordings of breathing, cough and speech which changes in a way we can predict as a person gets sicker or recovers. We will need to research the sounds we should record and how we should analyse them to get the most useful information. A study into how these sounds change over time will give us added information, not previously explored in any great depth. We have already worked with sounds from people with COVID-19, so we know lots of people will volunteer to take part and give us their sound data if we give them an app. We know this is a very cost-effective way to study how symptoms of a disease change over time. To be confident about using a machine learning system to treat patients, Doctors need to know if it is giving good advice. If they know a sound recording or a prediction is not very dependable, they can make sure they do extra checks or ask the patient to re-record their sounds. We plan to develop a machine learning system that can rate how reliable its own advice is each time. This will help doctors to know when to trust the system. Designing machine learning systems that can tell us about the quality of their advice is something new we will be exploring in this study. Our project will ask volunteers to use an app to collect speech and breathing sound data. They will be asked to make a recording when they are healthy and then another one every day if they get an RTI. The app will also collect other health information from them, such as any medication they take and any other illness they may have. The machine learning system will process the data to predict whether they are getting better or worse and rate its own confidence in its prediction. GPs will use patients' medical records to tell us which of the volunteers comes to see their doctor for treatment and whether anyone had to go to hospital. This will allow us to assess the quality of the advice from the machine learning system. Our aim is to develop a machine learning system that can assess if someone with an RTI should see their doctor for advice or can expect to get better without treatment.

This CDT will create a cohesive, internationally-leading, cross-domain training and research community fusing algebraic, geometric and quantum methods across Algebra, Geometry and Topology, Mathematical Physics, and their Interfaces. The scientific aim of our CDT is no less than to develop new foundations unifying all three disciplines, and in the process to bolster and future-proof UK capability in mathematics. The breadth of mathematical mastery necessary to achieve these aims, on which our training programme is based, is of the highest international standard, and training students in this area requires both the deep focus and the wide scope which only the resources of a CDT can enable. Our three scientific areas Algebra, Geometry and Quantum Fields are established, flagship, internationally-leading areas of UK mathematical strength. Algebra: quite simply *the* language, and controlling structure, of symbolic computation and symmetry. Geometry: the mathematically rigorous foundations of our human spatial and visual intuition. Quantum Fields: the mathematical incarnation of our quantum physical reality. A hallmark feature of 21st century mathematics is the dramatically increased synergy and inter-dependence between these three fundamental disciplines. Whereas in centuries past mathematics and physics interacted primarily through analysis and calculus, the advent of quantum mechanics posits a fundamentally different, fundamentally algebraic, set of laws for the universe. Geometry enters irrevocably when we pose quantum mechanical laws in the presence of fields, such as the electro-magnetic and gravitational fields, which permeate throughout time and space. A surprising and thrilling discovery of 21st century mathematics has been that the mathematically rigorous study of quantum fields yields some of the most powerful predictive theories within algebra and geometry, even to questions with no a priori physical formulation. These fundamental scientific developments have had a vast and direct impact on our modern world, and on a remarkably short timescale. Algebra, geometry and quantum fields are the driving force behind key developments such as internet search, quantum computation, machine learning, and both classical and quantum cryptography. Society and industry need the students we will train. Our graduates' skills are both fundamentally transferable and widely applicable across many external partnerships and stakeholders. The Deloitte report, commissioned by EPSRC, attributed 2.8M jobs and £200BN of the UK economy to mathematical sciences research, highlighting R&D, computing/tech, public administration, defence, aerospace and pharmaceuticals as economic sectors requiring graduates with advanced mathematical training. Sustainable energy consulting has since emerged as a further industry requiring ever-advanced mathematical sophistication. Crucially a physical and mathematical powerhouse needs to be a diverse powerhouse, yet the traditional structure of training in these areas has inhibited diversity of entrants, both to career academia and to industry. Building on our track record, and equipped with the resources and flexibility only a CDT can provide, we will create a diverse and confident cohort, equipped with the mathematical skillsets needed for our tech-led future to flourish, and able to influence a wide range of people, sectors and institutions.

The proposed EPSRC Centre for Doctoral Training in Sensor Technologies in an Uncertain World (Sensor CDT) will educate leaders who can effectively address the challenges of an increasingly uncertain, complex, and interconnected world. In recent years, society has faced a global pandemic, an energy crisis, and the consequences of war and the climate crisis. Sensor technologies play a vital role in addressing these challenges. They are essential tools for detecting changes in the world, protecting livelihoods, and improving well-being. Accurate sensory data are crucial for informing the public and enabling governments and policymakers to make evidence-based decisions. The new Sensor CDT is designed to train and inspire future sensor leaders with interdisciplinary and agile thinking skills to meet these challenges. Our students will learn to collaborate within and across cohorts, and co-create solutions with key stakeholders, including other scientists, industry partners, the third sector, and the public. The fully integrated 4-year Master + PhD program will be co-delivered by over 80 leading academics, over 25 industrial partners, and national research and policy agencies, and will cover the entire sensor value chain, from development over deployment and maintenance to end-of-life including middleware, and big data. Within the broader theme of uncertainty, we have identified three Focus Areas: I) Uncertainty in Sensory Data. According to the environmental sensor report published by UKRI in 2022, "data quality remains a major concern that hinders the widespread adoption of low-cost sensor technology". Through bespoke training in measurement science, statistical methods and AI, our students will learn to determine data quality and interpret imperfect, uncertain and constantly changing data. By acquiring hands-on design and prototyping skills and familiarising themselves with ubiquitous open technology platforms, they will learn how to construct more accurate and reliable sensors. II) Sensors in an Uncertain World. Environmental, economic and social uncertainties disproportionately impact low- and mid-income countries. Through collaboration with academic partners and policy agencies, the students will explore the impact of these interconnected uncertainties and pathways through which they can be mitigated by deploying low-cost sensor technologies. III) Uncertainty in Industry. UK industries deal with uncertainties in supply chains, variable process conditions and feedstocks, and they are subject to changing regulatory guidelines. Sensor data are critical to minimise the effect of such uncertainties on the quality of products and services. Through the provision of training in technical skills, systems thinking, leadership, and project management, our students will learn to innovate on rapidly changing timelines, and to work increasingly in collaboration and synergy with stakeholders in commerce and the public. Whilst prevention of future disasters is important, we recognise an increasing need to create resilience in a world facing rapid, often irreversible, change. Solutions must be co-created with society. The CDT will equip students with the confidence to collaborate across a range of fields, including arts and social sciences, skills that cannot be acquired in traditional, single student / single discipline PhD programmes. Finally, our programme will address a skills gap identified by UK industry and academia, who report a growing problem in recruiting suitably qualified candidates with the skills, disciplinary breadth and leadership qualities needed to drive innovation in the sensor field. In the UK alone, the sensor market contributes to ~£6bn in exports, underpins ~70,000 jobs, and connects to a global market estimated to reach £500bn in 2032 (Sensors KTN). Providing the skilled talent for the UK to succeed in this rapidly growing and competitive sector is a crucial goal of our programme.