Within the next few years the number of devices connected to each other and the Internet will outnumber humans by almost 5:1. These connected devices will underpin everything from healthcare to transport to energy and manufacturing. At the same time, this growth is not just in the number or variety of devices, but also in the ways they communicate and share information with each other, building hyper-connected cyber-physical infrastructures that span most aspects of people's lives. For the UK to maximise the socio-economic benefits from this revolutionary change we need to address the myriad trust, identity, privacy and security issues raised by such large, interconnected infrastructures. Solutions to many of these issues have previously only been developed and tested on systems orders of magnitude less complex in the hope they would 'scale up'. However, the rapid development and implementation of hyper-connected infrastructures means that we need to address these challenges at scale since the issues and the complexity only become apparent when all the different elements are in place. There is already a shortage of highly skilled people to tackle these challenges in today's systems with latest estimates noting a shortfall of 1.8M by 2022. With an estimated 80Bn malicious scans and 780K records lost daily due to security and privacy breaches, there is an urgent need for future leaders capable of developing innovative solutions that will keep society one step ahead of malicious actors intent on compromising security, privacy and identity and hence eroding trust in infrastructures. The Centre for Doctoral Training (CDT) 'Trust, Identity, Privacy and Security - at scale' (TIPS-at-Scale) will tackle this by training a new generation of interdisciplinary research leaders. We will do this by educating PhD students in both the technical skills needed to study and analyse TIPS-at-scale, while simultaneously studying how to understand the challenges as fundamentally human too. The training involves close involvement with industry and practitioners who have played a key role in co-creating the programme and, uniquely, responsible innovation. The implementation of the training is novel due to its 'at scale' focus on TIPS that contextualises students' learning using relevant real-world, global problems revealed through project work, external speakers, industry/international internships/placements and masterclasses. The CDT will enrol ten students per year for a 4-year programme. The first year will involve a series of taught modules on the technical and human aspects of TIPS-at-scale. There will also be an introductory Induction Residential Week, and regular masterclasses by leading academics and industry figures, including delivery at industrial facilities. The students will also undertake placements in industry and research groups to gain hands-on understanding of TIPS-at-scale research problems. They will then continue working with stakeholders in industry, academia and government to develop a research proposal for their final three years, as well as undertake internships each year in industry and international research centres. Their interdisciplinary knowledge will continue to expand through masterclasses and they will develop a deep appreciation of real-world TIPS-at-scale issues through experimentation on state-of-the-art testbed facilities and labs at the universities of Bristol and Bath, industry and a city-wide testbed: Bristol-is-Open. Students will also work with innovation centres in Bath and Bristol to develop novel, interdisciplinary solutions to challenging TIPS-at-scale problems as part of Responsible Innovation Challenges. These and other mechanisms will ensure that TIPS-at-Scale graduates will lead the way in tackling the trust, identity, privacy and security challenges in future large, massively connected infrastructures and will do so in a way that considers wider sosocial responsibility.

The UK's healthcare system faces unprecedented challenges. We are the most obese nation in Europe and our ageing population is especially at risk from isolation, depression, strokes and fractures caused by falls in the home. UK health expenditure is already very substantial and it is difficult to imagine the NHS budget rising to meet the future needs of the UK's population. NHS staff are under particular pressure to reduce hospital bed-days by achieving earlier discharge after surgery. However this inevitably increases the risk that patients face post operative complications on returning home. Hospital readmission rates have in fact grown 20% since 1998. Many look to technology to mitigate these problems - in 2011 the Health Minister asserted that 80% of face-to-face interactions with the NHS are unnecessary. SPHERE envisages sensors, for example: 1) That employ video and motion analytics to predict falls and detect strokes so that help may be summoned. 2) That uses video sensing to analyse eating behaviour, including whether people are taking their prescribed medication. 3) That uses video to detect periods of depression or anxiety and intervene using a computer-based therapy. The SPHERE IRC will take a interdisciplinary approach to developing these sensor technologies, in order that: 1) They are acceptable in people's homes (this will be achieved by forming User Groups to assist in the technology design process, as well as experts in Ethics and User-Involvement who will explore issues of privacy and digital inclusion). 2) They solve real healthcare problems in a cost-effective way (this will be achieved by working with leading clinicians in Heart Surgery, Orthopaedics, Stroke and Parkinson's Disease, and recognised authorities on Depression and Obesity). 3) The IRC generates knowledge that will change clinical practice (this will be achieved by focusing on real-world technologies that can be shown working in a large number of local homes during the life of the project). The IRC "SPHERE" proposal has been developed from day one with clinicians, social workers and clinical scientists from internationally-recognised institutes including the Bristol Heart Institute, Southampton's Rehabilitation and Health Technologies Group, the NIHR Biomedical Research Unit in Nutrition, Diet and Lifestyle and the Orthopaedic Surgery Group at Southmead hospital in Bristol. This proposal further includes a local authority that is a UK leader in the field of "Smart Cities" (Bristol City Council), a local charity with an impressive track record of community-based technology pilots (Knowle West Media Centre) and a unique longitudinal study (the world-renowned Avon Longitudinal Study of Parents and Children (ALSPAC), a.k.a. "The Children of the Nineties"). SPHERE draws upon expertise from the UK's leading groups in Communications, Machine Vision, Cybernetics, Data Mining and Energy Harvesting, and from two corporations with world-class reputations for research and development (IBM, Toshiba).

Bayesian inference is a process which allows us to extract information from data. The process uses prior knowledge articulated as statistical models for the data. We are focused on developing a transformational solution to Data Science problems that can be posed as such Bayesian inference tasks. An existing family of algorithms, called Markov chain Monte Carlo (MCMC) algorithms, offer a family of solutions that offer impressive accuracy but demand significant computational load. For a significant subset of the users of Data Science that we interact with, while the accuracy offered by MCMC is recognised as potentially transformational, the computational load is just too great for MCMC to be a practical alternative to existing approaches. These users include academics working in science (e.g., Physics, Chemistry, Biology and the social sciences) as well as government and industry (e.g., in the pharmaceutical, defence and manufacturing sectors). The problem is then how to make the accuracy offered by MCMC accessible at a fraction of the computational cost. The solution we propose is based on replacing MCMC with a more recently developed family of algorithms, Sequential Monte Carlo (SMC) samplers. While MCMC, at its heart, manipulates a single sampling process, SMC samplers are an inherently population-based algorithm that manipulates a population of samples. This makes SMC samplers well suited to the task of being implemented in a way that exploits parallel computational resources. It is therefore possible to use emerging hardware (e.g., Graphics Processor Units (GPUs), Field Programmable Gate Arrays (FPGAs) and Intel's Xeon Phis as well as High Performance Computing (HPC) clusters) to make SMC samplers run faster. Indeed, our recent work (which has had to remove some algorithmic bottlenecks before making the progress we have achieved) has shown that SMC samplers can offer accuracy similar to MCMC but with implementations that are better suited to such emerging hardware. The benefits of using an SMC sampler in place of MCMC go beyond those made possible by simply posing a (tough) parallel computing challenge. The parameters of an MCMC algorithm necessarily differ from those related to a SMC sampler. These differences offer opportunities for SMC samplers to be developed in directions that are not possible with MCMC. For example, SMC samplers, in contrast to MCMC algorithms, can be configured to exploit a memory of their historic behaviour and can be designed to smoothly transition between problems. It seems likely that by exploiting such opportunities, we will generate SMC samplers that can outperform MCMC even more than is possible by using parallelised implementations alone. Our interactions with users, our experience of parallelising SMC samplers and the preliminary results we have obtained when comparing SMC samplers and MCMC make us excited about the potential that SMC samplers offer as a "New Approach for Data Science". Our current work has only begun to explore the potential offered by SMC samplers. We perceive significant benefit could result from a larger programme of work that helps us understand the extent to which users will benefit from replacing MCMC with SMC samplers. We propose a programme of work that combines a focus on users' problems with a systematic investigation into the opportunities offered by SMC samplers. Our strategy for achieving impact comprises multiple tactics. Specifically, we will: use identified users to act as "evangelists" in each of their domains; work with our hardware-oriented partners to produce high-performance reference implementations; engage with the developer team for Stan (the most widely-used generic MCMC implementation); work with the Industrial Mathematics Knowledge Transfer Network and the Alan Turing Institute to engage with both users and other algorithmic developers.

The primary objective of the QC2 CDT is to train the upcoming generation of pioneering researchers, entrepreneurs, and business leaders who will contribute to positioning the UK as a global leader in the quantum-enabled economy by 2033. The UK government and industry have demonstrated their commitment by investing £1 billion in the National Quantum Technologies Programme (NQTP) since 2014. In its March 2023 National Quantum Strategy document, the UK government reaffirmed its dedication to quantum technologies, pledging £2.5 billion in funding over the next decade. This commitment includes the establishment of the UKRI National Quantum Computing Centre (NQCC). The fields of quantum computation and quantum communications are at a pivotal juncture, as the next decade will determine whether the long-anticipated technological advancements can be realized in practical, commercially-viable applications. With a wide-ranging spectrum of research group activities at UCL, the QC2 CDT is uniquely situated to offer comprehensive training across all levels of the quantum computation and quantum communications system stacks. This encompasses advanced algorithms and quantum error-correcting codes, the full range of qubit hardware platforms, quantum communications, quantum network architectures, and quantum simulation. The QC2 CDT has been co-developed through a partnership between UCL and a network of UK and international partners. This network encompasses major global technology giants such as IBM, Amazon Web Services and Toshiba, as well as leading suppliers of quantum engineering systems like Keysight, Bluefors, Oxford Instruments and Zurich Instruments. We also have end-users of quantum technologies, including BT, Thales, NPL, and NQCC, in addition to a diverse group of UK and international SMEs operating in both quantum hardware (IQM, NuQuantum, Quantum Motion, SeeQC, Pasqal, Oxford Ionics, Universal Quantum, Oxford Quantum Circuits and Quandela) and quantum software (Quantinuum, Phase Craft and River Lane). Our partners will deliver key components of the training programme. Notably, BT will deliver training in quantum comms theory and experiments, IBM will teach quantum programming, and Quantum Motion will lead a training experiment on semiconductor qubits. Furthermore, 17 of our partners will co-sponsor and co-supervise PhD projects in collaboration with UCL academics, ensuring a strong alignment between the research outcomes of the CDT and the critical research objectives of the UK quantum economy. In total the cash and in-kind contributions from our partners exceed £9.1 million, including £2.944 million cash contribution to support 46 co-sponsored PhD studentships. QC2 will provide an extensive cohort-based training programme. Our students will specialize in advanced research topics while maintaining awareness of the overarching system requirements for these technologies. Central to this programme is its commitment to interdisciplinary collaboration, which is evident in the composition of the leadership and supervisory team. This team draws expertise from various UCL departments, including Chemistry, Electronics and Electrical Engineering, Computer Science, and Physics, as well as the London Centre for Nanotechnology (LCN). QC2 will deliver transferable skills training to its students, including written and oral presentation skills, fostering an entrepreneurial mindset, and imparting techniques to maximize the impact of research outcomes. Additionally, the programme is committed to taking into consideration the broader societal implications of the research. This is achieved by promoting best practices in responsible innovation, diversity and inclusion, and environmental impact.

Our Centre brings together a world leading team of mathematicians, statisticians and clinicians with a range of industrial partners, patients and other stakeholders to focus on the development of new methods for managing and treating chronic health conditions using predictive mathematical models. This unique approach is underpinned by the expertise and breadth of experience of the Centre's team and innovative approaches to both the research and translational aspects. At present, many chronic disorders are diagnosed and managed based upon easily identifiable phenomena in clinically collected data. For example, features of the electrical activity of the heart of brain are used to diagnose arrhythmias and epilepsy. Sampling hormone levels in the blood is used for a range of endocrine conditions, and psychological testing is used in dementia and schizophrenia. However, it is becoming increasingly understood that these clinical observables are not static, but rather a reflection of a highly dynamic and evolving system at a single snapshot in time. The qualitative nature of these criteria, combined with observational data which is incomplete and changes over time, results in the potential for non-optimal decision-making. As our population ages, the number of people living with a chronic disorder is forecast to rise dramatically, increasing an already unsustainable financial burden of healthcare costs on society and potentially a substantial reduction in quality of life for the many affected individuals. Critical to averting this are early and accurate diagnoses, optimal use of available medications, as well as new methods of surgery. Our Centre will facilitate these through developing mathematical and statistical tools necessary to inform clinical decision making on a patient-by-patient basis. The basis of this approach is patient-specific mathematical models, the parameters of which are determined directly from clinical data obtained from the patient. As an example of this, our recent research in the field of epilepsy has revealed that seizures may emerge from the interplay between the activity in specific regions of the brain, and the network structures formed between those regions. This hypothesis has been tested in a cohort of people with epilepsy and we identified differences in their brain networks, compared to healthy volunteers. Mathematical analysis of these networks demonstrated that they had a significantly increased propensity to generate seizures, in silico, which we proposed as a novel biomarker of epilepsy. To validate this, an early phase clinical trial at King's Health Partners in London has recently commenced, the success of which could ultimately lead to a revolution in diagnosis of epilepsy by enabling diagnosis from markers that are present even in the absence of seizures; reducing time spent in clinic and increasing accuracy of diagnosis. Indeed it may even make diagnosis in the GP clinic a reality. However, epilepsy is just the tip of the iceberg! Patient-specific mathematical models have the potential to revolutionise a wide range of clinical conditions. For example, early diagnosis of dementia could enable much more effective use of existing medication and result in enhanced quality and quantity of life for millions of people. For other conditions, such as cortisolism and diabetes where a range of treatment options exist, identifying the optimal medication, and the pattern of its delivery, based upon the profile of the individual will enable us to maximise efficacy, whilst minimising unwanted side effects.