MathSys addresses two of EPSRC's CDT priority areas in Mathematical Sciences: "Mathematics of Highly Connected Real-World Systems" and "New Mathematics in Biology and Medicine". We will train the next generation of skilled applied mathematical researchers to use and develop cutting-edge techniques enabling them to address a range of challenges faced by science, industry and modern society. Our Centre for Doctoral Training will build on the experience and successes of the Complexity Science DTC at Warwick, while refining the scope of problems addressed. It will provide a supportive and stimulating environment for the students in which the common mathematical challenges underpinning problems from a variety of disciplines can be tackled. The need for mathematically skilled researchers, trained in an interdisciplinary environment, has never been greater and is viewed as a major barrier in both industry and government. This is supported by quotes from reports and business leaders: "Systems research needs more potential future leaders, both in academia and industry" (EPSRC workshop on Systems science towards Engineering, Feb 2011); Andrew Haldane (Bank of England, 2012) said "The financial crisis has taught us the importance of modelling and regulating finance as a complex, adaptive system. That will require skills currently rare or missing in the regulatory community - including, importantly, in the area of complexity science"; Paul Matthews (GlaxoSmithKline) stated "Scientists trained in statistical and computational approaches who have a sophisticated understanding of biologically relevant models are in short supply. They will be major contributors in the task of translating insights on human biology and disease into treatments and cures." Our CDT will address this need by training PhD students in the development and innovation of mathematics in the context of real-world systems and will operate in close collaboration with stakeholders from outside academia who will provide motivating problems and real-world experience. Common mathematical themes will include statistical behaviour of complex systems, tipping points, novel methods in control and resilience, hierarchical aggregation methods, model selection and sufficiency, implications of network structure, response to aperiodic forcing and shocks, and methods for handling complex data. Applications will be driven by local and external partner expertise in Epidemiology, Systems Biology, Crop Science, Healthcare, Operational Research, Systems Engineering, Network Science, Financial Regulation, Data Analysis and Social Behaviour. We believe that the merging of real-world applications with development of novel mathematics will have great synergy; applications will motivate and drive mathematical advances while novel mathematics will allow students to solve challenging real-world problems. The doctoral training programme will follow a 1+3 year MSc+PhD model that has proved successful in the Complexity Science DTC. The first year will consist of six months of taught training, followed by 3-month group research projects on problems set by external partners and a 3-month individual research project, leading to an MSc qualification. This preparation will enable the students to make rapid progress tackling their 3-year PhD research project, under the guidance of one mathematical and one application-oriented supervisor, alongside general skills training and group research projects. We have over 50 suitable supervisors with relevant mathematical expertise, all enthusiastic to contribute; they will be supported by a similar number of application-oriented supervisors from across campus and from external partners. The CDT seeks the equivalent of 7 full studentships per year from EPSRC and has commitment from non-RCUK sources for the equivalent of 3 full studentships per year.

Improving outcomes, minimising re-admissions, prioritising hospital resources and expanding home or community-based management are major objectives of the NHS. Patient care needs to be considered for the entire recovery process of patients and potential impact on life-long health and wellbeing. The future of surgery is therefore moving towards precision intervention, increasingly driven by focus on quality-of-life after surgery, as well as the need for taking a systems approach towards surgery. The aim of the proposed network is to establish a forum for surgical innovation with seamless integration of engineering research, clinical translation and industrial development by aligning EPSRC healthcare technologies with NIHR Healthcare Technology Co-operatives (HTCs) to accelerate the development and clinical adoption of new surgical and assistive devices that can improve the treatment, functional restoration, rehabilitation and quality-of-life for patients. The network is supported by NIHR HTCs, KTN, and a number of academic, NHS, industrial and healthcare stakeholders. The research and clinical bases to be covered by the proposed Technology Network include the following three areas: 1) Sensing for improved peri-operative care - which is a determining factor for mitigating against post-operative complications; 2) Smart surgical devices - for surgery with increased consistency and accuracy, streamlining intraoperative surgical decision making and circumventing potential post-operative complications and revisions; 3) Assistive devices and robots - to facilitate remote monitoring and managed rehabilitation in community or home care settings. The three areas share common engineering research challenges but need to be pursued under different clinical context. The planned activities of the network include 1) Network Events: Symposia and Focused Workshops; 2) Strategic Roadmap events and User Forums; 3) Support for Interdisciplinary Mobility and Industrial Secondment; 4) Proof-of-Concept Projects and Design Competitions; 5) Exhibitions and Patient/Public Engagement; and 6) Online Engagement, Web Forum and Social Media; and 7) Health Policy and High Level Engagement. The benefits for those involved in the proposed network include partnership with extensive industrial and clinical connections already established by the partnering HTCs, host institutions, clinically aligned research and development pathways addressing the future of surgery, engagement of healthcare stakeholders and policy makers, access to research expertise and young talents in this highly interdisciplinary area, early end-user involvement, and tapping into design expertise, access to user group feedback, deliver rapid results through HTCs' clinical network, match evidence to needs of NICE, strong commercial engagement.

Medicine is, within the UK, one of the most ethnically diverse professions but despite this, evidence suggests that ethnic minority doctors still face more challenges to their career progression than their white counterparts. The aim of this project is to increase our understanding of how ethnic minority doctors (and would-be doctors or 'aspirants') manage their transitions through the distinct stages of a medical career (from A level student to Consultant). We are seeking to discover what barriers they face and what strategies contribute to successfully being able to progress from one stage of a medical career to the next. We intend to use this knowledge to improve the career support to ethnic minority doctors and to help to improve doctor retention in the NHS. The NHS has long faced challenges with ensuring it has sufficient numbers of doctors. There are limited numbers of training places and doctors take many years to train and gain necessary experiences but there are issues of burnout and the number of doctors leaving the profession. In addition doctors are retiring earlier with the rate of early retirement of doctors tripling since 2008 (Moberley, 2021). These factors, combined with the impact of the pandemic on our health services, mean that the doctor shortage is likely to be exacerbated with fewer medics on hand to meet increased demand. Issues of retention and support for UK doctors are likely to increase in importance in the post-pandemic years As ethnic minority doctors are a key cohort of this workforce, and a group that has traditionally have faced problems with progression, then it is urgent and appropriate for us to examine in some depth how ethnic minority doctors transition through their careers. We recognise that there is a great deal of diversity within the category of 'ethnic minority' hence project will also help us to better understand the specific role that is played by other demographic features in the career of ethnic minority doctors (or aspirants). We want to examine whether barriers and strategies for success are different for ethnic minority doctors from different minority ethnic groups (e.g. do Black doctors, who are fewer in number, face different barriers or use different strategies to Asian doctors who are better represented?); different nationalities (e.g. what are the specific challenges and strategies for doctors who trained overseas?); and different social class backgrounds (e.g. how does coming from a family with fewer financial resources influence the way you navigate a career in medicine?). We will also look in detail at the extent to which male and female ethnic minority doctors face different barriers and use different strategies to transition through the career stages. We will examine the career transitions of early, mid and late career-stage doctors to deepen our understanding of the challenges faced and the strategies adopted to address those challenges are different career points. In addition, as within medicine, careerists often move through different career stages at similar ages, it will also provide us within insight into how different generations of ethnic minority professionals perceive the relevance of their ethnicity to their career transitions and whether the strategies they adopt differ. We will be able to reflect on whether changing narratives around ethnicity in society and the increasing importance placed on promoting diversity and inclusion has influenced the way in which different generations of medics reflect on career barriers and the strategies for progression.

PREMIERE will integrate challenges identified by the EPSRC Prosperity Outcomes and the Industrial Strategy Challenge Fund (ISCF) in healthcare (Healthy Nation), energy (Resilient Nation), manufacturing and digital technologies (Resilient Nation, Productive Nation) as areas to drive economic growth. The programme will bring together a multi-disciplinary team of researchers to create unprecedented impact in these sectors through the creation of a next-generation predictive framework for complex multiphase systems. Importantly, the framework methodology will span purely physics-driven, CFD-mediated solutions at one extreme, and data-centric solutions at the other where the complexity of the phenomena masks the underlying physics. The framework will advance the current state-of-the-art in uncertainty quantification, adjoint sensitivity, data-assimilation, ensemble methods, CFD, and design of experiments to 'blend' the two extremes in order to create ultra-fast multi-fidelity, predictive models, supported by cutting-edge experimental investigations. This transformative technology will be sufficiently generic so as to address a wide spectrum of challenges across the ISCF areas, and will empower the user with optimal compromises between off-line (modelling) and on-line (simulation) efforts so as to meet an a priori 'error bar' on the model outputs. The investigators' synergy, and their long-standing industrial collaborations, will ensure that PREMIERE will result in a paradigm-shift in multiphase flow research worldwide. We will demonstrate our capabilities using exemplar challenges, of central importance to their respective sectors in close collaboration with our industrial and healthcare partners. Our PREMIERE framework will provide novel and more efficient manufacturing processes, reliable design tools for the oil-and-gas industry, which remove conservatism in design, improve safety management, and reduce emissions and carbon footprint. This framework will also provide enabling technology for the design, operation, and optimisation of the next-generation nuclear reactors, and associated reprocessing, as well as patient-specific therapies for diseases such as acute compartment syndrome.

PIONEER aims to improve healthcare pathways and treatments by understanding the symptoms and diseases people have when they become unwell: whether they had been to hospital or other healthcare providers before with the same problems; the time it took to make a diagnosis; and the care they received. PIONEER enhances public trust in health data use, working with patients, the public and other stakeholders to ensure that governance of data access is transparent and in the public interest. PIONEER is commited to communicating these principles effectively to improve understanding, and raise the profile of, the value of health data research. PIONEER is improving the quality and accuracy of acute care health data by: working with healthcare providers; providing a secure and scalable data environment; and placing patients and the public at the heart of all data sharing decisions. PIONEER brings scale and efficiency to dataset aggregation and curation of anonymised routinely collected data relevant to unplanned and acute health care. PIONEER makes these datasets discoverable and appropriately accessible to research organisations, NHS bodies and those who are conducting innovation activities which will lead to direct patient benefit. PIONEER provides an environment of cross-sector collaboration with strong relationships between patients, the public, NHS, industry and academic researchers to support research, development and innovation.