SAMBa aims to create a generation of interdisciplinary mathematicians at the interface of stochastics, numerical analysis, applied mathematics, data science and statistics, preparing them to work as research leaders in academia and in industry in the expanding world of big models and big data. This research spectrum includes rapidly developing areas of mathematical sciences such as machine learning, uncertainty quantification, compressed sensing, Bayesian networks and stochastic modelling. The research and training engagement also encompasses modern industrially facing mathematics, with a key strength of our CDT being meaningful and long term relationships with industrial, government and other non-academic partners. A substantial proportion of our doctoral research will continue to be developed collaboratively through these partnerships. The urgency and awareness of the UK's need for deep quantitative analytical talent with expert modelling skills has intensified since SAMBa's inception in 2014. Industry, government bodies and non-academic organisations at the forefront of technological innovation all want to achieve competitive advantage through the analysis of data of all levels of complexity. This need is as much of an issue outside of academia as it is for research and training capacity within academia and is reflected in our doctoral training approach. The sense of urgency is evidenced in recent government policy (cf. Government Office for Science report "Computational Modelling, Technological Futures, 2018"), through the EPSRC CDT priority areas of Mathematical and Computational Modelling and Statistics for the 21st century as well as through our own experience of growing SAMBa since 2014. We have had extensive collaboration with partners from a wide range of UK industrial sectors (e.g. agri-science, healthcare, advanced materials) and government bodies (e.g. NHS, National Physical Laboratory, Environment Agency and Office for National Statistics) and our portfolio is set to expand. SAMBa's approach to doctoral training, developed in conjunction with our industrial partners, will create future leaders both in academia and industry and consists of: - A broad-based first year developing mathematical expertise across the full range of Statistical Applied Mathematics, tailored to each incoming student. - Deep experience in academic-industrial collaboration through Integrative Think Tanks: bespoke problem-formulation workshops developed by SAMBa. - Research training in a department which produces world-leading research in Statistical Applied Mathematics. - Multiple cohort-enhanced training activities that maximise each student's talents and includes mentoring through cross-cohort integration. - Substantial international opportunities such as academic placements, overseas workshops and participation in jointly delivered ITTs. - The opportunity for co-supervision of research from industrial and non-maths academic supervisors, including student placements in industry. This proposal will initially fund over 60 scholarships, with the aim to further increase this number through additional funding from industrial and international partners. Based on the CDT's current track record from its inception in 2014 (creating 25 scholarships to add to an initial investment of 50), our target is to deliver 90 PhD students over the next five years. With 12 new staff positions committed to SAMBa-core areas since 2015, students in the CDT cohort will benefit from almost 60 Bath Mathematical Sciences academics available for lead supervisory roles, as well as over 50 relevant co-supervisors in other departments.

Intelligent Visual and Interactive Technology allows us to perceive, understand and re-create the world around us. With it we can digitise the world with 3D cameras, use Artificial Intelligence (AI) to predict and enhance the health of people within our world or to educate and train them. It allows us to experience this world, or imagined ones, through immersive technologies, movies and video games, and interact with these worlds through technologies that analyse our movement and behaviour. There is a clear benefit to applying this technology across domains, for specific health or education purposes, but doing so requires coordinated action and genuine democratisation of the underpinning technologies, such that non-expert users are empowered. To address this challenge, CAMERA 2.0 will perform world-leading research in Intelligent Visual and Interactive Technology - underpinned by academic and partner expertise across Computer Vision, Computer Graphics, Human Computer Interaction (HCI) and AI - and engage a range of partners to generate impact and translate this technology across a range of themes. This multi-disciplinary approach is supported by academic and external partner expertise spanning healthcare, biomechanics, sports performance and psychology. These collaborations will allow us to carry out new research, create new impacts and develop further partnerships that would otherwise be impossible to achieve. This proposal builds on our highly successful Next Stage Digital Economy Centre for the Analysis of Motion Entertainment Research and Applications (CAMERA). Over the last 4 years, we have built a team of 14 academics and over 40 PhDs and researchers who have created real impact, alongside our partners, across themes of i) Entertainment; ii) Health, Rehabilitation and Assistive Technologies and; iii) Human Performance Enhancement. CAMERA 2.0 will also focus on three themes, supported by over 20 impact partners: i) Creative Science and Technology, ii) Digital Health and Assistive Technology and iii) Human Performance Enhancement. Furthermore, CAMERA 2.0 will work closely with our EPSRC CDT in Digital Entertainment and our new UKRI CDT in Accountable, Responsible and Transparent AI (ART-AI). Our research programme will deliver continuing impact through four primary mechanisms: (i) Theme Driven Impact Projects, (ii) Cross-Cutting Theme R&D Challenges, (iii) Reactive Impact Projects and (iv) Open Community Engagement. Theme Driven Impact Projects will be 12 to 24-month projects co-designed through sand-pits and co-delivered with partners. Although primarily aligned with a single theme they will overlap with at least one other. Our Cross-Cutting Theme R&D Challenges engage with R&D challenges shared by partners/academics across themes. Translating innovations across themes not only democratises and accelerates technology adoption but can significantly enhance impact. This will be addressed through key research projects, that support and feed into all other activities. Our reactive model allows us to carry out commercial projects as research impact vehicles at short notice - essential being able to work with the short-deadline driven creative sector. CAMERA 2.0 evolves our unique reactive impact model by placing our CAMERA student technical team at its core under the supervision of our experienced studio managers. Impact through Open Engagement. Our ambition is to raise the level of UK and international DE research through collaboration and technology democratisation. CAMERA 2.0 will operate an open-door model for reasonable access to facilities, data, software and training. In coordination with commitments from the University of Bath and external EU funding we are expanding our physical facilities and technical team to provide assisted motion capture and immersive technology training for free to over 100 creative industries, HEIs and healthcare companies.

Although British healthcare/biomedical manufacturing generates £70 billion/year and 240,000 jobs; its most important yield is a healthy, functional, thriving society. Unexpected externalities such as supply chain disruptions, sustainability requirements and socioeconomic circumstances (e.g. Brexit, COVID-19) pose a threat to this sector and more importantly to the wellbeing of Britain's population. To cope with these threats, it is imperative to develop new and strengthen existing technologies capable of manufacturing precise high-value, patient-personalised products in decentralised settings. Additive manufacturing technologies, such as 3D printing, have shown these characteristics as they enable prototyping and manufacturing customized products on-site in a rapid, and economic manner. Certainly, 3D printing has revolutionized manufacturing practices and generated tremendous economic benefits to economies worldwide; for instance, in the UK, 3D printing has a revenue of £2.4bn annually. Even so, this technology has major technical issues including, feedstock-performance dependency (printing needs to be calibrated depending of the plastic used), excessive plastic waste production (a major environmental concern), poor printing resolution (nanometer-size structures cannot be printed) and low flexibility in its operation mode (cannot produce long fibres, particles). These technical drawbacks significantly hinder the deployment of 3D printing in many healthcare/biomedical settings. Inspired by the response of organisms to environmental conditions, this project will develop a novel responsive additive technology (named eHD-3D printing) capable of responding autonomously to feedstock and product requirements, while addressing each of the challenges present in modern 3D printing technologies. To achieve these transformative characteristics, we will integrate bio-inspired modalities (e.g. sensing, thinking and moving). We will employ novel analytical tools that enable sensing the type of material/plastic fed into the unit. This information coupled with the characteristics of the product will allow an AI-algorithm to determine the best operating conditions and operation mode. Beyond conventional 3D printing, the eHD-3D unit will be able to generate particles (0D) and fibres (1D) with a nano-metric resolution, enabling the manufacture of complex multi-scaled structures. Moreover, to demonstrate the transformative features of the eHD-3D unit, a range of geometrically and structurally diverse tissue scaffolds will be manufactured.