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.

Despite dramatic advances in x-ray crystallography and electron microscopy, we do not have a way to visualise functional proteins in motion. This fellowship will lead the required breakthroughs and develop the first optical instrument to visualise proteins in real-time and at the level of single molecules. We propose to develop an instrument to probe single proteins in a specific and sensitive manner, while disturbing them as little as possible. The vision is to create a 'molecular scanner' that can characterise an arbitrary protein and its dynamics, a technology that is beyond the current state-of-the-art. Realising this sensor will lead to a new fundamental understanding of how the machinery of life functions. The micro-optical sensor will allow us to analyse proteins in entirely new ways. We will be able to detect proteins specifically, from optically-induced vibrational motions, on portable coin-sized laboratories. The advances I envisage will result in a completely new approach for the analysis and diagnosis of protein-misfolding diseases (proteinopathies) such as prion diseases, Alzheimer's disease, Parkinson's disease, amyloidosis, and a wide range of other disorders. Our sensor platform will be able to contribute to the development of artificial molecular machinery by providing laboratory test beds that observe the motions of nano-machines in real time. We will realise this instrument with optoplasmonic sensors. Optoplasmonic sensors enhance detection signals by reflection-driven circulation of the light. They concentrate the light at the nanoscale where they probe single proteins. We aim to scan the nanoscale light field across a single protein to provide information on the protein structure and its dynamics, resolving protein motions and vibrations at a temporal scale of nanoseconds and at a spatial scale of single bonds and atoms. The optical technique developed in this fellowship will instigate entirely new domains in protein analysis. It will measure and visualise protein structure and its dynamics in-situ, in solution and at surfaces. It will accomplish one of the "holy-grails" of proteomics. Also, this technique can be integrated on a chip, allowing the identification of misfolded proteins from a trace amount of sample, with minimal sample preparation. Thereby it will create new analysis methods, biomarkers and standards for the pharmaceutical and chemical analysis industries. A multitude of industries will be benefitted by the advances of this fellowship, including analytical sensing instrumentation, a $48.4 billion international market. The medical community desperately needs this analysis tool to rapidly detect and characterise intrinsically disordered proteins which cause the debilitating proteinopathies such as Parkinson's and Alzheimer's disease affecting more than 47 million worldwide, at an annual healthcare cost of ~$604 billion (WHO 2017).