With increasing take up of externally provisioned and managed services (from government, finance, entertainment), often hosted over Cloud computing infrastructure, there is a realisation that on-line electronic services can involve an interlinked range of providers. Gartner forecasts that cloud computing market will grow at a compound annual growth rate of 32% (2016-2019), with the potential for additional providers to emerge in the market place. Ofcom's "Communication Market Report" indicates total UK telecoms business revenue were 37.5bn in 2015, indicating significant contribution of mobile services to the UK economy. With the availability of additional mobile services and infrastructure, there is interest in new business models that can facilitate additional subscribers to make use of these services. However, from a user's perspective, trust in the use of these services remains limited, as highlighted in the Pew Research Centre report ("The Fate of Online Trust in the Next Decade", August 2017), which surveyed 1,233 respondents - 24% of these respondents predicted that trust in on-line services is likely to diminish over time. The report revealed that although billions of people use "cellphones" and the internet now, many still do not use that connectivity for shopping, banking, and other important transactions due to limited trust in on-line providers. Some of the respondents surveyed indicated that the use of new technology (such as Blockchains) and regulatory compliance (and industry changes) will help increase trust in on-line services. As more people move online globally over the next decade, both opportunities and threats grow. It is now likely that due to the wide adoption of Cloud based provisioning, some of these mobile services will exist at the network edge. Consider, for instance, a coffee chain that initially provided Wifi services to customers, now working in collaboration with data centre providers to offer additional services to users (e.g. edge data storage, multimedia caching, etc). Such scenarios have been proposed by a number of organisations involved in Mobile Edge Computing (e.g. the European ETSI and the NIST "Big Data" Working Group). This project addresses security and privacy requirements of such environments, where multiple Cloud computing providers need to work collaboratively to offer services to a user. Users of these services only interact with a Web interface rather than the larger, distributed service ecosystem, and are often unfamiliar with the "ecosystem" of providers that are involved in offering them a particular capability. Their visibility beyond the first service provider is often missing, requiring them to "trust" the provider in handling and managing their data. This is a significant challenge, and according to a recent report from the Pew Research Centre, often deters the use of on-line services (especially for data providers which are new in the market place). They often entrust their data and identity without realising that the service provider may share their data with several back-end services (Cloud hosted analytics, advertisers). While this has been a problem in the past, it will be greatly exacerbated by the expansion of internet connected devices. In order to address this, the General Data Protection Regulation (GDPR) will be implemented to ensure that non-expert users can make informed decisions about their privacy and thereby give 'informed consent' to the use, sharing and re-purposing of their personal data. There are a number of challenges to facilitating this, both for individuals who need to provide consent and for data controllers who need to obtain it. As a means of addressing this, we propose a technological solution in the form of a mobile software "container" that will ensure that all access instances are securely logged. This will improve transparency, enable an audit trail of providers and facilitate greater trust between users and service providers.

Probabilistic modelling permeates all branches of engineering and science, either in a fundamental way, addressing randomness and uncertainty in physical and economic phenomena, or as a device for the design of stochastic algorithms for data analysis, systems design and optimisation. Probability also provides the theoretical framework which underpins the analysis and design of algorithms in Data Science and Artificial Intelligence. The "CDT in Mathematics of Random Systems" is a new partnership in excellence between the Oxford Mathematical Institute, the Oxford Dept of Statistics, the Dept of Mathematics at Imperial College and multiple industry partners from the healthcare, technology and financial services sectors, whose goal is to establish an internationally leading PhD training centre for probability and its applications in physics, finance, biology and Data Science, providing a national beacon for research and training in stochastic modelling and its applications, reinforcing the UK's position as an international leader in this area and meeting the needs of industry for experts with strong analytical, computing and modelling skills. We bring together two of the worlds' best and foremost research groups in the area of probabilistic modelling, stochastic analysis and their applications -Imperial College and Oxford- to deliver a consolidated training programme in probability, stochastic analysis, stochastic simulation and computational methods and their applications in physics, biology, finance, healthcare and Data Science. Doctoral research of students will focus on the mathematical modelling of complex physical, economic and biological systems where randomness plays a key role, covering mathematical foundations as well as specific applications in collaboration with industry partners. Joint projects with industrial partners across several sectors -technology, finance, healthcare- will be used to sharpen research questions, leverage EPSRC funding and transfer research results to industry. Our vision is to educate the next generation of PhDs with unparalleled, cross-disciplinary expertise, strong analytical and computing skills as well as in-depth understanding of applications, to meet the increasing demand for such experts within the Technology sector, the Financial Service sector, the Healthcare sector, Government and other Service sectors, in partnership with industry partners from these sectors who have committed to co-funding this initiative. ALIGNMENT with EPSRC PRIORITIES This proposal reaches across various areas of pure and applied mathematics and Data Science and addresses the EPSRC Priority areas of (15. Mathematical and Computational Modelling), (22. Pure Mathematics and its Interfaces) ; however, the domain it covers is cross-disciplinary and broader than any of these priority areas taken in isolation. Probabilistic methods and algorithms form the theoretical foundation for the burgeoning area of Data Science and AI, another EPSRC Priority area which we plan to address, in particular through industry partnerships with AI/technology/data science firms. IMPACT By training highly skilled experts equipped to build, analyse and deploy probabilistic models, the CDT in Mathematics of Random Systems will contribute to - sharpening the UK's research lead in this area and training a new generation of mathematical scientists who can tackle scientific challenges in the modelling of complex, simulation and control of complex random systems in science and industry, and explore the exciting new avenues in mathematical research many of which have been pioneered by researchers in our two partner institutions; - train the next generation of experts able to deploy sophisticated data driven models and algorithms in the technology, finance and healthcare sectors

On a daily basis huge amounts of geospatial data and information that record location is created across a wide range of environmental, engineered and social systems. Globally approximately 2 quintillion bytes of data is generated daily which is location based. The economic benefits of geospatial data and information have been widely recognised, with the global geospatial industry predicted to be worth $500bn by 2020. In the UK the potential benefits of 'opening' up geospatial data is estimated by the government to be worth an additional £11bn annually to the economy and led to the announcement of a £80m Geospatial Commission. However, if the full economic benefits of the geospatial data revolution are to be realised, a new generation of geospatial engineers, scientists and practitioners are required who have the knowledge, technical skills and innovation to transform our understanding of the ever increasingly complex world we inhabit, to deliver highly paid jobs and economic prosperity, coupled with benefits to society. To seize this opportunity, the Centre for Doctoral Training in Geospatial Systems will deliver technically skilled doctoral graduates equipped with an industry focus, to work across a diverse range of applications including infrastructure systems, smart cities, urban-infrastructure resilience, energy systems, spatial mobility, structural monitoring, spatial planning, public health and social inclusion. Doctoral graduates will be trained in five core integrated geospatial themes: Spatial data capture and interpretation: modern spatial data capture and monitoring approaches, including Earth observation satellite image data, UAVs and drone data, and spatial sensor networks; spatial data informs us on the current status and changes taking place in different environments (e.g., river catchments and cities). Statistical and mathematical methods: innovative mathematical approaches and statistical techniques, such as predictive analytics, required to analyse and interpret huge volumes of geospatial data; these allow us to recognise and quantify within large volumes of data important locations and relationships. Big Data spatial analytics: cutting edge computational skills required for geospatial data analysis and modelling, including databases, cloud computing, pattern recognition and machine learning; modern computing approaches are the only way that vast volumes of location data can be analysed. Spatial modelling and simulation: to design and implement geospatial simulation models for predictive purposes; predictive spatial models allow us to understand where and when investment, interventions and actions are required in the future. Visualisation and decision support: will train students in modern methods of spatial data visualisation such as virtual and augmented reality, and develop the skills on how to deliver and present the outputs of geospatial data analysis and modelling; skills required to ensure that objective decisions and choices are made using geospatial data and information. The advanced training received by students will be employed within interdisciplinary PhD research projects co-designed with 40 partners ranging from government agencies, international engineering consultants, infrastructure operators and utility companies, and geospatial technology companies; organisations that are ideally positioned to leverage of the Big Data, Cloud Computing, Artificial Intelligence and Internet of Things (IoT) technologies that are predicted to be the key to "accelerating geospatial industry growth" into the future. Throughout their training and research, students will benefit from cohort-based activities focused on group-working and industry interaction around innovation and entrepreneurship to ensure that our outstanding researchers are able to deliver innovation for economic prosperity across the spectrum of the geospatial industry and applied user sectors.