There are many interesting open questions at the interface between applied mathematics, scientific computing and applied statistics. Mathematics is the language of science, we use it to describe the laws of motion that govern natural and technological systems. We use statistics to make sense of data. We develop and test computer algorithms that make these ideas concrete. By bringing these concepts together in a systematic way we can validate and sharpen our hypothesis about the underlying science, and make predictions about future behaviour. This general field of Uncertainty Quantification is a very active area of research, with many challenges; from intellectual questions about how to define and measure uncertainty to very practical issues concerning the need to perform intensive computational experiments as efficiently as possible. ICONIC brings together a team of high profile researchers with the appropriate combination of skills in modeling, numerical analysis, statistics and high performance computing. To give a concrete target for impact, the ICONIC project will focus initially on Uncertainty Quantification for mathematical models relating to crime, security and resilience in urban environments. Then, acknowledging that urban analytics is a very fast-moving field where new technologies and data sources emerge rapidly, and exploiting the flexibility built into an EPSRC programme grant, we will apply the new tools to related city topics concerning human mobility, transport and infrastructure. In this way, the project will enhance the UK's research capabilities in the fast-moving and globally significant Future Cities field. The project will exploit the team's strong existing contacts with Future Cities laboratories around the world, and with nonacademic stakeholders who are keen to exploit the outcomes of the research. As new technologies emerge, and as more people around the world choose to live and work in urban environments, the Future Cities field is generating vast quantities of potentially valuable data. ICONIC will build on the UK's strength in basic mathematical sciences--the cleverness needed to add value to these data sources--in order to produce new algorithms and computational tools. The research will be conducted alongside stakeholders--including law enforcement agencies, technical IT and infrastructure providers, utility companies and policy-makers. These external partners will provide feedback and challenges, and will be ready to extract value from the tools that we develop. We also have an international Advisory Board of committed partners with relevant expertise in academic research, policymaking, law enforcement, business engagement and public outreach. With these structures in place, the research will have a direct impact on the UK economy, as the nation competes for business in the global Future Cities marketplace. Further, by focusing on crime, security and resilience we will directly improve the lives of individual citizens.

There are many interesting open questions at the interface between applied mathematics, scientific computing and applied statistics. Mathematics is the language of science, we use it to describe the laws of motion that govern natural and technological systems. We use statistics to make sense of data. We develop and test computer algorithms that make these ideas concrete. By bringing these concepts together in a systematic way we can validate and sharpen our hypothesis about the underlying science, and make predictions about future behaviour. This general field of Uncertainty Quantification is a very active area of research, with many challenges; from intellectual questions about how to define and measure uncertainty to very practical issues concerning the need to perform intensive computational experiments as efficiently as possible. ICONIC brings together a team of high profile researchers with the appropriate combination of skills in modeling, numerical analysis, statistics and high performance computing. To give a concrete target for impact, the ICONIC project will focus initially on Uncertainty Quantification for mathematical models relating to crime, security and resilience in urban environments. Then, acknowledging that urban analytics is a very fast-moving field where new technologies and data sources emerge rapidly, and exploiting the flexibility built into an EPSRC programme grant, we will apply the new tools to related city topics concerning human mobility, transport and infrastructure. In this way, the project will enhance the UK's research capabilities in the fast-moving and globally significant Future Cities field. The project will exploit the team's strong existing contacts with Future Cities laboratories around the world, and with nonacademic stakeholders who are keen to exploit the outcomes of the research. As new technologies emerge, and as more people around the world choose to live and work in urban environments, the Future Cities field is generating vast quantities of potentially valuable data. ICONIC will build on the UK's strength in basic mathematical sciences--the cleverness needed to add value to these data sources--in order to produce new algorithms and computational tools. The research will be conducted alongside stakeholders--including law enforcement agencies, technical IT and infrastructure providers, utility companies and policy-makers. These external partners will provide feedback and challenges, and will be ready to extract value from the tools that we develop. We also have an international Advisory Board of committed partners with relevant expertise in academic research, policymaking, law enforcement, business engagement and public outreach. With these structures in place, the research will have a direct impact on the UK economy, as the nation competes for business in the global Future Cities marketplace. Further, by focusing on crime, security and resilience we will directly improve the lives of individual citizens.

Lancaster University (LU) proposes a Centre for Doctoral Training (CDT) whose goal is the development of international research leaders in statistics and operational research (STOR) through a programme in which industrial challenge is the catalyst for methodological advance. The proposal brings together LU's considerable academic strength in STOR with a formidable array of external partners, both academic and industrial. All are committed to the development of graduates capable of either leadership roles in industry or of taking their experience of and commitment to industrial engagement into academic leadership in STOR. The proposal develops an existing EPSRC-funded CDT (STOR-i) by a significant evolution of its mission which takes its degree of industrial engagement to a new level. This considerably enhanced engagement will further strengthen STOR-i's cohort-based training and will result in a minimum of 80% of students undertaking doctoral projects joint with industry, up from 50% in the current Centre. Industrial internships will be provided for those not following a PhD with industry. Industry will (i) play a role in steering the Centre, (ii) has co-designed the training programme, (iii) will co-fund and co-supervise industrial doctoral projects, (iv) will lead a programme of industrial problem-solving days and (v) will play a major role in the Centre's programme of leadership development. Industry's financial backing is providing for stipend enhancement and a range of infrastructure and training support as well as helping to bring STOR-i benefits to a wide audience. The total pledged support for STOR-i is over £5M (including £1.1M cash). The proposal addresses the priority area 'Industrially-Focussed Mathematical Modelling'. Within this theme we specifically target 'Statistics' (itself a priority area) and Operational Research (OR). This choice is motivated first by the pervasive need for STOR solutions within modern industrial problems and second by the widely acknowledged and long standing skills-shortage at doctoral level in these areas. Our partners' statements of support attest that the substantial recent growth in data acquisition and data-driven business and industrial decision-making have signalled a step change in the demand for high level STOR expertise and have opened the skills gap still wider. The current Centre has demonstrated that a high quality, industrially engaged programme of research training can create a high demand for places among the very ablest mathematically trained students, including many who would otherwise not have considered doctoral study in STOR. We believe that the new Centre will play a yet more strategic role than its predecessor in meeting the persistent skills gap. Our training programme is designed to do more than solve a numbers problem. There is an issue of quality of graduating doctoral students in STOR as much as there is one of quantity. Our goal is to develop research leaders who are able to secure impact for their work across academic, scientific and industrial boundaries; who can work alongside others who are differently skilled and who can communicate widely. Our external partners are strongly motivated to join us in achieving this through STOR-i's cohort-based training programme. We have little doubt that our graduates will be in great demand across a wide range of sectors, both industral and academic. The need for a Centre to deliver the training resides primarily in its guarantee of a critical mass of outstanding students. This firstly enables us to design a training programme around student cohorts in which peer to peer learning is a major feature. Second, we are able to attract and integrate the high quality contributions (both internal and external to LU) we need to create a programme of quality, scope and ambition.

Mathematics is a profound intellectual achievement with impact on all aspects of business and society. For centuries, the highest level of mathematics has been seen as an isolated creative activity, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. "Crowdsourcing" pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs that are just too long and complicated for any human to comprehend, using programs designed to verify hardware. Yet these techniques are currently used in stand-alone fashion, lacking integration with each other or with human creativity or fallibility. Social machines are new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity. Our long-term vision is to change mathematics, transforming the reach, pace, and impact of mathematics research, through creating a mathematics social machine: a combination of people, computers, and archives to create and apply mathematics. Thus, for example, an industry researcher wanting to design a network with specific properties could quickly access diverse research skills and research; explore hypotheses; discuss possible solutions; obtain surety of correctness to a desired level; and create new mathematics that individual effort might never imagine or verify. Seamlessly integrated "under the hood" might be a mixture of diverse people and machines, formal and informal approaches, old and new mathematics, experiment and proof. The obstacles to realising the vision are that (i) We do not have a high level understanding of the production of mathematics by people and machines, integrating the current diverse research approaches (ii) There is no shared view among the diverse re- search and user communities of what is and might be possible or desirable The outcome of the fellowship will be a new vision of a mathematics social machine, transforming the reach, pace and impact of mathematics. It will deliver: analysis and experiment to understand current and future production of mathematics as a social machine; designs and prototypes; ownership among academic and industry stakeholders; a roadmap for delivery of the next generation of social machines; and an international team ready to make it a reality.

Mathematics is a profound intellectual achievement with impact on all aspects of business and society. For centuries, the highest level of mathematics has been seen as an isolated creative activity, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. "Crowdsourcing" pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs that are just too long and complicated for any human to comprehend, using programs designed to verify hardware. Yet these techniques are currently used in stand-alone fashion, lacking integration with each other or with human creativity or fallibility. Social machines are new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity. Our long-term vision is to change mathematics, transforming the reach, pace, and impact of mathematics research, through creating a mathematics social machine: a combination of people, computers, and archives to create and apply mathematics. Thus, for example, an industry researcher wanting to design a network with specific properties could quickly access diverse research skills and research; explore hypotheses; discuss possible solutions; obtain surety of correctness to a desired level; and create new mathematics that individual effort might never imagine or verify. Seamlessly integrated "under the hood" might be a mixture of diverse people and machines, formal and informal approaches, old and new mathematics, experiment and proof. The obstacles to realising the vision are that (i) We do not have a high level understanding of the production of mathematics by people and machines, integrating the current diverse research approaches (ii) There is no shared view among the diverse re- search and user communities of what is and might be possible or desirable The outcome of the fellowship will be a new vision of a mathematics social machine, transforming the reach, pace and impact of mathematics. It will deliver: analysis and experiment to understand current and future production of mathematics as a social machine; designs and prototypes; ownership among academic and industry stakeholders; a roadmap for delivery of the next generation of social machines; and an international team ready to make it a reality.