"Software is the most prevalent of all the instruments used in modern science" [Goble 2014]. Scientific software is not just widely used [SSI 2014] but also widely developed. Yet much of it is developed by researchers who have little understanding of even the basics of modern software development with the knock-on effects to their productivity, and the reliability, readability and reproducibility of their software [Nature Biotechnology]. Many are long-tail researchers working in small groups - even Big Science operations like the SKA are operationally undertaken by individuals collectively. Technological development in software is more like a cliff-face than a ladder - there are many routes to the top, to a solution. Further, the cliff face is dynamic - constantly and quickly changing as new technologies emerge and decline. Determining which technologies to deploy and how best to deploy them is in itself a specialist domain, with many features of traditional research. Researchers need empowerment and training to give them confidence with the available equipment and the challenges they face. This role, akin to that of an Alpine guide, involves support, guidance, and load carrying. When optimally performed it results in a researcher who knows what challenges they can attack alone, and where they need appropriate support. Guides can help decide whether to exploit well-trodden paths or explore new possibilities as they navigate through this dynamic environment. These guides are highly trained, technology-centric, research-aware individuals who have a curiosity driven nature dedicated to supporting researchers by forging a research software support career. Such Research Software Engineers (RSEs) guide researchers through the technological landscape and form a human interface between scientist and computer. A well-functioning RSE group will not just add to an organisation's effectiveness, it will have a multiplicative effect since it will make every individual researcher more effective. It has the potential to improve the quality of research done across all University departments and faculties. My work plan provides a bottom-up approach to providing RSE services that is distinctive from yet complements the top-down approach provided by the EPRSC-funded Software Sustainability Institute. The outcomes of this fellowship will be: Local and National RSE Capability: A RSE Group at Sheffield as a credible roadmap for others pump-priming a UK national research software capability; and a national Continuing Professional Development programme for RSEs. Scalable software support methods: A scalable approach based on "nudging", to providing research software support for scientific software efficiency, sustainability and reproducibility, with quality-guidelines for research software and for researchers on how best to incorporate research software engineering support within their grant proposals. HPC for long-tail researchers: 'HPC-software ramps' and a pathway for standardised integration of HPC resources into Desktop Applications fit for modern scientific computing; a network of HPC-centric RSEs based around shared resources; and a portfolio of new research software courses developed with partners. Communication and public understanding: A communication campaign to raise the profile of research software exploiting high profile social media and online resources, establishing an informal forum for research software debate. References [Goble 2014] Goble, C. "Better Software, Better Research". IEEE Internet Computing 18(5): 4-8 (2014) [SSI 2014] Hettrick, S. "It's impossible to conduct research without software, say 7 out of 10 UK researchers" http://www.software.ac.uk/blog/2014-12-04-its-impossible-conduct-research-without-software-say-7-out-10-uk-researchers (2014) [Nature 2015] Editorial "Rule rewrite aims to clean up scientific software", Nature Biotechnology 520(7547) April 2015

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.

High Performance Embedded and Distributed Systems (HiPEDS), ranging from implantable smart sensors to secure cloud service providers, offer exciting benefits to society and great opportunities for wealth creation. Although currently UK is the world leader for many technologies underpinning such systems, there is a major threat which comes from the need not only to develop good solutions for sharply focused problems, but also to embed such solutions into complex systems with many diverse aspects, such as power minimisation, performance optimisation, digital and analogue circuitry, security, dependability, analysis and verification. The narrow focus of conventional UK PhD programmes cannot bridge the skills gap that would address this threat to the UK's leadership of HiPEDS. The proposed Centre for Doctoral Training (CDT) aims to train a new generation of leaders with a systems perspective who can transform research and industry involving HiPEDS. The CDT provides a structured and vibrant training programme to train PhD students to gain expertise in a broad range of system issues, to integrate and innovate across multiple layers of the system development stack, to maximise the impact of their work, and to acquire creativity, communication, and entrepreneurial skills. The taught programme comprises a series of modules that combine technical training with group projects addressing team skills and system integration issues. Additional courses and events are designed to cover students' personal development and career needs. Such a comprehensive programme is based on aligning the research-oriented elements of the training programme, an industrial internship, and rigorous doctoral research. Our focus in this CDT is on applying two cross-layer research themes: design and optimisation, and analysis and verification, to three key application areas: healthcare systems, smart cities, and the information society. Healthcare systems cover implantable and wearable sensors and their operation as an on-body system, interactions with hospital and primary care systems and medical personnel, and medical imaging and robotic surgery systems. Smart cities cover infrastructure monitoring and actuation components, including smart utilities and smart grid at unprecedented scales. Information society covers technologies for extracting, processing and distributing information for societal benefits; they include many-core and reconfigurable systems targeting a wide range of applications, from vision-based domestic appliances to public and private cloud systems for finance, social networking, and various web services. Graduates from this CDT will be aware of the challenges faced by industry and their impact. Through their broad and deep training, they will be able to address the disconnect between research prototypes and production environments, evaluate research results in realistic situations, assess design tradeoffs based on both practical constraints and theoretical models, and provide rapid translation of promising ideas into production environments. They will have the appropriate systems perspective as well as the vision and skills to become leaders in their field, capable of world-class research and its exploitation to become a global commercial success.

Our proposal builds on the successful start made by Cambridge Centre for Analysis (CCA), a current EPSRC Centre for Doctoral Training. We propose to develop further our activity in two important and rapidly evolving areas of analysis, namely mathematics of information and statistics of complex systems. Beginning with Newton, for whom the development of calculus and the mathematical understanding of bodies in motion were closely intertwined, the mathematics used to describe real phenomena consistently involves notions of continuity, rate of change, average value, and basic challenges such as the relationship between discrete and continuum objects. This is the domain of analysis, encompassing modelling by partial differential equations and by random processes, and the mathematical theory which guides effective computation for such models. The centrality of mathematical analysis in the relationship between mathematics and its applications has been acknowledged by successive International Reviews of Mathematics, as has the need to increase the capacity of UK PhD training in analysis. Mathematical Analysis and its Applications is an EPSRC Priority Area. Beyond the established and important uses of analysis in modelling physical phenomena, digital technology has created new areas where mathematical analysis, in guiding the extraction of knowledge from massive discrete systems, plays an essential role. These include the fields of high-dimensional statistics and the mathematics of information, including compressed sensing. In each of these, one is looking for a reliable means to interpret massive high-dimensional data. Already several CCA students are working in these areas. Big Data is one of the Eight Great Technologies championed by the Minister for Universities and Science. Statistics and Data to Knowledge are EPSRC Priority Areas. We propose a first year training programme based on our current successful model, now expanded by two further core courses, one in Statistics of Complex Systems and one in Mathematics of Information. These new courses will be paired with postgraduate level courses from the existing Cambridge Masters' (MASt), which students can use to consolidate their understanding. The core courses themselves are based on supervised student team assignments leading to student presentations. The other main components of the first year are research mini-projects (often the route to a PhD project) and an industry workshop. Years two to four are devoted mainly to the PhD thesis. First year training establishes a collaborative ethos in the cohort and, by mixing students with different prior skills, encourages cross-fertilization of ideas across the different threads of analysis. This is sustained in later years through a programme of seminars, workshops and training in transferable skills. The students appreciate that their collective understanding of a given problem using different skills will often exceed each individual's understanding. This makes cohort-based training especially valuable in analysis. We already expose all our students to the role of mathematics and the opportunities for mathematicians in industry and society, and we encourage first-hand engagement with applications through mini-projects, industrial seminars and study weeks, and, for some, PhD projects with industrial partners. The development of core skills and eventually the ability to generate new ideas is the hardest and crucial part of training as a research mathematician. This is necessarily our overriding task, in which we seek synergy and inspiration from user engagement. In the new CDT, our network of industrial connections will be further enhanced, along with our collaborations with Cambridge engineering colleagues, and our links with the Smith Institute for Industrial Mathematics.

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.