Examples of National Importance Statements

As part of our ongoing guidance on National Importance, we have worked with successful applicants to highlight good examples of National Importance statements. The paragraphs included below have been extracted from real proposals that have been through the EPSRC process in the Mathematical Sciences Theme.

There are several ways to articulate National Importance which can be seen in the examples below. There are a number of aspects of National Importance as described in our guidance for example social benefits, economic benefits or world leading science. As demonstrated by these case studies it is not always necessary to make a case against all of these.

For further information on National Importance when preparing your proposal.

For further examples on National Importance statements from other themes.

Grant Title: Multivariate Bayesian Modelling of Skewness and Kurtosis With Applications in Biostatistics

Mark Steel, Professor of Statistics, University of Warwick

One major set of contributions of this research would be in the development of statistical methodology. This is an area where the UK has traditionally been very strong, but in recent decades this comparative advantage has been somewhat eroded, as documented in the International Review of Mathematics (both in 2004 and 2010). In particular, the research proposed here would build upon key areas of strength of the UK research base in statistics (Bayesian modelling, computational statistics, biostatistics, longitudinal data analysis). This aspect of the research would contribute to the Mathematical Sciences portfolio of EPSRC (within the growth area of Statistics and Applied Probability).

An important second set of contributions would be in the specific areas of application in biomedical modelling. The joint modelling of longitudinal responses and the time to an event (such as death or the onset of a disease) is critical in understanding the evolution of many diseases, such as HIV, cardiovascular disease, renal disease or liver cirrhosis. In such situations, we also often wish to include additional recurrent events (such as opportunistic diseases or hospitalizations) in the model, as they are important indicators for quality of life. Allowing for flexible joint modelling of all these processes, formally taking into account model uncertainty and censored or missing observations would be an important advance in this area. In addition, we would make code freely available, so our methodology could be used by applied statisticians and medical practitioners.

Thus, we also contribute to substantive applications in the theme 'Healthcare Technologies: Techniques for Biomedical Understanding' highlighted in the EPSRC portfolio, which includes modelling which can be applied to biomedicine. Given the importance of enhancing our understanding of the progression of for example HIV and cardiovascular diseases, we expect this can also be of interest to non-academic organizations and decision-makers in health policy.

Grant Title: Special holonomy: geometric flow and boundary value problems

Jason Lotay, Lecturer in Pure Mathematics, University College London (UCL)

The proposed research is in Geometry, with a focus on using techniques from Geometric Analysis and electronic data systems (EDS) to study nonlinear partial differential equations (PDEs). The UK is internationally recognised as a leader in Geometry, which is a fundamental part of modern mathematics and has applications throughout the physical and life sciences, engineering and information and communication technologies (ICT). The International Review of Mathematical Sciences 2010 found that the part of geometry that most needs strengthening in the UK is the connection between geometric analysis and partial differential equations and recommended that opportunities should be exploited for fruitful collaborations between analysis and other fields of the mathematical sciences, most notably in geometry and topology. These sentiments are echoed in the findings of the EPSRC Pure Maths Workshop (2012).

Geometric flows are a major part of Geometric Analysis internationally and form a developing area of research in the UK. These flows play a central role in this proposal and have proven to be important tools not just within mathematics, where they have led to the resolution of longstanding famous conjectures, but also in engineering where Mean Curvature Flow provides a robust means for removing noise from empirical data (for example, in images of brains from various types of scanners). Another crucial part of the project is the use of elliptic boundary value problems, which occur in a variety of contexts both within mathematics and in physical applications such as modelling beam bending and the interactions between molecules and cells in biology. Overall, the national importance of the proposal will be to strengthen the research at the interface between Geometry and Analysis in the UK.

Grant Title: Boolean modelling of biochemical networks

Ozgur Akman, Senior Lecturer in Mathematics, University of Exeter

The UK Government’s Science & Innovation Framework 2004-2014 highlighted systems biology as one of its exemplar multidisciplinary research themes, with significant potential in economically critical areas such as medicine and crop breeding. In 2007, the Royal Academy of Engineering and the Academy of Medical Sciences jointly published an influential report further outlining the strategic importance of the area to the UK as a vehicle for advancing knowledge and building the nation’s wealth. Crucially, the report identified the construction of predictive mathematical models through iterative cycles of experiments and computational analysis to be a fundamental objective of both systems biology and its sister discipline synthetic biology. The development of robust techniques for building and validating quantitative models of complex dynamical networks is therefore a key challenge for physical scientists working in these fields, and is the general research theme within which this project lies. Moreover, the application of quantitative modelling methods to circadian biology is necessary to understand and predict the effects of climate change on key clock-regulated phenological processes in plants, such as photosynthesis, flowering time, seed germination and fruiting. This will inform rational strategies for breeding agronomically and ecologically important crops with improved performance under new climate scenarios. Conversely, quantifying the effect of temperature shifts on plant distributions will be important for accurate long-range predictions using climate change models. The proposed project thus aligns directly with the EPSRC’s strategic priorities in the Themes of Mathematical sciences (particularly Nonlinear systems and Complexity science) and Living with environmental change.

Grant Title: Theory of badly approximable sets

Dzmitry Badziahin, Lecturer of Mathematical Sciences, Durham University

The research proposed in this application primarily aims at developing new techniques and solving outstanding problems in the theory of Diophantine approximation. For decades this area of research has been a UK strength and has led to numerous breakthroughs, some of them being acknowledged by Fields medals (Roth, Baker). Nowadays the UK position in Diophantine approximation as well as in other research areas particularly close to the proposed research such that ergodic theory and dynamical systems are strong and represented across the country, for example at Bristol, Manchester, Warwick, York and other places. Doubtless the UK will continue to hold one of the world-leading positions in the area. The proposed research will help maintaining the UK leadership and contribute to the development of its research capability in this research area. This will highly likely remain important over the next 10-50 years as the various high-profile research activities in the area have only recently started unfolding. In particular, EPSRC is currently funding two large research programmes in the area: one at Bristol (EP/J00149X/1) and one at York (EP/J018260/1). After all, the proposed research is perfectly aligned with the current EPSRC portfolio of research: number theory and more broadly analysis are two currently active Themes within Mathematical Sciences.

Grant Title: Bringing set theory and algebraic topology together

Andrew Brooke-Taylor, EPSRC Early Career Fellow, University of Bristol

Set theory in the UK is currently a small but world class grouping, and is one of the four major areas of mathematical logic, which EPSRC plans to maintain. This project will significantly benefit the health of set theory, with new and strengthened connections to the central mathematical discipline of algebraic topology, and a refocusing of research on such connections. At the same time, the set theoretic tools of forcing and large cardinals which will play an important role in this project are notably also major features of the two current EPSRC funded classical set theory projects Inner Model Theory in Outer Models led by Philip Welch (Bristol), and Combinatorial set theory at the successor of a singular cardinal: a marriage of a forcing axiom and a reaction principle led by Mirna Dizamonja (UEA), so this project is a good fit for the current UK set theory landscape.

Algebraic topology is a central topic in the Geometry and Topology area, which was identified by the International Review of Mathematical Sciences 2010 as an area in which the UK is an international leader and which EPSRC has decided to maintain. The EPSRC Portfolio webpage for this area explicitly states a strategy to build upon growing connections with other mathematical disciplines and beyond, making this proposal particularly resonant with the strategy. It would of course ensure that the UK is at the very forefront of research bringing set-theoretic tools to bear on the area.

It should also be noted that the UK has a world-leading community in topos theory (with a strong showing for example in the Category Theory and Logic group in the Faculty of Mathematics at Cambridge). This is another topic that brings category theory together with logic, although generally non-classical logic rather than the classical logic in which this project is couched. Despite the differences between the subject matter of this proposal and the usual interests of the topos theory community, the general environment in the UK of excellence in category theory and the foundations of mathematics is something which this proposal would help to maintain and expand in new directions.

Regarding short term Social and Economic Impact, the UK has a particularly strong history of public engagement in science, with for example the internationally distributed New Scientist magazine based in the UK. Thus, the public engagement in science pathways described in the Pathways to Impact statement will be particularly relevant to the UK.