SIAM News Blog

Super-sized Study Groups with Industry

A Nonlinear Increase in Problem-solving Effectiveness

By Chris Breward and John Ockendon

Marking a milestone for industrial mathematics, the University of Oxford staged the 100th European Study Group with Industry during the week of April 7–11. This “Super-Sized Study Group” saw 200 participants attack ten problems of economic or social importance to the presenters, who represented sectors as diverse as manufacturing, agrifood, industrial processes, image processing, safety and security, and transport.

The interests of large multinationals, government agencies, and rapidly growing startups were all accommodated. The industrial reaction was more positive than ever: CrowdEmotion, a BBCWorldwide Labs startup, implemented a Study Group-generated algorithm in its software by the end of the final afternoon, and others were already discussing avenues for future collaboration. The registration fee was clearly no deterrent for the industrial participants.

"Do the simplest problem first." The process of a Study Group from raw problem to a useful outcome for the presenter can be tortuous.

The Study Group followed the tried and tested format of problem presentation, self-organised brainstorming, and reporting back. The mathematics evolved in the course of the week, following the universal Study Group pattern of repeated rephrasing of the raw problem in light of mathematical modelling until it made good scientific sense and would yield valuable practical insights. You would have to be present to grasp how tortuous this process can be, but the three following examples (and the accompanying photo) should give some idea.

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Raw Problem. A contaminant is released onto an urban surface, such as concrete or carpet. What is the best way to clean it up?

Processed Modelling Problem. Model the penetration of the contaminant into a porous substrate and the effect of a subsequent application of a chemically active cleanser to the substrate.

This led to a novel analysis of chemical reactions at the interface between two liquids in a porous medium. The key new insight was that cleansing is better when the reaction products are soluble in the cleanser rather than in the contaminant material. “The week was a great success,” said Anthony Arkell and Hasmitta Stewart of the UK Government Decontamination Service. “The outcomes . . . will allow us to target further research and development and provide better advice in the interim.”


Raw Problem. How can video searching be made quicker and more accurate?

Processed Modelling Problem. Identify models for colour perception most appropriate for jpeg and minimise the occurrence of subsequent encryption-generated artefacts.

This reminded the academic participants of the beautiful mathematical (geometrical) models of colour vision and provided new challenges for image processing. Suggested along the way were new algorithms for decompressing jpeg files that would make objects recognisable by sharpening the edges in the image and reducing computer-generated artefacts. “We now have a clear insight into how we may advance the state-of-the-art in automated scene analysis,” said Glynn Wright, CEO of the small company Aralia. “Some of the results promise to be of considerable significance to virtually everyone who uses digital images.”


Raw Problem. Design fibrous filters that optimise droplet removal from a two-phase gas/liquid flow.

Processed Modelling Problem. Model liquid transport along the exterior of fibres in networks and incorporate pinning and droplet formation.

Work on this problem provided a brand new twist to the theory of filters because of the high mobility of the filtrate. Proposed models ranged from generalised lubrication theories to Markov chains. Mark Hurwitz, from the multinational Pall Corporation, said that he was “highly gratified by the interest shown in our coalescence problem and the intense effort made by so many talented mathematicians. In a single week my thinking about this complicated subject has been significantly clarified, and the array of modelling approaches developed provide a powerful roadmap for further research.”

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Since their inception at Oxford in 1968, Study Groups have established themselves globally as a powerful mechanism for bringing mathematical thinking to bear on industrial problems (this site lists about 20 Study Groups yearly and will contain detailed reports on the ESGI100 problems in due course). Recent innovations include communications via social media and, especially important, the concept of pre-Study Group student modelling camps as pioneered in North America. 

Most Study Groups involve about five problems and 50–70 participants, the majority of whom are early-career researchers. The dramatic outcome at ESGI100 was the result of the scaling up in the number of participants and the corresponding nonlinear increase in the number of interactions, enabling brainstorming sessions to enhance both the novelty of the mathematics that was applied and the impact of the resulting new insights on the industrial problems. Somehow, people did not get lost in the crowd and managed to self-assemble into small teams within which leaders emerged to coordinate their outputs. The success of such brainstorming could be a great topic for psychological study!

An event on this scale could not have happened without strong support from many sources, including, crucially, the Smith Institute for Industrial Mathematics and System Engineering ( It provided the key infrastructure for drawing in the problems, and its wide network of leading academics, industrialists, and government policy-makers helped organise a panel discussion on the future of industrial mathematics.

The wide-ranging panel discussion identified a number of routes for enhancing the profile of industrial mathematics in the corridors of power, making it clear that the success of the subject crucially depends on the enthusiasm and commitment of early-career researchers. If such researchers are to be identified and encouraged, academics must continue to demonstrate the attractiveness of careers in which mathematicians can put their skills to genuine practical use in industry and society. The numerous Study Groups that occur throughout the world provide a forum that highlights how exciting and rewarding such careers can be.

Chris Breward is the the co-director of the EPSRC Centre for Doctoral Training in Industrially Focused Mathematical Modelling (InFoMM) and the associate director of the Oxford Centre for Collaborative Applied Mathematics, both at the Mathematical Institute at the University of Oxford. John Ockendon works at the Oxford Centre for Industrial and Applied Mathematics at the Mathematical Institute of the University of Oxford.

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