It all adds up

Never the sexiest of subjects, advanced mathematics can often end up coming far down the pecking order when

technology companies are looking for ways to improve the development or commercialisation of a new product. Seemingly more useful for solving exquisitely difficult mathematical puzzles than real-life problems, maths suffers from a bad image.

However, an initiative was launched last week to encourage UK companies to integrate mathematics into their research and help make the most of their technologies. The DTI’s latest Knowledge Transfer Network (KTN), the Industrial Mathematics KTN will be managed by The Smith Institute for Industrial Mathematics and System Engineering. Based at the Surrey Technology Centre in Guildford, the Smith Institute was established in 1997 to help companies improve their products, processes and services through cutting-edge mathematical modelling.

Network director Roger Leese said that it will be taking the best bits from the Faraday Partnership which preceded it. In his opinion both small and large UK technology firms are not making the most of industrial mathematics and are often not aware of the benefits it could bring to their business. ‘A knowledge transfer network puts people together who would not normally work together,’ said Leese. ‘Small companies in particular often have well-defined problems that they need to find out how to solve, usually in the design stage.’

For small businesses that can ill-afford to make costly mistakes at the design stage, the benefit lies in enabling them to make shrewd business decisions early on. The network organises European Study Groups which a small number of companies can present their design and data analysis problems to more than 100 international mathematicians.

There have been some early success stories. Through support from the Smith Institute a small medical devices firm called Lein Applied Diagnostics has managed to secure investment funding of around £1m for an innovative new technology to help in diabetes testing.

When Lein came to the study group it was struggling with an early design problem in its concept. The plan was to check for diabetes by analysing the amount of glucose present in the aqueous layer at the front of the eye. This liquid, which is blood plasma without any blood cells present, reflects light differently as the glucose level changes.

Unfortunately researchers at Lein were struggling to analyse the data that they were receiving from the instrument when they shone light into the patient’s eye.

‘It seemed to be working really well, but in real eyes you get a lot of additional information as well as the change in glucose which we did not want,’ said Dan Daley, the firm’s director.

Mathematicians from the Smith Institute helped Lein to analyse its data more efficiently and enabled it to understand what exactly the new system was measuring. With the problem solved, Lein successfully completed the prototype and has just finished recent trials with 14 patients. The technology is now heading into two years of clinical tests at hospitals before it is fully commercialised.

Industrial mathematics is nothing new, however. According to Leese, it was invented as a discipline in Oxford in the 1960s and is now one of the UK’s greatest intellectual exports. Leese sees it as a discipline that borrows from both pure and applied mathematics, but with a strict focus on solving real-life problems. Its approach is based on carefully constructing models and then using the necessary maths to solve the problem.

‘It is an important tool and it is telling that both China and India are now showing signs of wanting to advance their capability in industrial mathematics,’ he said.

The Smith Institute has seven trained mathematicians on its staff to tackle problems on a contract basis which need solving within weeks. Whereas academia can provide focused work over a couple of days, and for long-term projects the Institute can appoint a PhD student to work on them, it is in the intermediate timescale, weeks or months, that the Institute’s own in-house team tackles the problems.

‘One of our priorities is looking at the timescale in which a problem needs to be solved. There is no point in solving a problem if you then find that the world has moved on and it doesn’t need solving any more,’ said Leese. ‘The business world doesn’t work like that.’

An example of this in action was a project undertaken for the National Air Traffic Services (NATS). After approaching the Smith Institute to help it improve its radar accuracy analysis, mathematics experts at a European study group developed new analysis tools to help NATS make its radar analysis more robust and less reliant on human interpretation.

It is not only small-scale technology companies that have benefited from applying maths to their technology problems, however. BAE Systems has been working with the Smith Institute over the past three years to look at the complex problem of electromagnetic compatibility. Each of the hundreds of electronic systems on-board an aircraft or a ship emit varying amounts of electromagnetic radiation. At the same time, each of these systems contains sensitive electronics that are so susceptible to electromagnetic radiation that it can affect their overall performance.

Colin Sillence, a scientist at BAE’s advanced technology centre in Bristol, was on the Smith Institute’s industrial advisory board at its inception. He worked with the institute in modelling the main problems relating to electromagnetic emissions. ‘You have the unwanted emissions from your system and the fact that other platforms in the area can emit radiation that will mess up your own system,’ he said. ‘And there is the interoperability issue, meaning that within one system there are parts of it that can interfere with other parts and stop it working properly. Everything interferes with everything else.’

A project was set up to look at the maths that describes the statistics of electromagnetic radiation within cavities. One of the complications of electromagnetic radiation is that the amount emitted can depend on how tightly one screw has been fastened, for example.

While it is possible to carry out empirical tests and engineer around a problem, Sillence sees this as a needlessly costly approach. In his opinion, using this kind of mathematical analysis will allow engineers in the future to be able to engineer for electromagnetic compatibility at the very beginning of a project. ‘Simply relying on engineering best judgment can often cost businesses money as people are cautious and tend to over-engineer which costs in terms of weight or materials,’ he said.

Allowing mathematicians to get their hands on industrial design problems can often provide surprising results as the problem is taken apart and looked at in a completely new and abstract way. This can lead to unlikely collaborations and strange parallels being drawn across different industries. Last year mathematicians studying the development of a new flow-measuring device for use in a milking parlour, for example, quickly realised that the problem had already been solved and that the solution lay with the oil industry.

‘It is only when you look at the problem in an abstract way that you begin to see more and more parallels,’ said Leese.