Impact of our research

Mathematics is often perceived as abstract and theoretical, but it can make surprising appearances in the real-world. Here are some examples of the way in which York's maths research is useful in analysing practical problems.

How safe is your food?

Identifying the chemical and genetic constituents of foodstuffs requires more than just experimental measurements - there is a great deal of complex and subtle data processing to be done. Working with the Food and Environment Research Agency (Fera), Julie Wilson has developed advanced mathematical techniques which enable much better, more precise results to be obtained, so that Fera can be much more certain about exactly what you are eating!

How can the interference of users in wireless networks be managed?

In our digital world, wireless communication is used in all walks of life. The rapidly growing demand for network capacity unavoidably requires frequency-spectrum sharing and so causes interference between users, damaging overall performance. A recent breakthrough in solving this conundrum is the idea of 'Real Interference Alignment' (due to Motahari et al.), which makes use of mathematical properties of real numbers to design novel coding schemes. These have various benefits, including a higher number of degrees of freedom over a variety of channels, or the capability of converting a single antenna system to a Multiple Input Multiple Output (MIMO) system. The schemes are built upon the Khintchine-Groshev type theorem for nondegenerate manifolds that was independently established by Victor Beresnevich (at York) and Bernik, Kleinbock and Margulis, around the turn of the millennium. The theorem was originally a pure-mathematical advance, solving a long-standing problem in number theory but with no obvious applications. But in the light of this new development, a recent initiative by Beresnevich and Sanju Velani within their EPSRC Programme Grant aims at developing further new techniques in metric Diophantine approximation to improve electronic communication technologies.

How can we generate random numbers that are guaranteed to be random?

Random number generators are important in many applications: they are vital for simulations, and online casinos need them to run various games. In a classical world, there is no way to make random numbers even in principle; the best we can do is generate pseudo-random numbers (which satisfy certain randomness tests, but in fact contain subtle correlations). However, use of pseudo-randomness is dangerous, particularly for a casino where a shrewd gambler may be able to exploit the subtle correlations to make a large profit. Thus, the ability to certify the generation of truly random bits is highly desirable. When we move to the quantum world, random number generation ceases to be impossible. Roger Colbeck and collaborators have shown that by exploiting entanglement, a remarkable property of quantum systems that Einstein himself called "spooky", not only can we generate secure random numbers, but we can also certify their randomness based only on the laws of physics. Reassuring news for aspiring casino owners!

How can we fish in a more sustainable way?

In the future, we will need to harvest more fish from the seas to feed the growing population of the world. But over-fishing has already led to collapse in fish stocks. To square this circle, sustainable fisheries policies are needed. Mathematical models of fish growth and predation developed by Gustav Delius and Richard Law have given support to a radical new proposal of 'balanced harvesting', where a range of species and sizes of fish are caught, matched to distributions in the natural population. It turns out that balanced harvesting not only minimises disturbance to the ecosystem but also increases the total yield of fish. These ideas are influencing policy discussion at the EU level and elsewhere.

What is the right price for financial instruments which can be sold early?

The simplest financial 'options' (rights to buy or sell), and the more complex 'derivatives' which may be built from them, have a fixed strike date. But many derivatives nowadays may be exercised early (e.g. American options in equity markets or Bermudan options in interest rate markets) or even have multiple such features (e.g. 'swing' options in energy markets). Boda Kang has developed advanced computational techniques which bring their unpredictability and randomness under control, enabling a much faster and more accurate evaluation of their value. The techniques are able to handle multi-factor, multi-asset derivatives as well, and capture the price dynamics and volatility structures in many commodity and energy markets, including crude oil, gold, natural gas and Vix (the volatility index).

What are the right tactics for defensive air combat?

Niall MacKay, working with historians Ian Horwood and Chris Price (York St John University), has looked at some of the oldest 'Lanchester' mathematical warfare models, and their role in the development of the RAF's tactics leading up to the Battle of Britain. The conclusion, supported by data from this and other campaigns, is that air combat does not obey the Lanchester 'square law', which says that outnumbering the enemy is disproportionately important. Rather air combat is, in a precise mathematical sense, 'asymmetric warfare', - it is more like guerrilla war than conventional conflict. MacKay's work is used in teaching at the US Naval Postgraduate School, where he has given various guest lectures on the subject, and he continues to work with NPS colleagues on mathematical modeling of counterinsurgent warfare.

Are your children overweight, or just the right size?

There has been some controversy recently over whether the 'Body Mass Index', your weight divided by the square of your height, is a sensible measure of obesity. By adapting an old biomechanical argument, Niall MacKay suggested that, for growing children, the square of height should be replaced by a power of about 8⁄3 - in striking agreement with data from the UK and Hong Kong.

And finally,

Can you build a time machine or a warp drive?

Science fiction often makes crucial use of the ability to travel backwards in time or at speeds faster than light. But time machines and warp drives are not merely plot devices: they are based on real solutions of Einstein's equations for gravity. Unfortunately for sci-fi fans, the research of Bernard Kay and Chris Fewster shows that quantum theory imposes limits on such devices which make them impossible to create or make practical use of. Back to the drawing board...

 

Other ways in which our staff engage with industry and other partners outside academe are described on our consultancy page.

Photo: 'Fish' (resized) by Neil Turner, licensed under CC BY-SA 2.0