News

Wednesday, 10 August 2016

Mathematics enables faster computer simulations of biology

Numerous processes across both the physical and biological sciences are driven by diffusion, for example transport of proteins within living cells, and some drug delivery mechanisms. Diffusion is an unguided process which is of great importance at small spatial scales. Partial differential equations (PDEs) are a popular tool for modelling such phenomena deterministically, but it is often necessary to use stochastic (probabilistic) models instead to capture the behaviour of a system accurately, especially when the number of diffusing particles is low, such as in gene regulation.

Exploring the underlying mathematics behind these models is an important current area of research. Mathematicians need to understand these models better, so that they can be applied more meaningfully and so that they can be made more efficient while still preserving their accuracy (as computational power and time are often limiting factors). Oxford Mathematicians Paul Taylor and Ruth Baker, working with colleagues Christian Yates of the University of Bath and Matthew Simpson of the Queensland University of Technology, have been seeking to explore stochastic models of diffusion that are 'compartment-based'. In their paper, published in the Journal of Royal Society Interface, the domain under consideration is discretized into compartments, with particles jumping between compartments, possibly with constraints such as that a compartment cannot contain more than a certain number of particles. Previous work by these authors has concentrated on situations where the compartments all have the same size, but these can be unhelpfully restrictive for some applications, where it is important to focus at a high resolution in some parts but impractical to apply this same high resolution across the whole domain. This latest piece of work brings together a number of aspects, including allowing different compartments to have different sizes.

Crucially, this research demonstrates that these new approaches will be of value to researchers working on multi-scale systems, as they can speed up simulations while preserving precision where needed.

Friday, 29 July 2016

Summer (school) time in Oxford and the livin' is mathematical

This summer, about 200 teenagers will take part in mathematical summer schools hosted by Oxford Mathematics in the Mathematical Institute. Here is their story.
 
First to arrive were the 24 students from 15 countries across Europe who are taking part in PROMYS Europe, a six-week mathematical programme run by a partnership of PROMYS, the Mathematical Institute in Oxford, the Clay Mathematics Institute, and Wadham College, University of Oxford. As one student attending for the first time put it, "At PROMYS we do not learn Maths; we discover it. This gives us a much better understanding of the basics on which all other Maths is built".  

PROMYS has run in Boston, USA for more than 25 years, and this year sees the second occurrence of the new PROMYS Europe programme. Thanks to generous support from the organising partners and donors, selection for the programme is needs-blind, with partial and full financial support for those participants who would otherwise not be able to attend. The super-keen students are joined this summer by 7 undergraduate 'counsellors', also from across Europe (and including two current Oxford students), with teaching from Glenn Stevens (Boston University), Henry Cohn (Microsoft Research), Vicky Neale (Oxford) and David Conlon (Oxford), and guest lectures by mathematicians from Oxford and beyond. One counsellor, who also attended PROMYS as a student, observed "Three years ago, when I entered the PROMYS family, I learned one of the most important lessons - one should be taught how to think, not what to think - and this is exactly what this program does."
 
The Andrew Wiles Building is an ideal venue for hosting summer schools such as these, and indeed with careful planning can accommodate not one but three simultaneous events. The university's one-week UNIQ summer schools are for UK students about to enter their final year at school, to give them a taste of what it is like to study at Oxford, with priority being given to applicants from low socio-economic backgrounds and/or from areas with low progression to higher education. Demand for mathematics and statistics is high, and this year Rebecca Cotton-Barratt, the Schools Liaison Officer and Admissions Coordinator in the Mathematical Institute, and Mareli Grady, the Schools Liaison Officer in the Statistics Department, have between them coordinated three UNIQ summer schools, giving over 80 students the inspiring experience of studying Mathematics in Oxford. Reflecting at the end of the week, students commented "I thought I wasn’t good enough to apply but I will be applying now as I have gained more confidence", and "really enjoyable with lots of variety in various fields", and, interestingly, "I don’t want to go home now".
 
Later in the summer, we are looking forward to welcoming two summer schools organised by the UK Mathematics Trust. The National Mathematics Summer School and Summer School for Girls are each for around 40 students aged 15 and 16, invited to participate on the basis of their outstanding performance in national mathematics competitions. They give students a taste of mathematics beyond the school curriculum, as well as exploring more familiar material in depth, with an emphasis on problem solving and collaborative work. The teams of staff leading these summer schools include alumni, students and staff from Oxford Mathematics, and we are delighted to host these events.

All in all, the schools demonstrate that there is a passion for the subject of mathematics, a passion Oxford and its partners are keen to nurture for the long-term educational, scientific and economic benefits it will bring. 

Photo courtesy of Wadham College.

Tuesday, 19 July 2016

Dominic Joyce wins 2016 London Mathematical Society Fröhlich Prize

Oxford Mathematician Dominic Joyce FRS has won the 2016 LMS (London Mathematical Society) Fröhlich Prize "for his profound and wide-ranging contributions to differential and algebraic geometry." Dominic is Professor of Mathematics and Senior Research Fellow at Lincoln College. His research is, in his own words, "mostly in Differential Geometry, with occasional forays into some more esoteric areas of Theoretical Physics."

Tuesday, 19 July 2016

Oxford Mathematicians recognised at European Congress of Mathematics in Berlin

Oxford Mathematician James Maynard has been awarded a European Mathematical Society Prize at the 7th European Congress of Mathematics in Berlin. The prizes are awarded every four years in recognition of excellence in mathematics to ten individuals under the age of 35 living or working in Europe.

In the words of the judges James was awarded the prize for "his remarkable and deep results in analytic number theory, dealing especially with the distribution of primes. He is recognised in particular for his new proof, with improved estimates, of the 'small gaps between the primes theorem'."

In addition to James, Geordie Williamson, formerly a researcher in Oxford Mathematics was also awarded a prize for his "fundamental contributions to the representation theory of Lie algebra and algebraic groups, including his proof of Seorgel's conjecture on bimodules associated to Coxeter groups, and his startling counterexamples to the expected bounds in Lustig's conjecture on the characters of rational representations of algebraic groups." 

 

 

 

Thursday, 14 July 2016

Vicky Neale from Oxford Mathematics wins divisional teaching award

Vicky Neale from Oxford Mathematics has won an MPLS (Mathematical, Physical and Life Sciences) Teaching Award for her innovative and entertaining undergraduate teaching. Using blogs and tips to back up her lectures, Vicky's expansive approach has led to widespread praise from the toughest of critics, namely the students themselves.

Vicky is Whitehead Lecturer at Oxford, a post dedicated to the wider communication of mathematics. She regularly gives public lectures, including the prestigious London Mathematical Society Popular Lectures in 2013 and runs workshops for schools and teenagers including PROMYS Europe. She is also a regular guest on radio including BBC Radio 4's' Start the Week' and 'In Our Time'.

The MPLS awards are part of the University of Oxford's commitment to the highest standards of teaching across all its departments. 

Friday, 8 July 2016

Modelling genes: the backwards and forwards of mathematical population genetics - Public Lecture now online

How can we explain the patterns of genetic variation in the world around us? The genetic composition of a population can be changed by natural selection, mutation, mating, and other genetic, ecological and evolutionary mechanisms. How do they interact with one another, and what was their relative importance in shaping the patterns we see today? 

In our latest Oxford Mathematics Public Lecture Alison Etheridge FRS, Professor of Probability in the University of Oxford explores the remarkable power of simple mathematical caricatures in interrogating modern genetic data.

 

Wednesday, 6 July 2016

How weights and pulleys might explain the hunting techniques of toads

The motion of weights attached to a chain or string moving on a frictionless pulley is a classic problem of introductory physics used to understand the relationship between force and acceleration. In their recently published paper Oxford Mathematicians Dominic Vella and Alain Goriely and colleagues looked at the dynamics of the chain when one of the weights is removed and thus one end is pulled with constant acceleration.

This simple change has dramatic consequences for the ensuing motion. At a finite time, the chain ‘lifts off’ from the pulley, and the free end subsequently accelerates faster than the end that is pulled. Eventually, the chain undergoes a dramatic reversal of curvature reminiscent of the crack or snap of a whip. A key to this dynamic is its geometry. The imposed rotation of the chain around the pulley enables the end of the chain to ‘beat’ the free-fall that drives its motion.

Such insights have enabled the researchers to speculate more widely, notably on the peculiar hunting techniques of a variety of amphibians. Instead of throwing their tongue in a straight motion (as observed in chameleons), certain species of toads and salamanders adopt an unfurling tongue strategy. Of course, the reasons for such a mechanism are many and varied, but the researchers believe that, since the increase of tip velocity observed in the case of a chain has its origin in geometry, a similar effect is likely to reappear in more complicated problems involving, for example, a finite bending stiffness. It is then natural to wonder whether the geometrical amplification of acceleration may be used by these amphibians to allow them to maximise their chances of capturing a prey.

Image: Deban Laboratory

Thursday, 30 June 2016

The mathematics of poaching and gamekeeping

How do we stop poaching? You may think the answer lies in finding a way of giving gamekeepers an advantage over poachers. Oxford Mathematician Tamsin Lee and David Roberts from the University of Kent decided to look at the interaction between rhino poachers and a gamekeeper to predict the outcome of the battle. Their conclusions suggest alternative ways of tackling the problem.

Currently there are many methods used or under consideration for deterring the ever increasing number of poachers. These methods include dehorning, dyes, poisons, and inserting GPS tracking. All these methods devalue the horn considerably, but none of them remove the total value of the horn. Tamsin and David devised a simple model to test the effectiveness of each strategy.

The game has two players, who each have two strategies: the rhino manager may devalue horns or not, and poachers may only target rhinos with full horns, or behave indiscriminately. The game has two equilibriums, that is, either the manager wins or poachers win. The manager wins when devaluing deters poachers, and poachers move to another ranch; poachers win when the value of a damaged horn is still worth the kill, so the manager may as well conserve his/her resources and not devalue horns. A key feature is that poachers can choose their strategy instantaneously.

The model suggests that when devaluing the last few rhinos is expensive, due to sparsity of rhinos, it may not be worth devaluing all rhinos. However, for a poacher, as long as there are a few intact horns, a particular ranch is worth visiting. This is because the value of a rhino horn is so great - greater per unit weight than gold, diamonds or cocaine - that the risk for the poacher has little influence. The game can be tilted, unrealistically, to be in favour of the manager by increasing the risk to the poacher, or lowering the value of a partial horn. However, a poacher is still more likely to make a gain, or minimise loss, by killing rhinos indiscriminately.

In conclusion, the game appears to be challenging for the rhino manager to win. Therefore anti - poaching measures should not seem to tilt the game in the manager's favour, but instead change the game, for example, by legalising trade, or launching campaigns aimed at changing behaviour, although of course the latter may take some time to impact on rhino populations.

The team's research is presented in the Journal of Ecological Modelling and video outlining the paper is also available.

Friday, 24 June 2016

Heather Harrington to give LMS Popular Lectures

Oxford Mathematician Heather Harrington will be giving the London Mathematical Society (LMS) Popular Lectures this summer in London on 29 June and in September in Birmingham. The Lectures present exciting topics in mathematics and its applications to a wide audience and feature two lecturers who have been chosen for their mathematical distinction and communication skills.  

Heather's talk will be titled "the Shape of Data in Biology' and will focus on how computational developments in abstract mathematics can provide new insights in to the vast amounts of data generated by biological systems. The lectures are free but booking is required.

 

Thursday, 23 June 2016

Maria Bruna wins L'Oréal UK & Ireland Fellowship For Women in Science

Oxford Mathematician Maria Bruna has won a prestigious L'Oréal UK & Ireland Fellowship For Women in Science. Launched in January 2007, the Fellowships are awards offered by a partnership between L'Oréal UK & Ireland, the UK National Commission for UNESCO and the Irish National Commission for UNESCO, with the support of the Royal Society. Five Fellowships are awarded annually to outstanding female postdoctoral researchers. Each worth £15,000, the Fellowships are tenable at any UK or Irish university / research institute to support a 12-month period of postdoctoral research in any area of the life and physical sciences, mathematics and engineering.

The Fellowships have been designed to provide practical help for the winners to undertake research in their chosen fields. For example, winners may choose to spend their fellowship on buying scientific equipment, paying for child care costs, travel costs or indeed whatever they may need to continue their research.

Maria's research interests lie in the stochastic modelling of interacting particle systems, with applications for explaining how individual-level mechanisms give rise to population-level behaviour in biology and ecology. She is the first mathematician to win a fellowship.

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