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.

Monday, 20 June 2016

G is for Growth Tensor - the latest in our Oxford Mathematics Alphabet

A tree branch, a ram's horn, your hand - how have these distinct and consistent shapes come about? The growth and form of a biological entity is a complex matter that involves integrated activities across a number of length scales. Viewed at the scale of tissues, or large clusters of cells, understanding growth and form is a problem well suited for continuum mechanics and mathematical modelling.

Find out more about how this applies not only to your hands, but to rubber balls and even stalks of rhubarb in the latest in the Oxford Mathematics Alphabet series.


Thursday, 16 June 2016

Mathematical Institute receives a Gold Green Impact Award

Green Impact Awards - Bronze, Silver, Gold

The Mathematical Institute has struck gold in this years Green Impact Awards, adding to the silver and bronze awards received in the preceeding two years. The Mathematical, Physical and Life Sciences (MPLS) division as a whole continues to go from strength to strength and this year four departments received the highest level gold award. The scheme is now in its third year in the university and has grown to involve over 200 people representing over 40 departments/teams.

Green Impact, the University’s main engagement programme is all about making small changes that add up to make a big difference. Changes are made by staff and students within their working environment, whether a department or building, laboratory or college. Green Impact sees teams recognised at four levels: working towards bronze, bronze, silver, and gold. 45 teams took part across the University this year with 16 teams reaching the gold level, an outstanding achievement.

The evening was hosted by Pro-Vice-Chancellor William James and President of the Oxford University Student Union Becky Howe and took place at the new Blavatnik School of Government Building.

Guest presenters and speakers included: Vice-Chancellor Professor Louise Richardson; Neil Jennings, National Union of Students; Calum Miller Chief Operating Office of Blavatnik School of Government; last year’s Green Impact staff award winner Sue Henderson from the Chemistry Department; Paul Goffin, Director of Estates; Professor Mark Pollard, Associate Head of Social Sciences Division (Research); Professor Donal Bradley, Head of the Mathematical, Physical and Life Sciences (MPLS) Division; Professor Alastair Buchan, Dean of Medicine and Head of Medical Sciences Division; Alan Rusbridger, Principal of Lady Margaret Hall; and Harriet Waters, Head of Environmental Sustainability.

Tuesday, 14 June 2016

The Prime Number Theorem - Our latest Secrets of Mathematics Podcast

Prime numbers have fascinated mathematicians since there were mathematicians to be fascinated, and the Prime Number Theorem is one of the crowning achievements of the nineteenth century. The theorem answers, in a precise form, a seemingly basic question: how many prime numbers are there?

Up to small thresholds, we may search exhaustively. Up to a hundred, there are 25 primes; up to a thousand, there are 168; up to a million, there are 78,498. The proportion of numbers that are prime seems to be decreasing – from 0.25, to 0.17, to 0.08 – but how quickly? In this podcast, Simon Myerson, Sofia Lindqvist, Jamie Beacom and host Aled Walker reveal the answer, and discuss the collection of mathematical ideas which combine to give the theorem’s first remarkable proof. Listeners who enjoyed Marcus du Sautoy’s ‘The Music of the Primes’ will find similar themes examined in greater detail, but those without any background will find all the necessary terminology developed from first principles.

The story begins with Euclid’s proof of the existence of infinitely many primes. Although this is an argument of infamous elegance, the quantitative aspects are embarrassingly poor. Indeed, the argument only shows that there are at least log log x prime numbers up to a threshold x, and in particular only 5 primes less than a million! In the middle of the nineteenth century, Chebyshev invented methods for detecting many more primes, but he still fell short of the conjectured level of precision. It would take a revolutionary insight of Riemann (pictured), connecting the discrete theory of primes to the continuous theory of mathematical analysis, to uncover the exact distribution of the primes, and to prove the Prime Number Theorem.

This podcast is part of the Secrets of Mathematics series where the pleasure (and occassional) pain of the subject is communicated to a wide audience.

The podcast also forms part of the In Our Spare Time series, in which Oxford Mathematician Aled Walker chairs discussions between various panels of DPhil students, drawn from all the different academic spheres of the university. Current topics range from Oscar Wilde to Dark Matter to Cicero to Medieval Song.

Monday, 13 June 2016

SoapboxScience in Oxford - Data Science Demystified

Modern software allows us to draw symbols (such as Chinese characters, or mathematical symbols) that the computer will then recognise and turn into type. How can these systems be improved, so that they run faster and more accurately?

A key tool is machine learning, whereby the software is 'taught' on a large set of examples, and then draws on its learning to make predictions for subsequent examples. This sort of approach is very widespread, and understanding the mathematical underpinnings is crucial to being able to improve the software in future. Oxford Mathematician Dr Hao Ni is part of a research group working at the frontiers of this subject.

Dr Ni recently spoke at the Oxford Mathematics North meets South colloquium, which was started during this academic year, in which two early career researchers give short talks introducing their research area to the whole department, with the aim of fostering understanding and collaboration between mathematicians working in the north (pure mathematics) and south (applied mathematics) wings of the Andrew Wiles Building, the home of Oxford Mathematics. Dr Ni described how the theory of rough paths can be applied to the study of non-parametric statistics on streamed data and particularly to the problem of regression where the input variable is a stream of information and the dependent response is also (potentially) a path or a stream.  

To find out more and to hear Dr Ni speak about her work to the public, come to SoapboxScience in Oxford on Saturday 18th June. SoapboxScience is a novel public outreach platform for promoting women scientists and the science they do.

Monday, 6 June 2016

Oxford Mathematics awarded Regius Professorship for the Queen's 90th birthday

The Mathematical Institute at the University of Oxford has been awarded a new Regius Professorship as part of the Queen’s 90th birthday celebrations.

Twelve new Regius Professorships – rare, sovereign-granted titles recognising the most outstanding levels of research in their fields – were awarded to leading British universities to mark the milestone. This is the first time since 1842 that Oxford has been awarded a Regius Professorship.

The Vice-Chancellor of the University of Oxford, Professor Louise Richardson, said: "2016 is proving to be quite a year for the Mathematical Institute at Oxford, with the Abel Prize presented to Sir Andrew Wiles and Nigel Hitchin recently announced as Shaw Prize laureate. Being awarded a Regius Professorship in Mathematics is wonderful news for the University and another mark of distinction for Oxford Mathematics."

Professor Martin Bridson, Head of the Mathematical Institute at Oxford, said: "This is a special moment in the history of Oxford Mathematics. The award of this Regius Professorship is a wonderful recognition of all that we have achieved and of the exciting future that lies before us.

A noteworthy feature of the award is that it recognises both our pre-eminence in fundamental research and the enormous benefits that flow to society from mathematics. Progress at the frontiers of science and technology has always made great demands of mathematics, and today it reaches more deeply than ever into the core of the discipline. Oxford is proud of the way in which it embraces the power of this interaction."

Until now, only 14 Regius Professorships had been granted since the reign of Queen Victoria, including 12 to mark the Queen’s Diamond Jubilee. As in 2012, recipients of new Regius Professorships have been selected by open competition, judged by an independent panel of business and academic experts.

Each institution will assign the title to an existing professor in the chosen department or will appoint a new professor to take the chair and hold the title.

John Penrose, Minister for Constitution, said: "It is a privilege and an honour to announce these new Regius Professorships in recognition of the truly outstanding work of our universities and as a fitting tribute to mark Her Majesty’s 90th birthday. The 12 institutions can consider themselves truly deserving of this great honour."

In the past, Regius Professorships were created when a university chair was founded or endowed by a royal patron. Previously, they were limited to a handful of the ancient universities of the United Kingdom and Ireland, namely Oxford, Cambridge, St Andrews, Glasgow, Aberdeen, Edinburgh, and Trinity College, Dublin.

Announced in the government’s Productivity Plan in July, the new Regius Professorships will celebrate the increasingly important role of academic research in driving growth and improving productivity over the past 90 years.

The creation of Regius Professorships falls under the Royal Prerogative, and each appointment is approved by the monarch on ministerial advice.

Chancellor of the Exchequer George Osborne said: "I am passionate about promoting science and economic growth right across the country. That’s why I promised to push for prestigious new Regius Professorships, not just in London and Oxbridge but in other great centres of learning, including the Northern Powerhouse, Wales, Scotland and Northern Ireland. I’m delighted that promise is being honoured today."

Jo Johnson, Minister for Universities and Science, said: "The success of our economy is underpinned by the exceptional science and research taking place in our world-leading universities up and down the country, and I’m delighted these 12 institutions have been recognised for their achievements. We’ll continue to make sure pioneering science is recognised and supported to help improve the lives of millions across the country and beyond."

Thursday, 2 June 2016

Oxford's Victorian Savilian Professors of Geometry - the latest in our history series

Our latest Oxford Mathematicians are the three Savilian Professors of Geometry who dominated Oxford’s mathematical scene during the Victorian era: Baden Powell (1796–1860), Henry John Stephen Smith (1826–83) and James Joseph Sylvester (1814–97). None was primarily a geometer, but each brought a different contribution to the role. Find out more.

The Savilians are the fourth in our series exploring Oxford's mathematical heritage.


Wednesday, 1 June 2016

Scientists discover how a common garden weed expels its seeds at record speeds

Plants use many strategies to disperse their seeds, but among the most fascinating are exploding seed pods. Scientists had assumed that the energy to power these explosions was generated through the seed pods deforming as they dried out, but in the case of ‘popping cress’ (Cardamine hirsuta) this turns out not to be so. These seed pods don’t wait to dry before they explode. A recent paper in the scientific journal Cell offers new insights into the biology and mechanics behind this process.

Several teams of scientists from different disciplines and countries including Oxford Mathematicians Alain Goriely and Derek Moulton and colleagues from Oxford's departments of Plant Sciences, Zoology and Engineering and led by Angela Hay, a plant geneticist in the Department of Comparative Development and Genetics at the Max Planck Institute for Plant Breeding Research (MPIPZ), worked together to discover how the seed pods of popping cress explode. A rapid movement like this is rare among plants; since plants do not have muscles, most movements in the plant kingdom are extremely slow.

But the explosive shatter of popping cress pods is so fast that advanced high-speed cameras are needed to even see the explosion. Richard Bomphrey, of the Royal Veterinary College at the University of London, explains: “Because the seeds are so small, aerodynamic drag slows them down immediately.” To compensate, the seeds are accelerated away from the fruit and get up-to-speed extremely quickly. In fact, they accelerate from 0 to 10 metres per second in about half a millisecond, “which is super fast!” says Bomphrey.

Hay’s teams of scientists discovered that the secret to explosive acceleration in popping cress is the evolutionary innovation of a fruit wall that can store elastic energy through growth and expansion, and can rapidly release this energy at the right stage of development.

Previously, scientists had claimed that tension was generated by differential contraction of the inner and outer layers of the seed pod as it dried. So what puzzled the authors of the Cell paper was how popping cress pods exploded while green and hydrated, rather than brown and dry. Their surprising discovery was that hydrated cells in the outer layer of the seed pod actually used their internal pressure in order to contract and generate tension. The authors used a computational model of three-dimensional plant cells, to show that when these cells were pressurised, they expanded in depth while contracting in length, “like the way an air mattress expands in depth, when inflated, but contracts in width,” explains Richard Smith, a computer scientist at MPIPZ.



Another unexpected finding was how this energy was released. The authors found that the fruit wall wanted to coil along its length to release tension, but it had a curved cross-section preventing this. “This geometric constraint is also found in a toy called a slap bracelet,” explains Oxford Mathematics's Derek Moulton. In both the toy and the seed pod, the cross-section first has to flatten before the tension is suddenly released by coiling. Unexpectedly, this mechanism relies on a unique cell wall geometry in the seed pod. As Moulton explains, “This wall is shaped like a hinge, which can open,” causing the fruit wall to flatten in cross-section and explosively coil.

According to Hay, their most exciting discovery was the evolutionary novelty of this hinged cell wall. They had evidence from genetics and mathematical modelling that this hinge was needed for explosive pod shatter, “but finding the hinge only in plants with explosive seed dispersal was the smoking gun,” says Hay.

These findings reinforce the description of evolution as a "tinkerer, not an engineer", made by the scientist Francois Jacob. It appears that the sophisticated mechanism of explosive seed dispersal in popping cress evolved via tweaking the shape of already-existing cellular components.

When asked what implications their results will have for other researchers, Smith answered: “It is likely that other processes in plants that were previously attributed to passive shrinkage by drying are in fact active processes, especially in green, hydrated tissues.”

This study is a good example of how the recent trend towards interdisciplinary, collaborative science can lead to a global understanding of the biological and physical mechanisms at play in a complex process. The authors of this Cell paper built up a comprehensive picture of explosive seed dispersal by relating observations at the plant scale all the way down to the cellular and genetic scales, and systematically linking each scale. As Oxford Mathematics's Alain Goriely says, “this approach was only made possible by combining state-of-the-art modelling techniques with biophysical measurements and biological experiments.”

The image above is of a mathematical model explaining the explosive dispersal of seeds from a common garden weed.