Thursday, 20 October 2016

Savilian Professor Nigel Hitchin reflects

As he retires from the the Savilian Chair of Geometry, Oxford Mathematician Nigel Hitchin reflects in this interview with Martin Bridson. From early mathematical inspiration at school in Duffield, Derbyshire, Nigel recalls his often unplanned progress via Jesus College, Oxford, Princeton, Cambridge and Warwick, before his final return to Oxford.

Along the way such luminaries as Michael Atiyah and Simon Donaldson play their part as Nigel talks about time spent with physicists in Cambridge, the Eureka moments when the answers take shape, to his final reflections on a career where the name Hitchin is attached to so many of the tools of modern geometry and which culminated in the award of the 2016 Shaw Prize.





Wednesday, 19 October 2016

Fashion, Faith and Fantasy - Roger Penrose Public Lecture now online

What can fashionable ideas, blind faith, or pure fantasy have to do with the scientific quest to understand the universe? Surely, scientists are immune to trends, dogmatic beliefs, or flights of fancy? In fact, Roger Penrose argues that researchers working at the extreme frontiers of mathematics and physics are just as susceptible to these forces as anyone else.

In this lecture, based on his new book, Roger argues that fashion, faith, and fantasy, while sometimes productive and even essential, may be leading today's researchers astray, most notably in three of science's most important areas - string theory, quantum mechanics, and cosmology.





Tuesday, 18 October 2016

Hummingbirds, umbrellas and hopper poppers do it. But why not as quickly as expected?

Many elastic structures have two possible equilibrium states. For example umbrellas that become inverted in a sudden gust of wind, nanoelectromechanical switches, origami patterns and even the hopper popper, which jumps after being turned inside-out. These systems typically move from one state to the other via a rapid ‘snap-through’. Snap-through allows plants to gradually store elastic energy, before releasing it suddenly to generate rapid motions, as in the Venus flytrap . Similarly, the beak of the hummingbird snaps through to catch insects mid-flight, while technological applications are increasingly exploiting snap-through instabilities.

In all of these scenarios, it is the ability to repeatedly generate fast motions that gives snap-through its utility. However, estimates of the speed of snap-through suggest that it should occur more quickly than is usually observed. In their research published n Nature Physics, Oxford Mathematicians Michael GomezDominic Vella and Derek Moulton study the dynamics of snap-through in detail, showing that, even without dissipation, the dynamics slow down close to the snap-through transition. This is reminiscent of the slowing down observed in critical phenomena (for example the time taken for oscillations in the climate to die down is thought to grow larger as a ’tipping point’ is reached). As well as providing a handheld demonstration of such phenomena, the work provides a new tool for tuning dynamic responses in applications of elastic bistability: for example it shows that to obtain faster snap-through in applications such as robotics, the system needs to be pushed well beyond the snap-through transition. 


Tuesday, 4 October 2016

Using geometry to choose the best mathematical model

Across the physical and biological sciences, mathematical models are formulated to capture experimental observations. Often, multiple models are developed to explore alternate hypotheses.  It then becomes necessary to choose between different models.

Oxford Mathematician Heather Harrington and colleagues from the United States have explored the problem of model selection by regarding mathematical models as geometric objects in space. In general, model selection is a hard problem, but recasting it in geometric terms allows the authors to give a new methodology for selecting the best explanation of observed phenomena, thereby bringing recent groundbreaking developments in nonlinear algebra to the study of biological and other complex systems.

Specifically their paper, published today in the Royal Society Journal Interface, considers polynomial models (e.g., mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimisation using numerical algebraic geometry. The authors use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. This approach exploits the geometric structures relating models and data, and demonstrates its utility on examples from cell signalling, synthetic biology, and epidemiology.

Tuesday, 4 October 2016

Frances Kirwan wins Suffrage Science award

The Clinical Sciences Centre based at Imperial College in London has launched a new initiative to celebrate women in maths and computing. As a new branch of the existing Suffrage Science scheme, it will encourage women into science, and to reach senior leadership roles.

Women make up no more than four in ten undergraduates studying maths. Suffrage Science aims to make a difference. There are currently two sections, one for women in the Life Sciences, and one for those in Engineering and the Physical Sciences. Now there is a third specialism, for women in Maths and Computing. Twelve women will receive awards to celebrate their scientific achievements and ability to inspire others. Oxford Mathematician Frances Kirwan FRS is one of the first recipients of the award for Mathematics.

The awards themselves are pieces of jewellery, designed by students at the arts college Central Saint Martins-UAL, and inspired by science. One, a silver bangle, holds a secret. Engraved on the inside, and hidden beneath a layer of silver, is what many mathematicians consider the most beautiful equation in mathematics, Euler’s equation.


Wednesday, 21 September 2016

H is for Homology - The Oxford Mathematics Alphabet

A life belt, a coffee cup, a jumping ball, a beach ball. What do these objects have in common? What sets them apart? Questions like these come under the mathematical umbrella of topology. And the theory of homology enables us to explore and understand them. Find out more in the latest in our Oxford Mathematics Alphabet.

Saturday, 17 September 2016

Roger Heath-Brown in conversation with Ben Green

Roger Heath-Brown is one of Oxford's foremost mathematicians. His work in analytic number theory has been critical to the advances in the subject over the past thirty years and garnered Roger many prizes.

As he approached retirement, Roger gave this interview to Ben Green, Waynflete Professor of Mathematics in Oxford and himself a leading figure in the field of number theory. In the interview Roger reflects on his influences, his achievements and the pleasures that mathematics has given him.

Thursday, 8 September 2016

Marcus du Sautoy named one of London's most influential people

Oxford Mathematician and Charles Simonyi Professor for the Public Understanding of Science in the University of Oxford, Marcus du Sautoy, has been named one of London's most influential mathematicians in the London Standard Progress 1000 awards. The Progress 1000, in partnership with Citi, is an annual event hosted by The London Evening Standard to celebrate the people whose influence across many spheres of London life is felt most keenly by those who live in the City.

Marcus is not only a leading mathematician in his own right, but a driving force in the promotion and popularisation of mathematics and associated sciences. He has taken mathematics and science around the world, expressing its elegance, pleasures, and occasional pains, through lectures, theatre (his X & Y, a mathematical play written with Victoria Gould has been widely acclaimed) and most recently in his book "What We Cannot Know" where he tries to identify the frontiers to our knowledge. 


Sunday, 4 September 2016

Mathematics enables a better understanding of damage during brain surgery

For over a hundred years, when confronted by swelling in the brain, surgeons more often than not have resorted to decompressive craniectomy, the traditional route to reducing swelling by removing a large part of the skull. However, while this might be the standard procedure, its failure rate has been worryingly high, primarily because the consequences on the rest of the brain have been poorly understood. 
This is no longer just a challenge for neurosurgeons. Mathematicians are now able to study and model the impact of surgery at a cellular level and by so doing develop a more specific picture of the impact of surgery across the whole brain. In particular Oxford Mathematician Alain Goriely and colleagues Johannes Weickenmeier and Ellen Kuhl from Stanford University have looked at the issue by studying a standard physical problem: the problem of bulging in soft solids.

Bulging is due to the swelling of a material while constrained except at an opening, as would be the case when the skull is opened during surgery and the brain bulges out of the skull creating, potentially, deformations in another part of the brain, away from the immediate incision. To quantify possible deformations inside the brain, the team created a personalised finite element craniectomy model from high-resolution medical resonance imaging. Their study reveals three failure mechanisms which would suggest damage beyond the initial incision point: axonal stretch in the centre of the bulge, axonal compression at the edge of the craniectomy, and axonal shear around the opening. Strikingly, even small swelling volumes of 50ml can induce axonal strain in excess of 30% above reported damage thresholds in patients.

Such models suggest a possible mechanism for proving and identifying long-term damage. Indeed, this theoretical study is a first step towards gaining better insight into the complex mechanisms underlying craniectomy and opens the door for systematic personalised studies of craniectomy in patients. The next step is to combine this theoretical work with experimental and clinical work to enable surgeons to provide better-informed and more successful treatments.



A fuller explanation can be found in the following papers:

Physical Review Letters

Journal of the Mechanics and Physics of Solids

Computer Methods in Applied Mechanics and Engineering

Cornell University Library

Monday, 22 August 2016

Constructing reaction systems - an inverse problem in mathematics

There is a wide class of problems in mathematics known as inverse problems. Rather than starting with a mathematical model and analysing its properties, mathematicians start with a set of properties and try to obtain mathematical models which display them. For example, in mathematical chemistry researchers try to construct chemical reaction systems that have certain predefined behaviours. From a mathematical point of view, this can be used to create simplified chemical systems that can be used as test problems for different mathematical fields. From an experimental perspective, it is useful to create chemical systems that can be used as blueprints for constructing physical networks in synthetic biology, for example in the area of DNA computing.

Oxford Mathematicians Tomislav Plesa and Radek Erban, together with their colleague Tomáš Vejchodský of the Institute of Mathematics in the Czech Academy of Sciences, have recently published a paper in the Journal of Mathematical Chemistry developing the theory behind this. They have built on previous work to create an inverse problem framework suitable for constructing a reaction system, and have used this to construct certain two- and three-dimensional systems of particular interest. Their work concentrates primarily on networks modelled by systems of kinetic equations, a class of ordinary differential equations of a certain type. Such equations may display 'exotic phenomena', corresponding to specific biological functions in the underlying biochemical reaction networks, and so the inverse problem framework needs to be able to handle such behaviours.