Thursday, 25 May 2017

How do biomembranes form micro-structures in our cells?

The human body comprises an incredibly large number of cells. Estimates place the number somewhere in the region of 70 trillion, and that’s even before taking into account the microbes and bacteria that live in and around the body. Yet inside each cell, a myriad of complex processes occur to conceive and sustain these micro-organisms. One such process is the shaping of molecular membranes, known as lipid bilayers, to form protective barriers around important cellular parts and also to create spherical vessels and tubular networks to transport waste and nutrients at the microscopic level.

The mechanism believed to be responsible for the shaping of membranes involves the attachment of “curvature-inducing” proteins, whose role is to directly interact with the surface and bend it. By the cooperation of hundreds to tens of thousands of proteins, the membrane is shaped into the variety of micro-structures seen in the cell.

Previous efforts to gain a physical understanding of the dynamic shaping process required the use of supercomputers simulating thousands of molecules; a lengthy and costly process. However, recent research by Oxford Mathematicians James Kwiecinski, Jon Chapman and Alain Goriely shows that the problem can be formulated as an elegant mathematical model combining results from statistical and continuum mechanics – the first model of its kind. Yet despite the model’s simplicity, the phenomena exhibited are quite complex. James explains: “one of the surprising results from the model is that the types of tubes that can form and how stable they are in the face of thermodynamic fluctuations is completely determined by the mechanical stiffness of the proteins themselves. We were also expecting that the proteins would uniformly distribute themselves around the membrane, forming a scaffold structure, almost like a mould. However, this isn’t always true; there are some instances where the proteins can aggregate, forming these complex patterns which then merge and interact.”

Asked about the future of the work, James further commented: “the research is a significant first step into a fundamental problem of cellular mechanics, and one where we’re only getting started. There are still many more interesting geometries and unanswered questions to study.”

Thursday, 25 May 2017

The Sound of Symmetry - Marcus du Sautoy Public Lecture now online

From Bach’s Goldberg Variations to Schoenberg’s Twelve-tone rows, composers have exploited symmetry to create variations on a theme. But symmetry is also embedded in the very way instruments make sound. Marcus du Sautoy shares his passion for music, mathematics and their enduring and surprising relationship. The lecture culminates in a reconstruction of nineteenth-century scientist Ernst Chladni's exhibition that famously toured the courts of Europe to reveal extraordinary symmetrical shapes in the vibrations of a metal plate. 

Marcus du Sautoy is Charles Simonyi Professor for the Public Understanding of Science at Oxford University.





Wednesday, 24 May 2017

Andrew Wiles awarded the Royal Society's Copley Medal

Oxford Mathematics's Professor Andrew Wiles has been awarded the Copley Medal, the Royal Society's oldest and most prestigious award. The medal is awarded annually for outstanding achievements in research in any branch of science and alternates between the physical and biological sciences.

Andrew Wiles is one of the world's foremost mathematicians. His proof of Fermat's Last Theorem in the 1990s catapulted him to unexpected fame as both the mathematical and the wider world were gripped by the solving of a 300 year-old mystery. In 1637 Fermat had stated that there are no whole number solutions to the equation $x^n + y^n = z^n$ when n is greater than 2, unless xyz=0. Fermat went on to claim that he had found a proof for the theorem, but said that the margin of the text he was making notes on was not wide enough to contain it. 

After seven years of intense study in private at Princeton University, Andrew announced he had found a proof in 1993, combining three complex mathematical fields – modular forms, elliptic curves and Galois representations. However, he had not only solved the long-standing puzzle of the Theorem, but in doing so had created entirely new directions in mathematics, which have proved invaluable to other scientists in the years since his discovery. 

Educated at Merton College, Oxford and Clare College, Cambridge, where he was supervised by John Coates, Andrew made brief visits to Bonn and Paris before in 1982 he became a professor at Princeton University, where he stayed for nearly 30 years. In 2011 he moved to Oxford as a Royal Society Research Professor. Andrew has won many prizes including, in 2016, the Abel Prize, the Nobel Prize of mathematics. He is an active member of the research community at Oxford, where he is a member of the eminent number theory research group. In his current research he is developing new ideas in the context of the Langlands Program, a set of far-reaching conjectures connecting number theory to algebraic geometry and the theory of automorphic forms.

Thursday, 18 May 2017

The Real Butterfly Effect - Tim Palmer's Oxford Mathematics Public Lecture now online

Meteorologist Ed Lorenz was one of the founding fathers of chaos theory. In 1963 he showed with just three simple equations that the world around us could be both completely deterministic and yet practically unpredictable. In the 1990s, Lorenz’s work was popularised by science writer James Gleick who used the phrase “The Butterfly Effect” to describe Lorenz’s work. The notion that the flap of a butterfly’s wings could change the course of weather was an idea that Lorenz himself used. However, he used it to describe something much more radical - he didn’t know whether the Butterfly Effect was true or not.

In this lecture Tim Palmer discusses Ed Lorenz the man and his work, and compares and contrasts the meaning of the “Butterfly Effect" as most people understand it today, and as Lorenz himself intended it to mean. 

Tim Palmer is Royal Society Research Professor in Climate Physics at the University of Oxford.






Thursday, 18 May 2017

J is for Juggling - the latest in the Oxford Mathematics Alphabet

Juggling is the act of iteratively catching and throwing several objects. To a mathematician a juggling pattern can be described using a mathematical notation called siteswap. The idea of siteswap notation is to keep track of the order in which the objects are thrown. The notation does not indicate what kind of objects are being juggled (e.g. balls, rings, clubs, etc) or whether a special kind of throw is performed (e.g. under-the-leg or behind-the-back).

Want to know more? Let Data Scientist and Oxford Mathematician Ross Atkins explain all in the latest in our Oxford Mathematics Alphabet series.


Friday, 12 May 2017

Sandy Patel wins Best Support Staff award

Mathematicians, young and old, win awards, lots of them and Oxford mathematicians have their fair share. However, any university department is of course also home to a range of support staff whose job it is, on a good day, to enable academics to make the best use of their time.

To recognise this role the Oxford University Students Union (OUSU) has its own awards for best support staff, and this year we are delighted to announce that Oxford Mathematics's own Sandy Patel scooped a prize. Sandy is Graduate Studies Administrator and her role is to ensure that our over 200 Graduate Students have the best possible experience during their time in Oxford and together with their Faculty supervisors are able to produce the best research in the subject. Graduate Students are the critical component of any research university and giving them the best support is vital. 

Wednesday, 10 May 2017

Some advice for gamblers from Oxford Mathematics

We all know there is no guaranteed way of beating the bank in a casino or predicting the tossing of a coin. Well maybe. Perhaps a little more thought and a large dose of mathematics could help optimise our strategies.

Oxford Mathematicians Jan Obloj and colleagues looked at the optimal strategy of a gambler with cumulative prospect theory (CPT) preferences. CPT preferences capture, in particular, the empirically observed human tendency for being risk averse while winning but being risk seeking when losing. Their research showed that the performance, even of complex betting strategies, can be strictly improved by looking at past betting patterns and by tossing an independent coin. This improvement results from the lack of quasi-convexity of CPT preferences: given two choices we may prefer a mixture of them to either of them individually.

Even better news for gamblers is that if they go through a series of hypothetical choices to determine their particular risk appetites (and hence a numerical CPT representation of their preferences), Jan and colleagues can provide an algorithmic way to compute the bias of the coins which ought to be tossed by the gambler to optimally decide when to stop playing in the casino.

Tuesday, 9 May 2017

Philip Maini elected to the Academy of Medical Sciences

Oxford Mathematician Philip Maini has been elected to the Academy of Medical Sciences for 2017. The Academy's mission is to advance biomedical and health research and its translation into benefits for society and this year's elected Fellows, 46 in total, have expertise that spans women’s health, immunology, public health and infectious disease among many other fields.

Philip Maini FRS, who is Professor of Mathematical Biology and Director of the Wolfson Centre for Mathematical Biology here in Oxford, is a leading figure in the field of mathematical biology with research interests spanning the modelling of avascular and vascular tumours, normal and abnormal wound healing, applications of mathematical modelling in pattern formation in early development, as well as the theoretical analysis of the mathematical models that arise in all these applications.


Monday, 8 May 2017

Ulrike Tillmann elected member of the German National Academy of Sciences

Oxford Mathematics's Ulrike Tillmann has been elected a member of the German National Academy of Sciences. The Academy, Leopoldina, brings together the expertise of some 1,500 distinguished scientists to bear on questions of social and political relevance, publishing unbiased and timely scientific opinions. The Leopoldina represents the German scientific community in international committees and pursues the advancement of science for the benefit of humankind and for a better future.

Historically it was known under the German name Deutsche Akademie der Naturforscher Leopoldina until 2007, when it was declared a national academy of Germany. The Leopoldina is located in Halle. Founded in 1652, the Leopoldina claims to be the oldest continuously existing learned society in the world.

Monday, 8 May 2017

Mathematical Institute receives Athena Swan Silver Award

The Athena SWAN charter was establised in 2005 to encourage and recognise commitment to advancing the careers of women in science. In 2013 the Mathematical Institute here in Oxford was awarded a bronze medal and now, four years later, we are pleased to announce that we have been upgraded to silver.

Martin Bridson, Head of Department, said of the award: "Our Athena SWAN work supports the Department’s overarching aim of creating a working environment in which students and staff alike can achieve their full potential. This is a constant feature of all that we do, of course, but the process of self-reflection required in preparing our submission for this award provided a focus and stimulus to action that will benefit us all.

It is vital that the country’s leading departments be seen as beacons of commitment to supporting the work/life balance of their members and to redressing the under-representation of women in mathematics. This high-profile award does much to further our efforts in this direction."

Our application can be viewed here.