Thursday, 14 April 2016

Jake Taylor King wins Lee Segel Prize

Oxford Mathematician Jake Taylor King has won the Lee Segel Prize for Best Student Paper for his paper 'From birds to bacteria: Generalised velocity jump processes with resting states.' Jake worked on his research with Professor Jon Chapman. The prize is awarded annually by the Society for Mathematical Biology. One of Jake's co-authors on the paper, Gabs Rosser, previously also studied Mathematics at Oxford in the Wolfson Centre for Mathematical Biology.

Wednesday, 13 April 2016

Linus Schumacher wins Reinhart Heinrich Doctoral Thesis Award

Oxford Mathematician Linus Schumacher has won the prestigious Reinhart Heinrich Doctoral Thesis Award. The award is presented annually to the student submitting the best doctoral thesis in any area of Mathematical and Theoretical Biology. 

In the judges' view "Linus' thesis is an outstanding example of how mathematical modelling and analysis that is kept close to the experimental system can contribute efficiently to advance the understanding of complex biological questions. The roles of cellular heterogeneity, microenvironmental cues and cell-to-cell interactions, which are common themes in the study of biomedical systems, are skillfully dissected and analysed in relevant experimental model systems, leading to significant advances in the current understanding of said systems."

The judges concluded: "the modelling aims to derive generic, theoretical insights from specific, biological questions. The work has led to a number of excellent publications."

Friday, 8 April 2016

Predicting and managing energy use in a low-carbon future

If effectively harnessed, increased uptake of renewable generation, and the electrification of heating and transport, will form the bedrock of a low carbon future. Unfortunately, these technologies may have undesirable consequences for the electricity networks supplying our homes and businesses. The possible plethora of low carbon technologies, like electric vehicles, heat pumps and photovoltaics, will lead to increased pressure on the local electricity networks from larger and less predictable demands.

Stephen Haben and colleagues from the University of Oxford and colleagues from the University of Reading are working with the distribution network operator (DNO) Scottish and Southern Energy Power Distribution on the £30m Thames Valley Vision project. The aim is to develop sophisticated modelling techniques to help DNOs avoid expensive network reinforcement as the UK moves toward a low carbon economy. In other words, what are some of the smart alternatives to “keeping the lights on” without simply digging up the road and laying bigger cables?

With recent advanced monitoring infrastructures (such as smart meters) we can now start using mathematical and statistical techniques to better understand, anticipate and support local electricity networks. The team has been analysing smart meter data and employing clustering methods to better understand household energy usage and discover how many different types of behaviours exist. This is turn can lead to improvements in demand modelling, designing tariffs and other energy efficiency strategies (e.g. demand side response). The researchers found different types of behaviour with varying degrees of intra-day demand, seasonal variability and volatility. Each of these therefore has different types of possible strategies in terms of reducing energy and costs. An important discovery is that energy behavioural use has very weak links with the socio-demographics, tariffs or houses size. Hence to really understand your energy demand requires the monitoring of data available through smart meters.

Forecasts can help DNOs manage and plan the networks in many ways, in particular by anticipating extremes in demand (e.g. large amounts of local generation on a sunny day). The researchers have developed a range of point and probabilistic forecasts for a wide number of relevant applications. Long term, scenario forecasts are generated using agent based models to simulate the impact of low carbon technologies. Shorter term forecasts have been developed to estimate daily demands and thus create appropriate plans for the charging and discharging cycles of batteries, helping to reduce peak overloads. These algorithms have been successfully used in silico and will soon be deployed and tested on real storage devices on the network.

Most recently the team are working on understanding limits to their models when monitoring data is unavailable or sparse. This is desirable since acquiring data and installing monitoring equipment is expensive. Can households be accurately modelled with only limited access to monitored data? If so, how much monitoring is really necessary? They have found that local energy demand is very dependent on the number and proportion of commercial and domestic properties. Such insights will be used to device workable solutions so that a DNO can choose the most appropriate (i.e. least disruptive but most cost effective) solution for different network types. Whether, for example, that is installing batteries, introducing monitoring or investing in infrastructure upgrades.

In summary, the extra visibility of household level demand through higher resolution monitoring equipment has created new opportunities for better understanding energy behavioural usage and highlighted the need for novel analytics. Demand at the individual customer level is irregular and volatile in contrast to the high voltage demands that has traditionally been investigated and thus current methods may not be applicable.  The methods necessary to reduce energy demand and promote energy efficiency sit in many areas of applied mathematics, data science and statistics. This requires mathematicians to be at the forefront of designing and creating new methods and techniques for the future energy networks.

For more information see a list of publications and the Mathematics Matters article.

Wednesday, 6 April 2016

Endre Suli and Xunyu Zhou elected SIAM Fellows

The Society for Industrial and Applied Mathematics (SIAM) has announced that Professors Xunyu Zhou and Endre Suli from Oxford Mathematics are among its newly elected Fellows for 2016.

SIAM exists to ensure the strongest interactions between mathematics and other scientific and technological communities through membership activities, publication of journals and books, and conferences.

Saturday, 26 March 2016

D is for Diophantine Equations - the latest in the Oxford Mathematics Alphabet

diophantine equation is an algebraic equation, or system of equations, in several unknowns and with integer (or rational) coefficients, which one seeks to solve in integers (or rational numbers). The study of such equations goes back to antiquity. Their name derives from the mathematician Diophantus of Alexandria, who wrote a treatise on the subject, entitled Arithmetica.

The most famous example of a diophantine equation appears in Fermat’s Last Theorem. This is the statement, asserted by Fermat in 1637 without proof, that the diophantine equation has no solutions in whole numbers when n is at least 3, other than the 'trivial solutions' which arise when XYZ = 0. The study of this equation stimulated many developments in number theory. A proof of the theorem was finally given by Andrew Wiles in 1995.

The basic question one would like to answer is: does a given system of equations have solutions? And if it does have solutions, how can we find or describe them? While the Fermat equation has no (non-trivial) solutions, similar equations (for example ) do have non-trivial solutions. One of the problems on Hilbert’s famous list from 1900 was to give an algorithm to decide whether a given system of diophantine equations has a solution in whole numbers. In effect this is asking whether the solvability can be checked by a computer programme. Work of Martin Davis, Yuri Matiyasevich, Hilary Putnam and Julia Robinson, culminating in 1970, showed that there is no such algorithm. It is still unknown whether the corresponding problem for rational solutions is decidable, even for plane cubic curves. This last problem is connected with one of the Millennium Problems of the Clay Mathematics Institute (with a million dollar prize): the Birch Swinnerton Dyer Conjecture. 

To find out more about diophantine problems read Professor Jonathan Pila's latest addition to our Oxford Mathematics Alphabet.

Tuesday, 15 March 2016

Andrew Wiles awarded the Abel Prize

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2016 to Sir Andrew J. Wiles (62), University of Oxford, “for his stunning proof of Fermat’s Last Theorem by way of the modularity conjecture for semistable elliptic curves, opening a new era in number theory.”

The President of the Norwegian Academy of Science and Letters, Ole M. Sejersted, announced the winner of the 2016 Abel Prize at the Academy in Oslo today, 15 March. Andrew J. Wiles will receive the Abel Prize from H.R.H. Crown Prince Haakon at an award ceremony in Oslo on 24 May.

The Abel Prize recognizes contributions of extraordinary depth and influence to the mathematical sciences and has been awarded annually since 2003. It carries a cash award of NOK 6,000,000 (about EUR 600,000 or USD 700,000).

Andrew J. Wiles is one of very few mathematicians – if not the only one – whose proof of a theorem has made international headline news. In 1994 he cracked Fermat’s Last Theorem, which at the time was the most famous, and long-running, unsolved problem in the subject’s history.

Wiles’ proof was not only the high point of his career – and an epochal moment for mathematics – but also the culmination of a remarkable personal journey that began three decades earlier. In 1963, when he was a ten-year-old boy growing up in Cambridge, England, Wiles found a copy of a book on Fermat’s Last Theorem in his local library. Wiles recalls that he was intrigued by the problem that he as a young boy could understand, and yet it had remained unsolved for three hundred years. “I knew from that moment that I would never let it go,” he said. “I had to solve it.”

The Abel Committee says: “Few results have as rich a mathematical history and as dramatic a proof as Fermat’s Last Theorem.”

Wednesday, 9 March 2016

Comparing the social structure of different cities

People make a city. Each city is as unique as the combination of its inhabitants. Currently, cities are generally categorised by size, but research by Oxford Mathematicians Peter Grindrod and Tamsin Lee on the social networks of different cities shows that City A, which is twice the size of City B, may not necessarily be accurately represented as an amalgamation of two City Bs.

The researchers use Twitter data from ten different UK cities, showing reciprocal tweets within each city. By defining cities in terms of these social network structures, they break each city into its comprising modular communities. Next, they build virtual cities from the actual cities. For example, Bristol has 74 communities. Randomly sampling (with replacement) from these communities 145 times builds a virtual city the same size as Manchester - but made up of modular communities actually observed in Bristol. How much does our virtual Manchester network resemble the true Manchester network? The answer is very closely. So if one was trying to spread a message via Twitter through Manchester, or make other social interventions, it may prove beneficial to test the same activity in Bristol first.

However, sampling the Bristol communities to create a virtual city the same size as Leeds, which is smaller than Manchester, does not create a network of similar structure to the 'real' Leeds. This highlights that the relationship between social structures of cities is not immediately obvious, and requires further analysis. Furthermore, this relationship is not symmetrical: a virtual city created by randomly sampling 74 communities from the Leeds network, does in fact resemble the true Bristol social network. So Bristol could learn from Leeds but not vice versa.

In summary, we may sometimes replicate one city using the communities from another. However, some cities have a very diverse range of communities, making them difficult to replicate - Leeds is a good example of this. Perhaps cities can be put into classes where those cities in the same class are socially similar and so any experience of social phenomena or reactions to interventions in one such city may be relevant to another.

Tuesday, 8 March 2016

The Mirzakhani Society - Oxford Mathematics' society for female undergraduates

27% of mathematics undergraduates in Oxford are female. We would like the figure to be higher and we are putting a lot of resource in to making it so. However, it is also important that current female and non-binary Oxford mathematicians feel they have time and space to discuss and share experiences that may be specific to them.

The Mirzakhani Society is the society for women studying maths at Oxford, named after Maryam Mirzakhanithe first woman to win a Fields Medal (Maryam met the society in September 2015 on her visit to Oxford to collect her Clay Mathematics Institute Research Award).  With over 100 active members, it holds relaxed weekly ‘Sip and Solve’ meetings (aided by high-quality baking), and socials and talks. In a University where your immediate and regular contact is often limited to other members of your college, it is an invaluable way of broadening contacts and providing a support network. The society is open to both undergraduates and postgraduates, and is central in encouraging more women to take a fourth year (undergraduates currently can choose between the three and four year mathematics courses). Find out more about the society on their Facebook page

On Saturday 27 February 2016, the society (pictured) met up with their Cambridge University counterparts, the Emmy Noether Society, sharing experience of gender equality in the universities. Three speakers gave their perspectives: Anne Davis, a Professor of Mathematical Physics and the University Gender Equality Champion for STEMM subjects at Cambridge: Perla Sousi, a Lecturer in the Statistics Laboratory at Cambridge; and Christie Marr, Deputy Director of the Isaac Newton Institute. Thanks to the London Mathematical Society for funding the trip.

Tuesday, 23 February 2016

C is for Calabi-Yau manifolds - the latest in the Oxford Mathematics Alphabet

Model II 1a

Calabi-Yau manifolds have become a topic of study in both mathematics and physics, dissolving the boundaries between the two subjects.

A manifold is a type of geometrical space where each small region looks like normal Euclidean space. For example, an ant on the surface of the Earth sees its world as flat, rather than the curved surface of the sphere. Calabi-Yau manifolds are complex manifolds, that is, they can be disassembled into patches which look like flat complex space. What makes them so special is that these patches can only be joined together by the complex analogue of a rotation.

Proving a conjecture of Eugenio Calabi, Shing-Tung Yau has shown that Calabi-Yau manifolds have a property which is very interesting to physics. Einstein's equations show that spacetime curves according to the distribution of energy and momentum. But what if space is all empty? By Yau's theorem, not only is flat space a solution but so are Calabi-Yau manifolds. Furthermore, for this reason, Calabi-Yau spaces are possible candidates for the shape of extra spatial dimensions in String Theory.

Find out more from Oxford Mathematician Dr Andreas Braun in this latest instalment of our Oxford Mathematics Alphabet.


Monday, 22 February 2016

Well behaved cities - what all cities have in common

How are people, infrastructure and economic activity organised and interrelated? It is an intractable problem with ever-changing infinite factors of history, geography, economy and culture playing their part. But a paper by Oxford Mathematician Hyejin Youn and colleagues suggests “a mathematical function common to all cities.”

Think of the city as an ecosystem, types of businesses as species interacting in that system. Ecosystems in the natural world often share common patterns in distributions of species. That got the researchers thinking. Maybe the same consistency arises in the city too. Only instead of the food web, it’s people and money and businesses that require one another. We usually think of cities as unique. London is very different from Moscow. But, it turns out, what governs the distribution of their resources stays the same across the board.

The team analysed more than 32 million establishments in U.S. metro regions. An establishment, the unit of analysis of their study, indicates “a single physical location where business is conducted”. When the team measured relative sizes of business types (e.g. agriculture, finance, and manufacturing) in each and every city, and compared these distributions among cities, the universal law is found: despite widely different mixes of types of businesses and across different-sized cities, the shape of these distributions was completely universal. Cities have their own underlying dynamics. It doesn’t matter where they are, how old they are and who is in charge.

This underlying pattern allowed researchers to build a stochastic model. As cities grow, the total number of establishments is linearly proportional to its population size (more people, more businesses). When an establishment is created it differentiates from any existing types with a probability which determines how diversified a city is given its size. This probability turns out to be inversely proportional to city size: the more businesses, the harder it is to differentiate them from existing businesses. This process, with further research, displays an open-ended, never-ending, albeit slowing, diversification of businesses in a statistically predictable way, constituting a human eco-system.

For a fuller explanation of the work also see articles in Forbes and Next Cities.