Tuesday, 29 November 2016

Improving the quality and safety of x-rays

X-ray imaging is an important technique for a variety of applications including medical imaging, industrial inspection and airport security. An X-ray image shows a two-dimensional projection of a three-dimensional body. The original 3D information can be recovered if multiple images are given of the same object from different viewpoints. The process of recovering 3D information from a set of 2D X-ray projections is called Computed Tomography (CT).

Traditional CT scanners are based on a single moving source, rotating around the object to reconstruct. In this set-up, images are taken sequentially and the resulting reconstruction problem gives rise to a linear system of equations.

The innovation of X-ray emitter arrays allows for a novel type of X-ray scanning device with faster image acquisition due to multiple simultaneously emitting sources. Acquisition speed is an important factor in medical imaging because it can help to avoid artefacts from motion of the analysed tissue. Another major advantage of emitter arrays is that they result in light weight, highly mobile 3D imaging systems that can be taken to the patient rather than having to move the patient to a radiology suite.

However, two or more sources emitting simultaneously can yield measurements from spatially and temporally overlapping rays. This imposes a new type of image reconstruction problem based on nonlinear constraints that traditional linear image reconstruction methods cannot cope with.

Oxford Mathematicians Raphael Hauser and Maria Klodt have derived a mathematical model for this new type of image reconstruction problem, and developed a reconstruction method that allows the recovery of images from measurements with overlapping rays. Based on compressed sensing, the method allows for reconstruction from undersampled data, which means that the number of reconstructed densities is higher than the number of measurements, which enables reduced doses (see the full paper).

The method has been successfully applied to real X-ray measurements in cooperation with Gil Travish and Paul Betteridge from industrial partner Adaptix, an Oxford-based start-up company. The Adaptix scanners acquire images with a flat panel of comparatively small emitters with small opening angles of the emitter cones, arranged in a fixed grid which can allow for small devices with reduced doses.

The new image reconstruction method opens new possibilities for X-ray scanner design, because it allows for a new class of hand-held X-ray scanning devices, where emitter and detector positions cannot be aligned exactly, and overlapping of emitter cones cannot be avoided.

Friday, 25 November 2016

Maria Bruna wins the Women of the Future Science award

Oxford Mathematician Maria Bruna has won the Women of the Future Science award. The Women of the Future Awards, founded by Pinky Lilani in 2006, were conceived to provide a platform for the pipeline of female talent in the UK. Now in their 11th year they recognise the inspirational young female stars of today and tomorrow. They are open to women aged 35 or under and celebrate talent across categories including business, culture, media, technology and more.

Maria's work focuses on partial differential equations, stochastic simulation algorithms and the application of these techniques to the modelling of biological and ecological systems. 

Thursday, 24 November 2016

Random Walks 3 – The beauty and symmetry of ancient tiles

Beauty is in the eye of the beholder, but what about symmetry? In our final feature on mathematicians let loose in the Ashmolean Museum, Oxford Mathematician Balázs Szendrői investigates the beauty of symmetry in the Museum's Islamic art works. As he explains, no matter what the tile pattern may look like, its underlying symmetry configuration belongs to a small set of possibilities. 

If you are interested in the Random Walks series have a look at the previous films.








Friday, 18 November 2016

Random Walks 2 – Navigating the globe

From gigantic hanging tapestries to small pocket globes, the Ashmolean covers a whole range of navigational equipment. In the second of our Random Walks films featuring mathematicians let loose in the Ashmolean Museum, Vicky Neale from Oxford Mathematics demonstrates that she knows her place in the world. Through interactive examples that can be imitated at home, Vicky demonstrates the difficulties that cartographers have faced throughout the centuries.






Monday, 14 November 2016

Mitigating the impact of buy-to-let on the housing market

Much has been written about the buy-to-let sector and its role in encouraging both high levels of leverage and increases in house prices. Now Oxford Mathematician Doyne Farmer and colleagues from the Institute for New Economic Thinking at the Oxford Martin School and the Bank of England have modelled that impact. By looking at a large selection of micro-data, mostly from household surveys and housing market data sources, the team were able to model the individual behaviour and interactions of first-time buyers, home owners, buy-to-let investors, and renters from the bottom up, and observe the resulting aggregate dynamics in the property and credit markets. In turn a series of comparative statics exercises investigated the impact of the size of the rental/buy-to-let sector and different types of buy-to-let investors on housing booms and busts.

The results suggest that an increase in the size of the buy-to-let sector may amplify both house price cycles and increase house price volatility. Furthermore, in an effort to illustrate how this might be mitigated at a macro prudential level, the team modelled a loan-to-income portfolio limit which, encouragingly for policy-makers, attenuates the house price cycle. 


Friday, 11 November 2016

Random Walks: the Art of the Ashmolean through a mathematician’s eyes

The University of Oxford’s Ashmolean Museum is not only an exhibitor of art, but home to vital artistic research. The museum’s collections are investigated by some of the world’s leading historians, archaeologists, anthropologists and… mathematicians?

Throughout November 2016, the Ashmolean Museum and Oxford Mathematics proudly present Random Walks, a series of short films that present the historical world through mathematical eyes.

Our aim is to bring the humanities and sciences closer together, whilst demonstrating that historical museums are extremely useful for providing context to the development of logical thinking. What problems did humanity face throughout the millennia? How did science develop to surmount these problems? Why do remnants of these ideas remain important to this very day?

Join us as we answer these and many other questions and, hopefully, by the end, we will demonstrate that while mathematics may tell us how the universe began, it takes a museum to show us our place within it.

In our first film, Oxford Mathematics’ Thomas E. Woolley, takes you on a tour through the Ashmolean’s collection of mathematical tablets from the time of the ancient Babylonians. Thomas investigates how mistakes in mathematics can be just as illuminating as correct answers.

If you want to know more about the calculations presented in the film please click here

Friday, 11 November 2016

How can we understand our complex economy - Doyne Farmer Public Lecture now online

We are getting better at predicting things about our environment - the impact of climate change for example. But what about predicting our collective effect on ourselves? We can predict the small things, but we fail miserably when it comes to many of the big things. The financial crisis cost the world trillions, yet our ability to forecast and mitigate the next economic crisis is very low. Is this inherently impossible? Or perhaps we are just not going about it the right way? 

The complex systems approach to economics, which brings in insights from the physical and natural sciences, presents an alternative to standard methods. Doyne explains this new approach and give examples of its successes. He presents a vision of the economics of the future as it confronts the serious problems that our world will face.
J. Doyne Farmer is Director of the Complexity Economics programme at the Institute for New Economic Thinking at the Oxford Martin School and Professor in the Mathematical Institute at the University of Oxford.


Tuesday, 1 November 2016

Gui-Qiang Chen elected Fellow of the American Mathematical Society

Oxford Mathematician and Fellow of Keble College, Gui-Qiang G. Chen has been elected a Fellow of the American Mathematical Society in recognition of his contribution to partial differential equations, nonlinear analysis, fluid mechanics, hyperbolic conservation laws, and shock wave theory.

Professor Chen is Statutory Professor in the Analysis of Partial Differential Equations and Director of the EPSRC Centre for Doctoral Training in Partial Differential Equations in Oxford.


Tuesday, 1 November 2016

North meets South - helping mathematicians to understand each other

Mathematics can look like a foreign language to those who have not studied it in depth. Even for mathematicians, it can be difficult to understand the work of colleagues in other branches of mathematics, or indeed to know what questions they are seeking to answer in their research, because the vocabularies are so specialised and technical. A huge success of modern mathematics is that it is both broad and deep: mathematicians study a wide range of topics, and our knowledge in many of these areas is now so great that in order to work at the cutting edge of research one must specialise a lot. 

There is a tension, though, because while mathematicians need to immerse themselves in their research areas in order to make progress, at the same time they also need to be aware of developments in other areas that might help their work. Above all, and perhaps contrary to some perceptions, mathematics is highly interconnected and collaborative, and very often progress happens by making connections between research areas.

Oxford Mathematics seeks to address this in a number of ways. At the physical level, the splendid new home of the department, the Andrew Wiles Building, has been designed to facilitate both deliberate collaboration and also spontaneous exchanges of mathematical ideas through communal spaces (not least the excellent Café π).

Last year, Oxford Mathematics went one step further with a new initiative aimed at helping mathematicians to get to know what their Oxford colleagues are working on, and to give early career researchers the opportunity to share their work.

The new Fridays@4 project involves a programme of weekly sessions, aimed primarily but not exclusively at graduate students and postdocs, including a mix of colloquia, skills training, and advice on personal and career development. Part of this programme is the new ‘North meets South’ colloquium, organised by early career researchers and with early career researchers as invited speakers.

The colloquia happen once or twice each term. Each features two speakers, one from the north wing of the Andrew Wiles Building (roughly corresponding to pure mathematics, although that is a rather crude way to subdivide mathematics), and one from the south wing (roughly corresponding to applied mathematics). The speakers are asked to ensure that their talks are accessible to all the mathematicians in the department, not only those in their research areas.  Last year saw talks on a selection of topics: cluster algebras, modelling data streams, topological quantum field theory and defects in liquid crystals. This week (November 4) sees the first North meets South colloquium for this academic year, featuring Emilie Dufresne and Robert Van Gorder talking about their work. Interestingly, while both are working in Applied Mathematics, much of their work has also been in Pure Maths and Emilie's talk on separating sets in Invariant Theory is indeed Pure Mathematics. She and Robert are perhaps the ultimate North meets Southers, today's modern mathematicians. 

Heather Harrington and Brent Pym were instrumental in the setting up of North meets South. “We created this internal colloquium to learn what other young mathematicians here in Oxford are working on, and to form a network of early career researchers. Last year's speakers showed great skill, delivering exciting and accessible talks about research-level mathematics - and in only 30 minutes each! As organisers, we have observed that this experience is rewarding for the speakers, but even more so for Oxford Mathematics, as it brings together mathematicians from many subfields. We hope that North meetsSouth is another example of how such events can spark interactions that cross mathematical lines.”

The success of the North meets South colloquium is in itself a reminder of why mathematicians need to talk to each other, both to ensure that they make the most of the ideas and expertise around them, and, above all, to motivate them in their work. This is not a recreational add-on, but a core component of a modern mathematician's life.

Monday, 31 October 2016

A peek round the corner - introducing undergraduates to mathematical research

What is it like to do mathematical research? Many undergraduates wonder this, as they consider whether they would like to pursue graduate studies. There is no better way for the department to answer the question than to give undergraduates the opportunity to work on their own mathematical research projects. This summer the Oxford Mathematics enabled around 50 students to carry out such projects, working with faculty and postdocs in the department.

Eliza Casapopol (Balliol College) did a project with Dr Tom Sanders. "The summer project was a great opportunity for me as a mathematician. It has given me insight into what research is about and the biggest achievement was that it taught me to enjoy asking and answering my own questions. I think the project has given me a better idea about research and its challenges compared to what I knew so far, and it allowed me to see which areas of maths I am most interested in. Even if it seems like a difficult path, these past weeks have showed me that there is so much sense of fulfilment when you understand a proof or manage to come up with a new question or idea."

Rosemary Walmsley (Worcester College) worked with Professor Alison Etheridge, and said "my summer project has been a fantastic opportunity to experience mathematical research, and has given me a really valuable taste of what it would be like to do postgraduate study. It's been great to be able to get engrossed in an area I knew relatively little about beforehand - probabilistic models used in genetics - and to be able to explore it in a less prescribed way than I am used to with lecture courses. The project was more varied than I expected: reading papers, posing new questions, working on these questions, discussing ideas with my supervisor and DPhil students and writing up what I'd done. I would very much recommend doing a summer project!"

Shati Patel (Lady Margaret Hall) was part of a group of students who worked with Dr Jennifer Balakrishnan. "I really enjoyed doing a summer project as it's a completely different way of working compared to term time lectures and problem sheets. Not only was I introduced to some interesting theory about elliptic curves, I also got some general experience writing code and working with the command line. Our project involved about 10 people so it was incredibly useful to help each other and share ideas."

There is no doubt that this window on to a possible future is vital. Students not only learned about the process of research and its mix of personal focus and collaboration, they also were given a taste of new areas of mathematics beyond their current experience, the areas where Oxford mathematicians are leading the world in research and where these students might one day join them.

Three students received financial support from the London Mathematical Society. Eliza Casapopol (Balliol College), Daniel Fletcher (Oriel College) and Lorenzo Sarnataro (Worcester College) were among the 36 students selected nationally to receive funding, which was matched using funds from the Mathematical Institute and the Engineering and Physical Sciences Research Council (EPSRC). Further students were supported by EPSRC funding distributed through the Oxford Mathematical, Physical and Life Sciences Division. Oxford Mathematics' own funding enabled a significantly larger number of high-achieving students to experience what it is like to do mathematical research.