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This week's Radio 4 Inside Science programme includes a feature on the mathematics of the new Mathematical Institute here in Oxford. Professor Alain Goriely, Bruno Toledo from Architects Rafael Viñoly and Oxford Mathematics students discuss Penrose Tiling, arithmetical progressions and crystals.

Iain Smears, a third-year D.Phil student in the Mathematical Institute here in Oxford and a member of Worcester College has won one of the three SIAM Student Paper Prizes this year for his journal article “Discontinuous Galerkin Finite Element Approximation of Hamilton-Jacobi-Bellman Equations with Cordes Coefficients,” published in the SIAM Journal on Numerical Analysis.

The SIAM Student Paper Prizes will be awarded during the course of the 2014 SIAM Annual Meeting, to be held July 7-11 in Chicago, Illinois.

Oxford Mathematics now has its own Twitter account to keep you up to you date with all things mathematical.

https://twitter.com/OxUniMaths

What if you need to search through months of video files to identify a red car that was in shot for just a few seconds. Or how long do you have to scrub something before it can be considered clean? No big deal if it is the washing-up but what if there are hazardous chemicals in your workplace? 

The answer to both problems is mathematics.  Demonstrating this fact was the driving force for the 100th European Study Group with Industry which took place in Oxford from 7-11 April. Nine companies from sectors as diverse as chemicals, logistics, data processing, government and retail presented problems to a range of the world’s best mathematicians in an intensive week of brainstorming. The mathematicians’ brief was simple. Prove that mathematics can work in the real world and have a commercial application and value.

The result? The video search group came up with brand new algorithms for decompressing jpeg files to make objects recognisable by sharpening the edges in the image and reducing the computer-generated artefacts. Glynn Wright, CEO of Aralia, the company involved, said "we now have a clear insight into how we may advance the state-of-the-art in automated scene analysis. The range of skills brought to bear by graduates and professors alike forms a solid basis for our R&D that will keep Aralia busy for many months to come. Some of the results promise to be of considerable significance to virtually everyone who uses digital images."

In parallel the cleansing group modelled the movement of hazardous materials and decontaminants through carpets and concrete. The key new insight was that cleansing is better if the reaction produces products that are soluble in the decontaminant rather than the hazardous material. "The week was a great success" said Anthony Arkell and Hasmitta Stewart of the Government Decontamination Service. "The range of chemicals and types of surfaces proved to be an impossible task to prioritise and investigate within a laboratory but the outcomes from ESGI 100 will allow us to target further research and development and provide better advice in the interim. It was also a great pleasure to be involved with such a range of talented and enthusiastic people". These successes were repeated across the week as mathematicians and industrialists worked side by side on shared interests and goals. 

We often hear that mathematics underpins science. We hear less how it underpins industry. The 100th Study Group and its predecessors demonstrate that mathematics is a crucial industrial resource and that industrial R&D can provide fantastic challenges for mathematicians. For more information please contact Chris Breward (@email).

The Association for Symbolic Logic has announced Dr Jonathan Pila as among the winners of the Carol Karp Prize 2013. This prize is awarded every five years for an outstanding paper or book in the field of symbolic logic. It is made by the Association on recommendation of the ASL Committee on Prizes and Awards for a "connected body of research, most of which has been completed in the time since the previous prize was awarded," and consists of a cash award. Sharing the prize with Dr Pila are Moti Gitik, Ya'acov Peterzil, Segei Starchenko and Alex Wilkie. Alex Wilkie is presently a Logic Group visitor to the Mathematical Institute in Oxford and was a faculty member for many years before moving to Manchester.

Perhaps Bugs Bunny would not have taken a wrong turn at Albuquerque if he'd only known some more network analysis?  In a paper published in Physical Review E, Postdoctoral Researcher Sang Hoon Lee, Associate Professor Mason Porter, and their collaborator Mihai Cucuringu from UCLA reported the results of their network analysis of a rabbit warren in a paper on core-periphery structure.  Using measures of high-traffic and low-traffic areas in networks, including novel notions of "core" and "peripheral" junctions and pathways, they were able to characterise the rabbit social and breeding areas in a simple way.  One of the main points of the paper is that one can measure coreness based not only on notions of network density (which is the usual way of approaching the problem) but also on notions of transportation in a network. Lee, Cucuringu, and Porter compared density-based and transportation-based notions of core-periphery structure using a diverse set of applications: urban road networks, a European bank network, generative models for road-like networks, a US migration network, and more.

Jim Murray is one of the leading mathematical biologists of our times and the Inaugural Hooke Lecturer here in Oxford. In this wide-ranging interview with Philip Maini, Professor of Mathematical Biology in Oxford, Jim talks about his career, the range of his work, his successes and failures and his hopes and expectations for a subject that is the pointing the way for the future of applied mathematics.

This interview is the second in a series of interviews with distinguished Oxford Mathematicians, intended to shine a light on the work they do and the beauty and power of their subject. The first interview with Bryce McLeod is also available.

Arguably mathematicians are the scientific all-rounders, applying their skills to a range of subjects from chemistry and medicine to engineering and economics. In some cases these skills extend even further. Professor Alain Goriely, Statutory Professor of Mathematical Modelling in Oxford, has just won second prize in the Weird and Wonderful section of the 2014 National Science Photography Competition, organised by the Engineering and Physical Sciences Research Council (EPSRC) for his photograph of a gömböc. A  gömböc is a convex three-dimensional homogeneous body which, when resting on a flat surface, has just one stable and one unstable point of equilibrium. Its existence was conjectured by Russian mathematician Vladimir Arnold in 1995 and proven in 2006 by Hungarian scientists Gábor Domokos and Péter Várkonyi.

A limited edition Gömböc, labelled #2013, the year of the opening of the Andrew Wiles Building in Oxford, was purchased with generous support from Otto Albrecht and Tim and Leona Wong and can be found on display in the building. The Gömböc in Alain's photograph, a gift from Otto Albrecht, is made of plexiglass which generates intricate and intriguing light patterns. The mathematics of the Gömböc can be seen in the background.

Advances in quantum cryptography mean that we can protect our secrets even when our communications are being spied on or we are using devices built by our enemies, according to an Oxford University researcher.

Revelations of the extent of government surveillance have thrown a spotlight on the insecurity of our digital communications. Even today's encrypted data is vulnerable to technological progress. Writing in this week's Nature, Professor Artur Ekert of Oxford University and the National University of Singapore, and co-author Renato Renner of ETH Zurich, explore what physics tells us about keeping our secrets secret.In the history of secret communication, the efforts of code-makers have been matched time and again by the ingenuity of code-breakers. It is already believed that one of today's most widely used encryption systems, RSA, will become insecure once a quantum computer is built. But that story need not go on forever.

'Recent developments in quantum cryptography show that privacy is possible under stunningly weak assumptions about the freedom of action we have and the trustworthiness of the devices we use,' says Professor Ekert of Oxford University's Mathematical Institute, who is also Director of the Centre for Quantum Technologies at the National University of Singapore.

Over 20 years ago, Professor Ekert and others independently proposed a way to use the quantum properties of particles of light to share a secret key for secure communication. The key is a random sequence of 1s and 0s, derived by making random choices about how to measure the particles (and some other steps), that is used to encrypt the message. In the Nature Perspective, Ekert and Renner describe how quantum cryptography has since progressed to commercial prospect and into new theoretical territory.

Even though privacy is about randomness and trust, the most surprising recent finding is that we can communicate secretly even if we have very little trust in our cryptographic devices – imagine that you buy them from your enemy – and in our own abilities to make free choices – imagine that your enemy is also manipulating you. Given access to certain types of correlations (form the quantum world or elsewhere), and having a little bit of free will, we can protect ourselves. We can even protect ourselves against adversaries with superior technology that is unknown to us.

'As long as some of our choices are not completely predictable and therefore beyond the powers that be, we can keep our secrets secret,' says Renner, Professor of Theoretical Physics at ETH Zurich, Switzerland. This arises from a mathematical discovery by Renner and his collaborator about 'randomness amplification': they found that a quantum trick can turn some types of slightly-random numbers into completely random numbers. Applied in cryptography, such methods can reinstate our abilities to make perfectly random choices and guarantee security even if we are partially manipulated.

'As well as there being exciting scientific developments in the past few years, the topic of cryptography has very much come out of the shadows. It's not just spooks talking about this stuff now,' says Ekert.

The authors conclude: 'The days we stop worrying about untrustworthy or incompetent providers of cryptographic services may not be that far away'.

The Perspective article, entitled ‘The ultimate physical limits of privacy', is published in this week's Nature