Monday, 4 December 2017

Andrew Wiles London Public Lecture now online

In the first Oxford Mathematics London Public Lecture, in partnership with the Science Museum, world-renowned mathematician Andrew Wiles lectured on his current work around Elliptic Curves followed by an-depth conversation with mathematician and broadcaster Hannah Fry.

In a fascinating interview Andrew talked about his own motivations, his belief in the importance of struggle and resilience and his recipe for the better teaching of his subject, a subject he clearly loves deeply.









Friday, 1 December 2017

Modelling outbreaks of infectious disease - diagnostic tests key for epidemic forecasting

Precise forecasting in the first few days of an infectious disease outbreak is challenging. However, Oxford Mathematical Biologist Robin Thompson and colleagues at Cambridge University have used mathematical modelling to show that for accurate epidemic prediction, it is necessary to develop and deploy diagnostic tests that can distinguish between hosts that are healthy and those that are infected but not yet showing symptoms. The data derived from these tests must then be integrated into epidemic models.

“We used Ebola virus disease as the main case study in this paper" says co-author Nik Cunniffe, "since at the date of publication it was an important and very timely example of the type of disease we focus on in our research, i.e. one for which reporting is incomplete and where some epidemics die out naturally before infecting a large number of people.”

Robin is currently working on a probabilistic modelling framework for managing outbreaks of diseases such as bovine tuberculosis and foot-and-mouth disease: “I am investigating the optimal time to introduce control of a newly invading pathogen. Early control can be beneficial since the outbreak might be suppressed before the pathogen sweeps through the population. However, later control carries the advantage that it allows transmission parameters to be estimated more accurately and interventions to be optimised. Deciding when to initiate control is therefore an optimal stopping problem, and involves balancing the benefits of waiting against the potential costs of the pathogen becoming widespread.”

The team have won the PLoS Computational Biology Research Prize 2017 for the public impact of their work about diagnostic testing for Ebola. Robin is now a Junior Research Fellow at Christ Church in Oxford. He undertook this project as part of his PhD studies in Cambridge.

Wednesday, 29 November 2017

Assessing the impact of local planning on housing delivery and affordability

The investment decisions made by the construction sector have an obvious impact on the supply of housing. Furthermore, Local Planning Authorities play a fundamental role in shaping this supply via town planning and, in particular, by approving or rejecting planning applications submitted by developers. However, the role of these two factors, as well as their interaction, has so far been largely neglected in models of the housing market. Oxford Mathematicians Adrián Carro and Doyne Farmer, from the Institute for New Economic Thinking at the Oxford Martin School, have been working on a model that tries to capture this interaction. To this end, they have adapted a non-spatial agent-based model of the UK housing market previously developed in collaboration with the Bank of England in order to include all the necessary spatial aspects.

In particular, the new model includes different household types, a banking sector as a mortgage lender, a central government collecting taxes, a central bank setting mortgage regulation, a building sector providing new houses and a set of local governments approving or rejecting planning applications. Furthermore, it models both the sales and the rental market in detail, capturing the interactions between renters and buy-to-let investors. This is the first agent-based model of the housing market to explicitly include a dynamic, endogenous building sector endowed with its own behavioural rules, as well as a set of local governments influencing its activities.

Preliminary results suggest that the relationship between planning application approval rates and housing delivery is highly non-linear. In particular, the effect of a decrease in the approval rate in a certain Local Authority District is, to a certain extent, compensated by an increase in its local prices which encourages the building sector to file more planning applications there. Thus, the loss of housing stock due to a decrease in approval rates, while very significant, is found to be less important than the decrease itself. Finally, our results suggest that the increase in housing and rental prices due to a decrease in approval rates has strong social consequences, pushing a significant fraction of households towards social housing and strongly decreasing home ownership.

Wednesday, 29 November 2017

Developing particle-based software with Aboria

Over the last five decades, software and computation has grown to become integral to the scientific process, for both theory and experimentation. A recent survey of RCUK-funded research being undertaken in 15 Russell Group universities found that 92% of researchers used research software, 67% reported that it was fundamental to their research, and 56% said they developed their own software. As well as the practical use of performing numerical calculations impossible to produce by hand, software is vital for the communication of ideas and methods between scientific disciplines and for knowledge transfer to industry. While traditional scholarly publication can communicate the context, benefits and limitations of a given numerical method, the mathematical and computational details of implementation are often beyond non-specialised users, and software provides a formal language for encoding these ideas in such a way that they can be put to use immediately by potential users.

Biology is one of the many fields that increasingly uses software to inform and test new hypotheses. At smaller length-scales, molecular dynamics is used to model biomolecules to learn more about the structure and functional behaviour. For larger systems, coarse-graining is used to model whole molecules as single particles to study the emergent behaviour of chemical pathways at a sub-cellular level. For whole organs, differential equations are used to model the same pathways taking into account tissue mechanics and structure.

In order to support the wide variety of numerical methods used in biology, Oxford Mathematics researchers Martin Robinson and Maria Bruna have developed Aboria, a high performance software library for particle-based methods. In general, particle-based methods involve the calculation of interactions between particles in dimensional space, where the particles can describe either physical particles (e.g. molecular dynamics), a set of discretization points for solving differential equations (e.g. radial basis functions), or high dimensional data points (e.g. kernel methods in machine learning). Traditional particle-based methods such as molecular dynamics are enabled by complex, highly specialised software packages that are costly to develop and maintain. Within biology in particular, individual particle-based methods often require the development of custom particle interactions that are developed from scratch for each new project, making such high specialised packages unsuitable. Instead, Aboria provides an efficient and easy to use abstraction for the evaluation of both local and long range interactions, while at the same time allowing users to completely specify the nature of the both the particle interactions and how they are integrated over time.

Aboria has previously been used to simulate interacting elliptical particles in a molecular-scale liquid crystal model, diffusion through random porous media, and Brownian particles interacting via soft-sphere potentials. We are currently collaborating with Dyson and Ian Griffiths in Oxford to use Aboria to model how solid particles flow through a filter, and where they are trapped by the filter fibres. For this latter case Aboria is used to not only to evaluate the short-range interactions of particles with the fibres, but also to solve the fluid flow around the fibres, and the long-range electrostatic interactions of the system.

The main image shows a packing of polydisperse spheres using Aboria, where each sphere interacts with the others using a repulsive linear spring force. Each sphere is coloured by its radius.

The image below shows Filter simulation using Aboria. (Left) shows the solid particles in black that move with the flow and diffuse independently. The large coloured circles are the fibres of the filter that capture the solid particles (coloured by number of captured particles). The small red particles show where the solid particles were captured. (Middle) shows computational nodes where fluid flow is calculated, showing the flow inlet at the top, and the outlet at the bottom. (Right) plots the fluid flow at each of the nodes, coloured by velocity magnitude. 




Wednesday, 29 November 2017

Modelling the production of silicon in furnaces

How can solar panels become cheaper? Part of the cost is in the production of silicon, which is manufactured in electrode-heated furnaces through a reaction between carbon and naturally occurring quartz rock. Making these furnaces more efficient could lead to a reduction in the financial cost of silicon and everything made from it, including computer chips, textiles, and solar panels. Greater efficiency also means reduced pollution.

Oxford Mathematics' Ben Sloman is working with colleagues Colin Please, Robert Van Gorder, and collaborators at Norwegian silicon production company Elkem to better understand how the furnaces behave.

One problem in silicon production is the formation of a solid crust, which clogs up the furnace and prevents the raw materials from falling down the furnace to the hot region, where the necessary chemical reactions occur. Due to the high temperatures involved (around 2000 kelvin) it is difficult to observe how this clogging happens, so Elkem have carried out experiments. A mathematical model developed by Ben and colleagues captures the evolution of gas flow, temperature, and chemical reactions in these experimental furnaces. Numerical simulations demonstrate that the position of crust formation is largely driven by temperature, with the location moving upwards as the furnace becomes hotter. This effect is quantified in an asymptotic analysis of the model [1]. The furnace operators can change the type of raw materials used in the process and the energy input into the electrodes. Simulations of the model show that using more reactive carbon particles (for example charcoal) reduces the amount of silicon monoxide gas escaping from the furnaces, allowing more silicon to be produced from the quartz, and also reducing the build up of the furnace crust.

The image shows a sketch of a silicon furnace, reproduced from The Si Process Drawings, by Thorsteinn Hannesson.

[1] B. M. Sloman, C. P. Please, and R. A. Van Gorder. Asymptotic analysis of a silicon furnace model. Submitted. (2017).

The research is funded by the EPSRC Centre for Doctoral Training in Industrially Focused Mathematical Modelling here in Oxford in collaboration with Elkem.

Wednesday, 22 November 2017

Oxford Mathematics London Public Lecture with Andrew Wiles and Hannah Fry - watch it live

Andrew Wiles will be giving our first Oxford Mathematics London Public Lecture on Tuesday 28 November at 6.30pm in the Science Museum in London. Andrew will be talking about his current work and after the lecture he will be in conversation with mathematician and broadcaster Hannah Fry.

The event is now full but you can watch it live. It will also be streamed on the Oxford University Facebook page.

Tuesday, 21 November 2017

Four more universities join the Alan Turing Institute

The Alan Turing Institute is the national institute for data science, headquartered at the British Library. Five founding universities – Cambridge, Edinburgh, Oxford, UCL and Warwick – and the UK Engineering and Physical Sciences Research Council created The Institute in 2015. Now we are delighted to announce that four universities - Leeds, Manchester, Newcastle and Queen Mary University of London - are also set to join the Institute as university partners. The new universities will work with our growing network of partners in industry and government to advance the world-changing potential of data science.

Alan Wilson, CEO of the Institute, commented: “We are extending our university network in recognition of our role as a national institute and because we believe that increasing collaboration between researchers and private, public and third sector organisations will enable the UK to undertake the most ambitious, impactful research possible."

Peter Grindrod, Oxford Mathematics' nominee on the Turing board, said: “We are rightly proud to have launched the Alan Turing Institute in 2015, together with the other founding partners. The Turing is now on a journey to becoming a truly national endeavour, drawing in more universities and researchers and strengthening its international competitiveness. Data science and artificial intelligence will underpin many 21st century industry sectors; and, working with its partner universities, Turing is well placed to take a leading role in support of the Government’s Industrial Strategy.”


Tuesday, 21 November 2017

From Primes to Networks via Russia and ODEs - a sample of the latest books from Oxford Mathematics Faculty

When they aren't in their offices doing Maths our Faculty can be found in their offices writing books about doing Maths. Here is a recent sample of their labours. 

Richard Earl's 'Towards Higher Mathematics: A Companion' aims, as its title suggests, to bridge the gap between school and University, giving sixth-formers an insight into and preparation for the mathematics they will be studying at University.

By contrast Vicky Neale's 'Closing the Gap: the Quest to Understand Prime Numbers' is a mathematical thriller, a story of individual effort and innovative collaboration as the mathematical community tries to understand one of mathematics' great mysteries: Prime Numbers.

David Acheson's books aim to tell the world about the sheer excitement and pleasures of mathematics. His latest, 'the Calculus Story' does just that, giving the reader a tour of the mathematics of change via imaginary numbers, Isaac Newton and the electric guitar (amongst other mathematical things). You may even find yourself doing calculus.

Nick Trefethen is an expert in Numerical Analysis and one of the founders of the MATLAB-based Chebfun software project. Chebfun is at the heart of his latest book 'Exploring ODEs', an examination of the ubiquitous Ordinary Differential Equation.  

Christopher Hollings is an historian of mathematics and especially of Soviet Mathematics. His latest work 'Wagner’s Theory of Generalised Heaps' looks at the theories of the Russian mathematician V. V. Wagner (1908-1981). The book contains the first translation from Russian into English of a selection of Wagner’s papers.

Cornelia Drutu is an expert in geometric group theory and her forthcoming book on the subject (entitled 'Geometric Group Theory') attempts to make the subject accessible to students and researchers via proofs of many of its central tenets.

Renaud Lambiotte's 'A Guide to Temporal Networks' explores the fascinating world of networks and their profound and growing importance across the sciences, both physical and social. From the brain to Facebook, networks are at the heart of our interpretation of our world.

A full list of Faculty books is available.

Monday, 20 November 2017 Women in Technology Scholarships

Supporting female students is a priority for Oxford Mathematics, particularly on courses where women have historically been underrepresented.  We are delighted that, due to the support of, Oxford University can offer 10 scholarships to female Home/EU students studying MScs in mathematics, statistics and computer science in 2018-19. The scholarships will cover both fees and a stipend at the level of the national minimum doctoral stipend as set by the research councils. Scholarships are available to female applicants for the following MScs:

MSc Mathematical Sciences (OMMS)
MSc Statistical Science
MSc Mathematics and the Foundations of Computer Science
MSc Mathematical Modelling and Scientific Computing
MSc Mathematical and Theoretical Physics
MSc Computer Science
MSc Software Engineering
MSc Software and Systems Security

There is no separate application process for this scholarship. To be considered, submit your application for graduate study by Friday 19th January 2018. Selection is expected to take place by the end of April 2018. If you fulfil the eligibility criteria, you will be automatically considered for these scholarships.


Monday, 20 November 2017

West Nile Virus and understanding the spread of infection

West Nile virus (WNV) is responsible for viral encephalitis in humans, a condition that causes inflammation of the brain and can have longer-lasting physical effects. WNV is also related to similar viruses such as Dengue and Zika that are also of significant public health concern. Faced with the challenge of understanding how the virus reproduces within the host and its potential for epidemic, Oxford Mathematician Soumya Banerjee and colleagues have developed a computational method to determine characteristics of WNV infection even in the face of limited experimental data, an approach that could be applicable to other emerging diseases like the Zika virus for which there is little data.

Diseases that jump the species barrier from animals to humans affect millions worldwide. An understanding of how disease progression and immune response vary from species to species could have important public health benefits. In their work the team attempt to understand how immune function scales with body size, work which is a foundation for understanding scaling of immune response to other pathogens or in other animals. 

The team’s computational framework for infectious disease modelling at the within-host level leverages data from multiple species. This is likely to be of interest to modellers of infectious diseases that jump species barriers and infect multiple species – the method can be used to determine computationally the competency of a host to infect mosquitoes that will sustain West Nile virus infection. The models show that smaller Passerine species are more competent in spreading the disease than larger non-Passerine species. This suggests the role of host phylogeny as an important determinant of within-host pathogen replication.

Ultimately the team believes their work could be an important step in linking within-host viral dynamics models to the between-host models that predict spread of infectious disease between different hosts.