Friday, 3 February 2017

Modelling the impact of scientific collaboration

If nations are to grow, both economically and intellectually, they must foster scientific creativity. To do that they must create scientific environments that stimulate collaboration. This is especially true of developing countries as they seek to prosper in a global economy.

Oxford Mathematician Soumya Banerjee’s work looks at scientific collaboration networks, finding novel patterns and clusters in the data that may give insights and guidelines into how the scientific development of developing countries can create richer and more prosperous societies.  

Scientific collaboration networks are an important component of scientific output. Examining a dataset from a scientific collaboration network, Soumya analysed this data using a combination of machine learning techniques and dynamical models.

Soumya's results found a range of clusters of countries with different characteristics of collaboration and corresponding to nations at different stages of development (see figure). Some of these clusters were dominated by developed countries (e.g. the USA and the UK) that have higher numbers of self-connections compared with connections to other countries. Another cluster was dominated by developing nations (such as Liberia and El Salvador) that have mostly connections and collaborations with other countries, but fewer self-connections (shown by different clusters in the figure). 

The research has implications for policy. Countries like El Salvador have a low percentage of foreign connections (this could be a result of the protracted civil war). Consequently the development of active science and research programs in such nations is crucial in generating the concomitant foreign connections. By contrast, Liberia has 100% external connections, suggesting that more effort needs to be taken to develop its own scientific infrastructure. Both a thriving internal and external network are crucial to development.

Proposing a complex systems dynamical model that explains these characteristics, the research explains how the scientific collaboration networks of impoverished and developing nations change over time. The models suggest that developing nations can over time become as successful as the developed nations of today. Soumya also found interesting patterns in the behaviour of countries that may reflect past foreign policies and relations and contemporary geopolitics.

Clearly the model and analyses give food for thought as to how the scientific growth of developing countries can be guided and how it cannot be separated from their existing socio-economic environment and their future prosperity. Big data, machine learning and complexity science are enabling unprecedented computational power to be brought to bear on the fundamental developmental challenges facing humanity.

The figure above plots the percentage of external connections that each country has vs. the distinct number of countries each country is connected with. Clustering is done with k-means and shows three distinct clusters. Click on the image to enlarge.

Soumya's talk on his work can be found here together with his slides and code.


Monday, 30 January 2017

I is for Inverse Problems - the Oxford Mathematics Alphabet

All mathematical models require information to make their predictions; to get something out, you have to put something  in. To predict how an earthquake propagates through the ground, you have to know the material properties of the subsurface rocks. To predict the weather at noon, you have to give the initial conditions at dawn. To predict the drag coefficient of an aircraft, you have to specify its shape.

In many cases, however, we are faced with the opposite problem: given information about the outcome of a physical process, how did it come about? Such a problem is called an inverse problem, in contrast to the forward problems given above, for it inverts the relationship between cause and effect encoded in the underlying equations. Find out more in the latest in our Oxford Mathematics Alphabet.

Monday, 30 January 2017

Statistics: Why the Truth Matters - Tim Harford Public Lecture live podcast details

In our latest Public Lecture Tim Harford, Financial Times columnist and presenter of Radio 4's "More or Less", argues that politicians, businesses and even charities have been poisoning the value of statistics and data. Tim will argue that we need to defend the value of good data in public discourse, and will suggest how to lead the defence of statistical truth-telling.

For details and notification of the live podcast on 8 February at 4pm please click here.



Wednesday, 25 January 2017

Improving the performance of solar cells

Organometal halide perovskite (OMHP) is hardly a household name, but this new material is the source of much interest, not least for Oxford Applied Mathematicians Victor Burlakov and Alain Goriely as they model the fabrication and operation of solar cells.

One of the main advantages of OMHP is that the thin films on its base can be produced in a very inexpensive way via a solution deposition with subsequent heat treatment at moderate temperatures. Victor and Alain developed a generic theoretical framework for calculating surface coverage by a solid film of material de-wetting on the substrate. Using experimental data from OMHP thin films as an example, they calculated surface coverage for a wide range of annealing (heating) temperatures and film thicknesses. Their model accurately reproduced solution-cast thin film coverage (see the figure) and identified methods for both high and low levels of surface coverage.

Expanding their research Victor and Alain have also looked at the kinetics of photo-generated charge carriers in OMHP. By modelling the time decay of photoluminescence in the material, they extracted important information about charge carrier lifetime and concentration of intrinsic point defects. The latter are highly detrimental for the photo-voltaic performance of OMHP. The models, together with the experimental studies of colleagues, clarified the origin of the point defects and consequently identified a means of significantly decreasing their concentration.

Victor and Alain’s research can be explored in more detail on Victor and Alain's homepages. Their work reiterates the central importance of mathematical modelling in addressing real world problems.

Thursday, 19 January 2017

The impact of mathematics – human interactions!

Think of a mathematician and you might imagine an isolated individual fueled by coffee whose immaculate if incomprehensible papers may, in the fullness of time, via a decades-long dry chain of citations, be made use of by an industrialist (via one or two other dedicated mathematicians).

Not so, says new research by Oxford Mathematician and Computer Scientist Ursula Martin and evaluator Laura Meagher. Instead they reveal a vibrant and fertile environment where human interaction is the key.

Mathematics’ impact in every walk of life is astounding. Deloitte estimate that 10% of all UK jobs and 16% of total UK GDP is a direct result of mathematics. Ursula and Laura’s research puts the flesh on those figures, literally so as it demonstrates that mathematical impact is brought about above all by human interaction, long term relationships and close working with other disciplines and end users.  

In the context of an increasing interest in generating and measuring impacts across the academic and funding worlds, Ursula and Laura used the trove of data provided by the 2014 Research Excellence Framework (which assesses the quality and impact of research across higher education in the UK) to dig down into 209 examples of the impact of UK mathematics and statistics.

Complementing this with surveys and in-depth interviews, they identified a diverse ecosystem of people and ideas across mathematics, an ecosystem that includes the many other disciplines where mathematics is crucial as well as the many end users and beneficiaries of mathematical research. Their research also highlighted the role of specialist individuals in building long term relationships.

Moreover, the varieties of impact were striking, both the deep conceptual work that can reshape a whole field, and the detailed deployment of that work in a specific problem domain, both mathematical and beyond.

Finally, their work reinforced the crucial role of universities in developing a culture supportive of impact generation which reinforces the distinctive but all-pervasive nature of  mathematics, a discipline that is underpinning and influencing so many of the scientific, technological and social questions we are asking of our world.


Wednesday, 18 January 2017

Why the Truth Matters. Tim Harford's Oxford Mathematics Public Lecture 8 February

In our latest Public Lecture Tim Harford, Financial Times columnist and presenter of Radio 4's "More or Less", argues that politicians, businesses and even charities have been poisoning the value of statistics and data. Tim will argue that we need to defend the value of good data in public discourse, and will suggest how to lead the defence of statistical truth-telling.

8 February, 4pm, Mathematical Institute, Oxford. Please email to register




Monday, 16 January 2017

The magic of numbers - finding structure in randomness

Mathematics is full of challenges that remain unanswered. The field of Number Theory is home to some of the most intense and fascinating work. Two Oxford mathematicians, Ben Green and Tom Sanders, have recently made an important breakthrough in an especially tantalising problem relating to arithmetic structure within the whole numbers.

Imagine colouring every positive whole number with one of three colours, say red, green and blue. You might end up with this colouring: R1, G2, B3, B4, G5, R6, B7, R8, R9, G10, B11, B12, R13, G14, B15, B16, R17 ...

Or perhaps you chose one of the other infinitely many possibilities. Can you always pick two of these numbers, say x and y, so that x, y, x+y and xy all have the same colour?

For example, in our choice of colouring above we see that 3, 4, 3+4=7 and 3x4=12 are all blue, so it's possible for this colouring.  But will we always be able to do this, regardless of the colouring? And what if we use four colours, or even more, will we always be able to do it then too?

This is a well-known question in Ramsey theory, a branch of combinatorics that seeks to establish the existence of structure (such as the pattern x, y, x+y and xy all having the same colour) in randomness (such as all the many colourings). Results in Ramsey theory link with other areas of mathematics, and also have applications in other fields, notably in theoretical computer science.

A hundred years ago, the mathematician Issai Schur showed that if we colour every positive whole number with one of three or more colours then there are always two numbers, say x and y, so that x, y and x+y all have the same colour.  Extending this to handle multiplication as well as addition has turned out to be a significant challenge.

Ben and Tom have solved a sort of 'model' problem, where instead of colouring the integers they work with a finite analogue. This approach of considering a model problem has proved extremely fruitful for a number of other related questions, but it was far from clear how to proceed in this case. Ben and Tom introduced a number of new techniques in order to solve the problem in this finite model situation.

How does the finite analogue work?  Instead of colouring the positive whole numbers, Green and Sanders use a different system that shares similar arithmetic properties. Imagine a clock that shows 7 hours (rather than the familiar 12).  Every 7 hours, the hour hand gets back round to the top.  We can do arithmetic in this scenario too, for example 13 + 17 = 6 + 3 = 2 in this world, and 13 x 17 = 6 x 3 = 4. Ben and Tom showed that if the 7 values in this system are coloured using three or more colours then there must be many x and y for which x, y, x+y and xy all have the same colour, and similarly for any such system where the number of values is prime. Their work has been published in the new journal Discrete Analysis.

Indeed there has already been follow-up work, with Ben and his Oxford Graduate Student Sofia Lindqvist using similar ideas to resolve a question about monochromatic solutions to the equation $x+y=z^2$.

The original problem may remain unanswered, but mathematicians now have a way in and are working to establish whether Ben and Tom’s work provides the answer, both to this and maybe further problems in number theory. As so often, successes are incremental and hard-fought as mathematicians continue to map the structures that populate their and our world.

Wednesday, 11 January 2017

Stephen Hawking's Oxford Mathematics Public Lecture - live podcast CANCELLED



In recognition of a lifetime's contribution across the mathematical sciences, we are initiating a series of annual Public Lectures in honour of Roger Penrose. The first lecture will be given by his long-time collaborator and friend Stephen Hawking on 18th January at 5pm GMT. The lecture is sold out, but we will be podcasting live

Stephen Hawking is the former Lucasian Professor of Mathematics at the University of Cambridge and now the Dennis Stanton Avery and Sally Tsui Wong-Avery Director of Research at the Department of Applied Mathematics and Theoretical Physics and Founder of the Centre for Theoretical Cosmology at Cambridge.


Friday, 6 January 2017

The Mathematics of Visual Illusions - Christmas lecture online

Puzzling things happen in human perception when ambiguous or incomplete information is presented to the eyes. For example, illusions, or multistable figures occur when a single image can be perceived in several ways. 

In the Oxford Mathematics Christmas Public Lecture Ian Stewart demonstrates how these phenomena provide clues about the workings of the visual system, with reference to recent research which has modelled simplified, systematic methods by which the brain can make decisions.

Ian Stewart is Emeritus Professor of Mathematics in the University of Warwick.





Tuesday, 3 January 2017

18th Century Oxford Mathematics - Halley to Hornsby

In our final series of Oxford Mathematics History Posters we look at Oxford’s role in the development of Newtonian philosophy in the 18th Century. In particular we focus on Edmond Halley, the most famous English astronomer of his day and Savilian Professor of Geometry, and Thomas Hornsby, Sedleian Professor of Natural Philosophy and founder of the Radcliffe Observatory which appropriately now sits close to the new Mathematical Institute.

PDF icon Halley to Hornsby.pdf