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Researchers from the University of Oxford, the University of Limerick, and the Harvard School of Public Health have developed a mathematical model to examine online social networks, in particular the trade-off between copying our friends and relying on ‘best-seller’ lists.

The researchers examined how users are influenced in the choice of apps that they install on their Facebook pages by creating a mathematical model to capture the dynamics at play. By incorporating data from the installation of Facebook apps into their mathematical model, they found that users selected apps on the basis of recent adoptions by their friends rather than by using Facebook’s equivalent of a best-seller list of apps. The model suggests users tended to be swayed by recent activity—from their `friends’ on Facebook—that they saw on their Facebook feeds over the previous couple of days. The research, published in the journal, Proceedings of the National Academy of Sciences, finds that the “copycat” tendency in human behaviour is strong and that we can be influenced by the activities of others over a relatively short period of time.

The mathematical model examined data from an empirical study published in 2010, which had tracked 100 million installations of apps adopted by Facebook users during two months. In the 2010 study, based on data collected in 2007, all Facebook users were able to see a list of the most popular apps (similar to best-seller lists) on their pages, as well as being notified about their friends’ recent app installations. In the 2010 study (which included two of the authors of the new study), researchers found that in some cases, a user’s decision to install some apps seemed virtually unaffected by the activities of others, whereas sometimes they were strongly affected by the behaviour of others – even though the apps in these two categories did not appear to be distinguished by any particular characteristics. Instead, once an app reached some popularity threshold (as measured by the installation rate), its popularity tended to rise to stellar proportions.

In the new study, the researchers developed a mathematical model to distinguish between the consequences of two distinct, competing mechanisms that appeared to drive the dynamics behind the behaviour of the Facebook users. Using their model and extensive computer simulations, they looked behind the empirical data to see whether Facebook users’ behaviour could be modelled as being influenced primarily by the notifications of apps recently installed on their friends’ Facebook pages or mainly driven by which apps appeared on the best-seller list. Using the supercomputers of the Irish Centre for High-End Computing (ICHEC), the researchers ran thousands of simulations in which they varied the relative dominance of the two influences (recent installations versus cumulative popularity). It took the researchers 15,000 hours of computer processing to best match the results of the simulations with the characteristics of app installation that were observed in the earlier empirical study.

The researchers found that, although users seem to be influenced by both, the stronger effect on popularity dynamics was caused by the recent behaviour of others.The best-seller list did have a ‘mild’ effect on the behaviour of Facebook users, but an instinct to copy the behaviour of others was by far the more dominant instinct. 

Associate Professor Felix Reed-Tsochas, James Martin Lecturer in Complex Systems at the Said Business School and Director of Complexity Economics at the Institute for New Economic Thinking at the University of Oxford, said: ‘We have used sophisticated modelling techniques to show how it is possible to tease apart different causal mechanisms that underpin behaviour even when the empirical data are purely observational. This is significant because the assumption these days is that only experimental research designs can provide such answers. Here, we found that the “copycat” tendency plays a very important role in online behaviour. This might be because users need to make quick decisions in information-rich environments, but other research has identified similar imitative behaviour in the off-line world.’

Professor James Gleeson, from the Department of Mathematics and Statistics at the University of Limerick, said: ‘This study reveals how we can explore different scenarios using mathematical models to disentangle what drives people to behave the way they do using large data sets from the real online world. This opens up lots of new possibilities for studying human behaviour.’

Commenting on the significance of the method behind the study, Associate Professor Mason Porter, from the Mathematical Institute at University of Oxford, said: ‘We hope that our paper can help serve as a guide for modelling complex systems and how data can be incorporated directly into such modelling efforts. The importance of mathematical modelling often seems to be lost amidst the overabundance of empirical studies, and I cannot stress enough that mathematics is also crucial to help illustrate how things work.’

The other authors of the new study were Dr Davide Cellai (University of Limerick) and Assistant Professor Jukka-Pekka Onnela (Harvard).

For more information see the PNAS webpage, and contact the University of Oxford News and Information Office on:

+44 (0)1865 280534 or email: @email

NOTES FOR EDITORS

*The paper, ‘A simple generative model of collective online behavior’, by James P Gleeson. Davide Cellai, Jukka-Pekka Onnela, Mason A Porter and Felix Reed-Tsochas will be published by Proceedings of the National Academy of Sciences (PNAS).

*The data used by the research team contains no information about individuals, and only information about individual applications, so there are no implications in terms of the privacy of individual Facebook users.

Professor Ruth Baker has been awarded a Whitehead Prize by the London Mathematical Society for her outstanding contributions to the field of Mathematical Biology.

Congratulations to Kishan Patel who has won the 2014 Hansjoerg Wacker Prize of the European Consortium for Mathematics in Industry. This prize is awarded for a Masters thesis on Industrial Mathematics.  Kishan completed the MSc in Scientific Computing and Mathematical Modelling in 2012 at the University of Oxford and his dissertation on 'Imaging with X-Ray Emitter Arrays' was supervised by Raphael Hauser and sponsored by Radius Health. The chairman of the Prize Committee wrote: 'This year’s winner stands out due to a very impressive combination of different areas of mathematics, excellent algorithmic and programming skills together with a significant impact for an industrial imaging process.'

The Mathematical Institute was one of 12 departments who scooped a Bronze Award at the Universitys first ever Green Impact Awards Ceremony held on 18th June 2014 hosted at the Andrew Wiles Building, Mathematical Institute.

This award is in recognition for our achievements in a number of areas, including promoting green IT, recycling methods, sustainable energy efficient buildings, travel and cycling schemes and encouraging staff to reduce their energy usage.

The University signed up to Green Impact last year - an environmental accreditation and award scheme which helps departments improve their working environments for all, whilst gaining recognition for their efforts.

During this first successful year, 199 members of staff have formed 23 departmental teams across the University. These teams help deliver a range of sustainable initiatives - impacting over 5000 members of staff.

Vice Chancellor, Professor Andrew Hamilton attended to present awards alongside other representatives from across the University.

Many thanks to everyone who has contributed to our success. For more information about the scheme please contact a member of our building operations team.

Quotes from the Vice-Chancellor

"environmental sustainability is the responsibility of us all
it should be part of everything that we do
everyone wins and its fun
this initiative helps forge relationships and partnerships across the University these networks are important and help us learn from each other
also helps us connect with other universities

We are delighted to announce our latest Public lecture featuring the recently published book "Love and Math" by Edward Frenkel.

Edward Frenkel is a professor at the University of California at Berkeley, the winner of the Hermann Weyl Prize in mathematical physics, and a member of the American Academy of Arts and Sciences. His book "Love and Math" was a New York Times bestseller and was named one of the Best Books of 2013 by both Amazon and iBooks. It is currently being translated into nine languages.

7 July, 4:00-5:00pm:

Presentation and discussion in the Andrew Wiles Building, Mathematical Institute, University of Oxford

Moderator: Marcus du Sautoy, Simonyi Professor for the Public Understanding of Science, University of Oxford

Questions can be submitted by Twitter using the hashtag #loveandmath. The presentation will be followed by a book signing.

"Love and Math" tells two intertwined stories: the wonders of mathematics and one young man's journey learning and living it. The book shows that mathematics - far from occupying a specialist niche - goes to the heart of all matter, uniting us across cultures. Edward works on the Langlands correspondences. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Programme enables researchers to translate findings from one field to another so that they can solve hard problems that had seemed intractable before. "Love and Math" is an invitation to discover the hidden magic universe of mathematics. For more information, visit http://loveandmathbook.com/

The 2014 Ramanujan Prize has been awarded to Miguel Walsh of the Mathematical Institute in the University of Oxford for his outstanding contributions to Ergodic Theory and Number Theory, including a proof of the norm convergence of multiple polynomial or nilpotent ergodic averages, a long-standing problem in ergodic theory, and important results in inverse sieve problems leading to a sharp bound on the number of rational points on curves.  

In March Dr Walsh was awarded a Clay Research Fellowship, which he takes up on July 1.  He will hold the fellowship in Oxford. 

The Ramanujan Prize is awarded jointly by the International Centre for Theoretical Physics (ICTP) in Trieste, the Department of Science and Technology (Government of India) and the International Mathematical Union. More details can be seen on the ICTP website.

Congratulations and thanks to the following winners of the Mathematical Institute Teaching Awards:

Lifetime Teaching Awards: Prof. Karin Erdmann, Dr Jackie Stedall and Prof. David Stirzaker. 

Individual Teaching Awards: Prof. Peter Howell, Prof. Colin Macdonald, Prof. Michael Monoyios, Prof. Oliver Riordan and Prof. Paul Tod. 

The awards will be presented at the Undergraduate Welcome Party in the Michaelmas Term.

These two films explore the development of Sir Roger Penrose’s thought over more than 60 years, ending with his most recent theories and predictions.

In the first film, Roger Penrose explains the impact of his time at Cambridge in the 1950s. The interview brings out his highly unconventional choice of subjects for deep study, which completely ignored the boundary between ‘pure’ and ‘applied’ mathematics. Those familiar with his world-leading development of relativity theory in the 1960s may be surprised to learn how much he was influenced by quantum theory in the 1950s, and also by the early origin of his new ideas.

Roger also explains the influence of Dirac, Sciama and other leading figures of the 1950s, and goes on to characterise the emergence of twistor theory. Non-experts will be interested to hear how the ideas of his best-known work, The Emperor’s New Mind, also had an origin in this early period. He also adds fascinating detail about the psychology of mathematical discovery, explaining how he was very slow at school, needing extra time to think issues through for himself. The mystery of time, in physics and human consciousness, runs through the entire conversation, and lights up even the most technical aspects of the discussion. 

In the second film, the emphasis shifts to the recent developments in Roger Penrose’s thought. He gives a very clear outline of his argument for Conformal Cyclic Cosmology as the correct description of the Big Bang. However,  the conversation turns once again to the precursors of these ideas in the 1950s, with new anecdotes about Dirac and the origin of Roger Penrose’s geometrical innovations.

Bringing the discussion up to the present moment, Roger describes the impact of recent observations of primordial magnetic fields and also addresses the significance of his own predictions for the form of ‘dark matter’. And in a closing segment, the discussion turns to the current discoveries in neurology and biophysics relevant to Roger Penrose’s theory of microtubules as advanced in Shadows of the Mind. The discussion ends tantalisingly with renewed speculation on the foundations of quantum mechanics and its relation to general relativity.

Roger concludes: "to me eternity is not such a long time."

Associate Professor Mason Porter has won the 2014 Erdős–Rényi Prize. The prize is awarded to a selected young scientist (under 40 years old on the day of the nomination deadline) for their achievements in research activities in the area of network science, broadly construed. While the achievements can be both theoretical and experimental, the prize is aimed at emphasizing outstanding contributions relevant to the interdisciplinary progress of network science.

The prize awarding ceremony and lecture took take place in a special session at the conference portion of NetSci 2014 on Jun 2-6, 2014 in Berkeley California, at the Claremont Hotel and the Clark Kerr Campus of the University of California.

Congratulations to Professor Fernando Alday who won the Oxford University Student Union (OUSU) Teaching Award in the “Most Acclaimed Lecturer” category for the Mathematical, Physical & Life Sciences Division.