MOLTEN: Mathematics Of Large Technological Evolving Networks

Connections are important. In studying nature, technology, commerce and the social sciences it often makes sense to focus on the pattern of interactions between individual components. Within the UK's Digital Economy activities, for example, large, complex networks arisein energy: connecting power suppliers and users,in telecommunications: connecting mobile phone users,in transport: connecting train stations, airports or ports,in the World Wide Web: connecting web pages,in one-line social networking connecting cyberfriends, in retail trade: connecting sales of different products to the same customer.Improvements in computing power have made it possible to gather, store and analyze large data sets, especially in the areas of fast moving consumer goods (who bought what), telecommunications (who phoned who), mobile devices (who travelled where) , on-line social networks (who Twittered to who) and energy (who switched on when). The interdisciplinary field of Network Science has emerged as a means to understand and quantify these large networks and to extract useful information. By focussing on the underlying connectivity, mathematical techniques can be used to address common questions:Can we discover clusters of strongly connected individuals? This would allow us to break the network down into meaningful subunits.Do the network properties change when links are added or removed? This determines robustness/efficiency to attack/disease/malfunction and stability under evolution.Are some individuals or links especially important? `Hubs' are individuals with high-quality connections (e.g. web pages highly ranked by Google), `short-cuts' are links that join distinct subnetworks and `bottlenecks' are specific links that may become overloaded.Can we develop mathematical models that reproduce the features of a complex network?Given observed output (such as queuing times in a dynamic communication network) can we discover underlying, hidden, connectivity in a complex system?This proposal aims to add value to this important area by addressing an important feature that has fo far received very little attention from the mathematical community. Technological networks vary over time, and this dynamic element has important consequences. For example, if A phones B today and B phones C tomorrow, then a message may pass from A to C, but not from C to A. So there is an immediate lack of symmetry that makes much of the existing theory obsolete. .Moreover, the patterns of connectivity that we see today may be different tomorrow. So there is built-in uncertainty about the future. In this proposal we will develop new mathematical techniques to study the type of dynamically evolving networks that are relevant in the Digital Economy, allowing researchers to discover the important players, quantify the efficiency of a network and predict future behaviour. These ideas offer immediate benefits outside academia, allowing us to tackle questions such as: who are the important broadcasters or receivers of information? who should we target our advertising campaign at? what will the network look like next week or next year? is there any suspicious activity today? which networks users appear to be underage? which customers are likely to change brand loyalty? how quickly will a rumour or virus spread? what would be the effect of changing the way that customers are charged for network usage? Our objectives are to develop to practical, quantitative solutions to these issues by developing a new, underpinning mathematical framework that leads directly to useful computer software. In order to make sure that the results will have immediate benefit, we have put together a team of non-academic experts who use large technological networks in their businesses. These people will provide realistic data sets, pose specific challenges and provide regular feedback and advice throughout the project.

Because of its direct involvement with real data sets, and its built-in engagement with specific industrial partners, this project can provide immediate benefit for a number of contributors to and users of the digital economy. The concepts that drive the project revolve around the telecommunications and social networks paradigm: connectivity data produced by mobile device users, from the direct `who-called-who?' patterns to more indirect links, such as, `who-came-geographically-close-to-who?' and connections formed by on-line social interaction. However, the principles apply much more widely to a range of other scenarios where connections may be defined through correlated behaviour, including purchases, web searches and event attendance. In the dynamic network setting of this proposal, there is a clear and immediately implementable benefit for technology providers if we can produce computable measures that summarize the current state of the network. In the longer term, over two to three years, when suitably contextualized, the quantitative measures and inference techniques proposed here would be of interest to a range of e-businesses, health organisations and policy makers who have concerns such as: how quickly could a rumour or disease propagate around this dynamic network? what are the most vulnerable players/connections/times? can we identify players who are engaging in unusual or suspicious behaviour, e.g. in order to target `popular' or 'trendsetting' individuals or to investigate cybercrime? More generally, this type of quantifiable knowledge can improve the way that technological networks, such as `person-to-person' mobile phone, email, SMS or social network activity, `user-to-supplier' smart meter systems and `user-to-product' purchasing data are analysed, managed and expanded, and hence will positively The concrete, transferable skills developed by the Research Assistants on this project will provide them with an excellent grounding from which there are a range of employment opportunities. In particular, familiarity with both computational and statistical tools and an ability to work across disciplines are highly prized by employers, and these are the types of skilled personnel that are needed to boost the UK's high-tech digital service providing work force. At the end of the two year period we have specific plans to extend these methodologies to neruo-imaging (temporal brain activity networks) and smart metering (power usgae nehabior networks), where the proposers can exploit existing links. In addition to publications and conference presentations/posters, there are two formal dissemination routes built into the project. A workshop at the end of each of the two years will bring together academics and industrialists. All proposers have experience of interdisciplinary workshop and conference organisation. Also, a common project website will make computer codes and synthetic data sets available. The project has a Technology Strategy Advisor, Shail Patel, an independent consultant who was previously Director in Unilever R&D of an emerging Platform in Digital Consumers& Markets, which focused on understanding consumer complexity as well as building a new generation of personalised mass-scale consumer services. We also have commitments of time, know-how, software and data from industrial partners, who will (a) ensure that the project aligns with the challenges facing users of technolgoical network science, and (b) provide a fast route to exploitation and benefit for the new tools that are developed.