Networks: Emergence and dynamics

Lead Research Organisation: Imperial College London
Department Name: Dept of Mathematics

Abstract

The main objective of this proposal is capacity building in theoretical complexity science by coordinating and developing existing activities in the Departments of Mathematics, Physics and Bioengineering at Imperial. The RA hired for the project will be placed in the Institute for Mathematical Sciences (IMS) at Imperial. The IMS provides a venue for transdisciplinary research in mathematical sciences applied to real world problems. In this way the project will benefit from the other complexity activities hosted by the IMS as well as forging an inventive collaboration between researchers from various Departments. The proposed research will focus on network dynamics, a term that encompasses both dynamics on, and dynamics of, networks. Theoretical tools related to statistical mechanics, dynamical systems theory and stochastic processes will be developed to analyse and characterise the relationship between network structure and the emergence of collective network behaviour. In particular, the research will develop our understanding of the dynamical evolutionary processes leading to specific network structure and the properties of dynamical processes taking place on such networks. The theoretical modelling will be inspired by functional brain imaging data obtained experimentally by the Division of Clinical Neuroscience. The theoretical research will on the other hand motivate the experimental development.

Publications

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Doria V (2010) Emergence of resting state networks in the preterm human brain. in Proceedings of the National Academy of Sciences of the United States of America

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Evans TS (2009) Line graphs, link partitions, and overlapping communities. in Physical review. E, Statistical, nonlinear, and soft matter physics

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Expert P (2011) Uncovering space-independent communities in spatial networks. in Proceedings of the National Academy of Sciences of the United States of America

 
Description The main objective of this proposal was capacity building in theoretical complexity science by coordinating and developing existing activities in the Departments of Mathematics, Physics and Bioengineering at Imperial. The RA hired for the

project was placed in the Institute for Mathematical Sciences (IMS) at Imperial. The IMS provided a venue for transdisciplinary research in mathematical sciences applied to real world problems. In this way the project benefited from the other complexity activities hosted by the IMS as well as forged an inventive collaboration between researchers from various Departments. The proposed research focused on network dynamics, a term that encompasses both dynamics on, and dynamics of, networks. Theoretical tools related to statistical mechanics, dynamical systems theory and stochastic processes was developed to analyse and characterise the relationship between network structure and the emergence of collective network behaviour. In particular, the research developed our understanding of the how to identify community structures in complex networks and their role in properties of dynamical processes taking place on such networks. The project also led to the discovery that the fMRI signal from the brain exhibit self-similar fractal structure, which suggests that the dynamical processes taking place in the brain are also fractal in space and time.
Exploitation Route Any body who needs to understand the community structure of specific networks (costumers, social, interest etc.) will benefit for applying the techniques developed. Results have been published in high profile journals and the RA and PhD students involved are still actively working in collaborative projects with in UK and abroad.
Sectors Other