Warwick Complexity Science Doctoral Training Centre 2

It is a key challenge for our society to better understand, adapt, design and control complex systems. A complex system comprises many interacting components leading to multiple levels of collective structure and organization. Examples include natural systems ranging from bio-molecules and living cells to human social systems and the ecosphere, as well as sophisticated artificial systems such as the Internet, power grid or any large-scale distributed software system. Ongoing Research Themes:Complexity, Emergence & Upscaling. In mathematically oriented research we attempt to crystallise clear and appliable definitions of information content and emergent behaviour.Complex Fluids and Complex flows. How do a small fraction of interacting particles conspire to dominate their flow properties, and how do those properties influence particular flows? Clustering, Condensation and Jamming. Clustering phenomena are ubiquitous with applications ranging from raindrops to galaxies, and from facebook to traffic jams. Complex Networks & their dynamics. The interplay between the connectivity of a network and its dynamics are central to key challenges today, such as epidemiology, biodiversity, neuroscience and markets. Network Statistical Inference. The inference of network structure is a key approach we use in applications spanning multiple fields, from molecular biology to health and economics. New Applications of Statistical Mechanics. This well developed set of tools finds fresh use in molecular biology, traffic theory and opinion dynamics. Developing Areas include:Complex Systems in Social Science, Epidemiology and related Ecology, and Bioimaging.National Need.The financial crisis shows how urgently the UK needs people trained to understand systemic risk in a complex socio-technical system and to design regulation and incentives to get the economy going again. The debate on climate change shows how vital it is to the UK to have people trained in understanding the implications of policies on a large complex socio-economic-physical-biological system. Our partner BAS (British Antarctic Survey) explicitly recognises Complexity as a divisional aspect of their organisation: Natural Complexity Programme. The debate about management of the National Health Service shows how important it is to involve trained people in designing the incentive and monitoring system. The advances in ability to monitor gene expression provide a huge opportunity for people trained in discerning patterns to contribute to controlling many diseases, particularly cancer. The advances in ability to monitor brain activity create huge opportunities for people trained in understanding network function to contribute to controlling malfunctions such as epilepsy, Parkinson's disease and Alzheimer's disease.

i1 The long term but most direct strategic impact stems from the students we train and develop in research, whom we empower to apply their talent to solving real world problems and leading mathematically-based innovation. i2 Some of our student talent will stay in academia, but where they keep to the spirit of the research roots we are setting, they should eventually multiply impact through their later directed research and students trained. i3 Judging by project partnerships to date, we can anticipate employment impact in IT, Climate modelling, Finance, Health Improvement, Transport and more. i4 There is direct impact from individual PhD projects addressing such areas - they might change how you get treated for heart disease, how you store & retrieve data from your hard drive, or whether your children catch the next 'flu pandemic (examples based on current Complexity PhDs). i5 We also aim to inspire and engage the public with our endeavour. [Note academic beneficiaries are detailed in separate section.] See Pathways to Impact statement for implementation.