The University of Warwick leads the UK with a ground-breaking Centre for Complexity Science, to connect and develop interdisciplinary research in complexity science at all levels, train a new generation of complexity scientists via a doctoral training centre (DTC), understand, control and design complex systems, produce breakthroughs in the principles and applications of complexity science, link with end-users as sources of real-world problems and beneficiaries from the resulting knowledge and trainees, and sustain a lively intellectual and practically based environment for complexity science.
Research Groups
Complexity, Emergence & Upscaling
In mathematically-oriented research we attempt to crystallise clear and applicable definitions of a system being complex, in the sense of being more than the direct combination of its components. The notion of Emergent behaviour is a key focus of our attention, and connects to the question of forecastability versus chaos in complex systems and more mathematically to non-uniqueness of Gibbs phases. We are researching general methodologies for variable reduction on networks, the identification of continuum limits in particle systems, and of coherent phenomena in turbulent systems. Application areas include weather and climate.
Complex Fluids and Complex Flows
Complex fluids present two key challenges: how a small fraction of interacting particles conspire to dominate their flow properties, and how those properties influence particular flows. Application areas include flow of people, cars – granular materials – diagnosis of cancer, hypertension and heart disease.
Clustering, Condensation and Jamming
Clustering phenomena are ubiquitous with applications ranging from raindrops to galaxies, and from Facebook to traffic jams. A key question we address is: how fast and how large do clusters grow and what is their asymptotic shape? Problems such as traffic flow have conserved quantities but no absorbing state, leading to phase separation between a localised condensate (e.g. traffic jam) and a background (e.g. flowing traffic) at critical density: understanding these has applications to biology (molecular transport, ant trails), social sciences (traffic and transport modelling) and physics (granular media, Bose Einstein condensation).
Complex Networks and 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. Application areas include infectious diseases, neural computing, data storage, dynamics of opinions 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. We have developed novel methods and technical for network learning, including Bayesian approaches, MCMC and penalized likelihood methods. Application areas are diagnosis of cancer, hypertension, heart disease and data storage.
Statistical Mechanics
Here our strategy is to apply a well-developed set of tools to new contexts. In granular materials geometrical frustration is mapped onto pseudothermal fluctuations leading to new insights and scaling laws. In molecular biology we have brought together statistical mechanics, computational statistics and massively parallel single-cell expression assay data to shed light on how DNA sequences known to act in the regulation of gene transcription (CRMs) interact to control the expression of a key mammalian gene (MyoD1). In Social Dynamics we are exploring the relevance of statistical mechanics models of consensus formation – particularly the Axelrod Model – to social phenomena. Application areas are granular materials, dynamics of opinions and markets and molecular biology.
Research Degrees
PhD in Complexity Science
Duration: 3 years
We aim at training graduates able to understand, control and design complex systems, produce breakthroughs in the principles and applications of complexity science, link with end-users as sources of real-world problems.
Taught Master’s Degree
MSc in Complexity Science
Duration: 1 year
Places available: 12
The DTC teaches a coherent core of complexity science concepts which unify the field across disciplines: interacting agents and networks; probabilistic modelling and statistical inference; dynamics and chaos; statistical mechanics, emergence and self-organisation; simulation of complex systems; quantification of complexity, scaling and extreme events. Research projects range widely over areas such as informatics, biomolecules, distributed computing, complexity measures, ecology, economics, epidemiology, finance, gene expression, health, metabolic networks, neuroscience, operational research, plasma physics, production processes, transport (at levels from air, road and human to information and cell) and turbulence.
MSc in Complex Systems Science (Erasmus Mundus)
Duration: 2 years
Places available: 20
This is a joint MSc taught by the consortium: University of Warwick (UK), Chalmers University of Technology and University of Gothenburg (Sweden), Ecole Polytechnique (France)
We teach the tools to analyse complex systems and to understand their emergent behaviour. Students are offered a variety of research project opportunities to develop experience applying this to fresh challenges from the real world and within academic research. We offer an exceptional cross-disciplinary environment and experience, with the programme based around three leading research centres:
- Centre for Complexity Science (Warwick);
- Complex Systems Network (Paris);
- Complex Adaptive Systems (Gothenburg).
Mobility between these centres is a key aspect of the programme: all students spend extended time at two or more of the centres.
This programme is suitable for those who are willing to bridge the gap between theoretical and data-based projects, and mathematically-oriented students who are keen to experience science in a variety of European countries. Graduates are expected to go on and work in areas such as finance, biomedical research companies, forecasting agencies and academia.
