## The Complex Systems and Statistical Physics Group

## Our research

Although complex systems are, by their very nature, difficult to define precisely, they typically have the following characteristics. Firstly, they consist of a large number of agents (which may, for instance, be molecules, individuals, species or consumers) interacting with each other in many different ways. Secondly, interest focuses on collective properties of the system as a whole, which may result in emergent structures of great complexity at larger scales or after long times. Thirdly, random, or stochastic, effects are typically important: both determinism and chance are needed to describe reality. These properties are frequently found in the physical sciences, and are the domain of non-equilibrium statistical mechanics. In addition there may be a fourth property, most often found in the biological and social sciences, which is not found in the physical sciences: the system may be adaptive. For example, the stochasticity can lead to the production of "errors" (e.g. mutations) which may give rise to better variants and, through selection, eventually lead to complex structures.

The above discussion highlights the close relationship between the study of complex systems, non-equilibrium statistical mechanics and stochastic dynamics. To illustrate this, we summarise some of the current funded projects that group members are involved in.

**Resilience and interaction of networks in ecology and economics**

Connections between individuals (persons, firms, cities, countries, plants, ecosystems) facilitate the exchange of resources, goods and information, but they also expose them to the threats and dangers. A network is said to be resilient if it is able to benefit from the connections and if it does not collapse under external shocks and perturbations. We are using techniques from theoretical physics to study resilience in networks in ecology and economics. This work is being carried out with ecologists, economists and other theoretical physicists in Spain, the Netherlands and the UK.

See here for further details.

**Multi-scale dynamics and gene communities**

Evolution has mostly been studied in the context of the higher organisms, where the transfer of genetic material is almost always from parents to offspring. However some years ago it was discovered that bacteria, by contrast, are able to transfer genetic material directly between individuals. The first type of transfer is called vertical and the second type horizontal. We are developing novel mathematical methods to study models of horizontal gene transfer and related phenomena, based on techniques used in statistical physics and population genetics.

See here for further details.

**The Social Complexity of Immigration and Diversity**

This project seeks to integrate the two very different disciplines, social science and complexity science, in order to gain new understanding of complex social issues such as immigration and diversity. It will do this by building a series of agent-based computer simulation models of these social processes. Simplified versions of these models will be expressed in the language of nonlinear stochastic dynamics and will be analysed using tools and methodologies from this area.

See here for further details.

**Game theory and adaptive networks for smart evacuations**

In this project we investigate how social networks and ideas from game theory can be used to improve evacuation procedures. Does communication between evacuees (for example by mobile phones ?) and the use of social networking sites (e.g. Twitter) improve evacuation, or does it make it slower. How do agents use information do take decisions, for example what exit route to choose ? Can ideas from game theory be used to model the decision making of agents ? How can a disaster manager speed up evacuation by inocculating networks with appropriate information signals ? We address these questions through computer simulations, and where possible, analytical solutions of simple model system. The project is carried out with an interdisciplinary team of collaborators in the social sciences.

See here for further details.

**Characterizing complex nonlinear systems using quantum information theory**

The aim of this project is to explore connections between the field of complex and nonlinear systems and that of quantum information theory (QIT). In particular we study classical systems with quantitative techniques developed recently in QIT. In detail, we characterize multi-party probability distributions arising from classical complex and nonlinear systems, such as coupled chaotic maps or cellular automata. We are interested in exponential families and Gibbs measures generated by Hamiltonians of a given order of interaction.