"I think the next century will be the century of complexity." (Stephen Hawking, 2000)

The twentieth century saw huge successes using reductionist methods. However, to tackle the challenges facing modern society systemic approaches are proving increasingly effective. The complex systems domain spans sub-atomic interactions through to global systems and upwards. A key aspect is understanding how low-level interactions give rise to higher-level phenomena, and using tools to understand system dynamics. In most aspects of studying complex systems an interdisciplinary approach is integral. The organization of the Student Conference for Complexity Science reflects this interdisciplinary approach and is organized around the following themes:

Core research

Complexity

To date no consensus has been reached on the definition of a complex system. This issue is at the core of complex systems research, and encompasses questions such as which processes bring about complex behaviour and maintain their organization? Can a deeper understanding of these mechanisms be applied ubiquitously across disciplines?

The idea of emergent behaviour in complex systems and general methods related to investigating real world examples are key to complex systems science and research in this direction is crucial for developing the tools needed to understand the processes involved.

Formalisms and tools

Formalisms and tools are key to progress in most scientific endeavors. Study areas include networks, statistics and stochastic physics. Understanding networks through the study of their growth and connectivity is central to problems ranging from epidemiology, web science, markets, neuroscience and protein folding. Similarly, developing statistical tools and exploring the development and application of machine learning. Stochastic physics includes statistical mechanics whose applications range from the traditional to the frontiers of complexity science.

Simulation

Using computer based models to test hypotheses is well established throughout science. Simulation often has a central role in investigating complex systems of many interacting components. Themes within simulation include exploring how to get the best out of simulations, ensuring efficient use of computational resources in answering research questions through design of the simulation experiments and code. Both the availability of computational power as well as the scientific community's awareness and reliance on simulation are growing. Thus, investigating simulation methodology through the design of efficient algorithms, visualisation tools and data processing and storage tools are of growing importance.

Physical and engineered

Electrical energy systems

From resistor networks to the power grid, these systems are hugely important for modern society, but face a range of problems. These include assessing the impact of changes to conventional generation, distribution and transmission of energy as well as the generation from renewable sources and coping with fluctuations in demand.

Nanotechnology and devices

Advances in technology are increasingly enabled by understanding how very small devices can have huge capacities. Such advances in understanding are often gained by investigating several properties simultaneously, such as the electrical current, resulting temperature and structural expansion as well as coupling computational models at different length scales. Nanoscale devices are increasingly being used for convenience, medical purposes and to explore the environment.

Flows and turbulence

The study of turbulent flows is centred around the emergent properties of interacting components, specifically the non-additive nature of the interacting coherent structures. Small fractions of the interacting particles can dominate the flow properties in complex fluids. The non-linear phenomenon of turbulence can be characterised by the emergence of structures from a background of fluctuations of vorticity. The study of flows and turbulence is applicable to a wide range of applications such as the study of blood flow, design of vehicles and oceanography.

Quantum

Quantum techniques can be applied to systems across a range of sizes, from the subatomic to the molecular. Quantum chromodynamics concerns the ab initio study of the strong nuclear force and deals with the fundamental interactions that make up matter. Studying this field pertains to the standard model of physics and the interaction of quarks and gluons. Quantum dynamics attempts to fully model the behaviour of collections of particles. The study of these systems are of a fundamental nature, yet the interactions between pairs cannot be projected onto a many-particle system and retain predictive power. Larger systems have can also be addressed using quantum chemistry methods that are able to calculate the electron densities of systems with hundreds of constituent atoms. This allows the potentially accurate study of large molecular structures such as proteins and lipids. The analysis and development of new methodologies in these areas require the study of complex systems with non-linear dynamics that drive their behaviour.

Biological and environmental

Climate dynamics

The study of a simple climate model by Lorenz provided a compelling example of a complex system. In these times of approaching and seemingly dramatic changes to our climate this forms a highly pertinent area for research. Our climate is determined by the interaction of a myriad of factors and understanding the effect of perturbations on the system as a whole is a key area to which complexity science can be applied. These factors include the study of the atmosphere, oceans, biosphere and lithosphere, and require a wide array of modelling and analytical tools.

Evolution, ecology and ecosystems services

Ecological systems display great diversity in their biological complexity and thrive in almost every environment on the planet. The human influence on such systems can be immense and it is of great importance that we understand the complex interactions that take place within and across species. The properties of ecosystems are not fixed however and the drive of evolution generates change across a range of time scales. Complexity science addresses to what extent the existence of these systems as complex entities presents challenges and solutions to problems for the maintenance of life on earth. Biological systems have a long history of inspiring the design of human creations and this is no less true today with people looking to ecological systems for clues to the design of robust and adaptive systems.

This is all tied in to the concept of ecosystems services - the understanding and management of what ecological systems provide society, and our dependencies upon them. This has great influence in the shaping of policy towards natural resource management and such factors as food production, energy security and economic durability.

Protein structure, assembly and folding

Proteins act as powerful nanomachines within living organisms that undertake a huge range of processes, from catalysing chemical reactions to forming structural support networks. Proteins are composed of long chains of amino acids that fold to form complex three dimensional shapes that are key to their function. After, and even during, their manufacturing proteins begin to fold driven by the chemical properties of their constituent amino acids and often assisted by so-called chaperone proteins in their environment. There are many low energy configurations that an unfolded protein may adopt but only a small subset of these will give the protein in its functional form. Many pathological conditions arise where protein folding does not occur correctly, including Alzheimer's disease, amyloidosis and BSE/CJD.

But proteins do not exist in isolation. They form complex interacting metabolic pathways and aggregate together to form large specialised complexes to carry out processes within the cell. Studying the function of proteins demands that they cannot be considered in isolation but only through their behaviour as part of a wider system. This requires the development of novel experimental and computational approaches to appreciate the extent of their function within biological systems.

Biological and computational neuroscience

The study of neuroscience is a subject that can be approached on many different scales. Each neuron within the nervous system is capable of performing complex computations through the integration of multiple signals based on temporal and spatial locality. Studying the behaviour of an individual neuron however is entirely unable to account for phenomena at a psychological or behavioural level, as plausible as attempting to extrapolate the software being executed by a computer by examining the behaviour of a single transistor. Exciting advances in this area, including the advent of connectomics and computational approaches, has provided the scope for the interpretation of neuronal systems through the lens of network theory and complex systems approaches.

New visualisation techniques have allowed the mapping of connections within the brain at incredible levels of detail. It is becoming increasingly true however that there is an excess of raw data available in neuroscience. What is lacking however is a theoretical framework within which to interpret this data, a failing that complexity science is ideally positioned to address.

Genetics and disease

Sequencing of the genome provided an early and misplaced assurance in the power of the gene to explain human behaviour and disease. It is increasingly becoming apparent however that the development of phenotypes are driven not only by mutations within genes but also by changes in regulatory networks that determine the expression of a gene within an organism. The production of genes is controlled by complex regulatory networks and the prominence of epigenetic transgenerational mechanisms are increasingly becoming realised. These are particularly important during development when specific genes must be activated with temporal and spatial specificity. The dynamics of these networks are important for the physiological functioning of organisms and pertain to many disease states.

Socio-economic and socio-technological

Transport and infrastructure

By 2025 the estimated cost of traffic congestion in England is £22 billion and it forms a major problem in many urban centres. The intelligent design of modern infrastructure in the context of environmental and social constraints is perhaps not glamorous but carries great potential. The design of robust and dynamic infrastructures capable of withstanding terrorist or natural disasters will always be relevant and can have great economic and social benefit.

Economics and finance

Traditionally the study of markets and human economic behaviour has been based around simple models using crude caricatures of human behaviour. These models fail to capture much of the detail of such systems leaving phenomena within modern economic arenas unexplained. Modelling the behaviour of markets and investigating such features as crashes and growth could greatly improve the stability and reduce the risks associated with modern markets. Novel approaches, such as agent based modelling and game theoretic approaches, offered by complexity science attempt to replicate the emergent nature of markets and the behaviours they generate.

Demography and social policy

The challenges posed to society and the NHS in particular by an ageing population is a theme frequently explored by the media. Improvements in medical care and standards of living in developed countries are causing life expectancies to increase and driving the average age of populations upwards. Additionally changes in fertility levels and rising levels of divorce along with other factors are causing complex changes in the composition of society. Predicting the changes this will have in the future is important in order to intelligently shape the policy of today. The question of the provision of health care and social stability for future generations may require the modification of existing social frameworks and the development of novel societal models.

Language and learning

Language is a discipline for which the implications of complex systems theory are only beginning to emerge. While linguistic research is traditionally undertaken within clearly delimited modules focusing on specific aspects of language, its acquisition, and its use, the interactions between innate 'hardwired' linguistic knowledge, psycholinguistic processing mechanisms, non-linguistic cognitive systems, and linguistic, sociocultural, educational, or physical context may result in linguistic systems exhibiting complex nonlinear behaviour. Mapping out the specific contributions of these system components and the interactions between them will be of central importance to future understandings of the nature of grammars, language use, acquisition, and learning.