## Core Complex Systems ResearchThe theory, tools, methodologies and conceptual frameworks that are fundamental to complex systems simulation are research topics in their own right. What constitutes complexity? How should systems complexity be measured and characterised? Where does it originate? How can simulation methods best be used to augment mathematical modelling? Questions like these are addressed within three core research themes: ## ComplexityFamously poorly defined, understanding the nature of complexity remains one of the deepest challenges facing science. Historically, successive waves of research activity have attempted to formulate, reformulate and ultimately answer questions such as: what distinguishes complex systems from simple systems? what processes bring about complex systems, or maintain their organisation? how is complexity related to evolution, adaptation, agency, and cognition? how can notions of emergence and self-organisation be made to do useful scientific work? ## Case Study: Small-world Systems and Neural Complexity
Tononi, Edelman and Sporns' measure of neural complexity attempts to
characterise and measure a tension between the functional integration
of a whole system (e.g., a nervous system) and the relative functional
segregation of its parts (e.g., neural sub-systems). The measure
employs an information theoretic approach to identifying the degree of
segregation at different levels of description within a single system.
How does a network's topology impact on this measure of complexity?
Recent work shows that it is the ## Mathematics and StatisticsAs with any other scientific enterprise, mathematical tools, formalisms and analysis are a central building block for making progress. ## Case Study: Spatially Embedded Random Networks
Many real-world networks analysed in modern network theory have a natural spatial element; e.g., the Internet, social networks, neural networks, etc. Yet, aside from a comparatively small number of somewhat specialised and domain-specific studies, the spatial element is mostly ignored and, in particular, its relation to network structure disregarded. The Spatially Embedded Random Networks (SERN) construction is a model framework used to analyse the mediation of network structure by spatial embedding. It is not primarily intended as an accurate model of any specific class of real-world networks, but rather is intended to explore the effects of spatial embedding on network structure in general. SERN can be used to demonstrate the influence of spatial embedding on connectivity such as the effects of spatial symmetry on conditions for scale free degree distributions, and the existence of small-world spatial networks. One interesting result is the lack of a phase transition to a giant component that is characteristic of some other random graphs. Barnett, L., Di Paolo, E. A., and Bullock, S. (2007)
Spatially embedded random networks.
## Associated People:## SimulationWhile simulation modelling is as old as computational machinery we are still learning how best to make use of it alongside experimentation and mathematical modelling. As the availability of cheap computational power increases, the importance of simulation is growing. Finding effective, efficient, robust and explanatory simulation methodologies is an important part of this activity. The research into simulation methodology ranges from the development of efficient and effective algorithms, tools and programming languages, to the creation of new software engineering technologies, visualisation, data processing and storage methods, and even the philosophy and epistemology of simulation modelling. To exploit established hardware (including the local Iridis cluster and the UK`s high performance machine HECToR) we provide training from the Numerical Algorithms Group NAG) in MPI, OpenMP and general parallel software optimisation. The centre has an allocation of CPU time on HECToR reserved for its PhD students. We research emerging technologies such as GPU computing and its application to demanding simulations. ## Case Study: Parallel Multi-physics Simulations of Functional Nano-structuresProgressive minituarisation of nanodevices requires the simulation of different types of physics within the same model. For example, data in harddisks is currently stored by reversing small magnetic islands using an applied magnetic field. The next generation of magnetic media is likely to write data using spin-polalised currents, or the combination of a magnetic field and heat (for example from a laser which is focused on the area that should be written to) or superimposed AC-fields. From a simulation point of view, it is important to solve the
equations for all physical phenomena While for some application domains (such as fluid-structure interaction) such multi-physics codes exists, and general purpose tools such as Comsol and Ansys can carry out multi-physics simulations for a range of problem, there are other problems which need specialised (parallel) code, which we develop at Southampton. More examples of research activity in this theme here. ## Associated People: |
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