Winter School in Network Theory and Applications
Warwick Mathematics Institute
5-8 January 2011
All talks will take place in MS.02 on the ground floor in the Zeeman Building. Coffee/tea breaks, lunch and social events are in the Mathematics Common Room on the first floor in the same building.
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Poster Session with Dinner
- Thomas House (Warwick) Introduction to network statistics In some research contexts, maximal knowledge of the full structure of a network, including all available information about each node and link, is needed to make progress. Often, however, it is more informative to consider a family of networks, where the method of generation and statistical properties are well understood. Consideration of such families is also a useful route to understanding more about network theory. These lectures will start with arguably the best understood family of networks: the Erdos-Renyi random graph. Different statistics of networks that are defined for all graphs, including degree distribution, assortativity, clustering, path length and motif structure, will be introduced. Some standard statistical methods will be reviewed, including likelihoods for independent trials and Metropolis-Hastings sampling. Several families of (topological, undirected) networks often considered by researchers will be presented. These will include: exponential random graphs; configuration model networks and their assortative generalisation; networks with multiple levels of mixing; small-worlds networks; scale-free networks. Depending on time, examples of transmission models and generalisations to weighted, directed graphs will be suggested.
- Marc Timme (Göttingen) Spatio-Temporal Dynamics of Complex (Neural) Networks
In neural networks of the brain, robots controlled by sensory inputs, and modern dynamical systems providing new forms of computing devices, the connection topology of a network strongly influences its function. Although scientists are intensely working on the subject, there currently is no general theory of network dynamical systems, i.e. systems were many components interact on a non-trivial topology. In our group, we are trying to understand the structure and dynamics of complex networks in physics and biology with a focus on the analysis and modeling of the activity and computation of neural networks in the brain. We also develop mathematical tools required for understanding these highly complex systems. Furthermore, we work on foundations and applications in the areas of computer science, statistical physics of disordered systems, artificial neural networks and robotics, and, more recently, gene evolution and power grids.
In these lectures I will give an introduction to the emergence of spatio-temporal patterns in (neural) networks, and provide an example link bridging the statistical physics and the nonlinear dynamics of networks that exhibit synchronization and more complex spatio-temporal patterns.
- Eduardo Lopez (Oxford) Computational tools for network research: from real to random and from static to dynamic
One of the most important aspects of the revived study of networks in the last decade has been the introduction of new algorithms that, together with theoretical developments, have made the field a vibrant research area. In this sense, a large number of key articles in the field have introduced important concepts that help highlight the strength of network representations of practical problems (scientific, social, or other), together with algorithms that allow for the measurement of such concepts. Questions about network formation, optimal network structure for transport, network community and pattern detection, and flows/transport in networks are just a few key examples. In these lectures, I will focus on presenting algorithms for three different purposes: construction of ensembles of random networks, network structural analysis, and dynamics on networks. Such algorithms also have a natural split along the lines of model networks and networks based on data. If time allows, I will introduce additional algorithms for weighted networks and dynamic networks. The emphasis will be practical, with the aim of providing useful research algorithms.
- Ginestra Bianconi (Northeastern) Evolution of networks and biological evolution
Evolution ideas are pervasive in the study of complex systems. In fact the biological evolution paradigm explaines why complex systems evolve toward robust structures. The theory of complex networks and the theory of evolution are deeply related. In the first lesson I will show the state of the art of modeling evolution of biological as well as technological and social networks, stressing the similarities and differences with the theory of biological evolution. In the second lesson I will the new questions on biological evolution that are emerging from the recent experiments on epistatic interactions.
Notes: lecture1.pdf, lecture2.pdf
Mark Fricker (Oxford) : Biologically-inspired rules for adaptive network design (slides)
Amin Coja-Oghlan (Warwick) Spectral methods and regularity (slides)
Renaud Lambiotte (Imperial) Finding communities when lost in space (slides)
Elizabeth Leicht (Oxford) Community structure in networks: practice and significance (slides)
Michael Gastner (Imperial) Spatial networks: should we revive quantitative geography?
David Croydon (Warwick) Scaling limit of the Erdos-Renyi random graph and associated random walk (slides)