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Journal articlePruessner G, Cheang S, Jensen HJ, 2014,
Synchronization is a phenomenon observed in all of the living and in much of the nonliving world, for example in the heart beat, Huygens’ clocks, the flashing of fireflies and the clapping of audiences. Depending on the number of degrees of freedom involved, different mathematical approaches have been used to describe it, most prominently integrateand-fire oscillators and the Kuramoto model of coupled oscillators. In the present work, we study a very simple and general system of smoothly evolving oscillators, which continue to interact even in the synchronized state. We find that under very general circumstances, synchronization generically occurs in the presence of a (small) time delay. Strikingly, the synchronization time is inversely proportional to the time delay.
SoftwareEvans T, Lambiotte R, 2014,
This is code to implement our weighted line graphs, i.e. graphs whose nodes are the edges of the original graph which aslo capture the correct dynamical features of the original network. Weighted line graphs provide an alternative, valuable representation of the system's topology, and have important applications in community detection. The usual node partition of a line graph naturally leads to an edge partition of the original graph. This identification allows us to use traditional partitioning methods in order to address the long-standing problem of the detection of overlapping communities.Here we provide our simple C++ line graph code which takes in a graph as an edge list and outputs different types of line graph as another edge list. An executable suitable for most Windows machines is included as is basic documentation. This code been used successfully on a graph which produced 5.5e8 stubs in its line graph, though a special machine was used for this as it needs more than 4Gb of RAM memory. On a 4Gb machine a line graph with 4.5e7 stubs was created.We also have java based code which is part of a much bigger package.Discussions, papers and slides from talks:-Paper: Line Graphs, Link Partitions and Overlapping Communities, Phys.Rev.E 80 (2009) 016105 [arXiv:0903.2181].Conference Paper: Overlapping Communities, Link Partitions and Line Graphs, a very slightly altered version forECCS09.Slides from talk What am I? Finding Communities in Networks Using Line Graphs given at University of Warwick Complexity Forum, 28thOctober 2009.Slides from talk Overlapping Communities, Edge Partitions and Line Graphs given at ECCS09 (University of Warwick, 22nd September 2009).Paper: Edge Partitions and Overlapping Communities in Complex Networks, Eur. Phys. J. B 2010, 77, 265–272 [arXiv:0912.4389]. This covers in more detail the case where one is interested in the different line graphs of a weighted graph.Input used for the Les Miserable network and the correpsonding outputs
Journal articleJensen HJ, Viegas E, Cockburn SP, et al., 2014,
Journal articleRazak FA, Jensen HJ, 2014,
‘Causal’ direction is of great importance when dealing with complex systems. Often big volumes of data in the form of time series are available and it is important to develop methods that can inform about possible causal connections between the different observables. Here we investigate the ability of the Transfer Entropy measure to identify causal relations embedded in emergent coherent correlations. We do this by firstly applying Transfer Entropy to an amended Ising model. In addition we use a simple Random Transition model to test the reliability of Transfer Entropy as a measure of ‘causal’ direction in the presence of stochastic fluctuations. In particular we systematically study the effect of the finite size of data sets.
Journal articleRubin KJ, Pruessner G, Pavliotis GA, 2014,
Journal articleEvans TS, Rivers RJ, Rivers RJ, et al., 2014,
New approaches to Archaic Greek Settlement Structure, Les Nouvelles de l'archéologie, Vol: 135, Pages: 21-27, ISSN: 0242-7702
Recent developments in network theory have led to the creation of new Spatial Interaction Models (SIMs) and a reappraisal of existing models. Although not directed at the archaeology community, these models generalise the familiar gravitational models and Proximal Point Analysis (PPA) used by archaeologists for many years to help explain the archaeological record. However, a problem arises in archaeology that, with the increasing suite of plausible models that now exist, it is unclear how to choose one model over another. This can lead to the criticism that, if we hunt hard enough, we may be doing no more than finding a model which can be manipulated to conform to our preconceptions. In recent articles we have begun to address this criticism (Evans 2014, in press) with particular reference to the maritime networks of the MBA Aegean (Rivers 2014, in press). Different historical periods require different approaches and in this paper we continue this analysis by re-examining the onset of centralisation in mainland Greek city states of the 9th and 8th centuries BCE. Pioneering work on this archaic settlement structure was performed in 1987 by Rihll and Wilson (Rihll & Wilson 1987, 2: 5-32; 1991: 59-95), adapting a 'retail' model devised originally for urban planning. One alternative approach is given by a recent cost-benefit model termed ariadne, developed by ourselves (Evans, Knappett & Rivers 2009, 7: 451-79; Knappett, Evans & Rivers 2008, 82: 1009-84; 2011, 85: 1008-23), initially designed for Bronze Age maritime networks. A comparison of these models and other simpler SIMs for archaic settlements highlights the problems of modelling archaeological data. In particular we examine what constitutes model 'robustness' and the way in which different models handle 'contingency' when handling periods of rapid change.
Journal articleRochester CC, Lee AA, Pruessner G, et al., 2013,
Journal articleReiss DS, Price JJ, Evans TS, 2013,
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