Synchronizability determined by coupling strengths and topology on Complex Networks

We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we unveiled how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks. Here, we provide more evidence on this phenomenon extending the previous work to networks that interpolate between homogeneous and heterogeneous topologies. We also present new details on the path towards synchronization for the evolution of clustering in the synchronized patterns. Finally, we investigate the synchronization of networks with modular structure and conclude that, in these cases, local synchronization is first attained at the most internal level of organization of modules, progressively evolving to the outer levels as the coupling constant is increased. The present work introduces new parameters that are proved to be useful for the characterization of synchronization phenomena in complex networks.Comment: 11 pages, 10 figures and 1 table. APS forma

Identifying network communities with a high resolution

Community structure is an important property of complex networks. An automatic discovery of such structure is a fundamental task in many disciplines, including sociology, biology, engineering, and computer science. Recently, several community discovery algorithms have been proposed based on the optimization of a quantity called modularity (Q). However, the problem of modularity optimization is NP-hard, and the existing approaches often suffer from prohibitively long running time or poor quality. Furthermore, it has been recently pointed out that algorithms based on optimizing Q will have a resolution limit, i.e., communities below a certain scale may not be detected. In this research, we first propose an efficient heuristic algorithm, Qcut, which combines spectral graph partitioning and local search to optimize Q. Using both synthetic and real networks, we show that Qcut can find higher modularities and is more scalable than the existing algorithms. Furthermore, using Qcut as an essential component, we propose a recursive algorithm, HQcut, to solve the resolution limit problem. We show that HQcut can successfully detect communities at a much finer scale and with a higher accuracy than the existing algorithms. Finally, we apply Qcut and HQcut to study a protein-protein interaction network, and show that the combination of the two algorithms can reveal interesting biological results that may be otherwise undetectable.Comment: 14 pages, 5 figures. 1 supplemental file at http://cic.cs.wustl.edu/qcut/supplemental.pd

HTGR Unit Fuel Pebble k-infinity Results Using Chord Length Sampling

There is considerable interest in transport models that will permit the simulation of neutral particle transport through stochastic mixtures. Chord length sampling techniques that simulate particle transport through binary stochastic mixtures consisting of spheres randomly arranged in a matrix have been implemented in several Monte Carlo Codes [1-3]. Though the use of these methods is growing, the accuracy and efficiency of these methods has not yet been thoroughly demonstrated for an application of particular interest--a high temperature gas reactor fuel pebble element. This paper presents comparison results of k-infinity calculations performed on a LEUPRO-1 pebble cell. Results are generated using a chord length sampling method implemented in a test version of MCNP [3]. This Limited Chord Length Sampling (LCLS) method eliminates the need to model the details of the micro-heterogeneity of the pebble. Results are also computed for an explicit pebble model where the TRISO fuel particles within the pebble are randomly distributed. Finally, the heterogeneous matrix region of the pebble cell is homogenized based simply on volume fractions. These three results are compared to results reported by Johnson et al [4], and duplicated here, using a cubic lattice representation of the TRISO fuel particles. Figures of Merit for the four k-infinity calculations are compared to judge relative efficiencies

Complex networks: new trends for the analysis of brain connectivity

Today, the human brain can be studied as a whole. Electroencephalography, magnetoencephalography, or functional magnetic resonance imaging techniques provide functional connectivity patterns between different brain areas, and during different pathological and cognitive neuro-dynamical states. In this Tutorial we review novel complex networks approaches to unveil how brain networks can efficiently manage local processing and global integration for the transfer of information, while being at the same time capable of adapting to satisfy changing neural demands.Comment: Tutorial paper to appear in the Int. J. Bif. Chao

Detection of Complex Networks Modularity by Dynamical Clustering

Based on cluster de-synchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and real-world networks whose modular structure is already known or has been studied by means of other methods. The algorithm attains a high level of precision, especially when the modular units are very mixed and hardly detectable by the other methods, with a computational effort ${\cal O}(KN)$ on a generic graph with $N$ nodes and $K$ links.Comment: 5 pages, 2 figures. Version accepted for publication on PRE Rapid Communications: figures changed and text adde

Neutron time-of-flight measurements at the Rensselaer linac

Neutron transmission measurements of Ho, Er, Tm and Au samples have been made from thermal to several hundred eV and the data have been fitted with the SAMMY program. A 16-section NaI multiplicity detector has been used to measure simultaneously capture and scattering partial cross sections. These measurements are used to obtain accurate resonance parameters over this energy range for samples of Mo, Ho, Er, Tm and Au