Article
A small world of weak ties provides optimal global integration of selfsimilar modules in functional brain networks.
Levich Institute and Physics Department, City College of New York, New York, NY 10031, USA.
Proceedings of the National Academy of Sciences (Impact Factor: 9.81). 02/2012; 109(8):282530. DOI: 10.1073/pnas.1106612109 Source: PubMed

Article: IMDB Network Revisited: Unveiling Fractal and Modular Properties from a Typical SmallWorld Network.
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ABSTRACT: We study a subset of the movie collaboration network, http://www.imdb.com, where only adult movies are included. We show that there are many benefits in using such a network, which can serve as a prototype for studying social interactions. We find that the strength of links, i.e., how many times two actors have collaborated with each other, is an important factor that can significantly influence the network topology. We see that when we link all actors in the same movie with each other, the network becomes smallworld, lacking a proper modular structure. On the other hand, by imposing a threshold on the minimum number of links two actors should have to be in our studied subset, the network topology becomes naturally fractal. This occurs due to a large number of meaningless links, namely, links connecting actors that did not actually interact. We focus our analysis on the fractal and modular properties of this resulting network, and show that the renormalization group analysis can characterize the selfsimilar structure of these networks.PLoS ONE 08/2013; 8(6):e66443. · 3.53 Impact Factor 
Article: Linking human brain local activity fluctuations to structural and functional network architectures.
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ABSTRACT: Activity of cortical local neuronal populations fluctuates continuously, and a large proportion of these fluctuations are shared across populations of neurons. Here we seek organizational rules that link these two phenomena. Using neuronal activity, as identified by functional MRI (fMRI) and for a given voxel or brain region, we derive a single measure of full bandwidth brainoxygenationleveldependent (BOLD) fluctuations by calculating the slope, α, for the loglinear power spectrum. For the same voxel or region, we also measure the temporal coherence of its fluctuations to other voxels or regions, based on exceeding a given threshold, Θ, for zero lag correlation, establishing functional connectivity between pairs of neuronal populations. From resting state fMRI, we calculated wholebrain groupaveraged maps for α and for functional connectivity. Both maps showed similar spatial organization, with a correlation coefficient of 0.75 between the two parameters across all brain voxels, as well as variability with hodology. A computational model replicated the main results, suggesting that synaptic lowpass filtering can account for these interrelationships. We also investigated the relationship between α and structural connectivity, as determined by diffusion tensor imagingbased tractography. We observe that the correlation between α and connectivity depends on attentional state; specifically, α correlated more highly to structural connectivity during rest than while attending to a task. Overall, these results provide global rules for the dynamics between frequency characteristics of local brain activity and the architecture of underlying brain networks.NeuroImage 02/2013; · 6.25 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Clustering is typically measured by the ratio of triangles to all triples, open or closed. Generating clustered networks, and how clustering affects dynamics on networks, is reasonably well understood for certain classes of networks \cite{vmclust, karrerclust2010}, e.g., networks composed of lines and nonoverlapping triangles. In this paper we show that it is possible to generate networks which, despite having the same degree distribution and equal clustering, exhibit different higherorder structure, specifically, overlapping triangles and other orderfour (a closed network motif composed of four nodes) structures. To distinguish and quantify these additional structural features, we develop a new network metric capable of measuring orderfour structure which, when used alongside traditional network metrics, allows us to more accurately describe a network's topology. Three network generation algorithms are considered: a modified configuration model and two rewiring algorithms. By generating homogeneous networks with equal clustering we study and quantify their structural differences, and using SIS (SusceptibleInfectedSusceptible) and SIR (SusceptibleInfectedRecovered) dynamics we investigate computationally how differences in higherorder structure impact on epidemic threshold, final epidemic or prevalence levels and time evolution of epidemics. Our results suggest that characterising and measuring higherorder network structure is needed to advance our understanding of the impact of network topology on dynamics unfolding on the networks.Journal of Theoretical Biology 10/2013; · 2.35 Impact Factor
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