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      Persistent homology of time-dependent functional networks constructed from coupled time series

      1 , 1 , 1 , 2 , 3

      Chaos: An Interdisciplinary Journal of Nonlinear Science

      AIP Publishing

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          Most cited references 53

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          From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators

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            Network modelling methods for FMRI.

            There is great interest in estimating brain "networks" from FMRI data. This is often attempted by identifying a set of functional "nodes" (e.g., spatial ROIs or ICA maps) and then conducting a connectivity analysis between the nodes, based on the FMRI timeseries associated with the nodes. Analysis methods range from very simple measures that consider just two nodes at a time (e.g., correlation between two nodes' timeseries) to sophisticated approaches that consider all nodes simultaneously and estimate one global network model (e.g., Bayes net models). Many different methods are being used in the literature, but almost none has been carefully validated or compared for use on FMRI timeseries data. In this work we generate rich, realistic simulated FMRI data for a wide range of underlying networks, experimental protocols and problematic confounds in the data, in order to compare different connectivity estimation approaches. Our results show that in general correlation-based approaches can be quite successful, methods based on higher-order statistics are less sensitive, and lag-based approaches perform very poorly. More specifically: there are several methods that can give high sensitivity to network connection detection on good quality FMRI data, in particular, partial correlation, regularised inverse covariance estimation and several Bayes net methods; however, accurate estimation of connection directionality is more difficult to achieve, though Patel's τ can be reasonably successful. With respect to the various confounds added to the data, the most striking result was that the use of functionally inaccurate ROIs (when defining the network nodes and extracting their associated timeseries) is extremely damaging to network estimation; hence, results derived from inappropriate ROI definition (such as via structural atlases) should be regarded with great caution. Copyright © 2010 Elsevier Inc. All rights reserved.
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              Is Open Access

              Synchronization in complex networks

              Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.
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                Author and article information

                Journal
                Chaos: An Interdisciplinary Journal of Nonlinear Science
                Chaos
                AIP Publishing
                1054-1500
                1089-7682
                April 2017
                April 2017
                : 27
                : 4
                : 047410
                Affiliations
                [1 ]Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
                [2 ]Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095, USA
                [3 ]CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, United Kingdom
                Article
                10.1063/1.4978997
                © 2017
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