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Asymptotic scaling describing signal propagation in complex networks

Nature Physics volume 16, pages 1082–1083 (2020)Cite this article

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The Original Article was published on 02 November 2020

arising from C. Hens et al. Nature Physics https://doi.org/10.1038/s41567-018-0409-0 (2019)

The complex dynamics emergent in diverse systems are influenced not only by the network topologies but also by the interplay of these topologies with the dynamical mechanisms of interaction between nodes. Hens et al.1 established a general framework, novelly linking the universal topological features to the spatiotemporal propagation of signals in complex networks and analytically capturing the topological role in predicting local responses through the asymptotic scaling relationship. Although using an appropriate form of the asymptotic scaling can reveal universal characteristics in complex systems, it is likely to lead to biased or even incorrect predictions if the scaling form is not accurately estimated. It is possible, however, to achieve substantial improvements in the predictive power by including a suitable prefactor in the scaling.

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Fig. 1: Dynamic regimes of signal propagation for model \({\mathbb{M}}\) with the Epinions network.

References

  1. Hens, C., Harush, U., Haber, S., Cohen, R. & Barzel, B. Spatiotemporal signal propagation in complex networks. Nat. Phys. https://doi.org/10.1038/s41567-018-0409-0 (2019).

  2. Hens, C., Harush, U., Haber, S., Cohen, R. & Barzel, B. Reply to: Asymptotic scaling describing signal propagation in complex networks. Nat. Phys. https://doi.org/10.1038/s41567-020-1027-1 (2020).

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Acknowledgements

This work was supported by grants from National Key R&D Program of China (2018YFB0904500), Eastern Scholar, the National Natural Science Foundation of China (11925103, 11701096, 61932008, 62076071), STCSM (18DZ1201000, 2018SHZDZX01) and the Russian Ministery of Science and Education Agreement (N. 13.1902.21.0026). We thank Q. T. Hu for preliminary computations and D. Waxman for valuable discussions.

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Authors and Affiliations

  1. Institute of Science and Technology for Brain-inspired Intelligence and LCNBI, Fudan University, Shanghai, China

    Peng Ji & Wei Lin

  2. State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain Science, Institutes of Brain Science, Fudan University, Shanghai, China

    Peng Ji & Wei Lin

  3. Research Institute of Intelligent Complex Systems, Fudan University, Shanghai, China

    Peng Ji & Wei Lin

  4. School of Mathematical Sciences, SCMS and SCAM, Fudan University, Shanghai, China

    Wei Lin

  5. Potsdam Institute for Climate Impact Research (PIK), Potsdam, Germany

    Jürgen Kurths

  6. Nizhny Novgorod State University, Nizhny Novgorod, Russia

    Jürgen Kurths

  7. Saratov State University, Saratov, Russia

    Jürgen Kurths

Authors
  1. Peng Ji
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  2. Wei Lin
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  3. Jürgen Kurths
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Contributions

P.J. designed the research and contributed to the modelling. P.J., W.L. and J.K. contributed to the discussion and writing the paper.

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Correspondence to Peng Ji.

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Ji, P., Lin, W. & Kurths, J. Asymptotic scaling describing signal propagation in complex networks. Nat. Phys. 16, 1082–1083 (2020). https://doi.org/10.1038/s41567-020-1025-3

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