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Constructing minimal models for complex system dynamics

Nature Communications volume 6, Article number: 7186 (2015) | Download Citation

Abstract

One of the strengths of statistical physics is the ability to reduce macroscopic observations into microscopic models, offering a mechanistic description of a system’s dynamics. This paradigm, rooted in Boltzmann’s gas theory, has found applications from magnetic phenomena to subcellular processes and epidemic spreading. Yet, each of these advances were the result of decades of meticulous model building and validation, which are impossible to replicate in most complex biological, social or technological systems that lack accurate microscopic models. Here we develop a method to infer the microscopic dynamics of a complex system from observations of its response to external perturbations, allowing us to construct the most general class of nonlinear pairwise dynamics that are guaranteed to recover the observed behaviour. The result, which we test against both numerical and empirical data, is an effective dynamic model that can predict the system’s behaviour and provide crucial insights into its inner workings.

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Acknowledgements

This work was supported by the Templeton Foundation: Mathematical and Physical Sciences grant no. PFI-777; Army Research Laboratories (ARL) Network Science (NS) Collaborative Technology Alliance (CTA) grant: ARL NS-CTA W911NF-09-2-0053; European Union grant no. FP7 317532 (MULTIPLEX).

Author information

Affiliations

  1. Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel

    • Baruch Barzel
  2. Channing Division of Network Medicine, Brigham and Women’s Hospital, Harvard Medical School, Boston, Massachusetts 02115, USA

    • Yang-Yu Liu
  3. Center for Cancer Systems Biology, Dana-Farber Cancer Institute, Harvard Medical School, Boston, Massachusetts 02115, USA

    • Yang-Yu Liu
    •  & Albert-László Barabási
  4. Center for Complex Network Research and Departments of Physics, Computer Science and Biology, Northeastern University, Boston, Massachusetts 02115, USA

    • Albert-László Barabási
  5. Department of Medicine, Brigham and Women’s Hospital, Harvard Medical School, Boston, Massachusetts 02115, USA

    • Albert-László Barabási
  6. Center for Network Science, Central European University, Budapest 1052, Hungary

    • Albert-László Barabási

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Contributions

All authors designed the research and wrote the paper. B.B. analyzed the empirical data, and did the analytical and numerical calculations.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Yang-Yu Liu.

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DOI

https://doi.org/10.1038/ncomms8186

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