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  • 1Harbin Institute of Technology, Shenzhen, 518055 Guangdong, China.

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Summary
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This study introduces a new method to convert multivariate time series into multilayer networks, preserving data geometry. This approach helps identify dynamical transitions and measure information flow using interlayer entropy, equivalent to transfer entropy.

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Area of Science:

  • Complex systems analysis
  • Network science
  • Time series analysis

Background:

  • Transformations from time series to complex networks offer new insights into system dynamics.
  • Investigating complex systems often requires novel analytical perspectives.

Purpose of the Study:

  • To present a novel transformation from multivariate time series to multilayer networks for reciprocal characterization.
  • To ensure the preservation of underlying geometrical features of time series in their network representations.
  • To introduce and validate a new metric, interlayer entropy, for quantifying information flow and coupling strength in multilayer networks.

Main Methods:

  • Developed a transformation method mapping multivariate time series to multilayer networks.
  • Utilized network structure statistics to identify dynamical transitions in time series.
  • Defined and applied interlayer entropy to measure coupling strength between network layers.
  • Proved the equivalence of interlayer entropy and transfer entropy under specific conditions.

Main Results:

  • The proposed transformation preserves essential geometrical features of time series in the resulting multilayer networks.
  • Dynamical transitions within time series can be effectively identified through the analysis of network structural statistics.
  • Interlayer entropy is demonstrated to be a robust measure of coupling strength between network layers.
  • The study establishes the equivalence between interlayer entropy and transfer entropy for information flow measurement.

Conclusions:

  • The transformation from time series to multilayer networks provides a powerful tool for complex systems analysis.
  • Interlayer entropy offers a novel and effective method for quantifying information flow and interlayer coupling in multilayer networks.
  • This work bridges network science and time series analysis, offering complementary perspectives for understanding complex system dynamics.