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We developed a new method using permutation entropy to detect local mixing in time-series data. This technique helps identify the scale of mixing, crucial for accurate scientific measurements and data reporting.

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Area of Science:

  • Physical sciences
  • Data analysis
  • Information theory

Background:

  • Local mixing of data points is a common issue in physical experiments.
  • This mixing can arise from measurement apparatus or natural processes like diffusion.
  • Understudied effects of local mixing can impact data interpretation.

Purpose of the Study:

  • To propose a model-free technique for detecting local mixing in time-series data.
  • To quantify the scale at which data mixing occurs.
  • To provide a tool for scientists to set appropriate data measurement scales.

Main Methods:

  • Utilized permutation entropy, an information-theoretic technique.
  • Analyzed patterns by varying the temporal resolution of the calculation.
  • Validated the method on synthetic datasets and real-world experimental data.

Main Results:

  • Successfully detected local mixing in time-series data across various applications.
  • Quantified the scale of mixing, providing insights into data reliability.
  • Demonstrated the technique's effectiveness on chemistry experiments, methane records, and ice core data.

Conclusions:

  • Permutation entropy offers a robust, model-free approach to identify and scale local data mixing.
  • This method enhances the reliability of scientific data by informing measurement scale selection.
  • The technique is broadly applicable to diverse scientific fields dealing with time-series data.