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Quantifying Disorder in Data.

João Vitor Vieira Flauzino1,2,3,4, Thiago Lima Prado1,4, Norbert Marwan3,5,6

  • 1Federal University of Paraná, Department of Physics, 815 31-980 Curitiba, Brazil.

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|September 15, 2025
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Summary
This summary is machine-generated.

Quantifying data disorder is challenging. A new recurrence microstate analysis method reliably distinguishes chaotic, stochastic, and noisy signals, even in short time series, aiding scientific discovery.

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Area of Science:

  • Complex Systems Science
  • Data Analysis
  • Dynamical Systems Theory

Background:

  • Quantifying disorder in data is a persistent scientific challenge, especially with short datasets exhibiting complex behaviors.
  • Distinguishing between chaotic, stochastic, and noisy processes is difficult due to indistinguishable characteristics in data.
  • Existing methods struggle with short time series and identifying the nature of underlying processes.

Purpose of the Study:

  • To introduce a novel method for directly quantifying disorder in data using recurrence microstate analysis.
  • To develop a robust information entropy-based quantifier for differentiating signal types.
  • To apply the method to analyze paleoclimatic data and identify drivers of past climate transitions.

Main Methods:

  • Recurrence microstate analysis to quantify data disorder.
  • Leveraging information entropy to create a robust disorder quantifier.
  • Application to differentiate chaotic, correlated, and uncorrelated stochastic signals in small time series.
  • Analysis of paleoclimatic data to identify disorder minima correlating with Cenozoic era stage transitions.

Main Results:

  • The proposed method successfully quantifies disorder by maximizing recurrence microstates.
  • The information entropy-based quantifier reliably distinguishes between chaotic, correlated, and uncorrelated stochastic signals.
  • The method effectively characterizes corrupting noise in dynamical systems.
  • Disorder minima in paleoclimatic data align with known Cenozoic era stage transitions.

Conclusions:

  • Recurrence microstate analysis provides a robust framework for quantifying data disorder.
  • The developed quantifier offers a reliable tool for signal characterization, even with limited data.
  • The findings have implications for understanding dynamical systems, noise, and paleoclimatic change.