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Model selection for identifying power-law scaling.

Robert Ton1, Andreas Daffertshofer2

  • 1MOVE Research Institute, Department of Human Movement Sciences, VU Amsterdam, The Netherlands; Center for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, Roc Boronat 138, Barcelona 08018, Spain.

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Summary
This summary is machine-generated.

This study introduces a new algorithm to quantify and test power-law scaling in neural activity, improving upon detrended fluctuation analysis (DFA). The method accurately identifies scale-free dynamics and their presence range in complex signals.

Keywords:
DFAModel selectionPower law

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Area of Science:

  • Neuroscience
  • Complex Systems Analysis
  • Statistical Physics

Background:

  • Long-range temporal and spatial correlations are frequently observed in biological and physical systems.
  • Power-law scaling in neural activity is of significant interest for understanding brain function.
  • Existing methods like Detrended Fluctuation Analysis (DFA) have limitations in accurately quantifying and comparing scaling behaviors.

Purpose of the Study:

  • To develop a robust algorithm for quantifying power-law scaling in time series data.
  • To provide a method for testing power-law scaling against alternative models using Bayesian model comparison.
  • To enhance the analysis of neural activity and other complex signals exhibiting long-range correlations.

Main Methods:

  • The algorithm builds upon Detrended Fluctuation Analysis (DFA) by analyzing mean squared fluctuations.
  • It approximates the distribution of mean squared fluctuations per interval, avoiding assumptions of normal distribution.
  • Log-likelihood is estimated as a function of interval size, enabling robust model comparison.

Main Results:

  • The algorithm's validity and robustness were demonstrated using simulated signals with known Hurst exponents.
  • It successfully distinguished power-law scaling from other fluctuation types, including exponentially correlated and neural mass models.
  • The method was also illustrated for analyzing encephalographic (EEG) signals, accounting for finite signal size effects.

Conclusions:

  • The developed algorithm offers a straightforward and reliable approach to quantify power-law scaling.
  • It provides a superior alternative to conventional DFA for analyzing complex temporal dynamics.
  • This method facilitates accurate identification and characterization of power-law scaling in various scientific domains, particularly neuroscience.