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We developed a flexible Frequency Modulated Möbius (FMM) model for analyzing rhythmic patterns in complex data. This model accurately describes asymmetric oscillations found in biological and physical systems.

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Area of Science:

  • Physical Sciences
  • Biological Sciences
  • Data Analysis

Background:

  • Oscillatory systems commonly exhibit rhythmic patterns.
  • Standard sinusoidal models often fail to capture asymmetries present in real-world data.
  • There is a need for flexible models to analyze complex rhythmic phenomena.

Purpose of the Study:

  • To develop a novel parametric model, the Frequency Modulated Möbius (FMM) model.
  • To provide a flexible tool for describing and interpreting asymmetric rhythmic patterns in oscillatory systems.
  • To demonstrate the utility of the FMM model across diverse scientific applications.

Main Methods:

  • Developed the Frequency Modulated Möbius (FMM) model, a flexible parametric approach.
  • Applied the FMM model to analyze circadian clock gene expression data.
  • Utilized the FMM model for corticoptropin level data in depressed patients.
  • Employed the FMM model to study temporal light intensity patterns of distant stars.
  • Conducted analysis on synthetic data to validate model performance.

Main Results:

  • The FMM model accommodates asymmetries in sinusoidal shapes, offering greater flexibility than standard models.
  • Model parameters are easily estimated and interpretable for complex rhythmic data.
  • The FMM model demonstrated flexibility, scientific plausibility, and interpretability in all three applications.
  • Visual inspection and total mean squared error analysis confirmed excellent data fitting for the FMM model.

Conclusions:

  • The Frequency Modulated Möbius (FMM) model is a robust and versatile tool for analyzing rhythmic patterns in oscillatory systems.
  • The FMM model provides a scientifically plausible and interpretable approach for complex biological and physical data.
  • An R language software package is available for implementing the FMM model, facilitating its application in research.