Frequency Modulated Möbius Model Accurately Predicts Rhythmic Signals in Biological and Physical Sciences

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.