Using bundle embeddings to predict daily cortisol levels in human subjects.

Area of Science:

• * Dynamical systems analysis
• * Nonlinear time series analysis
• * Biological rhythms research

Background:

• * Biological variables often exhibit diurnal patterns, complicating data analysis.
• * Linear statistical methods may be inadequate for nonlinear biological dynamics.
• * Nonlinear lagged vector embeddings offer advanced analytical approaches.

Purpose of the Study:

• * To evaluate the efficacy of nonlinear lagged vector embeddings for analyzing diurnal biological data.
• * To compare sequentially weighted global linear maps (SMAP) and bundle embeddings for cortisol time series.
• * To assess the impact of time-of-day corrections on prediction accuracy.

Main Methods:

• * Collection of 126 consecutive urinary cortisol measurements from 10 participants (day and night).
• * Creation of lagged vector embeddings, including 'night,' 'day,' and time-of-day (TOD) corrected bundles.
• * Application of SMAP for predicting future cortisol values and comparison of global (linear) and local (nonlinear) predictions.

Main Results:

• * Night bundle embeddings provided the most accurate cortisol predictions, outperforming full and TOD-corrected embeddings.
• * Day bundle embeddings showed the poorest prediction accuracy.
• * Bundle embeddings indicated low dimensionality, suggesting processes within a single day, while day bundles had higher dimensions, implying longer processes or noise.

Conclusions:

• * The bundling approach effectively differentiates night and day cortisol patterns, surpassing conventional time-series methods.
• * Combining bundling with SMAP is beneficial for analyzing time-series data with periodic components.
• * This method enhances the understanding of diurnal variations in biological signals.