Early warning indicators via latent stochastic dynamical systems.

Area of Science:

• Complex Systems Science
• Dynamical Systems Theory
• Biomedical Data Analysis

Background:

• Abrupt dynamical transitions in complex systems pose risks in areas like brain diseases and natural disasters.
• Early detection of these transitions is crucial for timely intervention and mitigation.
• Existing methods often struggle with high-dimensional or latent dynamics.

Purpose of the Study:

• To develop a novel framework for detecting early warning indicators of abrupt dynamical transitions.
• To capture latent evolutionary dynamics in low-dimensional manifolds from high-dimensional data.
• To derive and validate effective warning signals for state transitions.

Main Methods:

• Developed a directed anisotropic diffusion map to uncover latent dynamics.
• Derived three warning signals: Onsager-Machlup, sample entropy, and transition probability indicators.
• Applied the framework to authentic electroencephalogram (EEG) data for validation.

Main Results:

• The proposed framework successfully identified tipping points during state transitions in EEG data.
• The derived early warning indicators demonstrated capability in detecting critical transition points.
• The methodology effectively bridges latent dynamics with real-world time-series data.

Conclusions:

• The novel framework provides effective early warning indicators for abrupt dynamical transitions.
• This approach shows potential for automatic labeling of complex high-dimensional time series.
• The findings have implications for predicting critical events in various complex systems, including neurological disorders.