Dynamical ergodicity DDA reveals causal structure in time series.

Area of Science:

• Neuroscience
• Complex Systems Analysis
• Nonlinear Dynamics

Background:

• Assessing synchronization, causality, and dynamical similarity in complex nonlinear systems, such as the brain, is difficult.
• Existing causality measures often fail for interdependent systems, limiting our understanding of brain interactions.
• The relationship between synchronization, causality, and dynamical similarity is obscured by the unknown deterministic structure of dynamical systems.

Purpose of the Study:

• To introduce a novel approach for assessing dynamical similarity and estimating causal interactions in time series data.
• To address the limitations of traditional causality measures in interdependent or synchronized systems.
• To apply the new methodology to both simulated and real-world neurological data.

Main Methods:

• Introduction of 'dynamical ergodicity' as a measure of dynamical similarity between time series.
• Combination of dynamical ergodicity with cross-dynamical delay differential analysis to estimate causal interactions.
• Validation using simulated data from coupled Rössler systems with known ground truth.
• Application to intracranial electroencephalographic (iEEG) data from epilepsy patients.

Main Results:

• The novel approach successfully assessed dynamical similarity and estimated causal interactions in simulated data.
• Distinct dynamical states were identified in the iEEG data of epilepsy patients.
• These identified dynamical states demonstrated high predictive power for epileptic seizures.

Conclusions:

• The proposed method, combining dynamical ergodicity and cross-dynamical delay differential analysis, offers a robust way to analyze complex systems.
• This approach provides new insights into brain dynamics and causal interactions.
• The findings suggest potential for improved seizure prediction in epilepsy.