From visibility graphs to cognition.

Area of Science:

• Complex systems analysis
• Network theory
• Statistical physics
• Physiological signal processing

Background:

• The natural visibility graph method (NVGM) is popular for creating complex networks.
• Previous studies often overlooked non-ergodic conditions in dynamical systems, especially those with turbulent or crucial events.
• Fractional Gaussian noise (FGN) is a theoretical model for such signals.

Purpose of the Study:

• To apply NVGM to complex networks, considering non-ergodic conditions and turbulent events.
• To investigate the impact of meditation on physiological signals using diffusion entropy analysis (DEA) with stripes.
• To reconcile ergodicity breaking with linear response theory using a master equation approach (MEA).

Main Methods:

• Utilized the natural visibility graph method (NVGM) to construct complex networks.
• Employed diffusion entropy analysis (DEA) with stripes to identify fractional Gaussian noise (FGN).
• Applied a non-Markov master equation approach (MEA) to model ergodicity breaking.

Main Results:

• In the long-time limit ($2<\mu <3$), non-ergodic signals resemble FGN.
• Meditation significantly reduces the scaling parameter $\delta$ in sick patients, unlike in healthy individuals.
• NVGM generates homogeneous networks, and the analysis reveals distinct patterns between healthy and sick patients.

Conclusions:

• Sick patients' heartbeats may exhibit FGN characteristics, indicated by a significant reduction in scaling after applying stripes.
• Meditation's effect on scaling reduction requires further investigation, potentially linking quantum mechanics and physiological processes.
• The study highlights the importance of analyzing physiological signals post-meditation, especially concerning ergodicity breaking.