A coupled node-network dynamics with Koopman and Krankheit-operators

Area of Science:

• Computational neuroscience
• Network science
• Systems biology

Background:

• The brain's connectome represents neural pathways and signal exchange.
• Krankheit-operators (K-operators) model neurological disorders.
• Koopman operators describe neural dynamics via lifted linear representations.

Purpose of the Study:

• To propose a coupled node-network model for brain dynamics.
• To integrate K-operators with Koopman operators for modeling neurological disorders.
• To computationally approximate and validate the proposed model.

Main Methods:

• Developing a coupled node-network model where K-operator induces structural changes on the functional connectome.
• Injecting K-operator information into node-level Koopman operators.
• Implementing a computational approximation by imposing K-operator network dynamics on local Koopman operators.

Main Results:

• Demonstrated improved time-series reconstruction using the K-operator as a nonlinear correction.
• Showed a statistically significant effect of Krankheit-Koopman coupling.
• Validated the model's potential in capturing complex brain dynamics.

Conclusions:

• The coupled node-network model offers a novel framework for understanding brain dynamics and neurological disorders.
• Nonlinear correction via the K-operator enhances predictive accuracy in neural time-series reconstruction.
• Further research into Krankheit-Koopman coupling may reveal deeper insights into brain function and dysfunction.