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Related Concept Videos

Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

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Publisher's Note: "Modeling a neurological disorder as the result of an operator acting on the brain: A first sketch based on network channel modeling" [Chaos 34, 053133 (2024)].

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Related Experiment Video

Updated: Jul 14, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

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

Maria Mannone1,2,3,4

  • 1ICAR, National Research Council of Italy (CNR), Palermo, Italy.

Chaos (Woodbury, N.Y.)
|July 13, 2026
PubMed
Summary

This study introduces a coupled node-network model for brain dynamics, integrating the Krankheit-operator (K-operator) with Koopman operators. The model improves time-series reconstruction by using K-operator for nonlinear correction in neurological disorder modeling.

Related Experiment Videos

Last Updated: Jul 14, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

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.