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K-operator for Modelling Neurodegeneration: Simulations, fMRI Application, Eigenvalue Analysis and Recurrence Plots.

Sofia Fazio1, Patrizia Ribino2, Francesca Gasparini3,4

  • 1Dipartimento di Fisica, Università Statale di Milano, Milano, Italy.

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|October 27, 2025
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Summary

This study models neurological disease progression using a physics-inspired operator K. We explore its matrix formulation to build predictive models for neurodegenerative diseases with machine learning.

Keywords:
K-operatorAlzheimer-Perusini’s disease progressionFunctional networkParkinsonpredictive models

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Area of Science:

  • Neuroscience
  • Mathematical Physics
  • Computational Biology

Background:

  • Neurological diseases cause brain network damage.
  • Physics-inspired mathematical models can represent this damage.

Purpose of the Study:

  • To develop a matrix formulation for the operator K, modeling brain damage.
  • To establish a framework for predictive models of neurodegenerative disease progression.
  • To integrate novel brain damage representations with machine learning.

Main Methods:

  • Exploration of the matrix formulation of operator K.
  • Analysis of eigenvalues and eigenvectors of K.
  • Heuristic considerations on approximation techniques for K.
  • Application of a case study with real-world data.

Main Results:

  • A foundational framework for modeling neurological disease progression is proposed.
  • The study analyzes the mathematical properties of the operator K.
  • Initial validation through a real-world data case study.

Conclusions:

  • The matrix formulation of operator K offers a novel approach to model brain damage.
  • This framework supports the development of advanced predictive models for neurodegenerative diseases.
  • Integration with machine learning is key for future advancements.