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Here, we explore the matrix formulation of\n                    <jats:italic>K<\/jats:italic>\n                    , analysing eigenvalues and eigenvectors, with heuristic considerations on different techniques to approximate it. The primary objective of this paper is to lay the foundational groundwork for an innovative framework aimed at the development of predictive models regarding the progression of neurodegenerative diseases. This endeavour will leverage the potential of integrating these novel representations of brain damage with advanced machine-learning techniques. A case study based on real-world data is presented here to support the proposed modelling.\n                  <\/jats:p>","DOI":"10.1007\/s10916-025-02244-6","type":"journal-article","created":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T00:45:52Z","timestamp":1761525952000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["K-operator for Modelling Neurodegeneration: Simulations, fMRI Application, Eigenvalue Analysis and Recurrence Plots"],"prefix":"10.1007","volume":"49","author":[{"given":"Sofia","family":"Fazio","sequence":"first","affiliation":[]},{"given":"Patrizia","family":"Ribino","sequence":"additional","affiliation":[]},{"given":"Francesca","family":"Gasparini","sequence":"additional","affiliation":[]},{"given":"Norbert","family":"Marwan","sequence":"additional","affiliation":[]},{"given":"Peppino","family":"Fazio","sequence":"additional","affiliation":[]},{"given":"Marco","family":"Gherardi","sequence":"additional","affiliation":[]},{"given":"Maria","family":"Mannone","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,10,27]]},"reference":[{"key":"2244_CR1","doi-asserted-by":"publisher","unstructured":"Sandrone, S., Bacigaluppi, M., Galloni, M.R., Cappa, S.F., Moro, V., Catani, M., Filippi, M., Monti, M.M., Perani, D., Martino, G.: Weighing brain activity with the balance: Angelo Mosso\u2019s original manuscripts come to light. 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ADNI would grant the research team access to the data for download through their website (\n                      \n                      ). More details about the ADNI project and data acquisition, and sharing policies and protocol can be found at\n                      \n                      PPMI sites received approval from an ethical standards committee on human experimentation before study initiation and obtained written informed consent for research from all participants in the study as stated in [\n                      \n                      ].","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}},{"value":"The authors declare no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"144"}}