{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:34:49Z","timestamp":1760060089799,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,1]],"date-time":"2025-08-01T00:00:00Z","timestamp":1754006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Italian Ministry of University and Research","award":["2022YMHNPY","P2022JAYMH"],"award-info":[{"award-number":["2022YMHNPY","P2022JAYMH"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Factor analysis is a well-known statistical method to describe the variability of observed variables in terms of a smaller number of unobserved latent variables called factors. Even though latent factors are conceptually independent of each other, their influence on the observed variables is often joint and synergistic. We propose to quantify the synergy of the joint influence of factors on the observed variables using O-information, a recently introduced metric to assess high-order dependencies in complex systems; in the proposed framework, latent factors and observed variables are jointly analyzed in terms of their joint informational character. Two case studies are reported: analyzing resting fMRI data, we find that DMN and FP networks show the highest synergy, consistent with their crucial role in higher cognitive functions; concerning HeLa cells, we find that the most synergistic gene is STK-12 (AURKB), suggesting that this gene is involved in controlling the HeLa cell cycle. We believe that our approach, representing a bridge between factor analysis and the field of high-order interactions, will find wide application across several domains.<\/jats:p>","DOI":"10.3390\/e27080820","type":"journal-article","created":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T15:09:53Z","timestamp":1754492993000},"page":"820","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Localizing Synergies of Hidden Factors in Complex Systems: Resting Brain Networks and HeLa GeneExpression Profile as Case Studies"],"prefix":"10.3390","volume":"27","author":[{"given":"Marlis","family":"Ontivero-Ortega","sequence":"first","affiliation":[{"name":"INFN, Sezione di Bari, Dipartimento Interateneo di Fisica, Universit\u00e0 degli Studi di Bari Aldo Moro, 70126 Bari, Italy"},{"name":"Cuban Center for Neuroscience, Havana 53-72637112, Cuba"}]},{"given":"Gorana","family":"Mijatovic","sequence":"additional","affiliation":[{"name":"Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3271-5348","authenticated-orcid":false,"given":"Luca","family":"Faes","sequence":"additional","affiliation":[{"name":"Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Serbia"},{"name":"Dipartimento di Ingegneria, Universit\u00e0 di Palermo, 90128 Palermo, Italy"}]},{"given":"Fernando E.","family":"Rosas","sequence":"additional","affiliation":[{"name":"Department of Informatics, Center for Consciousness Science, Sussex AI, University of Sussex, Brighton BN1 9RH, UK"},{"name":"Center for Psychedelic Research, Centre for Complexity Science, Department of Brain Science, Imperial College London, London SW7 2AZ, UK"},{"name":"Center for Eudaimonia and Human Flourishing, University of Oxford, Oxford OX1 2JD, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9803-0122","authenticated-orcid":false,"given":"Daniele","family":"Marinazzo","sequence":"additional","affiliation":[{"name":"Department of Data Analysis, Ghent University, 9000 Ghent, Belgium"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5873-8564","authenticated-orcid":false,"given":"Sebastiano","family":"Stramaglia","sequence":"additional","affiliation":[{"name":"INFN, Sezione di Bari, Dipartimento Interateneo di Fisica, Universit\u00e0 degli Studi di Bari Aldo Moro, 70126 Bari, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Everitt, S. 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