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Meas."],"published-print":{"date-parts":[[2022,8,31]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    <jats:italic>Objective.<\/jats:italic>\n                    In this work, an analytical framework for the multiscale analysis of multivariate Gaussian processes is presented, whereby the computation of Partial Information Decomposition measures is achieved accounting for the simultaneous presence of short-term dynamics and long-range correlations.\n                    <jats:italic>Approach.<\/jats:italic>\n                    We consider physiological time series mapping the activity of the cardiac, vascular and respiratory systems in the field of Network Physiology. In this context, the multiscale representation of transfer entropy within the network of interactions among Systolic arterial pressure (S), respiration (R) and heart period (H), as well as the decomposition into unique, redundant and synergistic contributions, is obtained using a Vector AutoRegressive Fractionally Integrated (VARFI) framework for Gaussian processes. This novel approach allows to quantify the directed information flow accounting for the simultaneous presence of short-term dynamics and long-range correlations among the analyzed processes. Additionally, it provides analytical expressions for the computation of the information measures, by exploiting the theory of state space models. The approach is first illustrated in simulated VARFI processes and then applied to H, S and R time series measured in healthy subjects monitored at rest and during mental and postural stress.\n                    <jats:italic>Main Results.<\/jats:italic>\n                    We demonstrate the ability of the VARFI modeling approach to account for the coexistence of short-term and long-range correlations in the study of multivariate processes. Physiologically, we show that postural stress induces larger redundant and synergistic effects from S and R to H at short time scales, while mental stress induces larger information transfer from S to H at longer time scales, thus evidencing the different nature of the two stressors.\n                    <jats:italic>Significance.<\/jats:italic>\n                    The proposed methodology allows to extract useful information about the dependence of the information transfer on the balance between short-term and long-range correlations in coupled dynamical systems, which cannot be observed using standard methods that do not consider long-range correlations.\n                  <\/jats:p>","DOI":"10.1088\/1361-6579\/ac826c","type":"journal-article","created":{"date-parts":[[2022,7,19]],"date-time":"2022-07-19T18:26:58Z","timestamp":1658255218000},"page":"085004","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":14,"title":["Multiscale partial information decomposition of dynamic processes with short and long-range correlations: theory and application to cardiovascular control"],"prefix":"10.1088","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0455-6466","authenticated-orcid":true,"given":"H\u00e9lder","family":"Pinto","sequence":"first","affiliation":[{"name":"Universidade do Porto"},{"name":"Centro de Matem\u00e1tica da Universidade do Porto (CMUP)"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9992-3221","authenticated-orcid":true,"given":"Riccardo","family":"Pernice","sequence":"additional","affiliation":[{"name":"University of Palermo"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2972-2050","authenticated-orcid":false,"given":"Maria","family":"Eduarda Silva","sequence":"additional","affiliation":[{"name":"Universidade do Porto"},{"name":"LIAAD-INESC TEC, Porto,"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7562-5193","authenticated-orcid":false,"given":"Michal","family":"Javorka","sequence":"additional","affiliation":[{"name":"Comenius University of Bratislava"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3271-5348","authenticated-orcid":true,"given":"Luca","family":"Faes","sequence":"additional","affiliation":[{"name":"University of Palermo"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3218-7001","authenticated-orcid":true,"given":"Ana Paula","family":"Rocha","sequence":"additional","affiliation":[{"name":"Universidade do Porto"},{"name":"Centro de Matem\u00e1tica da Universidade do Porto (CMUP)"}]}],"member":"266","published-online":{"date-parts":[[2022,8,12]]},"reference":[{"key":"pmeaac826cbib1","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/978-3-319-58709-7","type":"book","article-title":"Arfima-Garch Modeling of HRV: Clinical Application in Acute Brain Injury","author":"Almeida","year":"2017"},{"key":"pmeaac826cbib2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/07474939108800194","type":"journal-article","article-title":"State space modeling of multiple time series","volume":"10","author":"Aoki","year":"1991","journal-title":"Econometric Reviews"},{"key":"pmeaac826cbib3","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1016\/0304-4076(95)01732-1","type":"journal-article","article-title":"Long memory processes and fractional integration in econometrics","volume":"73","author":"Baillie","year":"1996","journal-title":"Journal of Econometrics"},{"key":"pmeaac826cbib4","first-page":"579","type":"book","article-title":"Generators of long-range dependent processes: a survey","author":"Bardet","year":"2003"},{"key":"pmeaac826cbib5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.91.040101","type":"journal-article","article-title":"Granger causality for state-space models","volume":"91","author":"Barnett","year":"2015","journal-title":"Phys. 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