{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T16:47:23Z","timestamp":1762015643976,"version":"build-2065373602"},"reference-count":52,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,3,16]],"date-time":"2021-03-16T00:00:00Z","timestamp":1615852800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The study of functional connectivity from magnetoecenphalographic (MEG) data consists of quantifying the statistical dependencies among time series describing the activity of different neural sources from the magnetic field recorded outside the scalp. This problem can be addressed by utilizing connectivity measures whose computation in the frequency domain often relies on the evaluation of the cross-power spectrum of the neural time series estimated by solving the MEG inverse problem. Recent studies have focused on the optimal determination of the cross-power spectrum in the framework of regularization theory for ill-posed inverse problems, providing indications that, rather surprisingly, the regularization process that leads to the optimal estimate of the neural activity does not lead to the optimal estimate of the corresponding functional connectivity. Along these lines, the present paper utilizes synthetic time series simulating the neural activity recorded by an MEG device to show that the regularization of the cross-power spectrum is significantly correlated with the signal-to-noise ratio of the measurements and that, as a consequence, this regularization correspondingly depends on the spectral complexity of the neural activity.<\/jats:p>","DOI":"10.3390\/axioms10010035","type":"journal-article","created":{"date-parts":[[2021,3,16]],"date-time":"2021-03-16T12:04:00Z","timestamp":1615896240000},"page":"35","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["The Role of Spectral Complexity in Connectivity Estimation"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4247-6192","authenticated-orcid":false,"given":"Elisabetta","family":"Vallarino","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Genova, via Dodecaneso 35, 16146 Genova, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3457-6780","authenticated-orcid":false,"given":"Alberto","family":"Sorrentino","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Genova, via Dodecaneso 35, 16146 Genova, Italy"},{"name":"CNR\u2013SPIN, Corso Ferdinando Maria Perrone 24, 16152 Genova, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1700-991X","authenticated-orcid":false,"given":"Michele","family":"Piana","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Genova, via Dodecaneso 35, 16146 Genova, Italy"},{"name":"CNR\u2013SPIN, Corso Ferdinando Maria Perrone 24, 16152 Genova, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1835-9399","authenticated-orcid":false,"given":"Sara","family":"Sommariva","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Genova, via Dodecaneso 35, 16146 Genova, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1103\/RevModPhys.65.413","article-title":"Magnetoencephalography\u2014theory, instrumentation, and applications to noninvasive studies of the working human brain","volume":"65","author":"Hari","year":"1993","journal-title":"Rev. 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