{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T09:51:01Z","timestamp":1773309061813,"version":"3.50.1"},"reference-count":62,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,6,30]],"date-time":"2023-06-30T00:00:00Z","timestamp":1688083200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Postgraduate Research &amp; Practice Innovation Program of Jiangsu Province","award":["KYCX19_0902"],"award-info":[{"award-number":["KYCX19_0902"]}]},{"name":"Postgraduate Research &amp; Practice Innovation Program of Jiangsu Province","award":["KYCX21_0743"],"award-info":[{"award-number":["KYCX21_0743"]}]},{"name":"Postgraduate Research &amp; Practice Innovation Program of Jiangsu Province","award":["KYCX22_0952"],"award-info":[{"award-number":["KYCX22_0952"]}]},{"name":"Postgraduate Research &amp; Practice Innovation Program of Jiangsu Province","award":["TK221003"],"award-info":[{"award-number":["TK221003"]}]},{"name":"Shandong Key Laboratory of Biophysics","award":["KYCX19_0902"],"award-info":[{"award-number":["KYCX19_0902"]}]},{"name":"Shandong Key Laboratory of Biophysics","award":["KYCX21_0743"],"award-info":[{"award-number":["KYCX21_0743"]}]},{"name":"Shandong Key Laboratory of Biophysics","award":["KYCX22_0952"],"award-info":[{"award-number":["KYCX22_0952"]}]},{"name":"Shandong Key Laboratory of Biophysics","award":["TK221003"],"award-info":[{"award-number":["TK221003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Network analysis is an important approach to explore complex brain structures under different pathological and physiological conditions. In this paper, we employ the multivariate inhomogeneous polynomial kernel Granger causality (MKGC) to construct directed weighted networks to characterize schizophrenia magnetoencephalography (MEG). We first generate data based on coupled autoregressive processes to test the effectiveness of MKGC in comparison with the bivariate linear Granger causality and bivariate inhomogeneous polynomial kernel Granger causality. The test results suggest that MKGC outperforms the other two methods. Based on these results, we apply MKGC to construct effective connectivity networks of MEG for patients with schizophrenia (SCZs). We measure three network features, i.e., strength, nonequilibrium, and complexity, to characterize schizophrenia MEG. Our results suggest that MEG of the healthy controls (HCs) has a denser effective connectivity network than that of SCZs. The most significant difference in the in-connectivity strength is observed in the right frontal network (p=0.001). The strongest out-connectivity strength for all subjects occurs in the temporal area, with the most significant between-group difference in the left occipital area (p=0.0018). The total connectivity strength of the frontal, temporal, and occipital areas of HCs exhibits higher values compared with SCZs. The nonequilibrium feature over the whole brain of SCZs is significantly higher than that of the HCs (p=0.012); however, the results of Shannon entropy suggest that healthy MEG networks have higher complexity than schizophrenia networks. Overall, MKGC provides a reliable approach to construct MEG brain networks and characterize the network characteristics.<\/jats:p>","DOI":"10.3390\/e25071006","type":"journal-article","created":{"date-parts":[[2023,6,30]],"date-time":"2023-06-30T00:43:30Z","timestamp":1688085810000},"page":"1006","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Schizophrenia MEG Network Analysis Based on Kernel Granger Causality"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9346-1126","authenticated-orcid":false,"given":"Qiong","family":"Wang","sequence":"first","affiliation":[{"name":"School of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"},{"name":"School of Physics and Information Engineering, Jiangsu Second Normal University, Nanjing 210013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7342-781X","authenticated-orcid":false,"given":"Wenpo","family":"Yao","sequence":"additional","affiliation":[{"name":"Smart Health Big Data Analysis and Location Services Engineering Research Center of Jiangsu Province, School of Geographic and Biologic Information, Nanjing University of Posts and Telecommunications, Nanjing 210023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1359-4819","authenticated-orcid":false,"given":"Dengxuan","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wanyi","family":"Yi","sequence":"additional","affiliation":[{"name":"School of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Yan","sequence":"additional","affiliation":[{"name":"Department of Psychiatry, Affiliated Nanjing Brain Hospital, Nanjing Medical University, Nanjing 210029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Wang","sequence":"additional","affiliation":[{"name":"Smart Health Big Data Analysis and Location Services Engineering Research Center of Jiangsu Province, School of Geographic and Biologic Information, Nanjing University of Posts and Telecommunications, Nanjing 210023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,30]]},"reference":[{"key":"ref_1","unstructured":"(2023, June 01). 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