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In the present paper, employing a homogeneous spherical conductor serving as an approximation of the brain, we provide a criterion which determines whether the measured surface potential is evoked by a single or multiple localized neuronal excitations. We show that the uniqueness of the inverse problem for a single dipole is closely connected with attaining certain relations connecting the measured data. Further, we present the necessary and sufficient conditions which decide whether the collected data originates from a single dipole or from numerous dipoles. In the case where the EEG data arouses from multiple parallel dipoles, an isolation of the source is, in general, not possible.<\/jats:p>","DOI":"10.1155\/2014\/232747","type":"journal-article","created":{"date-parts":[[2014,11,23]],"date-time":"2014-11-23T16:00:32Z","timestamp":1416758432000},"page":"1-8","source":"Crossref","is-referenced-by-count":11,"title":["Localizing Brain Activity from Multiple Distinct Sources via EEG"],"prefix":"10.1155","volume":"2014","author":[{"given":"George","family":"Dassios","sequence":"first","affiliation":[{"name":"Division of Applied Mathematics, Department of Chemical Engineering, University of Patras and FORTH\/ICE-HT, 26504 Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7458-0886","authenticated-orcid":true,"given":"Michael","family":"Doschoris","sequence":"additional","affiliation":[{"name":"Division of Applied Mathematics, Department of Chemical Engineering, University of Patras and FORTH\/ICE-HT, 26504 Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Konstantia","family":"Satrazemi","sequence":"additional","affiliation":[{"name":"Division of Applied Mathematics, Department of Chemical Engineering, University of Patras and FORTH\/ICE-HT, 26504 Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1097\/01.wnp.0000220079.61973.6c"},{"key":"2","year":"1998"},{"key":"3","first-page":"40","volume-title":"Fundamentals of dipole source potentials","year":"1990"},{"key":"4","year":"2006"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1002\/hbm.20851"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2011.08.104"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1111\/j.1749-6632.1982.tb50789.x"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1109\/10.362917"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1109\/10.486287"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1186\/1743-0003-5-25"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.bspc.2014.01.009"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1155\/2009\/656092"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/25\/3\/035001"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1002\/mma.2508"},{"key":"15","series-title":"Lecture Notes in Mathematics","volume-title":"Electric & magnetic activity of the brain in spherica l and ellipsoidal geometry","year":"1983"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/BF02476917"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/232747.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/232747.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/232747.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,28]],"date-time":"2016-07-28T13:11:52Z","timestamp":1469711512000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/232747\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":16,"alternative-id":["232747","232747"],"URL":"https:\/\/doi.org\/10.1155\/2014\/232747","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}