<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>2007-0705</journal-id>
<journal-title><![CDATA[Nova scientia]]></journal-title>
<abbrev-journal-title><![CDATA[Nova scientia]]></abbrev-journal-title>
<issn>2007-0705</issn>
<publisher>
<publisher-name><![CDATA[Universidad de La Salle Bajío A. C., Coordinación de Investigación]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2007-07052020000100011</article-id>
<article-id pub-id-type="doi">10.21640/ns.v12i24.2371</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Importance of the class of harmonic sources in the identification of sources in the inverse electroencephalographic problema]]></article-title>
<article-title xml:lang="es"><![CDATA[Importancia de la clase de fuentes armónicas en la identificación de fuentes en el problema inverso electroencefalográfico]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Mozqueda Lafarga]]></surname>
<given-names><![CDATA[Javier]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Fraguela Collar]]></surname>
<given-names><![CDATA[Andrés]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Soto Bajo]]></surname>
<given-names><![CDATA[Moisés]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Herrera Vega]]></surname>
<given-names><![CDATA[Javier]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Benemérita Universidad Autónoma de Puebla Facultad de Ciencias Físico Matemáticas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2020</year>
</pub-date>
<volume>12</volume>
<numero>24</numero>
<fpage>0</fpage>
<lpage>0</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2007-07052020000100011&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2007-07052020000100011&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2007-07052020000100011&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract  Introduction: In this work we discuss the relevance of the harmonic sources on the brain volume, which reproduce a given potential distribution on the scalp. These sources, apart from being a unicity class, they play a fundamental role in the resolution of the inverse problem of source identification with respect to any other sources class.  Method: We make use of the volume conductor model for the head, in order to relate sources and reproduced measurements. The problem is rewritten as an operational formulation which allows to characterize the admissible measurements with respect to any considered sources class.  Results: The admissible data set is characterized for the harmonic sources class on the brain volume. Also, the importance of this class in the context of the source estimation problem, with respect to any sources class, is shown. This is specifically illustrated considering the class of harmonic sources on a neighborhood of the cortex. Moreover, it is also shown the role the harmonic sources class on the brain plays when applying the Admissible Data Method (ADM) in order to get a general regularization scheme for the source estimation problem with respect to a unicity sources class.  Conclusion: A general resolution methodology for the source estimation problem in the context of the inverse electroencephalographic problem is proposed, in which the harmonic sources class on the brain volume is crucial. Namely, given an arbitrary sources unicity class (for this inverse problem), a general method is developed for identifying the source in this class whose reproduced potential distribution best approximates a given potential measurement on the scalp. We consider sources classes in connection with the electrical activity near the cortex.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen  Introducción: En este trabajo se estudiará la importancia de las fuentes armónicas en el volumen cerebral que reproducen una distribución de potencial en el cuero cabelludo determinada, las cuales además de ser clase de unicidad, tienen una importancia fundamental para la solución del problema inverso de identificación de fuentes en cualquier otra clase de fuentes, para reproducir la misma medición.  Método: Se propone el modelo de medio conductor para relacionar las mediciones con las fuentes que las reproducen. Se reduce el problema a un planteamiento operacional que nos permitirá caracterizar las llamadas mediciones admisibles con respecto a la clase de fuentes que se considere.  Resultados: Se caracteriza el conjunto de datos admisibles para la clase de fuentes armónicas en el volumen del cerebro y se ve la importancia de la clase de fuentes armónicas para la identificación de fuentes en otras clases de fuentes, lo cual se ejemplifica con la clase de fuentes armónicas en una vecindad de la corteza cerebral. También se muestra la importancia de la clase de fuentes armónicas en la aplicación del método de datos admisibles (MDA) a un esquema general de regularización para el problema de identificación de fuentes pertenecientes a clases de unicidad.  Conclusión: Se propone una metodología general de resolución del problema inverso electroencefalográfico de identificación de fuentes, haciendo uso de la clase de fuentes armónicas en el volumen cerebral. Dada una clase arbitraria  F de fuentes con la propiedad de unicidad para la solución del problema inverso, se desarrolla un método general para la identificación de la fuente en  F que mejor aproxima una medición del potencial sobre el cuero cabelludo.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[volume conductor model]]></kwd>
<kwd lng="en"><![CDATA[harmonic sources]]></kwd>
<kwd lng="en"><![CDATA[equivalent sources]]></kwd>
<kwd lng="en"><![CDATA[inverse electroencephalographic problema]]></kwd>
<kwd lng="en"><![CDATA[admissible data method]]></kwd>
<kwd lng="es"><![CDATA[modelo de medio conductor]]></kwd>
<kwd lng="es"><![CDATA[fuentes armónicas]]></kwd>
<kwd lng="es"><![CDATA[fuentes equivalentes]]></kwd>
<kwd lng="es"><![CDATA[problema inverso electroencefalográfico]]></kwd>
<kwd lng="es"><![CDATA[método de datos admisibles]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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