<?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>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332024000100001</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v31i1.53834</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Influencia en la detección de patrones de la solución del sistema no lineal en una transformada Shapelet discreta II]]></article-title>
<article-title xml:lang="en"><![CDATA[Influence on pattern detection for the solution of the nonlinear system on a discrete Shapelet transform II]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Valdés-Santiago]]></surname>
<given-names><![CDATA[Damián]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[León-Mecías]]></surname>
<given-names><![CDATA[Ángela M.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Díaz-Romañach]]></surname>
<given-names><![CDATA[Marta L. Baguer]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[González-Hidalgo]]></surname>
<given-names><![CDATA[Manuel]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Jaume-I-Capó]]></surname>
<given-names><![CDATA[Antoni]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de La Habana Facultad de Matemáticas y Computación ]]></institution>
<addr-line><![CDATA[ La Habana]]></addr-line>
<country>Cuba</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de La Habana Facultad de Matemáticas y Computación ]]></institution>
<addr-line><![CDATA[ La Habana]]></addr-line>
<country>Cuba</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad de La Habana Facultad de Matemáticas y Computación ]]></institution>
<addr-line><![CDATA[ La Habana]]></addr-line>
<country>Cuba</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad de las Islas Baleares  Departamento de Ciencias Matemáticas e Informática]]></institution>
<addr-line><![CDATA[Palma ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af5">
<institution><![CDATA[,Universidad de las Islas Baleares  Departamento de Ciencias Matemáticas e Informática]]></institution>
<addr-line><![CDATA[Palma ]]></addr-line>
<country>Spain</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2024</year>
</pub-date>
<volume>31</volume>
<numero>1</numero>
<fpage>1</fpage>
<lpage>25</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332024000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332024000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332024000100001&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen El uso de wavelets adaptadas para el reconocimiento de patrones es muy atractivo por la multiescalaridad de la transformada wavelet. Sin embargo, el buen desempeño de estos algoritmos en la detección de patrones depende fuertemente de la construcción de los filtros adaptados al patrón de interés. La Transformada Shapelet Discreta II (9) (DST-II) es un algoritmo inspirado en la transformada wavelet, que permite el diseño de filtros a la medida para la detección de patrones en señales unidimensionales. La construcción de estos filtros requiere la solución de un sistema de ecuaciones no lineales, que según (9) se puede efectuar mediante cualquier método iterativo. Esta investigación presenta un novedoso y exhaustivo estudio numérico que demuestra el impacto de la elección del método numérico adecuado para la solución del sistema no lineal en la DST-II. La eficacia de los filtros estimados repercute en el desempeño de esta transformada en la detección de patrones. Los mejores resultados se obtienen al combinar el método de Newton con preiteración mediante el algoritmo de continuación. La convergencia alcanzada para el 55, 37% de los patrones sugiere que la DST-II podría ser adecuada para patrones con formas específicas, de utilidad en aplicaciones sobre señales biomédicas.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The use of adapted wavelets for pattern recognition is very attractive because of the multiscalarity of the wavelet transform. However, the good performance of these algorithms in pattern detection strongly depends on the construction of the filters adapted to the pattern of interest. The Discrete Shapelet Transform II (9) (DST-II) is an algorithm inspired by the wavelet transform, which allows the design of tailored filters for pattern detection in one-dimensional signals. The construction of these filters requires the solution of a system of nonlinear equations, which according to (9) can be performed by any iterative method. This research presents a novel and comprehensive numerical study that demonstrates the impact of the choice of the appropriate numerical method for the solution of the nonlinear system in DST-II. The efficiency of the estimated filters has an impact on the performance of this transform in pattern detection. The best results are obtained by combining Newton&#8217;s method with preiteration using the continuation algorithm. The convergence achieved for 55,37% of the patterns suggests that DST-II could be suitable for patterns with specific shapes, useful in biomedical signal applications.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[diseño de filtros wavelet]]></kwd>
<kwd lng="es"><![CDATA[wavelet adaptada]]></kwd>
<kwd lng="es"><![CDATA[transformada shapelet discreta]]></kwd>
<kwd lng="es"><![CDATA[transformada wavelet discreta]]></kwd>
<kwd lng="en"><![CDATA[wavelet filter design]]></kwd>
<kwd lng="en"><![CDATA[matched wavelet]]></kwd>
<kwd lng="en"><![CDATA[discrete shapelet transform]]></kwd>
<kwd lng="en"><![CDATA[discrete wavelet transform.]]></kwd>
</kwd-group>
</article-meta>
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