Multidimensional scaling locus of memristor and fractional order elements
This paper combines the synergies of three mathematical and computational generalizations. The concepts of fractional calculus, memristor and information visualization extend the classical ideas of integro-differential calculus, electrical elements and data representation, respectively. The study em...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-09-01
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| Series: | Journal of Advanced Research |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090123220300047 |
| _version_ | 1818246973708304384 |
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| author | J.A. Tenreiro Machado António M. Lopes |
| author_facet | J.A. Tenreiro Machado António M. Lopes |
| author_sort | J.A. Tenreiro Machado |
| collection | DOAJ |
| description | This paper combines the synergies of three mathematical and computational generalizations. The concepts of fractional calculus, memristor and information visualization extend the classical ideas of integro-differential calculus, electrical elements and data representation, respectively. The study embeds these notions in a common framework, with the objective of organizing and describing the ''continuum'' of fractional order elements (FOE). Each FOE is characterized by its behavior, either in the time or in the frequency domains, and the differences between the FOE are captured by a variety of distinct indices, such as the Arccosine, Canberra, Jaccard and Sørensen distances. The dissimilarity information is processed by the multidimensional scaling (MDS) computational algorithm to unravel possible clusters and to allow a direct pattern visualization. The MDS yields 3-dimensional loci organized according to the FOE characteristics both for linear and nonlinear elements. The new representation generalizes the standard Cartesian 2-dimensional periodic table of elements. |
| first_indexed | 2024-12-12T14:57:19Z |
| format | Article |
| id | doaj.art-9dfaef6f425940d59900ecca7d9a9124 |
| institution | Directory Open Access Journal |
| issn | 2090-1232 |
| language | English |
| last_indexed | 2024-12-12T14:57:19Z |
| publishDate | 2020-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of Advanced Research |
| spelling | doaj.art-9dfaef6f425940d59900ecca7d9a91242022-12-22T00:20:53ZengElsevierJournal of Advanced Research2090-12322020-09-0125147157Multidimensional scaling locus of memristor and fractional order elementsJ.A. Tenreiro Machado0António M. Lopes1Institute of Engineering, Polytechnic of Porto, Dept. of Electrical Engineering, Porto, PortugalUISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, Porto, Portugal; Corresponding author.This paper combines the synergies of three mathematical and computational generalizations. The concepts of fractional calculus, memristor and information visualization extend the classical ideas of integro-differential calculus, electrical elements and data representation, respectively. The study embeds these notions in a common framework, with the objective of organizing and describing the ''continuum'' of fractional order elements (FOE). Each FOE is characterized by its behavior, either in the time or in the frequency domains, and the differences between the FOE are captured by a variety of distinct indices, such as the Arccosine, Canberra, Jaccard and Sørensen distances. The dissimilarity information is processed by the multidimensional scaling (MDS) computational algorithm to unravel possible clusters and to allow a direct pattern visualization. The MDS yields 3-dimensional loci organized according to the FOE characteristics both for linear and nonlinear elements. The new representation generalizes the standard Cartesian 2-dimensional periodic table of elements.http://www.sciencedirect.com/science/article/pii/S2090123220300047Fractional calculusMemristorInformation visualizationMultidimensional scalingProcrustes analysis |
| spellingShingle | J.A. Tenreiro Machado António M. Lopes Multidimensional scaling locus of memristor and fractional order elements Journal of Advanced Research Fractional calculus Memristor Information visualization Multidimensional scaling Procrustes analysis |
| title | Multidimensional scaling locus of memristor and fractional order elements |
| title_full | Multidimensional scaling locus of memristor and fractional order elements |
| title_fullStr | Multidimensional scaling locus of memristor and fractional order elements |
| title_full_unstemmed | Multidimensional scaling locus of memristor and fractional order elements |
| title_short | Multidimensional scaling locus of memristor and fractional order elements |
| title_sort | multidimensional scaling locus of memristor and fractional order elements |
| topic | Fractional calculus Memristor Information visualization Multidimensional scaling Procrustes analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2090123220300047 |
| work_keys_str_mv | AT jatenreiromachado multidimensionalscalinglocusofmemristorandfractionalorderelements AT antoniomlopes multidimensionalscalinglocusofmemristorandfractionalorderelements |