Rank of Hadamard powers of Euclidean distance matrices

Horvat, Boris; Jaklič, Gašper; Kavkler, Iztok; Randić, Milan

doi:10.1007/s10910-013-0291-z

Cited by 2 publications

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“…Hence, no single similarity table, be it the Clustal Omega approach, or the Four-color map approach, has claims to be "the solution" when it comes to similarity studies of biological objects. Clustal Omega approach 67 may have here an advantage because it compares bio-sequences that have been aligned. However, in view that the protein alignment problem and the related DNA alignment problems finally have been exactly solved using a very efficient algorithm, this open a novel direction in protein and DNA similarity studies.…”

Section: Resultsmentioning

confidence: 99%

On Map Representations of DNA

et al. 2013

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Abstract. We have constructed graphical (qualitative and visual) representations of DNA sequences as 2D maps and their numerical (quantitative and computational) analysis. The maps are obtained by transforming the four-letter sequences (where letters represent the four nucleic bases) via a spiral representation over triangular and square cells grids into a four-color map. The so constructed maps are then represented by distance matrices. We consider the use of several matrix invariants as DNA descriptors for determining the degree of similarity of a selection of DNA sequences.

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Section: Resultsmentioning

confidence: 99%

On Map Representations of DNA

et al. 2013

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“…In this paper we study completely positive factorizations of translations of Euclidean distance matrices corresponding to an arithmetic progression. Distance matrices have rich structural and spectral properties, and have been extensively studied in the literature [2,15,17]. Our work was particularly motivated by results on factorizations of distance matrices [14,21,22].…”

Section: Introductionmentioning

confidence: 99%

Completely positive factorizations associated with Euclidean distance matrices corresponding to an arithmetic progression

Bukovšek

Laffey

Šmigoc

2020

Linear Algebra and its Applications

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Euclidean distance matrices corresponding to an arithmetic progression have rich spectral and structural properties. We exploit those properties to develop completely positive factorizations of translations of those matrices. We show that the minimal translation that makes such a matrix positive semidefinite results in a completely positive matrix. We also discuss completely positive factorizations of such matrices over the integers. Methods developed in the paper can be used to find completely positive factorizations of other matrices with similar properties.

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Rank of Hadamard powers of Euclidean distance matrices

Cited by 2 publications

References 5 publications

On Map Representations of DNA

On Map Representations of DNA

Completely positive factorizations associated with Euclidean distance matrices corresponding to an arithmetic progression

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