Two applications of the divide&amp;conquer principle in the molecular sciences

Brinkmann, Gunnar; Dress, Andreas; Perrey, Sören W.; Stoye, Jens

doi:10.1007/bf02614312

Cited by 3 publications

(4 citation statements)

References 32 publications

(30 reference statements)

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“…The methods that use recursive partitioning (i.e. splitting the initial task into various subtasks until they become simple enough to be easily solved) successfully address different kinds of intricate problems [ 109 – 111 ]. The combination of different techniques that are based on this principle (i.e.…”

Section: Discussionmentioning

confidence: 99%

Divide and conquer! Data-mining tools and sequential multivariate analysis to search for diagnostic morphological characters within a plant polyploid complex (Veronica subsect. Pentasepalae, Plantaginaceae)

et al. 2018

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This study exhaustively explores leaf features seeking diagnostic characters to aid the classification (assigning cases to groups, i.e. populations to taxa) in a polyploid plant-species complex. A challenging case study was selected: Veronica subsection Pentasepalae, a taxonomically intricate group. The “divide and conquer” approach was implemented—that is, a difficult primary dataset was split into more manageable subsets. Three techniques were explored: two data-mining tools (artificial neural networks and decision trees) and one unsupervised discriminant analysis. However, only the decision trees and discriminant analysis were finally used to select diagnostic traits. A previously established classification hypothesis based on other data sources was used as a starting point. A guided discriminant analysis (i.e. involving manual character selection) was used to produce a grouping scheme fitting this hypothesis so that it could be taken as a reference. Sequential unsupervised multivariate analysis enabled the recognition of all species and infraspecific taxa; however, a suboptimal classification rate was achieved. Decision trees resulted in better classification rates than unsupervised multivariate analysis, but three complete taxa were misidentified (not present in terminal nodes). The variable selection led to a different grouping scheme in the case of decision trees. The resulting groups displayed low misclassification rates when analyzed using artificial neural networks. The decision trees as well as the discriminant analysis are recommended in the search of diagnostic characters. Due to the high sensitivity that artificial neural networks have to the combination of input/output layers, they are proposed as evaluation tools for morphometric studies. The “divide and conquer” principle is a promising strategy, providing success in the present case study.

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Section: Discussionmentioning

confidence: 99%

Divide and conquer! Data-mining tools and sequential multivariate analysis to search for diagnostic morphological characters within a plant polyploid complex (Veronica subsect. Pentasepalae, Plantaginaceae)

et al. 2018

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“…It appears that the method of sequences described here may also be useful in any algorithm that enumerates polycyclic maps with mixed ring sizes. Similar sequences are used in a fast algorithm 5 for enumerating fullerenes (polyhedral cubic maps with 12 pentagonal faces and all others hexagonal). The task of filling the disk inside the circuit C by a planar graph which is a part of a fullerene map with C as the boundary circuit is called the PentHex Puzzle.…”

Section: Introductionmentioning

confidence: 99%

“…The task of filling the disk inside the circuit C by a planar graph which is a part of a fullerene map with C as the boundary circuit is called the PentHex Puzzle. 5 Several known codes that represent boundary circuits of planar maps are equivalent to our sequences (see ref 6 for a short review). For example, the sequence a 1 a 2 ...a k is equivalent to a zero-one code 0 a1 10 a2 1...0 ak 1, where 0 a is a sequence of a zeros 7 and if a ) 0, the sequence 0 a is empty.…”

Section: Introductionmentioning

confidence: 99%

“…Similar sequences are used in a fast algorithm 5 for enumerating fullerenes (polyhedral cubic maps with 12 pentagonal faces and all others hexagonal). The task of filling the disk inside the circuit C by a planar graph which is a part of a fullerene map with C as the boundary circuit is called the PentHex Puzzle . Several known codes that represent boundary circuits of planar maps are equivalent to our sequences (see ref for a short review).…”

Section: Introductionmentioning

confidence: 99%

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Allowed Boundary Sequences for Fused Polycyclic Patches and Related Algorithmic Problems

Deza

Fowler

Grishukhin

2001

J. Chem. Inf. Comput. Sci.

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We consider sequences that encode boundary circuits of fused polycycles made up of polygonal faces with p sides, p < or = 6. We give a constructive algorithm for recognizing such sequences when p = 5 or 6. A simpler algorithm is given for planar hexagonal sequences. Hexagonal and pentagonal sequences of length at most 8 are tabulated, the former corresponding to planar benzenoid hydrocarbons CxHy with y up to 14.

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DCA: An efficient implementation of the divide-and-conquer approach to simultaneous multiple sequence alignment

1997

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Two applications of the divide&conquer principle in the molecular sciences

Cited by 3 publications

References 32 publications

Divide and conquer! Data-mining tools and sequential multivariate analysis to search for diagnostic morphological characters within a plant polyploid complex (Veronica subsect. Pentasepalae, Plantaginaceae)

Divide and conquer! Data-mining tools and sequential multivariate analysis to search for diagnostic morphological characters within a plant polyploid complex (Veronica subsect. Pentasepalae, Plantaginaceae)

Allowed Boundary Sequences for Fused Polycyclic Patches and Related Algorithmic Problems

DCA: An efficient implementation of the divide-and-conquer approach to simultaneous multiple sequence alignment

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