Sets of medians in the non-geodesic pseudometric space of unsigned genomes with breakpoints

Jamshidpey, Arash; Jamshidpey, Aryo; Sankoff, David

doi:10.1186/1471-2164-15-s6-s3

Cited by 8 publications

(15 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This construction produced a normalized sum of distances score of 2.25 instead of the median value of 2. (See reference [ 5 ] for a proof of the median value.) We then generalized this to k ≥ 3 input genomes, leading to better and better approximations to the median value of k − 1.…”

Section: Discussionmentioning

confidence: 99%

“…The value of the median as a prototype and as a component step for the construction of gene-order phylogenies has been undermined by simulations that show the median for a set of k ≥ 3 random input genomes tends, as genome length n increases, to coincide with any one of these k genomes themselves [ 3 , 5 ]. The median thus reflects no gene-order information from any of the other k − 1 genomes: the "medians in the corner" effect.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Near-medians that avoid the corners; a combinatorial probability approach

2014

Self Cite

View full text Add to dashboard Cite

BackgroundThe breakpoint median for a set of k ≥ 3 random genomes tends to approach (any) one of these genomes ("corners") as genome length increases, although there are diminishing proportion of medians equidistant from all k ("medians in the middle"). Algorithms are likely to miss the latter, and this has consequences for the general case where input genomes share some or many gene adjacencies, where the tendency for the median to be closer to one input genome may be an artifact of the corner tendency.ResultsWe present a simple sampling procedure for constructing a "near median" that represents a compromise among k random genomes and that has only a slightly greater breakpoint distance to all of them than the median does. We generalize to the realistic case where genomes share varying proportions of gene adjacencies. We present a supplementary sampling scheme that brings the constructed genome even closer to median status.ConclusionsOur approach is of particular use in the phylogenetic context where medians are repeatedly calculated at ancestral nodes, and where the corner effect prevents different parts of the phylogeny from communicating with each other.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Near-medians that avoid the corners; a combinatorial probability approach

2014

Self Cite

View full text Add to dashboard Cite

show abstract

“…They observed that as the size of permutations increases, the proportion of these medians far from the corners decreases. Jamshidpey et al [7] investigated this conjecture further and found a family of breakpoint median points using the new concept of accessible points. This concept may also help us to find a median far from corners.…”

Section: Introductionmentioning

confidence: 99%

“…

The notion of partial geodesic (or geodesic patch) was introduced by Jamshidpey et al in "Sets of medians in the non-geodesic pseudometric space of unsigned genomes with breakpoints" [7]. In this paper, we study the density of points on non-trivial partial geodesics between two permutations ξ (n) 1 and ξ (n) 2 * Partially supported by CNPq, FAPERJ and NSERC.

…”

mentioning

confidence: 99%

Partial geodesics on symmetric groups endowed with breakpoint distance

da Silva,

Jamshidpey,

Sankoff

2018

Preprint

Self Cite

View full text Add to dashboard Cite

The notion of partial geodesic (or geodesic patch) was introduced by Jamshidpey et al. in "Sets of medians in the non-geodesic pseudometric space of unsigned genomes with breakpoints" [7]. In this paper, we study the density of points on non-trivial partial geodesics between two permutations ξ (n) 1 and ξ (n) 2 * Partially supported by CNPq, FAPERJ and NSERC. DS holds the Canada Research Chair in Mathematical Genomics.

show abstract

“…For example, for k ≥3 random signed permutations of length n , and for d the “breakpoint distance”, the median tends to one or more of the given permutations as n increases [6–8]. …”

Section: Introductionmentioning

confidence: 99%

Compromise or optimize? The breakpoint anti-median

2016

Self Cite

View full text Add to dashboard Cite

BackgroundThe median of k≥3 genomes was originally defined to find a compromise genome indicative of a common ancestor. However, in gene order comparisons, the usual definitions based on minimizing the sum of distances to the input genomes lead to degenerate medians reflecting only one of the input genomes. “Near-medians”, consisting of equal samples of gene adjacencies from all the input genomes, were designed to restore the idea of compromise to the median problem.ResultWe explore adjacency sampling constructions in full generality in the case k=3, with given overlapping sets of adjacencies in the three genomes, where all adjacencies in two-way or three-way overlaps are included in the sample. We require the construction to be maximal, in the sense that no additional proportion of adjacencies from any of the genomes may be added without violating the local linearity of the genome. We discover that in incorporating as many adjacencies as possible, evenly from all the input genomes, we are actually maximizing, rather than minimizing, the sum of distances over all other maximal sampling schemes.ConclusionsWe propose to explore compromise instead of parsimony as the organizing principle for the small phylogeny problem.

show abstract

Sets of medians in the non-geodesic pseudometric space of unsigned genomes with breakpoints

Cited by 8 publications

References 6 publications

Near-medians that avoid the corners; a combinatorial probability approach

Near-medians that avoid the corners; a combinatorial probability approach

Partial geodesics on symmetric groups endowed with breakpoint distance

Compromise or optimize? The breakpoint anti-median

Contact Info

Product

Resources

About