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Counting All DCJ Sorting Scenarios
[chapter]

2009
*
Lecture Notes in Computer Science
*

Recently several works concerning the

doi:10.1007/978-3-642-04744-2_4
fatcat:3iqxdkbuibcufbc7jt3tc3z7ry
*DCJ*operation have been published, and in particular an algorithm was proposed to find an optimal*DCJ*sequence for*sorting*one genome into another one. ... Here we study the solution space of this problem and give an easy to compute formula that corresponds to the exact number of optimal*DCJ**sorting*sequences to a particular subset of instances of the problem ... In this model, the space of*all**sorting**scenarios*has been well characterized, allowing to group*sorting**scenarios*into classes of equivalence [2] . ...##
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Approximating the number of Double Cut-and-Join scenarios

2012
*
Theoretical Computer Science
*

A closed formula exists for

doi:10.1016/j.tcs.2012.03.006
fatcat:f3vn2cvcaranzocsfrntokurdi
*counting*the number of*DCJ**scenarios*between cotailed genomes, but no polynomial result has been published so far for arbitrary genomes. ... The MCMC can be used to quickly draw a sample of*DCJ**scenarios*from a prescribed distribution and test some hypotheses on genome evolution. ... In Section 4, we prove some partial results on*counting*the number of*DCJ**scenarios*. ...##
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Restricted DCJ-Indel Model Revisited
[chapter]

2013
*
Lecture Notes in Computer Science
*

We also present a simpler algorithm for computing an optimal restricted

doi:10.1007/978-3-319-02624-4_4
fatcat:wavtm5iu4vhtvfa6n4glejfhdu
*DCJ*-indel*sorting**scenario*in O(n log n) time. ... (BMC Bioinformatics 13, Suppl. 19, S14), but only an upper bound for the restricted*DCJ*-indel distance was provided. ... In Figure 1 we give examples of a general and a restricted*DCJ**sorting**scenarios*. ...##
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Genomic distance under gene substitutions

2011
*
BMC Bioinformatics
*

In these models, a deletion and a subsequent insertion that occur at the same position of the genome

doi:10.1186/1471-2105-12-s9-s8
pmid:22151231
pmcid:PMC3271670
fatcat:vic4mhkdcbgthli2llijakuzru
*count*for two*sorting*steps. ... A deletion and an insertion that occur at the same position of the genome can be modeled as a substitution,*counting*for a single*sorting*step. ...*scenario*with*DCJ*operations and indels. ...##
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Rearrangement Problems with Duplicated Genomic Markers
[article]

2014
*
arXiv
*
pre-print

Distances formulae as well as

arXiv:1410.5415v1
fatcat:t3slxmig65a6rihwxgvp66xqlu
*scenario*computing algorithms were established, along with their complexity proofs. ... This means that there exists a BI halving*scenario*S such that*all*BI operations in S, possibly excluding the last one, are equivalent to two successive*sorting**DCJ*operations. ... Moreover,*all*BI operations, possibly excluding the last one, are computed as pairs of compatible intervals, ie. pairs of*sorting**DCJ*operations, which ensures that the length of the*scenario*is n−C 2 ...##
###
The Problem of Chromosome Reincorporation in DCJ Sorting and Halving
[chapter]

2010
*
Lecture Notes in Computer Science
*

We study two problems in the double cut and join (

doi:10.1007/978-3-642-16181-0_2
fatcat:5wbkuahcdfaobebjqdzspvbiqy
*DCJ*) model:*sorting*-transforming one multilinear genome into another and halving -transforming a duplicated genome into a perfectly duplicated one. ... The*DCJ*model includes rearrangement operations such as reversals, translocations, fusions and fissions. ...*DCJ*distance and*scenarios*. A sequence of k*DCJ*operations transforming a given genome Π into Γ is called a*DCJ**scenario*of length k. ...##
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Algebraic double cut and join -- A group-theoretic approach to the operator on multichromosomal genomes
[article]

2014
*
arXiv
*
pre-print

In this paper, we realize the

arXiv:1409.7146v1
fatcat:ofwu2mpjd5ggpeov26le2cfg6i
*DCJ*operator as a group action on the space of multichromosomal genomes. ... We study this group action, deriving some properties of the group and finding group-theoretic analogues for the key results in the*DCJ*theory. ...*Counting*the optimal*sorting**scenarios*To*sort*a permutation π a into π b means to transform π a into π b through a sequence of allowed operations (in this case the*DCJ*operation). ...##
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Algebraic double cut and join

2014
*
Journal of Mathematical Biology
*

In this paper, we realize the

doi:10.1007/s00285-014-0852-1
pmid:25502846
fatcat:jpwbv7ac5fbepoe4fwg36jlaai
*DCJ*operator as a group action on the space of multichromosomal genomes. ... We study this group action, deriving some properties of the group and finding group-theoretic analogues for the key results in the*DCJ*theory. ...*Counting*the optimal*sorting**scenarios*To*sort*a permutation π a into π b means to transform π a into π b through a sequence of allowed operations (in this case the*DCJ*operation). ...##
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Bayesian sampling of genomic rearrangement scenarios via double cut and join

2010
*
Bioinformatics
*

Indeed, in some special cases, the total number of

doi:10.1093/bioinformatics/btq574
pmid:21037244
fatcat:lpijw5nkmfgk3pih44i7awm2mm
*DCJ**sorting**scenarios*can be analytically calculated, and uniformly distributed random*DCJ**scenarios*can be drawn in polynomial running time, while the ... Results: We use the computational facilities of the*DCJ*model to draw a sampling of HP*scenarios*. It is based on a parallel MCMC method that cools down*DCJ**scenarios*to HP*scenarios*. ... distribution of*all*possible*scenarios*is also hard. ...##
###
Parking Functions, Labeled Trees and DCJ Sorting Scenarios
[chapter]

2009
*
Lecture Notes in Computer Science
*

Here we give an exact formula for the number of double-cut-and-join (

doi:10.1007/978-3-642-04744-2_3
fatcat:drh2dphvm5cftp5737d66achje
*DCJ*) rearrangement*scenarios*of co-tailed genomes. ... We also construct effective bijections between the set of*scenarios*that*sort*a cycle and well studied combinatorial objects such as parking functions and labeled trees. ... Since each cycle is*sorted*independently, the number of global*scenarios*is enumerated by*counting*the number of sequences that contains ℓ m occurrences of the symbol S m , for 1 ≤ m ≤ C, which is*counted*...##
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Combinatorial Structure of Genome Rearrangements Scenarios

2010
*
Journal of Computational Biology
*

Here we give an exact formula for the number of double-cut-and-join (

doi:10.1089/cmb.2010.0126
pmid:20874400
fatcat:lc6mxfoerbc25njdctjrqzglka
*DCJ*) rearrangement*scenarios*between two genomes. ... We also construct effective bijections between the set of*scenarios*that*sort*a component as well studied combinatorial objects such as parking functions, labeled trees and prüfer codes. ... In the sequel, parsimonious*sorting**scenarios*are simply referred to as*sorting**scenarios*.*Sorting*cycle and paths independently A*DCJ*operation is*sorting*if it lowers the distance by 1. ...##
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DCJ-RNA - double cut and join for RNA secondary structures

2017
*
BMC Bioinformatics
*

The results, which are based on real datasets, show that the algorithm is able to

doi:10.1186/s12859-017-1830-6
pmid:29072145
pmcid:PMC5657034
fatcat:yn6jvykgknhjlliyqgdo43ynzm
*count*the minimum number of rearrangement operations, as well as to report an optimum*scenario*that can increase the similarity ... Sequences can be different, but they*all*share the same structure and, therefore, the same functionality. ...*Sorting**scenario*One related issue is identifying a*sorting**scenario*for the given distance, which provides the operations themselves. ...##
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Rearrangement Models and Single-Cut Operations
[chapter]

2009
*
Lecture Notes in Computer Science
*

We show that for any optimal SCJ uni

doi:10.1007/978-3-642-04744-2_8
fatcat:v2negq2yjjespmwaifthtifmxq
*sorting**scenario*that creates a circular chromosome in an intermediate step, there exists a*sorting**scenario*of equal length without a circular chromosome. ... The*DCJ*model is a superset of*all*the other models in the cube, and is thus the most general. ...##
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Rearrangement Models and Single-Cut Operations

2010
*
Journal of Computational Biology
*

Among our results is that

doi:10.1089/cmb.2010.0091
pmid:20874405
fatcat:2isezqge4jb67o5cqn2tbnkybe
*sorting*in the HP model is equivalent to*sorting*in the reversal model when the initial and final genomes are linear unichromosomal. ... The*dcj*model is a superset of*all*the other models in the cube, and is thus the most general. ... Let A and B be two circular genomes, and let R be a*dcj*-*sorting*event on A. Then R 2*dcj*circ . Proof. ...##
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Sampling and counting genome rearrangement scenarios

2015
*
BMC Bioinformatics
*

Contribution: In this paper, we give a mini-review about the state-of-the-art of sampling and

doi:10.1186/1471-2105-16-s14-s6
pmid:26452124
pmcid:PMC4603625
fatcat:prugvnwdyffvtojt5l3m5lwwfm
*counting*rearrangement*scenarios*, focusing on the reversal,*DCJ*and SCJ models. ... Even for moderate size inputs, there are a tremendous number of optimal rearrangement*scenarios*, regardless what the model is and which specific question is to be answered. ... to calculate the number of most parsimonious*sorting**scenarios*between G 1 and G 2 . ...
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