6,471 research outputs found
A Rearrangement Distance for Fully-Labelled Trees
The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the widely studied setting of classical phylogenetics, where trees are leaf-labelled, tumoral trees are fully labelled, i.e., every vertex has a label.
In this paper we provide a rearrangement distance measure between two fully-labelled trees. This notion originates from two operations: one which modifies the topology of the tree, the other which permutes the labels of the vertices, hence leaving the topology unaffected. While we show that the distance between two trees in terms of each such operation alone can be decided in polynomial time, the more general notion of distance when both operations are allowed is NP-hard to decide. Despite this result, we show that it is fixed-parameter tractable, and we give a 4-approximation algorithm when one of the trees is binary
On Two Measures of Distance Between Fully-Labelled Trees
The last decade brought a significant increase in the amount of data and a variety of new inference methods for reconstructing the detailed evolutionary history of various cancers. This brings the need of designing efficient procedures for comparing rooted trees representing the evolution of mutations in tumor phylogenies. Bernardini et al. [CPM 2019] recently introduced a notion of the rearrangement distance for fully-labelled trees motivated by this necessity. This notion originates from two operations: one that permutes the labels of the nodes, the other that affects the topology of the tree. Each operation alone defines a distance that can be computed in polynomial time, while the actual rearrangement distance, that combines the two, was proven to be NP-hard.
We answer two open question left unanswered by the previous work. First, what is the complexity of computing the permutation distance? Second, is there a constant-factor approximation algorithm for estimating the rearrangement distance between two arbitrary trees? We answer the first one by showing, via a two-way reduction, that calculating the permutation distance between two trees on n nodes is equivalent, up to polylogarithmic factors, to finding the largest cardinality matching in a sparse bipartite graph. In particular, by plugging in the algorithm of Liu and Sidford [ArXiv 2020], we obtain an ??(n^{4/3+o(1}) time algorithm for computing the permutation distance between two trees on n nodes. Then we answer the second question positively, and design a linear-time constant-factor approximation algorithm that does not need any assumption on the trees
Regenerative tree growth: structural results and convergence
We introduce regenerative tree growth processes as consistent families of
random trees with n labelled leaves, n>=1, with a regenerative property at
branch points. This framework includes growth processes for exchangeably
labelled Markov branching trees, as well as non-exchangeable models such as the
alpha-theta model, the alpha-gamma model and all restricted exchangeable models
previously studied. Our main structural result is a representation of the
growth rule by a sigma-finite dislocation measure kappa on the set of
partitions of the natural numbers extending Bertoin's notion of exchangeable
dislocation measures from the setting of homogeneous fragmentations. We use
this representation to establish necessary and sufficient conditions on the
growth rule under which we can apply results by Haas and Miermont for
unlabelled and not necessarily consistent trees to establish self-similar
random trees and residual mass processes as scaling limits. While previous
studies exploited some form of exchangeability, our scaling limit results here
only require a regularity condition on the convergence of asymptotic
frequencies under kappa, in addition to a regular variation condition.Comment: 23 pages, new title, restructured, presentation improve
Synchronisation Properties of Trees in the Kuramoto Model
We consider the Kuramoto model of coupled oscillators, specifically the case
of tree networks, for which we prove a simple closed-form expression for the
critical coupling. For several classes of tree, and for both uniform and
Gaussian vertex frequency distributions, we provide tight closed form bounds
and empirical expressions for the expected value of the critical coupling. We
also provide several bounds on the expected value of the critical coupling for
all trees. Finally, we show that for a given set of vertex frequencies, there
is a rearrangement of oscillator frequencies for which the critical coupling is
bounded by the spread of frequencies.Comment: 21 pages, 19 Figure
Using F-structures in machine translation evaluation
Despite a growing interest in automatic evaluation methods for Machine Translation (MT) quality, most existing automatic metrics are still limited to surface comparison of translation and reference strings. In this paper we
show how Lexical-Functional Grammar (LFG) labelled dependencies obtained from an automatic parse can be used to assess the quality of MT on a deeper linguistic level, giving as a result higher correlations with human judgements
Limited Lifespan of Fragile Regions in Mammalian Evolution
An important question in genome evolution is whether there exist fragile
regions (rearrangement hotspots) where chromosomal rearrangements are happening
over and over again. Although nearly all recent studies supported the existence
of fragile regions in mammalian genomes, the most comprehensive phylogenomic
study of mammals (Ma et al. (2006) Genome Research 16, 1557-1565) raised some
doubts about their existence. We demonstrate that fragile regions are subject
to a "birth and death" process, implying that fragility has limited
evolutionary lifespan. This finding implies that fragile regions migrate to
different locations in different mammals, explaining why there exist only a few
chromosomal breakpoints shared between different lineages. The birth and death
of fragile regions phenomenon reinforces the hypothesis that rearrangements are
promoted by matching segmental duplications and suggests putative locations of
the currently active fragile regions in the human genome
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