Related papers: Perfect Reconstruction of Oncogenetic Trees
An inductive theorem proving method for constrained term rewriting systems, which is based on rewriting induction, needs a decision procedure for reduction-completeness of constrained terms. In addition, the sufficient complete property of…
One of the goals of phylogenetic research is to find the species tree describing the evolutionary history of a set of species. But the trees derived from geneti data with the help of tree inference methods are gene trees that need not…
Repetitions within a given genealogical tree provides some information about the degree of consanguineity of a population. They can be analyzed with techniques usually employed in statistical physics when dealing with fixed point…
In order to construct a representation of the tangle category one needs an enhanced R-matrix. In this paper we define a sufficient and necessary condition for enhancement that can be checked easily for any R-matrix. If the R-matrix can be…
We show that every polycube tree can be unfolded with a 4x4 refinement of the grid faces. This is the first constant refinement unfolding result for polycube trees that are not required to be well-separated.
Phylogenetic networks generalize phylogenetic trees by allowing the modelization of events of reticulate evolution. Among the different kinds of phylogenetic networks that have been proposed in the literature, the subclass of binary…
Gene tree/species tree reconciliation is a recent decisive progress in phylo-genetic methods, accounting for the possible differences between gene histories and species histories. Reconciliation consists in explaining these differences by…
We describe a method that will reconstruct an unrooted binary phylogenetic level-1 network on n taxa from the set of all quartets containing a certain fixed taxon, in O(n^3) time. We also present a more general method which can handle more…
Recovering a tree that represents the evolutionary history of a group of species is a key task in phylogenetics. Performing this task using sequence data from multiple genetic markers poses two key challenges. The first is the discordance…
In a reconfiguration problem, given a problem and two feasible solutions of the problem, the task is to find a sequence of transformations to reach from one solution to the other such that every intermediate state is also a feasible…
We give a precise description of combed trees in terms of Kelly-Mac Lane graphs. We show that any combed tree is uniquely expressed as an allowable Kelly-Mac Lane graph of a certain shape. Conversely, we show that any such Kelly-Mac Lane…
We provide a fundamental result for bucket increasing trees, which gives a complete characterization of all families of bucket increasing trees that can be generated by a tree evolution process. We also provide several equivalent…
Phylogenies depicting the evolutionary history of genetically heterogeneous subpopulations of cells from the same cancer, i.e., cancer phylogenies, offer valuable insights about cancer development and guide treatment strategies. Many…
Motivation: Millions of genes in the modern species belong to only thousands of `gene families'. A gene family includes instances of the same gene in different species (orthologs) and duplicate genes in the same species (paralogs). Genes…
We give in this article necessary and sufficient conditions on the topology of rationally and polynomially convex domains.
The reconstruction of a species phylogeny from genomic data faces two significant hurdles: 1) the trees describing the evolution of each individual gene--i.e., the gene trees--may differ from the species phylogeny and 2) the molecular…
This paper concerns the reconstruction of possibly complex-valued coefficients in a second-order scalar elliptic equation posed on a bounded domain from knowledge of several solutions of that equation. We show that for a sufficiently large…
Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data is generated by a mixture model has stimulated considerable recent…
We consider the phylogenetic tree reconstruction problem with insertions and deletions (indels). Phylogenetic algorithms proceed under a model where sequences evolve down the model tree, and given sequences at the leaves, the problem is to…
The aim of this article is to show the existence, and also give an explicit construction, of infinite sets of orthogonal exponentials for certain families of convex polytopes which include simple-rational polytopes and also non simple…