626,408 research outputs found
Extracting Conflict-free Information from Multi-labeled Trees
A multi-labeled tree, or MUL-tree, is a phylogenetic tree where two or more
leaves share a label, e.g., a species name. A MUL-tree can imply multiple
conflicting phylogenetic relationships for the same set of taxa, but can also
contain conflict-free information that is of interest and yet is not obvious.
We define the information content of a MUL-tree T as the set of all
conflict-free quartet topologies implied by T, and define the maximal reduced
form of T as the smallest tree that can be obtained from T by pruning leaves
and contracting edges while retaining the same information content. We show
that any two MUL-trees with the same information content exhibit the same
reduced form. This introduces an equivalence relation in MUL-trees with
potential applications to comparing MUL-trees. We present an efficient
algorithm to reduce a MUL-tree to its maximally reduced form and evaluate its
performance on empirical datasets in terms of both quality of the reduced tree
and the degree of data reduction achieved.Comment: Submitted in Workshop on Algorithms in Bioinformatics 2012
(http://algo12.fri.uni-lj.si/?file=wabi
Inferring Species Trees from Incongruent Multi-Copy Gene Trees Using the Robinson-Foulds Distance
We present a new method for inferring species trees from multi-copy gene
trees. Our method is based on a generalization of the Robinson-Foulds (RF)
distance to multi-labeled trees (mul-trees), i.e., gene trees in which multiple
leaves can have the same label. Unlike most previous phylogenetic methods using
gene trees, this method does not assume that gene tree incongruence is caused
by a single, specific biological process, such as gene duplication and loss,
deep coalescence, or lateral gene transfer. We prove that it is NP-hard to
compute the RF distance between two mul-trees, but it is easy to calculate the
generalized RF distance between a mul-tree and a singly-labeled tree. Motivated
by this observation, we formulate the RF supertree problem for mul-trees
(MulRF), which takes a collection of mul-trees and constructs a species tree
that minimizes the total RF distance from the input mul-trees. We present a
fast heuristic algorithm for the MulRF supertree problem. Simulation
experiments demonstrate that the MulRF method produces more accurate species
trees than gene tree parsimony methods when incongruence is caused by gene tree
error, duplications and losses, and/or lateral gene transfer. Furthermore, the
MulRF heuristic runs quickly on data sets containing hundreds of trees with up
to a hundred taxa.Comment: 16 pages, 11 figure
Folding and unfolding phylogenetic trees and networks
Phylogenetic networks are rooted, labelled directed acyclic graphs which are commonly used to represent reticulate evolution. There is a close relationship between phylogenetic networks and multi-labelled trees (MUL-trees). Indeed, any phylogenetic network can be "unfolded" to obtain a MUL-tree and, conversely, a MUL-tree can in certain circumstances be "folded" to obtain a phylogenetic network that exhibits . In this paper, we study properties of the operations and in more detail. In particular, we introduce the class of stable networks, phylogenetic networks for which is isomorphic to , characterise such networks, and show that they are related to the well-known class of tree-sibling networks.We also explore how the concept of displaying a tree in a network can be related to displaying the tree in the MUL-tree . To do this, we develop a phylogenetic analogue of graph fibrations. This allows us to view as the analogue of the universal cover of a digraph, and to establish a close connection between displaying trees in and reconcilingphylogenetic trees with networks
Dynamics of Controlled Hybrid Systems of Aerial Cable-Ways
Dynamics of the hybrid systems of aerial cable-ways is investigated. The
eigenvalue problems are considered for such hybrid systems with different
assumptions. An overview of different methods for eigenvalue problems is given.
In the research, the method of the normal fundamental systems is applied, which
turns out to be very effective for the considered problems. Changes of
dynamical characteristics of the systems depending on the controlled parameter
are studied.Comment: Accepted (15-May-2006) to the Proceedings of the "International
Conference of Hybrid Systems and Applications", The University of Louisiana,
Lafayette, LA, USA, May 22-26 2006, to be published in the journal "Nonlinear
Analysis: Hybrid Systems and Applications
Letter from Julia to family June 4, 1942
In this letter Julia tells about Howard breaking his arm in a fall from a mul
Componentwise and Cartesian decompositions of linear relations
Let be a, not necessarily closed, linear relation in a Hilbert space
\sH with a multivalued part \mul A. An operator in \sH with \ran
B\perp\mul A^{**} is said to be an operator part of when A=B \hplus
(\{0\}\times \mul A), where the sum is componentwise (i.e. span of the
graphs). This decomposition provides a counterpart and an extension for the
notion of closability of (unbounded) operators to the setting of linear
relations. Existence and uniqueness criteria for the existence of an operator
part are established via the so-called canonical decomposition of . In
addition, conditions are developed for the decomposition to be orthogonal
(components defined in orthogonal subspaces of the underlying space). Such
orthogonal decompositions are shown to be valid for several classes of
relations. The relation is said to have a Cartesian decomposition if
A=U+\I V, where and are symmetric relations and the sum is
operatorwise. The connection between a Cartesian decomposition of and the
real and imaginary parts of is investigated
Multiple sampling and interpolation in the classical Fock space
We study multiple sampling, interpolation and uniqueness for the classical
Fock space in the case of unbounded mul-tiplicities
MUL-Tree Pruning for Consistency and Compatibility
A multi-labelled tree (or MUL-tree) is a rooted tree leaf-labelled by a set of labels, where each label may appear more than once in the tree. We consider the MUL-tree Set Pruning for Consistency problem (MULSETPC), which takes as input a set of MUL-trees and asks whether there exists a perfect pruning of each MUL-tree that results in a consistent set of single-labelled trees. MULSETPC was proven to be NP-complete by Gascon et al. when the MUL-trees are binary, each leaf label is used at most three times, and the number of MUL-trees is unbounded. To determine the computational complexity of the problem when the number of MUL-trees is constant was left as an open problem.
Here, we resolve this question by proving a much stronger result, namely that MULSETPC is NP-complete even when there are only two MUL-trees, every leaf label is used at most twice, and every MUL-tree is either binary or has constant height. Furthermore, we introduce an extension of MULSETPC that we call MULSETPComp, which replaces the notion of consistency with compatibility, and prove that MULSETPComp is NP-complete even when there are only two MUL-trees, every leaf label is used at most thrice, and every MUL-tree has constant height. Finally, we present a polynomial-time algorithm for instances of MULSETPC with a constant number of binary MUL-trees, in the special case where every leaf label occurs exactly once in at least one MUL-tree
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