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Ubiquitous Parameterization  Invitation to FixedParameter Algorithms
 In Proc. 29th MFCS, volume 3153 of LNCS
, 2004
"... Problem parameters are ubiquitous. In every area of computer science, we find all kinds of "special aspects" to the problems encountered. ..."
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Problem parameters are ubiquitous. In every area of computer science, we find all kinds of "special aspects" to the problems encountered.
Breakpoint Distance and PQTrees
"... Abstract. The PQtree is a fundamental data structure that can encode large sets of permutations. It has recently been used in comparative genomics to model ancestral genomes with some uncertainty: given a phylogeny for some species, extant genomes are represented by permutations on the leaves of th ..."
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Abstract. The PQtree is a fundamental data structure that can encode large sets of permutations. It has recently been used in comparative genomics to model ancestral genomes with some uncertainty: given a phylogeny for some species, extant genomes are represented by permutations on the leaves of the tree, and each internal node in the phylogenetic tree represents an extinct ancestral genome, represented by a PQtree. An open problem related to this approach is then to quantify the evolution between genomes represented by PQtrees. In this paper we present results for two problems of PQtree comparison motivated by this application. First, we show that the problem of comparing two PQtrees by computing the minimum breakpoint distance among all pairs of permutations generated respectively by the two considered PQtrees is NPcomplete for unsigned permutations. Next, we consider a generalization of the classical Breakpoint Median problem, where an ancestral genome is represented by a PQtree and p permutations are given, with p ≥ 1, and we want to compute a permutation generated by the PQtree that minimizes the sum of the breakpoint distances to the p permutations. We show that this problem is FixedParameter Tractable with respect to the breakpoint distance value. This last result applies both on signed and unsigned permutations, and to unichromosomal and multichromosomal permutations. 1
Informationtheoretic indices and an approximate significance test for testing the molecular clock hypothesis with genetic distances. Mol Phylogenet Evol
"... a b s t r a c t Distancebased phylogenetic methods are widely used in biomedical research. However, distancebased dating of speciation events and the test of the molecular clock hypothesis are relatively underdeveloped. Here I develop an approximate test of the molecular clock hypothesis for dist ..."
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a b s t r a c t Distancebased phylogenetic methods are widely used in biomedical research. However, distancebased dating of speciation events and the test of the molecular clock hypothesis are relatively underdeveloped. Here I develop an approximate test of the molecular clock hypothesis for distancebased trees, as well as informationtheoretic indices that have been used frequently in model selection, for use with distance matrices. The results are in good agreement with the conventional sequencebased likelihood ratio test. Among the informationtheoretic indices, AICu is the most consistent with the sequencebased likelihood ratio test. The confidence in model selection by the indices can be evaluated by bootstrapping. I illustrate the usage of the indices and the approximate significance test with both empirical and simulated sequences. The tests show that distance matrices from protein gel electrophoresis and from genome rearrangement events do not violate the molecular clock hypothesis, and that the evolution of the third codon position conforms to the molecular clock hypothesis better than the second codon position in vertebrate mitochondrial genes. I outlined evolutionary distances that are appropriate for phylogenetic reconstruction and dating.