The Experts below are selected from a list of 222 Experts worldwide ranked by ideXlab platform
Peter F. Stadler - One of the best experts on this subject based on the ideXlab platform.
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From event-labeled gene trees to species trees
BMC Bioinformatics, 2012Co-Authors: Maribel Hernandez-rosales, Marc Hellmuth, Nicolas Wieseke, Katharina T. Huber, Vincent Moulton, Peter F. StadlerAbstract:Background Tree reconciliation problems have long been studied in phylogenetics. A particular variant of the reconciliation problem for a gene tree T and a species tree S assumes that for each Interior Vertex x of T it is known whether x represents a speciation or a duplication. This problem appears in the context of analyzing orthology data.
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From event-labeled gene trees to species trees
BMC Bioinformatics, 2012Co-Authors: Maribel Hernandez-rosales, Marc Hellmuth, Nicolas Wieseke, Katharina T. Huber, Vincent Moulton, Peter F. StadlerAbstract:Abstract Background Tree reconciliation problems have long been studied in phylogenetics. A particular variant of the reconciliation problem for a gene tree T and a species tree S assumes that for each Interior Vertex x of T it is known whether x represents a speciation or a duplication. This problem appears in the context of analyzing orthology data. Results We show that S is a species tree for T if and only if S displays all rooted triples of T that have three distinct species as their leaves and are rooted in a speciation Vertex. A valid reconciliation map can then be found in polynomial time. Simulated data shows that the event-labeled gene trees convey a large amount of information on underlying species trees, even for a large percentage of losses. Conclusions The knowledge of event labels in a gene tree strongly constrains the possible species tree and, for a given species tree, also the possible reconciliation maps. Nevertheless, many degrees of freedom remain in the space of feasible solutions. In order to disambiguate the alternative solutions additional external constraints as well as optimization criteria could be employed.
Salvador Segura Gomis - One of the best experts on this subject based on the ideXlab platform.
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Subdivisions of rotationally symmetric planar convex bodies minimizing the maximum relative diameter
Journal of Mathematical Analysis and Applications, 2016Co-Authors: Antonio Cañete, Uwe Schnell, Salvador Segura GomisAbstract:Abstract In this work we study subdivisions of k -rotationally symmetric planar convex bodies that minimize the maximum relative diameter functional. For some particular subdivisions called k -partitions, consisting of k curves meeting in an Interior Vertex, we prove that the so-called standard k-partition (given by k equiangular inradius segments) is minimizing for any k ∈ N , k ⩾ 3 . For general subdivisions, we show that the previous result only holds for k ⩽ 6 . We also study the optimal set for this problem, obtaining that for each k ∈ N , k ⩾ 3 , it consists of the intersection of the unit circle with the corresponding regular k -gon of certain area. Finally, we also discuss the problem for planar convex sets and large values of k , and conjecture the optimal k -subdivision in this case.
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Subdivisions of rotationally symmetric planar convex bodies minimizing the maximum relative diameter
arXiv: Metric Geometry, 2015Co-Authors: Antonio Cañete, Uwe Schnell, Salvador Segura GomisAbstract:In this work we study subdivisions of $k$-rotationally symmetric planar convex bodies that minimize the maximum relative diameter functional. For some particular subdivisions called $k$-partitions, consisting of $k$ curves meeting in an Interior Vertex, we prove that the so-called \emph{standard $k$-partition} (given by $k$ equiangular inradius segments) is minimizing for any $k\in\mathbb{N}$, $k\geq 3$. For general subdivisions, we show that the previous result only holds for $k\leq 6$. We also study the optimal set for this problem, obtaining that for each $k\in\mathbb{N}$, $k\geq 3$, it consists of the intersection of the unit circle with the corresponding regular $k$-gon of certain area. Finally, we also discuss the problem for planar convex sets and large values of $k$, and conjecture the optimal $k$-subdivision in this case.
Katharina T. Huber - One of the best experts on this subject based on the ideXlab platform.
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Reconstructing fully-resolved trees from triplet cover distances
arXiv: Combinatorics, 2014Co-Authors: Katharina T. Huber, Mike SteelAbstract:It is a classical result that any finite tree with positively weighted edges, and without vertices of degree 2, is uniquely determined by the weighted path distance between each pair of leaves. Moreover, it is possible for a (small) strict subset L of leaf pairs to suffice for reconstructing the tree and its edge weights, given just the distances between the leaf pairs in L. It is known that any set L with this property for a tree in which all Interior vertices have degree 3 must form a cover for T {that is, for each Interior Vertex v of T, L must contain a pair of leaves from each pair of the three components of T v. Here we provide a partial converse of this result by showing that if a set L of leaf pairs forms a cover of a certain type for such a tree T then T and its edge weights can be uniquely determined from the distances between the pairs of leaves in L. Moreover, there is a polynomial-time algorithm for achieving this reconstruction. The result establishes a special case of a recent question concerning `triplet covers', and is relevant to a problem arising in evolutionary genomics.
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Tree Reconstruction from Triplet Cover Distances
The Electronic Journal of Combinatorics, 2014Co-Authors: Katharina T. Huber, Mike SteelAbstract:It is a classical result that any finite tree with positively weighted edges, and without vertices of degree 2, is uniquely determined by the weighted path distance between each pair of leaves. Moreover, it is possible for a (small) strict subset $\mathcal{L}$ of leaf pairs to suffice for reconstructing the tree and its edge weights, given just the distances between the leaf pairs in $\mathcal{L}$. It is known that any set ${\mathcal L}$ with this property for a tree in which all Interior vertices have degree 3 must form a cover for $T$ - that is, for each Interior Vertex $v$ of $T$, ${\mathcal L}$ must contain a pair of leaves from each pair of the three components of $T-v$. Here we provide a partial converse of this result by showing that if a set ${\mathcal L}$ of leaf pairs forms a cover of a certain type for such a tree $T$ then $T$ and its edge weights can be uniquely determined from the distances between the pairs of leaves in ${\mathcal L}$. Moreover, there is a polynomial-time algorithm for achieving this reconstruction. The result establishes a special case of a recent question concerning 'triplet covers', and is relevant to a problem arising in evolutionary genomics.
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From event-labeled gene trees to species trees
BMC Bioinformatics, 2012Co-Authors: Maribel Hernandez-rosales, Marc Hellmuth, Nicolas Wieseke, Katharina T. Huber, Vincent Moulton, Peter F. StadlerAbstract:Background Tree reconciliation problems have long been studied in phylogenetics. A particular variant of the reconciliation problem for a gene tree T and a species tree S assumes that for each Interior Vertex x of T it is known whether x represents a speciation or a duplication. This problem appears in the context of analyzing orthology data.
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From event-labeled gene trees to species trees
BMC Bioinformatics, 2012Co-Authors: Maribel Hernandez-rosales, Marc Hellmuth, Nicolas Wieseke, Katharina T. Huber, Vincent Moulton, Peter F. StadlerAbstract:Abstract Background Tree reconciliation problems have long been studied in phylogenetics. A particular variant of the reconciliation problem for a gene tree T and a species tree S assumes that for each Interior Vertex x of T it is known whether x represents a speciation or a duplication. This problem appears in the context of analyzing orthology data. Results We show that S is a species tree for T if and only if S displays all rooted triples of T that have three distinct species as their leaves and are rooted in a speciation Vertex. A valid reconciliation map can then be found in polynomial time. Simulated data shows that the event-labeled gene trees convey a large amount of information on underlying species trees, even for a large percentage of losses. Conclusions The knowledge of event labels in a gene tree strongly constrains the possible species tree and, for a given species tree, also the possible reconciliation maps. Nevertheless, many degrees of freedom remain in the space of feasible solutions. In order to disambiguate the alternative solutions additional external constraints as well as optimization criteria could be employed.
Harald Woracek - One of the best experts on this subject based on the ideXlab platform.
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Spectral Multiplicity of Selfadjoint Schrödinger Operators on Star-Graphs with Standard Interface Conditions
Integral Equations and Operator Theory, 2013Co-Authors: Sergey Simonov, Harald WoracekAbstract:We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schrodinger operator on a star-shaped graph with continuity and Kirchhoff conditions at the Interior Vertex. We compute the multiplicity of the singular spectrum in terms of the spectral measures of the Weyl functions associated with the single (independently considered) boundary relations. This result is a generalization and refinement of a Theorem of I.S.Kac.
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Spectral multiplicity of selfadjoint Schroedinger operators on star-graphs with standard interface conditions
arXiv: Spectral Theory, 2012Co-Authors: Sergey Simonov, Harald WoracekAbstract:We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schroedinger operator on a star-shaped graph with continuity and Kirchhoff conditions at the Interior Vertex. We compute the multiplicity of the singular spectrum in terms of the spectral measures of the Weyl functions associated with the single (independently considered) boundary relations. This result is a generalization and refinement of Theorem of I.S. Kac.
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Eigenvalue Asymptotics for a Star-Graph Damped Vibrations Problem
Asymptotic Analysis, 2011Co-Authors: Vyacheslav Pivovarchik, Harald WoracekAbstract:We consider a boundary value problem generated by Sturm-Liouville equations on the edges of a star-shaped graph. Thereby a continuity condition and a condition depending on the spectral parameter is imposed at the Interior Vertex, corresponding to the case of damping in the problem of small transversal vibrations of a star graph of smooth inhomogeneous strings. At the pendant vertices Dirichlet boundary conditions are imposed. We describe the eigenvalue asymptotics of the problem under consideration. AMS Classification Numbers: Primary 34B45. Secondary 34B07, 34B24
Maribel Hernandez-rosales - One of the best experts on this subject based on the ideXlab platform.
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From event-labeled gene trees to species trees
BMC Bioinformatics, 2012Co-Authors: Maribel Hernandez-rosales, Marc Hellmuth, Nicolas Wieseke, Katharina T. Huber, Vincent Moulton, Peter F. StadlerAbstract:Background Tree reconciliation problems have long been studied in phylogenetics. A particular variant of the reconciliation problem for a gene tree T and a species tree S assumes that for each Interior Vertex x of T it is known whether x represents a speciation or a duplication. This problem appears in the context of analyzing orthology data.
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From event-labeled gene trees to species trees
BMC Bioinformatics, 2012Co-Authors: Maribel Hernandez-rosales, Marc Hellmuth, Nicolas Wieseke, Katharina T. Huber, Vincent Moulton, Peter F. StadlerAbstract:Abstract Background Tree reconciliation problems have long been studied in phylogenetics. A particular variant of the reconciliation problem for a gene tree T and a species tree S assumes that for each Interior Vertex x of T it is known whether x represents a speciation or a duplication. This problem appears in the context of analyzing orthology data. Results We show that S is a species tree for T if and only if S displays all rooted triples of T that have three distinct species as their leaves and are rooted in a speciation Vertex. A valid reconciliation map can then be found in polynomial time. Simulated data shows that the event-labeled gene trees convey a large amount of information on underlying species trees, even for a large percentage of losses. Conclusions The knowledge of event labels in a gene tree strongly constrains the possible species tree and, for a given species tree, also the possible reconciliation maps. Nevertheless, many degrees of freedom remain in the space of feasible solutions. In order to disambiguate the alternative solutions additional external constraints as well as optimization criteria could be employed.