Computing Geodesic Distances in Tree Space

Megan Owen

doi:10.1137/090751396

Computing Geodesic Distances in Tree Space

SIAM Journal on Discrete Mathematics ◽

10.1137/090751396 ◽

2011 ◽

Vol 25 (4) ◽

pp. 1506-1529 ◽

Cited By ~ 18

Author(s):

Megan Owen

Keyword(s):

Tree Space ◽

Geodesic Distances

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A Fast Algorithm for Computing Geodesic Distances in Tree Space

IEEE/ACM Transactions on Computational Biology and Bioinformatics ◽

10.1109/tcbb.2010.3 ◽

2011 ◽

Vol 8 (1) ◽

pp. 2-13 ◽

Cited By ~ 80

Author(s):

Megan Owen ◽

J Scott Provan

Keyword(s):

Fast Algorithm ◽

Tree Space ◽

Geodesic Distances

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An Efficient Algorithm for Approximating Geodesic Distances in Tree Space

IEEE/ACM Transactions on Computational Biology and Bioinformatics ◽

10.1109/tcbb.2010.121 ◽

2011 ◽

Vol 8 (5) ◽

pp. 1196-1207 ◽

Cited By ~ 1

Author(s):

S. Battagliero ◽

G. Puglia ◽

S. Vicario ◽

F. Rubino ◽

G. Scioscia ◽

...

Keyword(s):

Efficient Algorithm ◽

Tree Space ◽

Geodesic Distances

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Geodesic distances in the intrinsic dimensionality estimation using packing numbers

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2014.4.4 ◽

2014 ◽

Vol 19 (4) ◽

pp. 578-591 ◽

Cited By ~ 1

Author(s):

Rasa Karbauskaitė ◽

◽

Gintautas Dzemyda ◽

Keyword(s):

Geodesic Distances ◽

Intrinsic Dimensionality

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Faculty Opinions recommendation of Stochastic models for horizontal gene transfer: taking a random walk through tree space.

Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature ◽

10.3410/f.1026516.323363 ◽

2005 ◽

Author(s):

Jeffrey Thorne

Keyword(s):

Random Walk ◽

Gene Transfer ◽

Horizontal Gene Transfer ◽

Stochastic Models ◽

Tree Space

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Projections on Tree-Like banach Spaces

Canadian Journal of Mathematics ◽

10.4153/cjm-1985-049-2 ◽

1985 ◽

Vol 37 (5) ◽

pp. 908-920

Author(s):

A. D. Andrew

Keyword(s):

Banach Space ◽

Linear Operator ◽

Banach Spaces ◽

Bounded Linear Operator ◽

Unconditional Basis ◽

Reflexive Banach Space ◽

Separable Space ◽

Bounded Linear ◽

Tree Space

1. In this paper, we investigate the ranges of projections on certain Banach spaces of functions defined on a diadic tree. The notion of a “tree-like” Banach space is due to James 4], who used it to construct the separable space JT which has nonseparable dual and yet does not contain l1. This idea has proved useful. In [3], Hagler constructed a hereditarily c0 tree space, HT, and Schechtman [6] constructed, for each 1 ≦ p ≦ ∞, a reflexive Banach space, STp with a 1-unconditional basis which does not contain lp yet is uniformly isomorphic to for each n.In [1] we showed that if U is a bounded linear operator on JT, then there exists a subspace W ⊂ JT, isomorphic to JT such that either U or (1 — U) acts as an isomorphism on W and UW or (1 — U)W is complemented in JT. In this paper, we establish this result for the Hagler and Schechtman tree spaces.

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