Colby Edward Long

Works (4)

Updated: July 5th, 2023 15:41

2017 journal article

L-INFINITY OPTIMIZATION TO LINEAR SPACES AND PHYLOGENETIC TREES

SIAM JOURNAL ON DISCRETE MATHEMATICS, 31(2), 875–889.

By: D. Bernstein* & C. Long*

author keywords: distance-based methods; tree metric; ultrametric; subdominant ultrametric; oriented matroid; zonotope
TL;DR: It is shown that the $l^\infty$-closest point in alinear space is unique if and only if the underlying matroid of the linear space is uniform. (via Semantic Scholar)
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15. Life on Land (Web of Science)
Source: Web Of Science
Added: August 6, 2018

2015 journal article

BOUNDS ON THE EXPECTED SIZE OF THE MAXIMUM AGREEMENT SUBTREE

SIAM JOURNAL ON DISCRETE MATHEMATICS, 29(4), 2065–2074.

By: D. Bernstein n, L. Ho, C. Long n, M. Steel, K. St John  n & S. Sullivant n 

Contributors: D. Bernstein n, L. Ho, C. Long n, M. Steel, K. St. John  n & S. Sullivant n 

author keywords: random trees; agreement subtrees; Yule-Harding distribution
TL;DR: It is proved polynomial upper and lower bounds on the expected size of the maximum agreement subtree of two random binary phylogenetic trees under both the uniform distribution and Yule-Harding distribution are positive. (via Semantic Scholar)
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
15. Life on Land (Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2015 journal article

Identifiability of 3-class Jukes-Cantor mixtures

ADVANCES IN APPLIED MATHEMATICS, 64(1), 89–110.

By: C. Long n & S. Sullivant n 

Contributors: C. Long n & S. Sullivant n 

author keywords: Phylogenetic mixture models; Identifiability; Tropical geometry; Disentangling number
TL;DR: The proof uses ideas from algebraic statistics, in particular: finding phylogenetic invariants that separate the varieties associated to different triples of trees; computing dimensions of the resulting phylogenetic varieties; and using the disentangling number to reduce to trees with a small number of leaves. (via Semantic Scholar)
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
15. Life on Land (Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2015 journal article

Tying up loose strands: defining equations of the strand symmetric model

J. Algebr. Stat., 6(1), 17–23.

By: C. Long* & S. Sullivant* 

TL;DR: The set of known phylogenetic invariants for the general strand symmetric model of the three leaf claw tree entirely defines the ideal, and it is shown that the known equations generate a prime ideal of the correct dimension using elimination theory. (via Semantic Scholar)
Sources: NC State University Libraries, ORCID, NC State University Libraries
Added: August 6, 2018

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