Daniel I. Bernstein

Works (7)

Updated: July 5th, 2023 15:39

2017 journal article

Completion of tree metrics and rank 2 matrices

LINEAR ALGEBRA AND ITS APPLICATIONS, 533, 1–13.

By: D. Bernstein n

author keywords: Low-rank matrix completion; Algebraic matroids; Tropical geometry; Tree-metric completion
TL;DR: This work gives a combinatorial description of the collections of pairwise distances between several taxa that may be arbitrarily prescribed while still allowing the resulting dissimilarity map to be completed to a tree metric. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

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

2017 journal article

Unimodular hierarchical model sand their Graver bases

Journal of Algebraic Statistics, 8(2), 29–43.

By: D. Bernstein* & C. O'Neill  n

Source: NC State University Libraries
Added: August 6, 2018

2016 journal article

Normal Binary Hierarchical Models

EXPERIMENTAL MATHEMATICS, 26(2), 153–164.

By: D. Bernstein n & S. Sullivant n 

Contributors: D. Bernstein n & S. Sullivant n 

author keywords: algebraic statistics; contingency tables; Hilbert basis; Groebner basis; combinatorics
TL;DR: This work studies the normality of these vector configurations including a description of operations on simplicial complexes that preserve normality, constructions of families of minimally nonnormal complexes, and computations classifying all of the normal complexes on up to six vertices. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2016 journal article

Unimodular binary hierarchical models

JOURNAL OF COMBINATORIAL THEORY SERIES B, 123, 97–125.

By: D. Bernstein n & S. Sullivant n 

Contributors: D. Bernstein n & S. Sullivant n 

author keywords: Graver basis; Algebraic statistics; Log-linear models; Hierarchical models; Toric ideal
TL;DR: The main theorem provides both a construction of all unimodular binary hierarchical models and a characterization in terms of excluded minors, where the definition of a minor allows the taking of links and induced complexes. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
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)
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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

On three sets with nondecreasing diameter

DISCRETE MATHEMATICS, 338(8), 1328–1344.

By: D. Bernstein n, D. Grynkiewicz * & C. Yerger*

author keywords: Monochromatic; Ramsey; Erdos-Ginzburg-Ziv; Diameter; Integer; Nondecreasing; m-set
Source: Web Of Science
Added: August 6, 2018

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