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Ubiquity of synonymity: almost all large binary trees are not uniquely identified by their spectra or their immanantal polynomials

Overview of attention for article published in Algorithms for Molecular Biology, May 2012
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Title
Ubiquity of synonymity: almost all large binary trees are not uniquely identified by their spectra or their immanantal polynomials
Published in
Algorithms for Molecular Biology, May 2012
DOI 10.1186/1748-7188-7-14
Pubmed ID
Authors

Frederick A Matsen, Steven N Evans

Abstract

There are several common ways to encode a tree as a matrix, such as the adjacency matrix, the Laplacian matrix (that is, the infinitesimal generator of the natural random walk), and the matrix of pairwise distances between leaves. Such representations involve a specific labeling of the vertices or at least the leaves, and so it is natural to attempt to identify trees by some feature of the associated matrices that is invariant under relabeling. An obvious candidate is the spectrum of eigenvalues (or, equivalently, the characteristic polynomial).

Twitter Demographics

The data shown below were collected from the profile of 1 tweeter who shared this research output. Click here to find out more about how the information was compiled.

Mendeley readers

The data shown below were compiled from readership statistics for 17 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
United Kingdom 1 6%
United States 1 6%
New Zealand 1 6%
Unknown 14 82%

Demographic breakdown

Readers by professional status Count As %
Researcher 7 41%
Professor > Associate Professor 3 18%
Student > Master 2 12%
Student > Ph. D. Student 2 12%
Librarian 1 6%
Other 2 12%
Readers by discipline Count As %
Agricultural and Biological Sciences 8 47%
Computer Science 3 18%
Mathematics 2 12%
Unspecified 2 12%
Biochemistry, Genetics and Molecular Biology 1 6%
Other 1 6%

Attention Score in Context

This research output has an Altmetric Attention Score of 1. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 10 July 2012.
All research outputs
#7,801,209
of 12,434,464 outputs
Outputs from Algorithms for Molecular Biology
#99
of 181 outputs
Outputs of similar age
#66,959
of 119,888 outputs
Outputs of similar age from Algorithms for Molecular Biology
#1
of 3 outputs
Altmetric has tracked 12,434,464 research outputs across all sources so far. This one is in the 23rd percentile – i.e., 23% of other outputs scored the same or lower than it.
So far Altmetric has tracked 181 research outputs from this source. They receive a mean Attention Score of 2.9. This one is in the 39th percentile – i.e., 39% of its peers scored the same or lower than it.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 119,888 tracked outputs that were published within six weeks on either side of this one in any source. This one is in the 32nd percentile – i.e., 32% of its contemporaries scored the same or lower than it.
We're also able to compare this research output to 3 others from the same source and published within six weeks on either side of this one. This one has scored higher than all of them