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

Biology – Quantitative Biology – Populations and Evolution

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

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). We show for any of these choices of matrix that the fraction of binary trees with a unique spectrum goes to zero as the number of leaves goes to infinity. We investigate the rate of convergence of the above fraction to zero using numerical methods. For the adjacency and Laplacian matrices, we show that that the {\em a priori} more informative immanantal polynomials have no greater power to distinguish between trees.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Ubiquity of synonymity: almost all large binary trees are not uniquely identified by their spectra or their immanantal polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Ubiquity of synonymity: almost all large binary trees are not uniquely identified by their spectra or their immanantal polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ubiquity of synonymity: almost all large binary trees are not uniquely identified by their spectra or their immanantal polynomials will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-113695

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.