1,543 research outputs found
A metric of Yukawa potential as an exact solution to the field equations of general relativity
It is shown that, by defining a suitable energy momentum tensor, the field
equations of general relativity admit a line element of Yukawa potential as an
exact solution. It is also shown that matter that produces strong force may be
negative, in which case there would be no Schwarzschild-like singularityComment: Latex 4 pages (some changes in notation, and a discussion on a
repulsive term that may be related to the charge of a particle
Consistency and convergence rate of phylogenetic inference via regularization
It is common in phylogenetics to have some, perhaps partial, information
about the overall evolutionary tree of a group of organisms and wish to find an
evolutionary tree of a specific gene for those organisms. There may not be
enough information in the gene sequences alone to accurately reconstruct the
correct "gene tree." Although the gene tree may deviate from the "species tree"
due to a variety of genetic processes, in the absence of evidence to the
contrary it is parsimonious to assume that they agree. A common statistical
approach in these situations is to develop a likelihood penalty to incorporate
such additional information. Recent studies using simulation and empirical data
suggest that a likelihood penalty quantifying concordance with a species tree
can significantly improve the accuracy of gene tree reconstruction compared to
using sequence data alone. However, the consistency of such an approach has not
yet been established, nor have convergence rates been bounded. Because
phylogenetics is a non-standard inference problem, the standard theory does not
apply. In this paper, we propose a penalized maximum likelihood estimator for
gene tree reconstruction, where the penalty is the square of the
Billera-Holmes-Vogtmann geodesic distance from the gene tree to the species
tree. We prove that this method is consistent, and derive its convergence rate
for estimating the discrete gene tree structure and continuous edge lengths
(representing the amount of evolution that has occurred on that branch)
simultaneously. We find that the regularized estimator is "adaptive fast
converging," meaning that it can reconstruct all edges of length greater than
any given threshold from gene sequences of polynomial length. Our method does
not require the species tree to be known exactly; in fact, our asymptotic
theory holds for any such guide tree.Comment: 34 pages, 5 figures. To appear on The Annals of Statistic
On the convergence of the maximum likelihood estimator for the transition rate under a 2-state symmetric model
Maximum likelihood estimators are used extensively to estimate unknown
parameters of stochastic trait evolution models on phylogenetic trees. Although
the MLE has been proven to converge to the true value in the independent-sample
case, we cannot appeal to this result because trait values of different species
are correlated due to shared evolutionary history. In this paper, we consider a
-state symmetric model for a single binary trait and investigate the
theoretical properties of the MLE for the transition rate in the large-tree
limit. Here, the large-tree limit is a theoretical scenario where the number of
taxa increases to infinity and we can observe the trait values for all species.
Specifically, we prove that the MLE converges to the true value under some
regularity conditions. These conditions ensure that the tree shape is not too
irregular, and holds for many practical scenarios such as trees with bounded
edges, trees generated from the Yule (pure birth) process, and trees generated
from the coalescent point process. Our result also provides an upper bound for
the distance between the MLE and the true value
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