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Linear functionals of eigenvalues of random matrices
Let Mn be a random n×n unitary matrix with distribution given by Haar measure on the unitary group. Using explicit moment calculations, a general criterion is given for linear combinations of traces…
Probability and Real Trees
- S. Evans
Around the Continuum Random Tree.- R-Trees and 0-Hyperbolic Spaces.- Hausdorff and Gromov-Hausdorff Distance.- Root Growth with Re-Grafting.- The Wild Chain and other Bipartite Chains.- Diffusions on…
Construction of markovian coalescents
Estimating Allele Age and Selection Coefficient from Time-Serial Data
A likelihood method to jointly estimate the selection coefficient and the age of an allele from time-serial data is developed and is illustrated with an application to several loci encoding coat color in horses, a pattern that has previously been linked with domestication.
Non-equilibrium theory of the allele frequency spectrum.
Rayleigh processes, real trees, and root growth with re-grafting
The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as infinite total edge length and vertices with infinite branching degree.…
The phylogenetic Kantorovich–Rubinstein metric for environmental sequence samples
- S. Evans, Frederick Albert Matsen IV
- MathematicsJournal of the Royal Statistical Society. Series…
- 11 May 2010
It is established that, if the authors equate a metagenomic sample with its empirical distribution on a reference phylogenetic tree, then the weighted UniFrac distance between two samples is just the classical Kantorovich-Rubinstein, or earth mover's, distance between the corresponding empirical distributions.
Invariants of Some Probability Models Used in Phylogenetic Inference
Edge Principal Components and Squash Clustering: Using the Special Structure of Phylogenetic Placement Data for Sample Comparison
Two new complementary methods that leverage how this microbial community data sits on a phylogenetic tree and illustrate their use with data from the human microbiome are presented.
Measure-Valued Branching Diffusions with Singular Interactions
Abstract The usual super-Brownian motion is a measure-valued process that arises as a high density limit of a system of branching Brownian particles in which the branching mechanism is critical. In…