Related papers: Exact formulas for the variance of several balance…
We obtain an exact formula for the probability that a uniformly random spanning tree of the $2$-by-$n$ square grid is ``balanced'' in the sense that it has an edge whose removal partitions its vertices into two sets of equal size. We…
In recent years, there has been an effort to extend the classical notion of phylogenetic balance, originally defined in the context of trees, to networks. One of the most natural ways to do this is with the so-called $B_2$ index. In this…
While balancing covariates between groups is central for observational causal inference, selecting which features to balance remains a challenging problem. Kernel balancing is a promising approach that first estimates a kernel that captures…
Given a gene-tree labeled topology $G$ and a species tree $S$, the "ancestral configurations" at an internal node $k$ of $S$ represent the combinatorially different sets of gene lineages that can be present at $k$ when all possible…
The Wiener index is maximized over the set of trees with the given vertex weight and degree sequences. This model covers the traditional "unweighed" Wiener index, the terminal Wiener index, and the vertex distance index. It is shown that…
This article introduces a flexible and adaptive nonparametric method for estimating the association between multiple covariates and power spectra of multiple time series. The proposed approach uses a Bayesian sum of trees model to capture…
Using topological summaries of gene trees as a basis for species tree inference is a promising approach to obtain acceptable speed on genomic-scale datasets, and to avoid some undesirable modeling assumptions. Here we study the…
In phylogenomics, species-tree methods must contend with two major sources of noise; stochastic gene-tree variation under the multispecies coalescent model (MSC) and finite-sequence substitutional noise. Fast agglomerative methods such as…
Covariate balancing is a popular technique for controlling confounding in observational studies. It finds weights for the treatment group which are close to uniform, but make the group's covariate means (approximately) equal to those of the…
A new method is proposed for determining the critical indices of the deconfinement transition in gauge theories, based on the finite-size scaling analysis of simple lattice operators, such as the plaquette. A precise determination of the…
We study two fringe subtree counting statistics, the number of cherries and that of pitchforks for Ford's $\alpha$ model, a one-parameter family of random phylogenetic tree models that includes the uniform and the Yule models, two tree…
Multivariate time series exhibit two types of dependence: across variables and across time points. Vine copulas are graphical models for the dependence and can conveniently capture both types of dependence in the same model. We derive the…
In a rooted tree, we call a vertex {\em balanced} if it is at equal distance from all its descendant leaves. We count balanced vertices in three different tree varieties. For decreasing binary trees, we can prove that the probability that a…
We introduce a new method for determining the critical indices of the deconfinement transition in gauge theories. The method is based on the finite size scaling behavior of the expectation value of simple lattice operators, such as the…
We design exact polynomial expansions of a class of Feynman--Kac particle distributions. These expansions are finite and are parametrized by coalescent trees and other related combinatorial quantities. The accuracy of the expansions at any…
We consider general Gaussian latent tree models in which the observed variables are not restricted to be leaves of the tree. Extending related recent work, we give a full semi-algebraic description of the set of covariance matrices of any…
A phylogenetic variety is an algebraic variety parameterized by a statistical model of the evolution of biological sequences along a tree. Understanding this variety is an important problem in the area of algebraic statistics with…
Cayley's formula states that there are $n^{n-2}$ spanning trees in the complete graph on $n$ vertices; it has been proved in more than a dozen different ways over its 150 year history. The complete graphs are a special case of threshold…
We study counting statistics of number of transitions in a stochastic process. For mesoscopic systems, a path integral formulation for the counting statistics has already been derived. We here show that it is also possible to derive the…
Bayesian phylogenetics is vital for understanding evolutionary dynamics, and requires accurate and efficient approximation of posterior distributions over trees. In this work, we develop a variational Bayesian approach for ultrametric…