相关论文: On asymptotic joint distributions of cherries and …
We propose a statistical method to test whether two phylogenetic trees with given alignments are significantly incongruent. Our method compares the two distributions of phylogenetic trees given by the input alignments, instead of comparing…
Bayesian hierarchical models are used to share information between related samples and obtain more accurate estimates of sample-level parameters, common structure, and variation between samples. When the parameter of interest is the…
Inferring evolutionary histories (phylogenetic trees) has important applications in biology, criminology and public health. However, phylogenetic trees are complex mathematical objects that reside in a non-Euclidean space, which complicates…
We derive tractable criteria for the consistency of Bayesian tree reconstruction procedures, which constitute a central class of algorithms for inferring common ancestry among DNA sequence samples in phylogenetics. Our results encompass…
We consider the creation conditions of diverse hierarchical trees both analytically and numerically. A connection between the probabilities to create hierarchical levels and the probability to associate these levels into a united structure…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
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…
Here we show that deciding whether two rooted binary phylogenetic trees on the same set of taxa permit a cherry-picking sequence, a special type of elimination order on the taxa, is NP-complete. This improves on an earlier result which…
We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new…
Phylogenetic networks provide a general framework for modeling reticulate evolutionary processes such as hybridization, recombination, and horizontal gene transfer. In this paper, we study the asymptotic counting of binary phylogenetic…
We consider a population with non-overlapping generations, whose size goes to infinity. It is described by a discrete genealogy which may be time non-homogeneous and we pay special attention to branching trees in varying environments. A…
The properties of scale-free random trees are investigated using both preconditioning on non-extinction and fixed size averages, in order to study the thermodynamic limit. The scaling form of volume probability is found, the connectivity…
We present a new technique for proving logarithmic upper bounds for diameters of evolving random graph models, which is based on defining a coupling between random graphs and variants of random recursive trees. The advantage of the…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
In 1986, Janson showed that the number of edges in the union of $k$ random spanning trees in the complete graph $K_n$ is a shifted Poisson distribution. Using results from the theory of electrical networks, we provide a new proof of this…
Analyzing data collected from multiple sources to estimate common and heterogeneous structures through a hierarchical model is a central task in Bayesian inference, and to this end, Bayesian factor models are one of the most widely used…
A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…
We study several enumeration problems connected to linear trees, a broad class which includes stars, paths, generalized stars, and caterpillars. We provide generating functions for counting the number of linear trees on $n$ vertices,…
We introduce Joint Probability Trees (JPT), a novel approach that makes learning of and reasoning about joint probability distributions tractable for practical applications. JPTs support both symbolic and subsymbolic variables in a single…
A popular line of research in evolutionary biology is the use of time-calibrated phylogenies for the inference of diversification processes. This requires computing the likelihood of a given ultrametric tree as the reconstructed tree…