Related papers: On joint subtree distributions under two evolution…

Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…

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 probability distribution d on the truth assignments to a uniform binary AND-OR tree. Liu and Tanaka [2007, Inform. Process. Lett.] showed the following: If d achieves the equilibrium among independent distributions (ID) then d is…

We investigate the distribution of the depth of a node containing a specific key or, equivalently, the number of steps needed to retrieve an item stored in a randomly grown binary search tree. Using a representation in terms of mixed and…

A wide variety of stochastic models of cladogenesis (based on speciation and extinction) lead to an identical distribution on phylogenetic tree shapes once the edge lengths are ignored. By contrast, the distribution of the tree's edge…

The occurrence and the distribution of patterns of trees associated to natural numbers are investigated. Bounds from above and below are proven for certain natural quantities.

We study the distribution and the popularity of left children on sets of treeshelves avoiding a pattern of size three. (Treeshelves are ordered binary increasing trees where every child is connected to its parent by a left or a right link.)…

We study the problem of probability distribution matching and sampling on near-term quantum computers, aiming to construct parameterized circuits that generate samples from a target distribution while minimizing resource overhead. This task…

We study the number of random records in an arbitrary split tree (or equivalently, the number of random cuttings required to eliminate the tree). We show that a classical limit theorem for convergence of sums of triangular arrays to…

We present an approach to model-based hierarchical clustering by formulating an objective function based on a Bayesian analysis. This model organizes the data into a cluster hierarchy while specifying a complex feature-set partitioning that…

We study a random recursive tree model featuring complete redirection called the random friend tree and introduced by Saram\"aki and Kaski. Vertices are attached in a sequential manner one by one by selecting an existing target vertex and…

In this work, we characterize the solution of a system of elliptic integro-differential equations describing a phenotypically structured population subject to mutation, selection and migration between two habitats. Assuming that the effects…

We give a parity reversing involution on noncrossing trees that leads to a combinatorial interpretation of a formula on noncrossing trees and symmetric ternary trees in answer to a problem proposed by Hough. We use the representation of…

Ancestral mixture model, proposed by Chen and Lindsay (2006), is an important model to build a hierarchical tree from high dimensional binary sequences. Mixture trees created from ancestral mixture models involve in the inferred…

The problem of how to estimate diffusion on a graph effectively is of importance both theoretically and practically. In this paper, we make use of two widely studied indices, geodesic distance and mean first-passage time ($MFPT$) for random…

In this article, we construct a generalization of the Blum-Fran\c{c}ois Beta-splitting model for evolutionary trees, which was itself inspired by Aldous' Beta-splitting model on cladograms. The novelty of our approach allows for asymmetric…

Phylogenetic diversity is a measure for describing how much of an evolutionary tree is spanned by a subset of species. If one applies this to the (unknown) subset of current species that will still be present at some future time, then this…

Diffusion processes on trees are commonly used in evolutionary biology to model the joint distribution of continuous traits, such as body mass, across species. Estimating the parameters of such processes from tip values presents challenges…

We study a general model of recursive trees where vertices are equipped with independent weights and at each time-step a vertex is sampled with probability proportional to its fitness function (a function of its weight and degree) and…

We investigate an AND-OR tree T and a probability distribution d on the truth assignments to the leaves. Tarsi (1983) showed that if d is an independent and identical distribution (IID) such that probability of a leaf having value 0 is…