相关论文: Limiting Behaviour of Fr\'echet Means in the Space…

We investigate two stochastic models of a growing population subject to selection and mutation. In our models each individual carries a fitness which determines its mean offspring number. Many of these offspring inherit their parent's…

One regards spaces of trees as stratified spaces, to study distributions of phylogenetic trees. Stratified spaces with may have cycles, however spaces of trees with a fixed number of leafs are contractible. Spaces of trees with three leafs,…

A multi-type branching process is defined as a random tree with labeled vertices, where each vertex produces offspring independently according to the same multivariate probability distribution. We demonstrate that in realizations of the…

Fr\'echet regression is becoming a mainstay in modern data analysis for analyzing non-traditional data types belonging to general metric spaces. This novel regression method is especially useful in the analysis of complex health data such…

We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all…

Nested (or reconciled) phylogenetic trees model co-evolutionary systems in which one evolutionary history is embedded within another. We introduce a geometric framework for such systems by defining $\sigma$-space, a moduli space of fully…

Much evidence from biological theory and empirical data indicates that, gene tree, phylogenetic trees reconstructed from different genes (loci), do not have to have exactly the same tree topologies. Such incongruence between gene trees…

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…

Quasistatic simple shearing flow of random monodisperse soap froth is investigated by analyzing Surface Evolver simulations of spatially periodic foams. Elastic-plastic behavior is caused by irreversible topological rearrangements (T1s)…

Discovering the latent structure from many observed variables is an important yet challenging learning task. Existing approaches for discovering latent structures often require the unknown number of hidden states as an input. In this paper,…

Rearrangement operations transform a phylogenetic tree into another one and hence induce a metric on the space of phylogenetic trees. Popular operations for unrooted phylogenetic trees are NNI (nearest neighbour interchange), SPR (subtree…

Many discrete mathematics problems in phylogenetics are defined in terms of the relative labeling of pairs of leaf-labeled trees. These relative labelings are naturally formalized as tanglegrams, which have previously been an object of…

We study the behavior of phylogenetic tree shapes in the tropical geometric interpretation of tree space. Tree shapes are formally referred to as tree topologies; a tree topology can also be thought of as a tree combinatorial type, which is…

We extend the classical coding of measured $\mathbb R$-trees by continuous excursion-type functions to c\`adl\`ag excursion-type functions through the notion of parametric representations. The main feature of this extension is its…

This paper investigates the Fr\'echet mean of the Erd\H{o}s-R\'enyi random graph $G_{n,p}$ with respect to the Frobenius distance on graph Laplacians, a metric that captures global structural information beyond local edge flips. We first…

Background: The reconstruction of the phylogenetic tree topology of four taxa is, still nowadays, one of the main challenges in phylogenetics. Its difficulties lie in considering not too restrictive evolutionary models, and correctly…

The existing Fr\'echet regression is actually defined within a linear framework, since the weight function in the Fr\'echet objective function is linearly defined, and the resulting Fr\'echet regression function is identified to be a linear…

We compute higher derivatives of the Fr\'{e}chet function on spheres with an absolutely continuous and rotationally symmetric probability distribution. Consequences include (i)~a practical condition to test if the mode of the symmetric…

Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer.…

Phylogenetic trees represent the evolutionary relationships between extant lineages, where extinct or non-sampled lineages are omitted. Extending the work of Stadler and collaborators, this paper focuses on the branch lengths in…