Related papers: A branching process approach to level-$k$ phylogen…
Local convergence of bounded degree graphs was introduced by Benjamini and Schramm. This result was extended further by Lyons to bounded average degree graphs. In this paper, we study the convergence of a random tree sequence where the…
Construction of phylogenetic trees and networks for extant species from their characters represents one of the key problems in phylogenomics. While solution to this problem is not always uniquely defined and there exist multiple methods for…
Dynamical processes taking place on real networks define on them evolving subnetworks whose topology is not necessarily the same of the underlying one. We investigate the problem of determining the emerging degree distribution, focusing on…
We study a broad class of random labelled trees in which integer-valued labels evolve along the edges according to increments in $\{-1, 0, 1\}$. These models include e.g. branching random walks, embedded complete and incomplete binary…
An out-branching of a directed graph is a rooted spanning tree with all arcs directed outwards from the root. We consider the problem of deciding whether a given directed graph D has an out-branching with at least k leaves (Directed…
It was recently shown that a large class of phylogenetic networks, the `labellable' networks, is in bijection with the set of `expanding' covers of finite sets. In this paper, we show how several prominent classes of phylogenetic networks…
We prove an invariance principle for a general class of continuous time critical branching processes with finite variance (non-local) branching mechanism. We show that the genealogical trees, viewed as random compact metric measure spaces,…
Study of random networks generally requires the nodes to be independently and uniformly distributed such as a Poisson point process. In this work, we venture beyond this standard paradigm and investigate a stochastic forest obtained from a…
Tree-based phylogenetic networks, which may be roughly defined as leaf-labeled networks built by adding arcs only between the original tree edges, have elegant properties for modeling evolutionary histories. We answer an open question of…
We consider the branch-length estimation problem on a bifurcating tree: a character evolves along the edges of a binary tree according to a two-state symmetric Markov process, and we seek to recover the edge transition probabilities from…
Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…
Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…
Phylogenetic networks are a type of leaf-labelled, acyclic, directed graph used by biologists to represent the evolutionary history of species whose past includes reticulation events. A phylogenetic network is tree-child if each non-leaf…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
We study a model of random $\mathcal{R}$-enriched trees that is based on weights on the $\mathcal{R}$-structures and allows for a unified treatment of a large family of random discrete structures. We establish distributional limits…
In this note we consider the $k$th level of the uniform random recursive tree after $n$ steps, and prove that the proportion of nodes with degree greater than $t\log n$ converges to $(1-t)^k$ almost surely, as $n\to\infty$, for every…
We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…
We introduce a new phylogenetic reconstruction algorithm which, unlike most previous rigorous inference techniques, does not rely on assumptions regarding the branch lengths or the depth of the tree. The algorithm returns a forest which is…
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…
This Master's thesis examines the properties of large degree vertices in random recursive directed acyclic graphs (RRDAGs), a generalization of the well-studied random recursive tree (RRT) model. Using a novel adaptation of Kingman's…