Related papers: Counting Phylogenetic Networks with Few Reticulati…
In our previous work, we introduced the random $k$-cut number for rooted graphs. In this paper, we show that the distribution of the $k$-cut number in complete binary trees of size $n$, after rescaling, is asymptotically a periodic function…
Tree containment problem is a fundamental problem in phylogenetic study, as it is used to verify a network model. It asks whether a given network contain a subtree that resembles a binary tree. The problem is NP-complete in general, even in…
In networks that grow by isotropic redirection (IR), a new node selects an initial target node uniformly at random and attaches to a randomly chosen neighbor of the target. The emerging networks exhibit leaf proliferation, in which the…
An important and well-studied problem in phylogenetics is to compute a \emph{consensus tree} so as to summarize the common features within a collection of rooted phylogenetic trees, all whose leaf-sets are bijectively labeled by the same…
Growing network models with preferential attachment dependent on both age and degree are proposed to simulate certain features of citation network noted in \cite{red2}. In this directed network, a new node gets attached to an older node…
Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of non-treelike evolutionary events, like recombination, hybridization, or lateral gene transfer. In a recent series of papers devoted to the…
We analyze an evolving network model of Krapivsky and Redner in which new nodes arrive sequentially, each connecting to a previously existing node b with probability proportional to the p-th power of the in-degree of b. We restrict to the…
Phylogenetic networks are often constructed by merging multiple conflicting phylogenetic signals into a directed acyclic graph. It is interesting to explore whether a network constructed in this way induces biologically-relevant…
Convolutional neural networks typically consist of many convolutional layers followed by one or more fully connected layers. While convolutional layers map between high-order activation tensors, the fully connected layers operate on…
Galled networks, directed acyclic graphs that model evolutionary histories with reticulation cycles containing only tree nodes, have become very popular due to both their biological significance and the existence of polynomial time…
The presence of reticulate evolutionary events in phylogenies turn phylogenetic trees into phylogenetic networks. These events imply in particular that there may exist multiple evolutionary paths from a non-extant species to an extant one,…
Let $\mathcal{T}$ be an unrooted binary tree with $n$ distinctly labelled leaves. Deriving its name from the field of phylogenetics, a convex character on $\mathcal{T}$ is simply a partition of the leaves such that the minimal spanning…
Rooted phylogenetic networks are used to describe evolutionary histories that contain non-treelike evolutionary events such as hybridization and horizontal gene transfer. In some cases, such histories can be described by a phylogenetic…
Collapse Lineage Tree (CLTree) is a software tool that annotates, roots, and evaluates phylogenetic trees by using lineages. A recursive algorithm was designed to annotate the branches by the common taxonomic lineage of its descendants in a…
One class of random walks with infinite memory, so called elephant random walks, are simple models describing anomalous diffusion. We present a surprising connection between these models and bond percolation on random recursive trees. We…
The evolutionary relationships between species are typically represented in the biological literature by rooted phylogenetic trees. However, a tree fails to capture ancestral reticulate processes, such as the formation of hybrid species or…
An important problem in phylogenetics is the construction of phylogenetic trees. One way to approach this problem, known as the supertree method, involves inferring a phylogenetic tree with leaves consisting of a set $X$ of species from a…
Genetic and comparative genomic studies indicate that extant genomes are more properly considered to be a fusion product of random mutations over generations and genomic material transfers between individuals of different lineages. This has…
A graph is called set-sequential if its vertices can be labeled with distinct nonzero vectors in $\mathbb{F}_2^n$ such that when each edge is labeled with the sum$\pmod{2}$ of its vertices, every nonzero vector in $\mathbb{F}_2^n$ is the…
Phylogenetics is the study of the evolutionary relationships between organisms. One of the main challenges in the field is to take biological data for a group of organisms and to infer an evolutionary tree, a graph that represents these…