Related papers: Constructing a Minimum-Level Phylogenetic Network …

In phylogenetics, phylogenetic trees are rooted binary trees, whereas phylogenetic networks are rooted arbitrary acyclic digraphs. Edges are directed away from the root and leaves are uniquely labeled with taxa in phylogenetic networks. For…

Let $X$ be a finite set, $\mathcal N$ be a reticulation-visible network on $X$, and $\mathcal T$ be a rooted binary phylogenetic tree. We show that there is a polynomial-time algorithm for deciding whether or not $\mathcal N$ displays…

Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this…

In this paper we study a polynomial time algorithms that for an input $A\subseteq {B_m}$ outputs a decision tree for $A$ of minimum depth. This problem has many applications that include, to name a few, computer vision, group testing, exact…

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…

Phylogenetic trees and networks are graphs used to model evolutionary relationships, with trees representing strictly branching histories and networks allowing for events in which lineages merge, called reticulation events. While the…

Phylogenetic networks are necessary to represent the tree of life expanded by edges to represent events such as horizontal gene transfers, hybridizations or gene flow. Not all species follow the paradigm of vertical inheritance of their…

It is a known fact that, given two rooted binary phylogenetic trees, the concept of maximum acyclic agreement forests is sufficient to compute hybridization networks with minimum hybridization number. In this work, we demonstrate by first…

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…

Arboreal networks are multi-rooted phylogenetic networks whose underlying graph is a tree. We give an encoding of stack-free arboreal networks in terms of triplets and the novel concept of a duet. This yields a polynomial time algorithm to…

'Tree-based' phylogenetic networks proposed by Francis and Steel have attracted much attention of theoretical biologists in the last few years. At the heart of the definitions of tree-based phylogenetic networks is the notion of 'support…

Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…

We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as $O(n^{\omega+\epsilon})$ time matrix multiplication, and in…

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…

In phylogenetics, it is important for the phylogenetic network model parameters to be identifiable so that the evolutionary histories of a group of species can be consistently inferred. However, as the complexity of the phylogenetic network…

This paper presents an algorithm for searching for the minimum number of neurons in fully connected layers of an arbitrary network solving given problem, which does not require multiple training of the network with different number of…

This paper deals with gene networks whose dynamics is assumed to be generated by a continuous-time, linear, time invariant, finite dimensional system (LTI) at steady state. In particular, we deal with the problem of network reconstruction…

Phylogenetic networks can represent evolutionary events that cannot be described by phylogenetic trees. These networks are able to incorporate reticulate evolutionary events such as hybridization, introgression, and lateral gene transfer.…

We consider the NP-hard Tree Containment problem that has important applications in phylogenetics. The problem asks if a given leaf-labeled network contains a subdivision of a given leaf-labeled tree. We develop a fast algorithm for the…

Given a finite set $X$, a collection $\mathcal{T}$ of rooted phylogenetic trees on $X$ and an integer $k$, the Hybridization Number problem asks if there exists a phylogenetic network on $X$ that displays all trees from $\mathcal{T}$ and…