Related papers: Popping Bubbles in Pangenome Graphs
Motivation: The abundance of gene flow in the Tree of Life challenges the notion that evolution can be represented with a fully bifurcating process, as this process cannot capture important biological realities like hybridization,…
DNA sequencing is the process of determining the exact order of the nucleotide bases of an individual's genome in order to catalogue sequence variation and understand its biological implications. Whole-genome sequencing techniques produce…
Rapid developments in genetics and biology have led to phylogenetic methods becoming an important direction in the study of cancer and viral evolution. Although our understanding of gene biology and biochemistry has increased and is…
Normalizing flows model complex probability distributions using maps obtained by composing invertible layers. Special linear layers such as masked and 1x1 convolutions play a key role in existing architectures because they increase…
We construct a partial order relation which acts on the set of 3-cliques of a maximal planar graph G and defines a unique hierarchy. We demonstrate that G is the union of a set of special subgraphs, named `bubbles', that are themselves…
Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred…
Phylogenetic networks extend phylogenetic trees to allow for modeling reticulate evolutionary processes such as hybridization. They take the shape of a rooted, directed, acyclic graph, and when parameterized with evolutionary parameters,…
Combining a set of phylogenetic trees into a single phylogenetic network that explains all of them is a fundamental challenge in evolutionary studies. Existing methods are computationally expensive and can either handle only small numbers…
Given an $n$-vertex pseudorandom graph $G$ and an $n$-vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, i.e.\ an embedding $\varphi\colon V(H)\to V(G)$ so that $\varphi(u)\varphi(v)\in E(G)$ for all…
Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of $n$ objects scales factorially in $n$. One recent way that has been used to reduce storage complexity has been to exploit…
Graph invariants are a useful tool in graph theory. Not only do they encode useful information about the graphs to which they are associated, but complete invariants can be used to distinguish between non-isomorphic graphs. Polynomial…
Bidirected graphs are a common generalisation of directed graphs where arcs can also be incoming to both their incident nodes, or outgoing from both their incident nodes. Such arcs allow a walk to change direction. Some algorithms can…
Phylogenetic (evolutionary) trees and networks are leaf-labeled graphs that are widely used to represent the evolutionary relationships between entities such as species, languages, cancer cells, and viruses. To reconstruct and analyze…
Phylogenetic networks are a generalization of phylogenetic trees to leaf-labeled directed acyclic graphs that represent ancestral relationships between species whose past includes non-tree-like events such as hybridization and horizontal…
A permutation graph is a graph whose edges are given by inversions of a permutation. We study the Abelian sandpile model (ASM) on such graphs. We exhibit a bijection between recurrent configurations of the ASM on permutation graphs and the…
Continuous-time branching processes (CTBPs) are powerful tools in random graph theory, but are not appropriate to describe real-world networks, since they produce trees rather than (multi)graphs. In this paper we analyze collapsed branching…
A major ambition of systems science is to uncover the building blocks of any biological network to decipher how cellular function emerges from their interactions. Here, we introduce a graph representation of the information flow in these…
The dominant paradigm for learning on graph-structured data is message passing. Despite being a strong inductive bias, the local message passing mechanism suffers from pathological issues such as over-smoothing, over-squashing, and limited…
Phylogenetic networks are a generalization of evolutionary trees that are used by biologists to represent the evolution of organisms which have undergone reticulate evolution. Essentially, a phylogenetic network is a directed acyclic graph…
There is growing interest in graph pattern mining (GPM) problems such as motif counting. GPM systems have been developed to provide unified interfaces for programming algorithms for these problems and for running them on parallel systems.…