Related papers: Parking functions, labeled trees and DCJ sorting s…
In this paper, we survey some properties, encoding, and bijections involving combinatorial maps, double occurrence words, and chord diagrams. We particularly study quasi-trees from a purely combinatorial point of view and derive a…
A semiorder is a partially ordered set $P$ with two certain forbidden induced subposets. This paper establishes a bijection between $n$-element semiorders of length $H$ and $(n+1)$-node ordered trees of height $H+1$. This bijection…
Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…
The edit distance under the DCJ model can be computed in linear time for genomes with equal content or with Indels. But it becomes NP-Hard in the presence of duplications, a problem largely unsolved especially when Indels are considered. In…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
DNA rearrangement processes recombine gene segments that are organized on the chromosome in a variety of ways. The segments can overlap, interleave or one may be a subsegment of another. We use directed graphs to represent segment…
Recombining trinomial trees are a workhorse for modeling discrete-event systems in option pricing, logistics, and feedback control. Because each node stores a state-dependent quantity, a depth-$D$ tree naively yields $\mathcal{O}(3^{D})$…
Background: Tree reconciliation problems have long been studied in phylogenetics. A particular variant of the reconciliation problem for a gene tree T and a species tree S assumes that for each interior vertex x of T it is known whether x…
We analyze models of genome evolution based on both restricted and unrestricted double-cut-and-join (DCJ) operations. We compare the number of operations along the evolutionary trajectory to the DCJ distance of the genome from its ancestor…
There are several combinatorial objects that are known to be in bijection to the spanning trees of a graph G. These objects include G-parking functions, critical configurations of G, and descending traversals of G. In this paper, we extend…
The ongoing explosion of genome sequence data is transforming how we reconstruct and understand the histories of biological systems. Across biological scales, from individual cells to populations and species, trees-based models provide a…
Metabolites, small molecules that are involved in cellular reactions, provide a direct functional signature of cellular state. Untargeted metabolomics experiments usually relies on tandem mass spectrometry to identify the thousands of…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
Nested dichotomies are used as a method of transforming a multiclass classification problem into a series of binary problems. A tree structure is induced that recursively splits the set of classes into subsets, and a binary classification…
A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees. Previous work on this similarity measure is only concerned with the comparison of labeled trees of two…
Decision trees are popular machine learning models that are simple to build and easy to interpret. Even though algorithms to learn decision trees date back to almost 50 years, key properties affecting their generalization error are still…
Parking sequences (a generalization of parking functions) are defined by specifying car lengths and requiring that a car attempts to park in the first available spot after its preference. If it does not fit there, then a collision occurs…
Genome rearrangement distances are an established method in genome comparison. Works in this area may include various rearrangement operations representing large-scale mutations, gene orientation information, the number of nucleotides in…
The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…
Some genes can change their relative locations in a genome. Thus for different individuals of the same species, the orders of genes might be different. Such jumping genes are called transposons. A practical problem is to determine…