Related papers: Vector encoding of phylogenetic trees by ordered l…
Orchard and tree-child networks share an important property with phylogenetic trees: they can be completely reduced to a single node by iteratively deleting cherries and reticulated cherries. As it is the case with phylogenetic trees, the…
Many common sequential data sources, such as source code and natural language, have a natural tree-structured representation. These trees can be generated by fitting a sequence to a grammar, yielding a hierarchical ordering of the tokens in…
Latent Dirichlet Allocation (LDA) is a foundational model for discovering latent thematic structure in discrete data, but its Dirichlet prior cannot represent the rich correlations and hierarchical relationships often present among topics.…
``Algorithms with predictions'', or ``learning-augmented algorithms'', has proved to be an extremely useful paradigm for combining machine learning with traditional algorithms. One of the textbook settings for this is searching a sorted…
Ranked tree-child networks are a recently introduced class of rooted phylogenetic networks in which the evolutionary events represented by the network are ordered so as to respect the flow of time. This class includes the well-studied…
Phylogenetic networks are generalizations of phylogenetic trees that allow the representation of reticulation events such as horizontal gene transfer or hybridization, and can also represent uncertainty in inference. A subclass of these,…
The evolutionary relationships among organisms have traditionally been represented using rooted phylogenetic trees. However, due to reticulate processes such as hybridization or lateral gene transfer, evolution cannot always be adequately…
Phylogenetic networks are a type of directed acyclic graph that represent how a set $X$ of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of reticulate evolution,…
The notion of transducer integer sequences is considered through a series of examples. By definition, transducer integer sequences are integer sequences produced, under a suitable interpretation, by finite automata encoding tree morphisms…
One strategy for reconstruction of phylogenetic networks is to solve the phylogenetic network problem, which involves inferring phylogenetic trees first and subsequently computing the smallest phylogenetic network that displays all the…
We look at a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this…
Phylogenetic networks are a generalization of phylogenetic trees that are used to represent non-tree-like evolutionary histories that arise in organisms such as plants and bacteria, or uncertainty in evolutionary histories. An…
Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…
We present a $\lg n + 2 \lg \lg n+3$ ancestry labeling scheme for trees. The problem was first presented by Kannan et al. [STOC 88'] along with a simple $2 \lg n$ solution. Motivated by applications to XML files, the label size was improved…
It was recently observed by de Vienne et al. that a simple square root transformation of distances between taxa on a phylogenetic tree allowed for an embedding of the taxa into Euclidean space. While the justification for this was based on…
Null models of binary phylogenetic trees are useful for testing hypotheses on real world phylogenies. In this paper we consider phylogenies as binary trees without edge lengths together with a sampling measure and encode them as algebraic…
Phylogenetic trees are used to model evolution: leaves are labelled to represent contemporary species ("taxa") and interior vertices represent extinct ancestors. Informally, convex characters are measurements on the contemporary species in…
Despite the recent progress in genome sequencing and assembly, many of the currently available assembled genomes come in a draft form. Such draft genomes consist of a large number of genomic fragments (scaffolds), whose order and/or…
We introduce a simple algorithm for reconstructing phylogenies from multiple gene trees in the presence of incomplete lineage sorting, that is, when the topology of the gene trees may differ from that of the species tree. We show that our…
The weighted ancestor problem on a rooted node-weighted tree $T$ is a generalization of the classic predecessor problem: construct a data structure for a set of integers that supports fast predecessor queries. Both problems are known to…