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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…
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…
We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than…
The asymmetric tropical distance is a distance measure on the tropical torus $\mathbb{R}^n/\mathbb{R}\mathbf{1}$ and in particular on the Bergman fan $B(K_N) \subseteq \mathbb{R}^{\binom{N}{2}}/\mathbb{R}\mathbf{1}$ of the complete…
The history of gene families -- which are equivalent to event-labeled gene trees -- can to some extent be reconstructed from empirically estimated evolutionary event-relations containing pairs of orthologous, paralogous or xenologous genes.…
In this paper, we consider the problem of reconstructing trees from traces in the tree edit distance model. Previous work by Davies et al. (2019) analyzed special cases of reconstructing labeled trees. In this work, we significantly expand…
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…
Recursive partitioning is the core of several statistical methods including CART, random forest, and boosted trees. Despite the popularity of tree based methods, to date, there did not exist methods for combining multiple trees into a…
Rotation distances measure the differences in structure between rooted ordered binary trees. The one-dimensional skeleta of associahedra are rotation graphs, where two vertices representing trees are connected by an edge if they differ by a…
In this paper, we provide a polynomial time algorithm to calculate the probability of a {\it ranked} gene tree topology for a given species tree, where a ranked tree topology is a tree topology with the internal vertices being ordered. The…
A classical problem in comparative genomics is to compute the rearrangement distance, that is the minimum number of large-scale rearrangements required to transform a given genome into another given genome. While the most traditional…
Ultrametric trees are trees whose leaves lie at the same distance from the root. They are used to model the genealogy of a population of particles co-existing at the same point in time. We show how the boundary of an ultrametric tree, like…
A BC-tree (block-cutpoint-tree) is a tree (with at least two vertices) where the distance between any two leaves is even. Motivated from the study of the "core" of a graph, BC-trees provide an interesting class of trees. We consider…
In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In particular, given a population of cells sampled from such a…
We consider the problem of estimating the evolutionary history of a set of species (phylogeny or species tree) from several genes. It is known that the evolutionary history of individual genes (gene trees) might be topologically distinct…
In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general…
Computing the similarity between two data points plays a vital role in many machine learning algorithms. Metric learning has the aim of learning a good metric automatically from data. Most existing studies on metric learning for…
We introduce a new phylogenetic reconstruction algorithm which, unlike most previous rigorous inference techniques, does not rely on assumptions regarding the branch lengths or the depth of the tree. The algorithm returns a forest which is…
There are several tools available to infer phylogenetic trees, which depict the evolutionary relationships among biological entities such as viral and bacterial strains in infectious outbreaks, or cancerous cells in tumor progression trees.…
Graphs are interesting structures: extremely useful to depict real-life problems, extremely easy to understand given a sketch, extremely complicated to represent formally, extremely complicated to compare. Phylogeny is the study of the…