Related papers: Comparing and Aggregating Partially Resolved Trees
This article presents a new way to understand the descriptive ability of tree shape statistics. Where before tree shape statistics were chosen by their ability to distinguish between macroevolutionary models, the ``resolution'' presented in…
The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired…
There are several interrelated notions of discrete curvature on graphs. Many approaches utilize the optimal transportation metric on its probability simplex or the distance matrix of the graph. In this survey article, we compute formulas…
Measuring tree morphology for phenotyping is an essential but labor-intensive activity in horticulture. Researchers often rely on manual measurements which may not be accurate for example when measuring tree volume. Recent approaches on…
We introduce the tree distance, a new distance measure on graphs. The tree distance can be computed in polynomial time with standard methods from convex optimization. It is based on the notion of fractional isomorphism, a characterization…
When we apply comparative phylogenetic analyses to genome data, it is a well-known problem and challenge that some of given species (or taxa) often have missing genes. In such a case, we have to impute a missing part of a gene tree from a…
Optimal transport (\OT) theory defines a powerful set of tools to compare probability distributions. \OT~suffers however from a few drawbacks, computational and statistical, which have encouraged the proposal of several regularized variants…
We study various measure theories using the classical approach and then compute the Hausdorff dimension of some simple objects and self-similar fractals. We then develop a nonstandard approach to these measure theories and examine the…
Motivated by applications to low-rank matrix completion, we give a combinatorial characterization of the independent sets in the algebraic matroid associated to the collection of $m\times n$ rank-2 matrices and $n\times n$ skew-symmetric…
This paper introduces decorated merge trees (DMTs) as a novel invariant for persistent spaces. DMTs combine both $\pi_0$ and $H_n$ information into a single data structure that distinguishes filtrations that merge trees and persistent…
The root is an important organ of a plant since it is responsible for water and nutrient uptake. Analyzing and modelling variabilities in the geometry and topology of roots can help in assessing the plant's health, understanding its growth…
In the decision tree computation model for Boolean functions, the depth corresponds to query complexity, and size corresponds to storage space. The depth measure is the most well-studied one, and is known to be polynomially related to…
We provide a new approach for proving the indistinguishability of connected components of random one-or-two-ended oriented forests on unimodular random graphs. In particular, this approach leads to a new and simpler proof for the wired…
This paper introduces \textit{measurement trees}, a novel class of metrics designed to combine various constructs into an interpretable multi-level representation of a measurand. Unlike conventional metrics that yield single values,…
We describe a kernel of size 9k-8 for the NP-hard problem of computing the Tree Bisection and Reconnect (TBR) distance k between two unrooted binary phylogenetic trees. We achieve this by extending the existing portfolio of reduction rules…
Tree comparison metrics have proven to be an invaluable aide in the reconstruction and analysis of phylogenetic (evolutionary) trees. The path-length distance between trees is a particularly attractive measure as it reflects differences in…
Quartet Reconstruction, the task of recovering a phylogenetic tree from smaller trees on four species called \textit{quartets}, is a well-studied problem in theoretical computer science with far-reaching connections to statistics, graph…
Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional…
We look for partition theorems for large subtrees for suitable uncountable trees and colourings. We concentrate on sub-trees of $^{\kappa \ge} 2$ expanded by a well ordering of each level. Unlike earlier works, we do not ask the embedding…
Persistent Topology studies topological features of shapes by analyzing the lower level sets of suitable functions, called filtering functions, and encoding the arising information in a parameterized version of the Betti numbers, i.e. the…