Erin Wolf Chambers
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View article: Counting Triangulations of Fixed Cardinal Degrees
Counting Triangulations of Fixed Cardinal Degrees Open
A fixed set of vertices in the plane may have multiple planar straight-line triangulations in which the degree of each vertex is the same. As such, the degree information does not completely determine the triangulation. We show that even i…
View article: Burning or Collapsing the Medial Axis is Unstable
Burning or Collapsing the Medial Axis is Unstable Open
The medial axis of a set consists of the points in the ambient space without a unique closest point in the original set. Since its introduction, the medial axis has been used extensively in many applications as a method of computing a skel…
View article: Bounding the interleaving distance for mapper graphs with a loss function
Bounding the interleaving distance for mapper graphs with a loss function Open
Data consisting of a graph with a function mapping into $${\mathbb {R}}^d$$ arise in many data applications, encompassing structures such as Reeb graphs, geometric graphs, and knot embeddings. As such, the ability to compare and clust…
View article: A Stable and Theoretically Grounded Gromov-Wasserstein Distance for Reeb Graph Comparison using Persistence Images
A Stable and Theoretically Grounded Gromov-Wasserstein Distance for Reeb Graph Comparison using Persistence Images Open
Reeb graphs are a fundamental structure for analyzing the topological and geometric properties of scalar fields. Comparing Reeb graphs is crucial for advancing research in this domain, yet existing metrics are often computationally prohibi…
View article: A scoping review of health co-benefit tests in the setting of a screening or health programme: Limited data to inform their potential use to address inequities
A scoping review of health co-benefit tests in the setting of a screening or health programme: Limited data to inform their potential use to address inequities Open
Objective: The aim of this scoping review is to assess the extent, range and nature of health co-benefit tests and their application to address inequities in a screening or other health programme setting and to inform their potential use f…
View article: Drawing Reeb Graphs
Drawing Reeb Graphs Open
Reeb graphs are simple topological descriptors with applications in many areas like topological data analysis and computational geometry. Despite their prevalence, visualization of Reeb graphs has received less attention. In this paper, we…
View article: Braiding vineyards
Braiding vineyards Open
In this work, we introduce and study what we believe is an intriguing and, to the best of our knowledge, previously unknown connection between two areas in computational topology, topological data analysis (TDA) and knot theory. Given a fu…
View article: A Distance for Geometric Graphs via the Labeled Merge Tree Interleaving Distance
A Distance for Geometric Graphs via the Labeled Merge Tree Interleaving Distance Open
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric g…
View article: Metric and Path-Connectedness Properties of the Frechet Distance for Paths and Graphs
Metric and Path-Connectedness Properties of the Frechet Distance for Paths and Graphs Open
The Frechet distance is often used to measure distances between paths, with applications in areas ranging from map matching to GPS trajectory analysis to handwriting recognition. More recently, the Frechet distance has been generalized to …
View article: Bounding the Interleaving Distance for Mapper Graphs with a Loss Function
Bounding the Interleaving Distance for Mapper Graphs with a Loss Function Open
Data consisting of a graph with a function mapping into $\mathbb{R}^d$ arise in many data applications, encompassing structures such as Reeb graphs, geometric graphs, and knot embeddings. As such, the ability to compare and cluster such ob…
View article: Clinical Significance of Quantitative Viral Load in Patients Positive for SARS-CoV-2
Clinical Significance of Quantitative Viral Load in Patients Positive for SARS-CoV-2 Open
Cycle threshold (CT) refers to the number of cycles in a reverse transcriptase polymerase chain reaction (RT-PCR) assay needed to amplify viral RNA and can be used to indicate viral load. CT is inversely related to viral load, where lower …
View article: Distances Between Immersed Graphs: Metric Properties
Distances Between Immersed Graphs: Metric Properties Open
Graphs in metric spaces appear in a wide range of data sets, and there is a large body of work focused on comparing, matching, or analyzing collections of graphs in different ambient spaces. In this survey, we provide an overview of a dive…
View article: Aggregating community maps
Aggregating community maps Open
This paper is motivated by a practical problem: many U.S. states have public hearings on "communities of interest" as part of their redistricting process, but no state has as yet adopted a concrete method of spatializing and aggregating co…
View article: Comparing Embedded Graphs Using Average Branching Distance
Comparing Embedded Graphs Using Average Branching Distance Open
Graphs drawn in the plane are ubiquitous, arising from data sets through a variety of methods ranging from GIS analysis to image classification to shape analysis. A fundamental problem in this type of data is comparison: given a set of suc…
View article: Research Networks for Women
Research Networks for Women Open
Research Networks for Women is a recent effort led by the Association for Women in Mathematics to increase gender diversity in specific research areas of mathematics through a grassroots effort to build mentoring and collaborative relation…
View article: On Complexity of Computing Bottleneck and Lexicographic Optimal Cycles in a Homology Class
On Complexity of Computing Bottleneck and Lexicographic Optimal Cycles in a Homology Class Open
Homology features of spaces which appear in applications, for instance 3D meshes, are among the most important topological properties of these objects. Given a non-trivial cycle in a homology class, we consider the problem of computing a r…
View article: TopoRoot: a method for computing hierarchy and fine-grained traits of maize roots from 3D imaging
TopoRoot: a method for computing hierarchy and fine-grained traits of maize roots from 3D imaging Open
Background 3D imaging, such as X-ray CT and MRI, has been widely deployed to study plant root structures. Many computational tools exist to extract coarse-grained features from 3D root images, such as total volume, root number and total ro…
View article: Constructing monotone homotopies and sweepouts
Constructing monotone homotopies and sweepouts Open
This article investigates when homotopies can be converted to monotone homotopies without increasing the lengths of curves. A monotone homotopy is one which consists of curves which are simple or constant, and in which curves are pairwise …
View article: Reeb Graph Metrics from the Ground Up
Reeb Graph Metrics from the Ground Up Open
The Reeb graph has been utilized in various applications including the analysis of scalar fields. Recently, research has been focused on using topological signatures such as the Reeb graph to compare multiple scalar fields by defining dist…
View article: TopoRoot: A method for computing hierarchy and fine-grained traits of maize roots from X-ray CT images
TopoRoot: A method for computing hierarchy and fine-grained traits of maize roots from X-ray CT images Open
Background 3D imaging, such as X-ray CT and MRI, has been widely deployed to study plant root structures. Many computational tools exist to extract coarse-grained features from 3D root images, such as total volume, root number and total ro…
View article: Realizable piecewise linear paths of persistence diagrams with Reeb graphs
Realizable piecewise linear paths of persistence diagrams with Reeb graphs Open
Reeb graphs are widely used in a range of fields for the purposes of analyzing and comparing complex spaces via a simpler combinatorial object. Further, they are closely related to extended persistence diagrams, which largely but not compl…
View article: Realizable piecewise linear paths of persistence diagrams with Reeb\n graphs
Realizable piecewise linear paths of persistence diagrams with Reeb\n graphs Open
Reeb graphs are widely used in a range of fields for the purposes of\nanalyzing and comparing complex spaces via a simpler combinatorial object.\nFurther, they are closely related to extended persistence diagrams, which\nlargely but not co…
View article: Covering a Curve with Subtrajectories.
Covering a Curve with Subtrajectories. Open
We study subtrajectory clustering under the Frechet distance. Given a polygonal curve $P$ with $n$ vertices, and parameters $k$ and $\ell$, the goal is to find $k$ center curves of complexity at most $\ell$ such that every point on $P$ is …
View article: Subtrajectory Clustering: Finding Set Covers for Set Systems of Subcurves
Subtrajectory Clustering: Finding Set Covers for Set Systems of Subcurves Open
We study subtrajectory clustering under the Fréchet distance. Given one or more trajectories, the task is to split the trajectories into several parts, such that the parts have a good clustering structure. We approach this problem via a ne…