172 citations · 564 across the 31 of their papers we have counts for
36 papers
Gromov--Hausdorff Distance Between Euclidean Unit Balls
Henry Adams, Kushagri Sharma
What is the Gromov--Hausdorff distance between Euclidean unit balls of different dimensions, denoted by $d_\gh(B^m,B^n)$, for ? Note that the lower bound coming from the stabi…
Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes
Henry Adams, Johnathan Bush, Nate Clause +13
We explore emerging relationships between the Gromov--Hausdorff distance, Borsuk--Ulam theorems, and Vietoris--Rips simplicial complexes. The Gromov--Hausdorff distance between two…
Čech complexes of hypercube graphs
Henry Adams, Samir Shukla, Anurag Singh
A Čech complex of a finite simple graph is a nerve complex of balls in the graph, with one ball centered at each vertex. More precisely, let the Čech complex …
A Primer on Topological Data Analysis to Support Image Analysis Tasks in Environmental Science
Lander Ver Hoef, Henry Adams, Emily J. King +1
Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science. In this work, we seek to provide an intuitive…
Vietoris thickenings and complexes have isomorphic homotopy groups
Henry Adams, Florian Frick, Žiga Virk
We study the relationship between metric thickenings and simplicial complexes associated to coverings of metric spaces. Let be a cover of a separable metric space …
The Persistent Topology of Optimal Transport Based Metric Thickenings
Henry Adams, Facundo Mémoli, Michael Moy +1
A metric thickening of a given metric space is any metric space admitting an isometric embedding of . Thickenings have found use in applications of topology to data analysis…
Counting Rocks! An Introduction to Combinatorics
Henry Adams, Kelly Emmrich, Maria Gillespie +2
This textbook, "Counting Rocks!", is the written component of an interactive introduction to combinatorics at the undergraduate level. Throughout the text, we link to videos where…
The topology of projective codes and the distribution of zeros of odd maps
Henry Adams, Johnathan Bush, Florian Frick
We show that the size of codes in projective space controls structural results for zeros of odd maps from spheres to Euclidean space. In fact, this relation is given through the to…
Topology Applied to Machine Learning: From Global to Local
Henry Adams, Michael Moy
Through the use of examples, we explain one way in which applied topology has evolved since the birth of persistent homology in the early 2000s. The first applications of topology…
Geometric Approaches on Persistent Homology
Henry Adams, Baris Coskunuzer
We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence…
On Vietoris--Rips complexes of hypercube graphs
Michał Adamaszek, Henry Adams
We describe the homotopy types of Vietoris-Rips complexes of hypercube graphs at small scale parameters. In more detail, let be the vertex set of the hypercube graph with $2^…
Operations on Metric Thickenings
Henry Adams, Johnathan Bush, Joshua Mirth
Many simplicial complexes arising in practice have an associated metric space structure on the vertex set but not on the complex, e.g. the Vietoris-Rips complex in applied topology…
Efficient Evader Detection in Mobile Sensor Networks
Henry Adams, Deepjyoti Ghosh, Clark Mask +2
Suppose one wants to monitor a domain with sensors, each sensing a small ball-shaped region, but the domain is hazardous enough that one cannot control the placement of the sensors…
Lions and contamination, triangular grids, and Cheeger constants
Henry Adams, Leah Gibson, Jack Pfaffinger
Suppose each vertex of a graph is originally occupied by contamination, except for those vertices occupied by lions. As the lions wander on the graph, they clear the contamination…
Representations of Energy Landscapes by Sublevelset Persistent Homology: An Example With n-Alkanes
Joshua Mirth, Yanqin Zhai, Johnathan Bush +8
Encoding the complex features of an energy landscape is a challenging task, and often chemists pursue the most salient features (minima and barriers) along a highly reduced space,…
Support vector machines and Radon's theorem
Henry Adams, Elin Farnell, Brittany Story
A support vector machine (SVM) is an algorithm that finds a hyperplane which optimally separates labeled data points in into positive and negative classes. The data…
Capturing Dynamics of Time-Varying Data via Topology
Lu Xian, Henry Adams, Chad M. Topaz +1
One approach to understanding complex data is to study its shape through the lens of algebraic topology. While the early development of topological data analysis focused primarily…
An Adaptation for Iterative Structured Matrix Completion
Henry Adams, Lara Kassab, Deanna Needell
The task of predicting missing entries of a matrix, from a subset of known entries, is known as \textit{matrix completion}. In today's data-driven world, data completion is essenti…
Metric thickenings and group actions
Henry Adams, Mark Heim, Chris Peterson
Let be a group acting properly and by isometries on a metric space ; it follows that the quotient or orbit space is also a metric space. We study the Vietoris-Rips and…
Metric Thickenings, Borsuk-Ulam Theorems, and Orbitopes
Henry Adams, Johnathan Bush, Florian Frick
Thickenings of a metric space capture local geometric properties of the space. Here we exhibit applications of lower bounding the topology of thickenings of the circle and more gen…
Multidimensional Scaling on Metric Measure Spaces
Henry Adams, Mark Blumstein, Lara Kassab
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We o…
The persistent homology of cyclic graphs
Henry Adams, Ethan Coldren, Sean Willmot
We give an algorithm for computing the -dimensional persistent homology of a filtration of clique complexes of cyclic graphs on vertices. This is nearly q…
A torus model for optical flow
Henry Adams, Johnathan Bush, Brittany Carr +2
We propose a torus model for high-contrast patches of optical flow. Our model is derived from a database of ground-truth optical flow from the computer-generated video \emph{Sintel…
A fractal dimension for measures via persistent homology
Henry Adams, Manuchehr Aminian, Elin Farnell +6
We use persistent homology in order to define a family of fractal dimensions, denoted for each homological dimension , assigned to a proba…