4 citations · 6 across the 14 of their papers we have counts for
23 papers
Real Tree Vineyards have Vines
Michael Hull, Thomas Payne, Thomas Weighill
We show that every vineyard can be decomposed into vines, that is, every path in the space of persistence diagrams can be decomposed into a sequence of paths in $\mat…
Measuring Spatial Clustering via Metropolis-Hastings Diffusion Distance
Thomas Weighill, Chidinma Williams
We propose a novel measure of the discrepancy between two probability distributions and on a graph - which we call the diffusion distance - that measures the rate of conver…
Topological optimization with birth and death cochains
Thomas Weighill, Ling Zhou
We introduce the notion of birth and death cochains as generalized versions of birth and death simplices in persistent cohomology. We show that birth and death cochains (unlike bir…
Through the Grapevine: Vineyard Distance as a Measure of Topological Dissimilarity
Alvan Arulandu, Daniel Gottschalk, Thomas Payne +2
We introduce a new measure of distance between datasets, based on vineyards from topological data analysis, which we call the vineyard distance. Vineyard distance measures the exte…
Classification of Firn Data via Topological Features
Sarah Day, Jesse Dimino, Matt Jester +2
In this paper we evaluate the performance of topological features for generalizable and robust classification of firn image data, with the broader goal of understanding the advanta…
Generalized Dimension Reduction Using Semi-Relaxed Gromov-Wasserstein Distance
Ranthony A. Clark, Tom Needham, Thomas Weighill
Dimension reduction techniques typically seek an embedding of a high-dimensional point cloud into a low-dimensional Euclidean space which optimally preserves the geometry of the in…
Topological analysis of U.S. city demographics
Jakini A. Kauba, Thomas Weighill
We apply persistent homology, the main method in topological data analysis, to the study of demographic data. Persistence diagrams efficiently summarize information about clusters…
Coarse embeddings of quotients by finite group actions
Thomas Weighill
We prove that for a metric space and a finite group acting on by isometries, if coarsely embeds into a Hilbert space, then so does the quotient . A crucial ste…
Reconfiguration of Polygonal Subdivisions via Recombination
Hugo A. Akitaya, Andrei Gonczi, Diane L. Souvaine +2
Motivated by the problem of redistricting, we study area-preserving reconfigurations of connected subdivisions of a simple polygon. A connected subdivision of a polygon $\mathcal{R…
Coarse embeddability of Wasserstein space and the space of persistence diagrams
Neil Pritchard, Thomas Weighill
We prove an equivalence between open questions about the embeddability of the space of persistence diagrams and the space of probability distributions (i.e.~Wasserstein space). It…
Measuring Segregation via Analysis on Graphs
Moon Duchin, James M. Murphy, Thomas Weighill
In this paper, we use analysis on graphs to study quantitative measures of segregation. We focus on a classical statistic from the geography and urban sociology literature known as…
Geometric averages of partitioned datasets
Tom Needham, Thomas Weighill
We introduce a method for jointly registering ensembles of partitioned datasets in a way which is both geometrically coherent and partition-aware. Once such a registration has been…
Three Applications of Entropy to Gerrymandering
Larry Guth, Ari Nieh, Thomas Weighill
This preprint is an exploration in how a single mathematical idea - entropy - can be applied to redistricting in a number of ways. It's meant to be read not so much as a call to ac…
Political Geography and Representation: A Case Study of Districting in Pennsylvania
Jonathan Rodden, Thomas Weighill
This preprint offers a detailed look, both qualitative and quantitative, at districting with respect to recent voting patterns in one state: Pennsylvania. We investigate how much t…
The (homological) persistence of gerrymandering
Moon Duchin, Tom Needham, Thomas Weighill
We apply persistent homology, the dominant tool from the field of topological data analysis, to study electoral redistricting. Our method combines the geographic information from a…
Geometry of Graph Partitions via Optimal Transport
Tara Abrishami, Nestor Guillen, Parker Rule +4
We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition compon…
Lifting coarse homotopies
Thomas Weighill
Coarse geometry, and in particular coarse homotopy theory, has proven to be a powerful tool for approaching problems in geometric group theory and higher index theory. In this pape…
Coarse quotients by group actions and the maximal Roe algebra
Logan Higginbotham, Thomas Weighill
For a discrete metric space (or more generally a large scale space) and an action of a group on by coarse equivalences, we define a type of coarse quotient space ,…
A characterization of Gromov hyperbolicity via quasigeodesic subspaces
Thomas Weighill
By a geodesic subspace of a metric space we mean a subset of such that any two points in can be connected by a geodesic in . It is easy to check that a geodesic…
Extension theorems for large scale spaces via coarse neighbourhoods
Jerzy Dydak, Thomas Weighill
We introduce the notion of (hybrid) large scale normal space and prove coarse geometric analogues of Urysohn's Lemma and the Tietze Extension Theorem for these spaces, where contin…
Monotone-light factorizations in coarse geometry
Jerzy Dydak, Thomas Weighill
We introduce large scale analogues of topological monotone and light maps, which we call coarsely monotone and coarsely light maps respectively. We show that these two classes of m…
Mal'tsev objects, -spaces and ultrametric spaces
Thomas Weighill
In this paper we introduce a notion of Mal'tsev object, and the dual notion of co-Mal'tsev object, in a general category. In particular, a category is a Mal'tsev categ…
On spaces with connected Higson coronas
Thomas Weighill
In this paper, we characterise metric spaces which have topologically connected Higson coronas. The characterisation is given by a natural categorical condition applied in the coar…