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09/05/2023
From Curves to Words and Back Again: Geometric Computation of Minimum-Area Homotopy
Let γ be a generic closed curve in the plane. Samuel Blank, in his 1967 ...
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07/26/2023
The Weighted Euler Characteristic Transform for Image Shape Classification
The weighted Euler characteristic transform (WECT) is a new tool for ext...
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12/26/2022
Efficient Graph Reconstruction and Representation Using Augmented Persistence Diagrams
Persistent homology is a tool that can be employed to summarize the shap...
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08/10/2022
Persistent Homology Transform Cosheaf
We employ the recent discovery of functoriality for persistent homology ...
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04/01/2022
Differentiating small-scale subhalo distributions in CDM and WDM models using persistent homology
The spatial distribution of galaxies at sufficiently small scales will e...
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03/17/2022
Extremal Event Graphs: A (Stable) Tool for Analyzing Noisy Time Series Data
Local maxima and minima, or extremal events, in experimental time series...
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06/03/2021
Combinatorial Conditions for Directed Collapsing
The purpose of this article is to study directed collapsibility of direc...
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05/25/2021
A Domain-Oblivious Approach for Learning Concise Representations of Filtered Topological Spaces for Clustering
Persistence diagrams have been widely used to quantify the underlying fe...
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12/29/2019
Persistence Diagrams for Efficient Simplicial Complex Reconstruction
Topological descriptors have been shown to be useful for summarizing and...
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12/18/2019
Reconstructing Embedded Graphs from Persistence Diagrams
The persistence diagram (PD) is an increasingly popular topological desc...
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12/06/2019
Topological and Geometric Reconstruction of Metric Graphs in R^n
We propose an algorithm to estimate the topology of an embedded metric g...
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11/28/2019
Threshold-Based Graph Reconstruction Using Discrete Morse Theory
Discrete Morse theory has recently been applied in metric graph reconstr...
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12/29/2018
Approximate Nearest Neighbors in the Space of Persistence Diagrams
Persistence diagrams are important tools in the field of topological dat...
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11/28/2018
Challenges in Reconstructing Shapes from Euler Characteristic Curves
Shape recognition and classification is a problem with a wide variety of...
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05/27/2018
Learning Simplicial Complexes from Persistence Diagrams
Topological Data Analysis (TDA) studies the shape of data. A common topo...
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04/04/2018