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Combinatorial Conditions for Directed Collapsing
The purpose of this article is to study directed collapsibility of direc...
06/03/2021 ∙ by Robin Belton, et al. ∙
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A Domain-Oblivious Approach for Learning Concise Representations of Filtered Topological Spaces
Persistence diagrams have been widely used to quantify the underlying fe...
05/25/2021 ∙ by Yu Qin, et al. ∙
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Persistence Diagrams for Efficient Simplicial Complex Reconstruction
Topological descriptors have been shown to be useful for summarizing and...
12/29/2019 ∙ by Brittany Terese Fasy, et al. ∙
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Reconstructing Embedded Graphs from Persistence Diagrams
The persistence diagram (PD) is an increasingly popular topological desc...
12/18/2019 ∙ by Robin Lynne Belton, et al. ∙
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Topological and Geometric Reconstruction of Metric Graphs in R^n
We propose an algorithm to estimate the topology of an embedded metric g...
12/06/2019 ∙ by Brittany Terese Fasy, et al. ∙
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Threshold-Based Graph Reconstruction Using Discrete Morse Theory
Discrete Morse theory has recently been applied in metric graph reconstr...
11/28/2019 ∙ by Brittany Terese Fasy, et al. ∙
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Approximate Nearest Neighbors in the Space of Persistence Diagrams
Persistence diagrams are important tools in the field of topological dat...
12/29/2018 ∙ by Brittany Terese Fasy, et al. ∙
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Challenges in Reconstructing Shapes from Euler Characteristic Curves
Shape recognition and classification is a problem with a wide variety of...
11/28/2018 ∙ by Brittany Terese Fasy, et al. ∙
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Learning Simplicial Complexes from Persistence Diagrams
Topological Data Analysis (TDA) studies the shape of data. A common topo...
05/27/2018 ∙ by Robin Lynne Belton, et al. ∙
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Functional Summaries of Persistence Diagrams
One of the primary areas of interest in applied algebraic topology is pe...
04/04/2018 ∙ by Eric Berry, et al. ∙
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