Combinatorial Hodge theory for equitable kidney paired donation

Mike, Joshua L.; Maroulas, Vasileios

doi:10.3934/fods.2019004

Cited by 2 publications

(1 citation statement)

References 16 publications

(21 reference statements)

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“…In recent years, topology and geometry blended with statistical methods have seen increasing application to the study of data analysis, visualization, and dimensionality reduction [1][2][3][4][5][6][7][8][9]. These applications range from classification and clustering in fields such as action recognition [10], handwriting analysis [11], and biology [12][13][14][15][16], to classification of high entropy alloy [17] and gas separation [18], to the analysis of complex biological networks [19], and other complex dynamical systems [20,21] and sensor networks [22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Quantum Persistent Homology

Bernardo¹,

Maroulas²,

Siopsis³

2022

Preprint

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Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such topological features is often a rather formidable task necessitating the sub-sampling the underlying data. To remedy this, we develop an efficient quantum computation of persistent Betti numbers, which track topological features of data across different scales. Our approach employs a persistent Dirac operator whose square yields the persistent combinatorial Laplacian, and in turn the underlying persistent Betti numbers which capture the persistent features of data. We also test our algorithm on point cloud data.

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