Spatio–Spectral Limiting on Replacements of Tori by Cubes

Title: Spatio–Spectral Limiting on Replacements of Tori by Cubes
Creator: Hogan, Jeffrey A.; Lakey, Joseph D.
Relation: Mathematics Vol. 11, Issue 23, no. 4714
Publisher Link: http://dx.doi.org/10.3390/math11234714
Publisher: MDPI AG
Resource Type: journal article
Date: 2023
Description: A class of graphs is defined in which each vertex of a discrete torus is replaced by a Boolean hypercube in such a way that vertices in a fixed subset of each replacement cube are adjacent to corresponding vertices of a neighboring replacement cube. Bases of eigenvectors of the Laplacians of the resulting graphs are described in a manner suitable for quantifying the concentration of a low-spectrum vertex function on a single vertex replacement. Functions that optimize this concentration on these graphs can be regarded as analogues of Slepian prolate functions that optimize concentration of a bandlimited signal on an interval in the classical setting of the real line. Comparison to the case of a simple discrete cycle shows that replacement allows for higher concentration.
Subject: boolean cube; discrete torus; replacement graph; spatio-spectral limiting; spectral graph theory
Identifier: http://hdl.handle.net/1959.13/1496709
Identifier: uon:54216
Identifier: ISSN:2227-7390
Rights: x
Language: eng
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