Hyper G-Matrix Pairs and Applications in Dentistry

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Keleş H., Keleş E.

PROOF, vol.5, pp.94-105, 2025 (Peer-Reviewed Journal)

• Publication Type: Article / Article
• Volume: 5
• Publication Date: 2025
• Doi Number: 10.37394/232020.2025.5.13
• Journal Name: PROOF
• Page Numbers: pp.94-105
• Karadeniz Technical University Affiliated: Yes

Abstract

This study investigates the application of Hyper G-matrix pairs from linear algebra to dental

microbiology. A mathematical framework is presented for modeling the complex interaction networks

of the oral microbiome. Hyper G-matrix pairs quantitatively express the relationship between microbial

interactions under two different clinical conditions. The presented numerical examples demonstrate that

this approach can be used for assessing caries risk and predicting treatment effectiveness. Both approx-

imate and exact Hyper G-matrix pairs are examined, and their clinical interpretations are explained in

detail. The study is based on recent publications on Hyper G-matrices.