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Title: A CHEMO-MECHANO-BIOLOGICAL MODEL OF CARTILAGE IN FEBIO: STUDIES OF PATHOLOGICAL LOADING, HOMEOSTATIC ADAPTATION AND BIO-CHEMICAL TREATMENTS
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Award ID(s):
1662429
PAR ID:
10479422
Author(s) / Creator(s):
Corporate Creator(s):
Editor(s):
a
Publisher / Repository:
ASME
Date Published:
Journal Name:
Proceedings of the Summer Biomechanics, Bioengineering and Biotransport Conference
Edition / Version:
1
Volume:
1
Issue:
1
Page Range / eLocation ID:
1
Subject(s) / Keyword(s):
1
Format(s):
Medium: X Size: 1 Other: 1
Size(s):
1
Sponsoring Org:
National Science Foundation
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    A unified approach to the determination of eigenvalues and eigenvectors of specific matrices associated with directed graphs is presented. Matrices studied include the new distance matrix, with natural extensions to the distance Laplacian and distance signless Laplacian, in addition to the new adjacency matrix, with natural extensions to the Laplacian and signless Laplacian. Various sums of Kronecker products of nonnegative matrices are introduced to model the Cartesian and lexicographic products of digraphs. The Jordan canonical form is applied extensively to the analysis of spectra and eigenvectors. The analysis shows that Cartesian products provide a method for building infinite families of transmission regular digraphs with few distinct distance eigenvalues. 
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