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Comparisons of GEO3D with 500 vertices for higher graph densities (up to 0.4) suggest that the score becomes more stable, although slowly increasing (Supplementary Material).
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Output given number of genes with highest graph centrality as the new unified breast cancer signature.
Finally, we get reliable gene signatures that are consisted by the genes with high graph centrality.
Full list of genes in these graph centrality based signatures are provided in Table 2. 54 genes with highest graph centrality in the context-constrained PIN are selected to consist new breast cancer gene signatures.
They also give interesting conditions for topological higher rank graphs and P-graphs, and apply to the new Cuntz C⁎-algebra QN arising from the "ax+b -semigroup over N.
In contrast, a high neighbourhood graph density reflects a high degree of functional homogeneity within the seed's neighbourhood which indicates a higher likelihood of the seed being in a protein complex core, e.g., vertex 1 in Figure 1.
We compute the K-theory of the Toeplitz algebra of a finitely aligned higher rank graph and of a higher rank Exel Laca algebra under condition (II).
With these observations as motivation, one defines a higher rank graph, as follows.
At a very low throughput, the successive transmission probability of a node is lower for a higher degree graph as given by (5).
Figure 2B ('hours') shows a higher resolution graph that displays bloodstains deposited 15 minutes to 2 days prior to analysis.
The Dow Jones industrials and Standard & Poor's 500 reached their highest levels in nearly five years, while the Dow Transports reached all-time highs (see graph).
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