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The graph theoretically shows that no cracks are anticipated to take place in this new deck.
The tool's graph theoretically can show that no cracks are anticipated to take place in this designed concrete bridge deck.
Since Brouwer's fixed-point theorem has been approached graph theoretically with hexagonal lattices [13] or using results on graph colorings like the Sperner lemma [14], it is natural to inquire for a direct combinatorial analogue on graphs without relating to any Euclidean structure.
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Modules under such definition might not be graph-theoretically intuitive.
Besides, inspection of modularity-based communities reveals that these communities are graph-theoretically meaningful yet not reflective of specific biological functions.
This contribution aims at extending VQ to the quantization of graphs in a theoretically principled way in order to overcome practical limitations known in the context of prototype-based clustering of graphs.
The orbifold framework will introduce sufficient mathematical structure to allow an extension of VQ to graph quantization in a theoretically sound way without discarding the relational information of the graphs.
Given the PCR protocol, the midpoint cycle number (where the template concentration is half that of the final concentration) can be theoretically determined and graphed for a variety of initial DNA concentrations.
Convergence is not theoretically guaranteed for general graphs; however, the algorithm often does converge for real-world graphs in practice.
We combine the schemes with the two random graph generation models and investigate the proposed algorithms theoretically.
We theoretically prove that the uniform random graph is the optimal topology for this botnet, and demonstrate its high efficiency and stealth with various simulations.
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