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We will assume w.l.o.g. that G is a complete graph (if there is no edge between two nodes, we can add it with an infinite cost).
If an edge is allowed between two nodes, we immediately score and relax the edge, resetting the best score and best-path back-pointer in the later node when appropriate.
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Here we are interested in a static problem where we are given nodes and edges, except for the edge between two nodes (A) and (B), and we must then predict whether there is an edge between (A) and (B).
The numerical model is amenable to any molecular force that depends on the distance between two nodes, however, for this paper, we assume that the polymer chain segments that connect the filler particles obey a simple two-force model, i.e. a constant force required to stretch a single polymer chain and a force arising from the binding energy between a polymer chain and a filler particle surface.
Here, instead of searching for the shortest route between two nodes (e.g. genes), we use it to find the alternative path between those two nodes with the best throughput.
If the distance between two nodes falls into the transmission range, we add a link between them.
Ideally, we should consider the hierarchical structure of GO when we computed concept consistency between two nodes.
If the distance between two nodes falls into the transmission range (250 m), we add a link between them.
We have analyzed correlations between two nodes appearing in selective combinations.
For each path in a tree, we define the distance between two nodes as the number of edges between them.
We note that we assume a uniform distribution of the distance between two nodes.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com