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Yet, our construction is fully generalized and can be applied to analyze signals on any undirected, connected, weighted graph.
We compared these to our fully connected, weighted network using a receiver operating characteristic (ROC) curve.
These correlations may be interpreted as a fully connected, weighted graph, typically represented as a simpler discrete network by a process of edge removal based on the strength or significance of the correlations 92 (e.g. Fig. 1C).
72 However, studying the evolution of such graphs is tricky – it depends on how the fully connected, weighted graph is simplified, which may involve arbitrary thresholds, or approaches such as minimal spanning trees (MSTs, Fig. 1C).
To facilitate the proof of this theorem, we build a fully connected weighted graph 𝒢 in which each node corresponds to a tree for integration, and the weight of each edge corresponds to the weight increase (initially, this is the cohesion score) for integrating the corresponding trees.
Given a fully connected, weighted network, let w x be the vector of similarity scores between x and all other nodes in the network; i.e. w x [ i]= S x, i), where S x, i) is the similarity between sequences x and i.
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Every subgraph of a differential bicluster of degree at least L is a differential bicluster of degree at least L. In every connected, weighted-edge graph G = (V, E, w) where θ(G) = α ≥ 1/2 there is a node v ∈ V such that G − v is connected and θ(G − v ≥α.
In our setting, we obtain the following results where G − v is the subgraph of G which results from removing v and all edges incident to v: Every subgraph of a differential bicluster of degree at least L is a differential bicluster of degree at least L. In every connected, weighted-edge graph G = (V, E, w ) where θ(G ) = α ≥ 1/2 there is a node v ∈ V such that G − v is connected and θ(G − v )≥α.
The neurons of one layer to the neurons of pre-and-after layerare connected through weighted links.
ANN units are connected by weighted links that pass information and store the required knowledge in hidden layers.
Genes are connected with weighted directed edges.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com