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After the young mouse networks (YNG) and middle-aged mouse networks (MID) networks were created and clustered, three integrated networks were generated: the union of clusters of density ≥65% from YNG and MID, the union of clusters of density ≥6 = 75% from YNG and MID, and the union of clusters of density ≥85% from YNG and MID.
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SWC and DECOMP both use a simple voting-based aggregative strategy, called COMBINE, to take the union of the clusters produced by multiple clustering algorithms.
Then, K clusters are selected and tested whether their union is equal to the set, S. The maximal comparison time for calculating the union of two clusters is M 2 n because the maximal number of elements in a cluster is M and the dimension of an element is n.
Thus the authors of the PBT model [24] focus on the union of the clusters of angles-of-departure from the transmit array, denoted Θ T, and the union of the clusters of angles-of-arrival to the receive array, Θ R. Because a linear array aligned to the z-axis array can only resolve the z-component, the intervals of interest are Ψ T ={cosθ:θ∈Θ T } and Ψ R ={cosθ:θ∈Θ R }.
Thus, the maximal comparison time for the union of K clusters is (K ‐ 1)M 2 n.
It can be seen in Figure 6 that the support of the distribution is the union of four clusters where each of them represents the support of the distribution of only one of the eigenvalues.
Then we take the union of the clusters produced by the three approaches.
The union of AGO clusters for all experiments was computed and filtered for overlap with Ensembl-annotated 3′ UTRs, using the 'merge' and 'intersectBED' utilities, respectively, found in BEDTools v2.20.1 (parameter '-s') (Quinlan and Hall, 2010 ).
For any cluster C produced by any of these clustering algorithms, we define its score as its weighted density: s c o r e C = d e n s C = ∑ u ∈ C, v ∈ C w u, v C C - 1 We also use a simple voting-based aggregative strategy COMBINED, which takes the union of the clusters produced by the six algorithms above.
To construct the boundary of the clot, we first use the 3D morphological dilation method [20] to define a ball around each voxel of the cluster, resulting in the union of a cluster of balls in 3D.
It is worthy to note that both [ z ) and ( w ] can be considered as unions of order clusters. Given two preordered sets ( X, ≽ X ) and ( U, ≽ U ), we say that a single valued mapping f : X → U is order-increasing (or order-preserving) if x ≼ X y in X implies f ( x ) ≼ U f ( y ) in U.
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