To generalize the fixed point theorems from posets to preordered sets, Xie et al. in [1] introduced the concepts of order cluster and order-clustered fixed point for order-cluster preserving mappings.
23, 24 For the space-time analyses, Software for Spatial and Space-Time Statistics (SaTScan) identifies and orders clusters according to their likelihood ratio test statistic.
Both the long-range order lamella and local order cluster in the membranes are significantly affected by the radiation-induced cross-linking.
We denote by [ x ∗ ] C the order cluster in ( C, ≽ X ) containing x ∗.
After distance-sensitive ordering, cluster structure is shown in the diagonal block structure of connectivity matrix.
Since F is order cluster preserving, from u ∈ [ x ∗ ] C, it implies F ( x ∗, u ) ∈ [ F ( x ∗, x ∗ ) ].
So x ∈ [ x ] ∈ P ˜, for every x ∈ P. In the case that z ∼ w, we have [ z, w ] = [ z ], which is the order cluster containing z.
Sometimes, first-order cluster roots branch to give second order cluster roots.
Based on the definition of second-order clustering, connected network components within the same second-order cluster show coordinated activities, which implies their functional relevance.
For each ordered label and each ordered cluster tree, a TI is computed.
