In triangulated graph, each 3-node loop (which is not part of any larger clique) represents 3-node clique, and each edge (which is not part of any 3-node clique) represents 2-node clique.
For instance, in the PJT in Figure 3b, the node 10 (due to the non-triangulated 4-node loop: 3 9 5 10), and the node 7 (due to the appearance of 4-node clique: 2 6 5 7) do not satisfy the RIP.
aAccording to our empirical analysis, the number of these loops is relatively small (e.g., just one 4-node loop in Figure 2b .bWe implicitly assumed that q C i 1 ( x C i ) = 0 if the state of one of the clique nodes is out of the deployment area.cIn practical circumstances, we can set ϵ = 0.dNote that these values do not represent the mean value and the standard deviation of the distance.
Following selection of candidate blisters, the other components such as needle, bypass and mouthpiece were dimensioned on the basis of node-loop operations and validation experiments.
With regard to hysteresis-loop bursters, the class of smallest complexity is subH/FLC (c16), which exists close to the codim-2 Bautin bifurcation as outlined by Golubitsky et al. Class SN/SH (c2) lives close to the codim-2 Saddle-Node-Loop bifurcation [17], but this bifurcation is not local and the lowest codimension singularity for this class is the codim-3 deg.
Here the limit cycle vanishes and we have a curve of saddle-homoclinic bifurcations SH l, which starts at TB l and terminates on SN r giving rise to the codim-2 saddle-node-loop bifurcation SNLs r. 's' denotes a small limit cycle, in the sense that it does not surround all the fixed points.
The main benefit of the thin graph is that it mainly includes 3-node loops.
Two types of constraints are employed: a constraint between consecutive nodes ((j = i + 1)) and that between non-sequential nodes (loop-closing constraints).
Thus, for n-node loops (n > 3), we form maximum n 2-node cliques, using each edge (which is not already subset of any 3-node clique) of the loop as a clique.
Nonetheless, given that so many of the key motifs identified so far are either complete 3-node loops or contain them [37], [38], the global topology will have a high clustering coefficient, and will most likely be a small-world network.
The Intermediate test covers the topics: object nodes, control nodes, activity partitions, structured activity nodes, conditional and loop nodes, and exception handlers.
