The labels n and m index the quadrature points, per eqn. (16). The nodes on the third level of the tree (8-15) have S α ′ vectors defined as the sum of their children's S α ′ vectors, e.g. the S α ′ for node 8 is the sum of those in nodes 16 and 17. This accumulation process is repeated all the way up to the nodes 2 and 3 in the first level of the tree. From here, the interaction between a particle at the origin with all others in 18 and 19 can be evaluated using the vectors from node 9. Similarly, the cumulative effect of particles in 20-23 can be obtained from node 5, with nodes 24-31 described by vectors in node 3.