HCA is a grouping method, which allows arranging the tested objects into clusters, basing on the mathematically derived distances between them.
For the weighting scheme based on the frequencies of variants in cases, we receive the following distance vectors for cases and controls: with the elements and representing the derived distances between the weighted variant positions.
We compared the PRE derived distances between the 5′-radical center and the H6 cytidine distances with mean values obtained from various HIV-1 TAR RNA structures deposited in the PDB comprising nine structures with different ligands bound (Supporting Table 1, Supporting Information).
Distance-based method ("Neighbor Joining") was used to derive distance estimate between the isolates and branch assignments were validated using bootstrap.
One notable difference between PRE derived distances and MD derived distances is posed by C33, a nucleotide that is rather far away in the sequence but according to our experimental data seems to sample states of closer distance to the radical.
The method's principle is to minimize the entropy-derived distance between annotation-based partitions and all available hierarchical partitions.
Once adjacency has been stipulated, a distance function can be easily derived: the distance between \(p\) and \ q\), \(d p,q)\), is the smallest number of "links" in a chain of points connecting \(p\) and \ q\) such that each one is adjacent to the previous one.
By this approach we could measure global changes in Alu and LINE-1 methylation on all cytosine residues in a 220 bp Alu amplicon and a 429 bp LINE-1 amplicon (benchmark lengths derived from distance between primers in the consensus sequences) (Additional file 4).
Several practical mechanisms have been proposed for wireless nodes to perform direct distance measurements [57], and the most common current approach is to derive the distance between the transmitter and the receiver based on the signal strengths (RSS) of the received signals [37].
For example if the entries in F are derived from distances between cities then the dimension will be no higher than r = 2.
Likewise, if the entries are derived from distances between atoms in a molecule or stars in space, then the maximum dimension is r = 3.
