Overlapping clusters

Figure 6 A schematic representation of two clustering methods, m which each point represents a single molecular conformation and the circles are the similarity cutoff distances used to define the clusters, (a) Three clusters are defined when overlapping clusters are grouped together, (h) Five clusters are defined when the overlaps are removed from one of the overlapping clusters.

Blankenstein, T. Krawinkel, U. (1987). Immunoglobulin VH region genes of the mouse are organized in overlapping clusters. Eur. J. Immunol. 17,1351-1357. 

In the region where the reciprocal approximation holds, Equation 7 also predicts that the intensity is independent of dose. It is found, however, that the intensity is proportional to dose. This dose dependence could arise in this kinetic scheme if the species causing luminescence are in non-overlapping clusters or spurs and an increase in dose simply results in a proportionate increase in the number of such clusters. However, this cluster model would imply that virtually all triplets must be formed in the clusters, and there is as yet no other evidence for this. 

This statistical law makes it possible to correlate single cluster behavior to that of a collection of many clusters and, alternatively, to derive nucleation and growth laws from observations involving many overlapping clusters. The validity of Eq. (32) requires a random distribution of a large number of clusters, in which, each must be small with respect to the total available electrode area. 

Linear regression analysis allows to find a well defined, and in some way optimum decision plane even for overlapping clusters. 

After completing the process of claim construction, POE, and the NPTF-IG key phrases extraction methodology, the target patent and the related prior art patents are analyzed to identify patent novelty. An invention is patentable if it satisfies specifications for novelty. Novelty is defined in Section 102 of the US Patent Law The invention is novel if it was not previously patented, described in a publication, in public use, or on sale by others before the inventor invented it. Trappey et al. [35] use non-exhaustive overlap clustering to analyze patent documents with multiple technical descriptions of the invention. The results show that key phrases... 

Substantial (nearby seeds can cause overlapping windows) Incomplete (requires additional steps to revisit skipped nodes) Poor (can be widely varying depending on adjacent net degree) Mediocre (overlapping clusters cannot be solved simultaneously)... 

In structures where n = 7 or above, overlapping clusters are not observed, and maximum separation of the clusters occurs consistent with the composition, dimensions and symmetries of the unit cell. Furthermore, relaxation of the cation sublattice is observed to be maximized. In particular, although in the = 7 structures double vacancies do occur along <11 1) across metal atoms and where no metal atoms separate them, the latter are not found in any other known structures, even for = 9. The only intermediate compound reported for the actinide oxides is the iota phase, An70j2 (see sections 2 and 3). However, efforts to prepare other phases have not been extensive. They might occur in the heavier oxides of the series from Pu to Es since these may possess both the 3 -F and 4+ oxidation states. The structural principles appropri-... 

Number or letter the H s on the remaining structure and use these to assign each unique type of H to a cluster on the spectrum. (Note that there are some overlapping clusters near 7.4 ppm.)... 

---