The phrase "analyses of the cluster" is correct and usable in written English.
It can be used when discussing the examination or evaluation of a specific group or collection of items, data, or phenomena referred to as a "cluster."
Example: "The analyses of the cluster revealed significant patterns that were previously unnoticed."
Alternatives: "examinations of the cluster" or "evaluations of the cluster."
This analysis reduces to previous analyses of the cluster problem for unconstrained optimization under suitable assumptions.
This article extends previous analyses of the cluster problem in unconstrained global optimization (Du and Kearfott 1994; Wechsung et al. in J Glob Optim 58(3):4201438, 2014) to the constrained setting based on a recently-developed notion of convergence order for convex relaxation-based lower bounding schemes.
The analyses described in this article were not part of the original analyses of the cluster randomized control trial and were therefore performed as secondary analyses.
Synteny conservation, nucleotide composition, and phylogenetic analyses of the cluster genes indicate that the B. cinerea cluster was acquired via horizontal transfer from a Fusarium donor.
Blast analyses of the cluster as well as the corresponding region of the other SDSE strains, three in Lancefield group G and one in Lancefield group A, indicated that these clusters showed identity with those of bacteria carrying group C, G, and A antigens, respectively (table 1).
This view has been supported by a vast number of analyses of the clustering of infrared galaxies, at scales up to a few degrees, in various surveys.
Using ultra-fast clustering followed by automated analyses of the clusters, we were able to quickly analyze a very large metagenomic dataset.
However, in the clustering process and in subsequent analyses of the clusters, we consider only nodes with more than three interacting partners in the network; consequently, we consider only edges with both end nodes having degree of more than three.
Taken together, functional analyses of the clusters revealed that light generally increases cellular metabolism (Clusters 3a and 3b), and at the same time causes significant oxidative stress to the organism.
Detailed analyses of the clusters for transport systems and transcriptional regulators allow the conclusion that despite the conservation of enzymes in catabolic pathways, the transport systems and transcriptional regulators are not conserved.
On the other hand, GO analyses of the magenta cluster revealed genes linked to "neuron development" such as CNTN1, FAIM2, which were also hub-genes in the magenta cluster.
