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Each data point is allocated to at most one cluster and the clusters are disjoint.
Second, we prove that the sequence ({ (hat{x}^{k},hat{y}^{k}) }) has at most one cluster point.
After computing the weighted sum rate R ̂ ( c ) for all the candidate BS clusters in, the CU schedules a set of non-overlapping BS clusters, where each BS belongs to at most one cluster. .
In detail, by defining a j, c = 1, j ∈ J c, 0, otherwise, x c = 1, CU schedules candidate cluster J c, 0, otherwise, we consider that each BS belongs to at most one cluster, i.e., we impose ∑ c ∈ C a j, c x c ≤ 1, j ∈ J. (17).
In other words, the set of matepairs and mapped locations have a one-to-many relationship, while each mapped location is a member of at most one cluster.
We have also identified potential non-moonlighting proteins by applying essentially the opposite criteria to above: 1) proteins that have at least eight GO terms in the UniProt annotation; 2) proteins that have at most one cluster at a SS Rel of 0.1; 3) proteins that have at most one cluster at 0.5 SS Rel.
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In the Affymetrix annotation a probe set is represented by at most one UniGene cluster, while, conducting our own mapping of Affymetrix probes onto UniGene, we observed that in a number of cases multiple UniGene identifiers can be associated to a given probe set.
In terms of RMSD, this conformation exhibits the strongest deviation from the most prevalent one (Cluster 1).
Therefore ({x_{n}}) has at most one weak-cluster point.
Moreover, ({x_{n}}) has at most one weak-cluster point.
From this we conclude that ({x_{n}}) has at most one weak-cluster point.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com