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These measures are either based on the RMSD (root mean squared deviation: average squared distance between homologous alpha carbons) or the dRMSD (distance RMSD: average square difference of distances between equivalent pairs of amino acids) like the DALI score (Holm and Sander, 1995), APDB (O'Sullivan et al., 2003) or the iRMSD (Armougom et al., 2006a).
It is defined as the square root of the minimum value of the average squared distance between each pair of corresponding atoms, over all the possible rotations and translations.
Since is fixed, minimizing RSS is equivalent to minimizing the average squared distance, a measure of how well centroids represent their documents.
The k-means method is a widely used clustering technique that seeks to minimize the average squared distance between points in the same cluster.
Then, the average squared distance from a CH to the BS is similarly given by Equation (2).
Therefore, the average squared distance from an LN to its CH within a cluster can be calculated as follow.
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The average square distance, taken over all molecules and a measure of the average distance a molecule travels, gives us the mean square displacement (MSD).
The average square distance between two consecutive broken fibers is (|langle Delta r^{2}rangle ^{1/2}|=L/sqrt {6}) [Stormo et al. (2013)].
Moreover in the Additional file 1, we give a detailed comparison of the distance method applied here with some of the most used genetic distance measures based on microsatellite analysis, such as the Nei distance [14], the Cavalli-Sforza distance [15], the Goldstein distance [14] and the average square distance [16].
The weight of each gene is computed based on its minimum distance to any known functional group (e.g. a pathway) where the distance is defined as the average square distance from this gene to all the genes in the group.
Diversity and haplotype connectivity scores for the sampling locations pictured in Figure 5, ranked according to normalized average square-distance diversity score (AD*).
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