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We then computed all pairwise distances between the vectors, using the standardized Euclidean distance as the distance measure, i.e., weighting each coordinate by the inverse of its variance.
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For every interest point of P i, the best match is determined by minimizing the Euclidean distance between the two descriptor vectors (using the keypoint matching approach presented in [13]).
Similarity between flux graphs is quantified through the distances between corresponding vectors, using the cosine coefficient and a novel graph-distance metric taking into account the magnitude of each flux and the activity distribution of different fluxes.
Trees based on amino acid content were constructed from the matrix of Euclidean distances between frequency vectors using the NEIGHBOR program of the PHYLIP package [ 100].
Proposition 1 states that an estimation of the inner product between two vectors, using the matrix of sparse random projections (4), are correct in expectation and have bounded variance.
Norm optimal iterative learning control is an optimization-based approach where, in contrast to other such approaches, a term in the cost function is a measure of the difference between the control vectors used on successive trials.
It is then straightforward to define a distance between two sequences S i and S j as the distance between these frequency vectors, using some standard distance metric on vector spaces.
The differences in trajectories of shape changes were analyzed by comparing the angle between the species-specific multivariate regression vectors using VecCompare6 (IMP-software).
The covariance between the vectors is used as a way to determine how dominant a particular vector will be in the proposed linear combination.
When taking into account more than three eigenvectors, to assess more precisely the distances between the vectors, we used a decision-making tool based on calculation of the root mean square (Supplementary Table 2, see section on supplementary data given at the end of this article).
The relationship between body-shape and swimming performance was tested by comparing the variable vector with the shape vector, using the permutation test available in TpsPls.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com