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In [28], the proof is based on a recursive formula for the distance of the vector of regrets to the negative orthant.
Here, we only provide a brief sketch of these proofs: (1) Huang and Krishnamuthy [24] prove convergence indirectly by proving an inequality which is originated from the Blackwell's sufficient condition for approachability (2) In [28], the proof is based on a recursive formula for the distance of the vector of regrets to the negative orthant.
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It is based on the Hamming distance of the vectors presence or absence of an ortholog for every E. coli protein in each of the compiled genomes.
Any nonrandom pattern in the performance of experiments could impose a pattern on the distances of the vector metrics of affected runs from the center.
To verify the necessary condition, i.e. whether the experimentally determined feature vector lies on the boundary of the Newton polytope, we calculated the distance of the feature vector from the boundary of the polytope using the 'p_poly_dist' MATLAB function (Yoshpe, 2006).
K-means performs the clustering by minimizing the distances of the vectors to their cluster prototype.
For each transmit channel, implement a numerical research to determine which difference vectors providing d min. Equalize all difference distances of the vectors in step (ii) to obtain analytic solutions of the power allocation matrix Σ.
(ii) For each transmit channel, implement a numerical research to determine which difference vectors providing d min. (iii) Equalize all difference distances of the vectors in step (ii) to obtain analytic solutions of the power allocation matrix Σ. .
The Mahalanobis distance [41] is used in a classification procedure to measure the distance of the feature vector of an object to the centroid of each class.
The approximate solution in fact maximizes the product of two Euclidean distances, namely, the distance of the mean vector to both the lower and the higher genuine interval boundaries.
If any distance is smaller than the distance of the corresponding vector to its own cluster prototype, it is evidence that k-means has potential to operate between the clusters.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com