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since the user data rates are independent from each other, i.e., it is enough to optimize the individual user data rates in order to optimize the sum of the user data rates.
More specifically, we focus on choosing a set of jobs to reject and constructing a schedule for the remaining jobs so as to optimize the sum of the weighted completion times of the jobs scheduled plus the sum of the penalties of the jobs rejected.
This alignment scheme aims to optimize the sum of the semi-global (overlap-detection) alignment scores on each side of a fixed split position in the transcript gap region.
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In this case however, we have to optimize the sum rate and cannot optimize the rate for each user.
Other variants like c- optimality (optimize estimation of a linear combination of parameters) or a- optimality (optimize the sum of individual variances of parameter estimates) exist, but these are less common and will not be covered here.
The crux of this scalarization method is to optimize the weighted sum of the two objectives with different weight vectors.
This means that we do not attempt to jointly optimize the sum rate of all users; notice, though, that for single-stream beamforming, it has been shown in [62, 63] that such an approach can still achieve the maximal sum-rate, provided the leakage constraints are appropriately selected.
Finally, the unregistered images are non-linearly registered to their synthetic reference counterparts by optimizing the sum of squared differences (SSD).
The best forest mitigation strategy is the one that optimizes the sum of all mitigation options in a given (policy-determined) time frame, a complex task whose solution is very much country-specific (e.g., [6, 37]).
The MSA program optimizes the sum of all of the pairs of characters at each position in the alignment (the so-called sum of pair score) and has been implemented in a software program for constructing multiple sequence alignments.
We conducted multiple-sequence alignment using MUSCLE (4 ) and optimized the sum of all of the pairs of characters manually.
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