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Similar pairs of constraints are generated after lifting and partial projection are performed over the remaining variables.
Zahour et al. [32] proposed a partial projection procedure: they partitioned an input page into columns and drew horizontal strokes in each column.
Instead, only a partial projection of the lifted problem is carried out which leads to the following two extra constraints: (3).
It can be observed that by including the extra constraints derived from the partial projection and performing a simple branching over the linear relaxation of the extended problem, the results obtained are very close to the optimal value.
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(A ) Partial projections of expression patterns of Split GAL4 lines are visualized by mCD8 GFP (green).
E, F : insets are partial projections showing t1 cell body clusters.
Full projections of entire spindles are shown on the left and partial projections of insets chosen to highlight particular features of spindle organization are on the right.
Dynein cups chromosomes, sometimes found enriched on the side facing away from the pole ('asterisks') and sometimes around the entire chromosome ('arrowheads'); partial projections are shown to highlight particular chromosomes.
These bundles are apparent in images that are partial projections of z-stacks immediately surrounding individual bivalents; in full projections other microtubules in the spindle often obscure the bundles (which is the case in most of our images in the current manuscript).
In partial projections (focused on particular sets of separating chromosomes), bundles of microtubules could be observed on both sides of the chromosomes, with a lower density of microtubules in between the separating pair, suggesting that chromosomes may move through 'channels' as they segregate.
The map functions were used to filter and back-project subsets of projections, and reduce functions to aggregate that partial back-projection into the whole volume.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com