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The proposed method generates an assignment order for the whole planes that corresponds to assignment priority.

To assess possible affects of subdivision, we generated an assignment matrix (C) with values that equaled zero (0) if populations belonged to a cluster identified by Structure and one (1) if populations belonged to different clusters.

Through minimizing the overall loss on both labeled and unlabeled data, we generate a label assignment pool.

As mentioned in [ 25], the factorization of the consensus matrix will generate a clustering assignment matrix that could capture the cluster structure inherent in the network.

If the similarity matrix was well constructed (each element reflected the co-cluster similarity), the factorization of the similarity matrix would generate a clustering assignment matrix that could well capture the cluster structure inherent in the network representation.

An accurate investigation of the assignments of the OAK discloses failures and shows that the OAK is not able to generate a substructure preserving assignment of the atoms in some cases.

It works by first blocking SampleType only to generate a pool of assignment setups, and then select the optimal one with most homogeneous cross-batch strata (i.e., SampleType, Race and AgeGrp) distribution.

The alternative algorithm (implemented in function optimal.blcok) sought to first block specified variables (e.g., list of variables of primary interests) to generate a pool of assignment setups, then select the optimal one which minimize the objective functions based on all variables considered (including those variables which are not included in the block randomization step).

The default algorithm (implemented in function optimal.shuffle) sought to first block all variables considered to generate a single initial assignment setup, then identify the optimal one which minimizes the objective functions (i.e., the one with most homogeneous cross-batch strata distribution) through shuffling the initial setup.

The default algorithm implemented in OSAT will first block three variables considered (i.e., SampleType, Race and AgeGrp) to generate a single initial assignment setup, and then identify the optimal one with most homogeneous cross-batch strata distribution through shuffling the initial setup.

The computer program generates a treatment assignment and a study ID number associated with each eligible subject's name and birth date, and documents these in an uneditable form with a date stamp.

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