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This scatterplot is coupled with a unique partition slider which allows users to move color coordinated bands on the scatterplot to indicate grade ranges.
In other words, we ensure that all current paths are contained completely either in a unique partition matrix or in the coupling matrix.
Perhaps we will not always end up with a unique partition to which the Principle of Indifference is to be applied, but it would already be progress if we ended up with only a handful of partitions.
Based on the observations above, we remark that each ordered partition from can be transformed, in a finite number of steps, to the unique partition from which satisfies the condition in (7).
There exist a unique partition T = {C 1, C 2, …, C p }of the state space S into SCCs (communicating classes in MDP theory), that can be classified into some levels (see Fig. 1).
This process leads to a unique partition of covariance between the outcome and all covariates.
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With three clusters (K = 3), there are only two unique partitions.
This unique partitioning of data enables researchers to focus on the hard matching problems of face recognition within the database.
The unique partitioning pattern observed for the Chlorellales clearly indicates that the chloroplast genome followed a distinctive evolutionary pathway in this algal group.
Note that the initial assignment of a particular paralog to the first or second column is arbitrary, meaning that there are 2 n – possible unique partitioning of the duplicates into columns.
It is sufficient to check (3) for "minimal balanced collections" (and these collections turn out to yield a unique fractional partition).
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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