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But once we define the hero, simply, as the purposeful and dynamic protagonist who carries the story – someone who exhibits certain patterns of behaviour or characteristics – then there's no reason the hero can't be a woman.
Once we define an optimisation target, i.e. find parameters which minimise cross-validation error estimate, our aim is to find the optimal solution.
Once we define the participations of a user, we define also: the sum of moves, sum of duration, mean of moves and mean of duration and mean of moves per second (average user MPS over each participation).
Once we define a norm in the moment tensor eigenvalue space, points in the three-dimensional space can be projected onto a two-dimensional surface of unit "size" (A = 1); this is the basic process of producing a source-type diagram.
An example: when we have defined the rationals, and then defined the reals as the collection of Dedekind cuts, how do we define the square root of 2? It is reasonably straightforward to show that ({x ∈ Q | x < 0 ∨ x2 < 2}, {x ∈ Q | x > 0 & x2 ≥ 2}) is a cut and (once we define arithmetic operations) that it is the positive square root of two.
Once we define the set of consistent values of these meta-variables, we can define a transition probability between them.
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Once again, we define a few rules: 1.
Once we have defined the set of learning objectives and mapped them to the knowledge units, we perform a similar mapping of learning objectives to assessments.
Once we have defined the set of points of interest, we track these points over the next frames using optical flow techniques.
Once we have defined resonances it is natural to estimate the number of resonances.
Once we have defined a reduction strategy, it is natural to ask whether one can improve it.
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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