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Theorem 2 Suppose φ ∈ C ( I, I ) and α ∈ C 1 ( I, I ) are increasing functions with α ( t ) ≤ t, α ( 0 ) = 0, ∀ t ∈ I.
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From (2.12) we can easily prove that (G(I)) is decreasing and (H(I)) is increasing.
To see that f ∗ ∈ F, note that since each f i is increasing, so is f ∗.
For fixed, (i) is increasing with respect to, (ii)if, then is Schur-concave with respect to.
Throughout the paper, we assume that the function (f(I)) satisfies the following condition: (A1): (f(I)) is increasing for (I>0), and (f(0)>0).
We assume that θ i is increasing for 0≤ i≤ N−1.
As a consequence, z i is increasing and each root can be identified by this property, which means each value of y i can be obtained.
For example, if one component of f (i) is increased, other components will decrease because of the normalization.
In order to counter this effect, the value of the maximal synaptic conductance g i is increased so as to effectively increase the strength of synaptic inhibition.
Thus the waiting time before each block i is increased by the minimum of Θ i earliness, Θ i slack, and Θ i + 1 waiting (Lines 3 7).
On the other hand, if instance Ins m and those in M have different values on the the gene i, then W i is increased.
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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