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In their model, the stochastic problem is transformed into a deterministic one by replacing the random demand with its average values.
The first example is Weibull-Cauchy{exponential} distribution which can be obtained by replacing the random variable T in (9) with Weibull(c, γ) random variable.
The second example is Lomax-Cauchy{log-logistic} distribution which can be obtained by replacing the random variable T in (11) with Lomax random variable.
D-Flooding differentiates from flooding by replacing the random jitter mechanism used in the latter to reduce collisions by a distance-based delay similar to the one used by PAMPA.
MCML was enhanced by replacing the random number generator with the Mersenne Twister pseudorandom number generator in the Intel Math Kernel Library MKLL).
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In this way, (14) should be changed by replacing the normal random number r1 with the random number r from lévy distribution function.
By replacing the unknown random factors of factor analysis with observed macroeconomic variables, the arbitrage pricing theory (APT) is recast as a multivariate nonlinear regression model with across-equation restrictions.
As an alternative to the random methods, it has been suggested that lower error and improved convergence may be obtained by replacing the pseudo-random sequences with more uniformly distributed sequences known as quasi-random.
Hence, recent papers suggest replacing the random perturbed cost by a (deterministic) Taylor approximation of the average perturbed cost function.
When she realized that the area under the desk looked kind of naked, she covered her tracks by replacing the shoes with random objects.
The data owner then can deidentify his dataset by replacing the PHI with the random key.
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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