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This can be formulated as a random field (RF) model according to the Bayes theorem (1).
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The proposed problems are formulated as a fuzzy random production planning (FRPP) model by maximizing the mean chance of the total costs less than a given allowable investment level.
The correct question for the WMW test can be formulated as: Is a random sample from one of the distributions likely to be less than a random sample from the other distribution?
Each entry ( a_{ij},;j in J_{i} ) is formulated as a symmetric and bounded random variable ( tilde{a}_{ij},;j in J_{i} ) (Ben-Tal and Nemirovski 2000) that takes on values ( left[ {a_{ij} - hat{a}_{ij},a_{ijij} + hat{a}_{ij} } right].
The problem is formulated as a discrete-time optimal control problem with a random terminal time and probabilistic state constraints.
This problem is formulated as a binary labeling problem based on a Markov random field (MRF) framework, the solution of which is a binary map for each exposure image, which identifies the pixels to be excluded in the fusion process.
Haneveld (1988) and Peters et al. (1977) considered the production planning problem with limited production capacity and random demand for multiple products formulated as a stochastic programming.
The synthesis problem is formulated as a mixed-integer nonlinear programming (MINLP) problem, which is solved by simulated annealing algorithm under a random procedure to explore the optimal operating parameters and the distillation sequence structure.
The queuing problem is formulated as a GI/M/1 Markov chain where the exact queue length and delay statistics for the GBN-ARQ protocol can be obtained by using matrix geometric methods under random feedback delay values.
The test for discrimination can be formulated as a "but for" question.
The FARED is formulated as a robust optimization problem.
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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