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In order to experimentally quantify the effects of microstructure on local BIF, systems which have a minimum number of variables which influence fracture must be used.
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A minimum number of random variables were chosen from a sensitivity analysis to reduce the computational cost.
In short, PCA is an unsupervised statistical method that aims at pooling together a maximum amount of variance in a minimum number of independent variables.
It is essential for bifurcation analysis that any mass conservations in a model are identified and used to write the model in a form with a minimum number of independent variables.
This table shows the groups of a minimum number of state variables used as outputs for the parameter estimation which leads to the convergence to the true parameter point.
A result from Kishi and Katajini in 1967 is that the absolute minimum number of variables required to describe the behaviour of the network is given by the maximum distance between any two spanning forests of the network graph.
The term F, called the variance, or degrees of freedom, describes the minimum number of variables that must be fixed in order to define a particular condition of the system.
B-RDBC and Müller and Welsh method based on Mallows' quasi-likelihood estimator select the same model based on the minimum number of variables.
To determine the minimum number of variables describing the geographic distribution of each species we ran a stepwise-mixed logistic regression analysis, which combines both forward and backward variable selection, on the training dataset (JMP v5.1), with county area as a covariate and a tolerance threshold for entering and keeping a variable in the model at P≤0.10.
These important assumptions in our model are made to ensure that only the minimum number of variables is included in our system of equations in order to answer the main questions of interest.
However, even upon assessing the models on the minimum number of variables included as indicated by the report and the number of events in the full sample (and therefore the maximum events per variable), all of the papers had a strong likelihood of presenting results that were overfitted to the data.
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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