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As a robustness check, we alternatively define excess cash (Excess CashALT) with the predicted values from the fixed effect model (2) in Table 3 that includes additional firm characteristic variables.
We could alternatively define a separate probability distribution for the first d nucleotides.
There is therefore considerable incentive to identify biomarkers that will have impact across the broad lupus portfolio, or alternatively define unique SLE subsets that may require and respond to different therapies.
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In model (7), we deploy alternatively defined excess cash (Excess CashALT) and obtain a similar result.
When the variable is a differentiable function of the parameter, the sensitivity index may be alternatively defined using partial derivatives.
Additionally, the PSD function can be alternatively defined using the spectral representation of time series, that is, (4).
The variable E 1i is alternatively defined as indicating whether individual i has ever started a business or whether individual i has ever started a business that was ultimately successful.
Comparing the baker's map and the symmetric tent map functions, the baker's map can be alternatively defined via the symmetric tent map function as follows: begin{array}{*{20}l} left[ begin{array}{c} x y end{array} right]= F u,v)= left[ begin{array}{c} G u) G_{mathsf{sign} u)}^{-1} v) end{array} right], -1 leq u, v leq 1. end{array} (3).
Alternatively, defined amounts of bovine serum albumin (BSA; Sigma) served as standard for semi-quantitative determination of protein concentration after SDS-PAGE and Coomassie Blue staining.
When the main exposure variable was alternatively defined as the sum of 16 glycol ethers, excluding propylene glycol, the likelihood of the four respective outcomes were essentially very similar to those posed by sum of 17 glycol ethers including propylene glycol (Table 4).
We alternatively defined the Sophophora glob2 and the Sophophora glob3 stem lineages as foreground branches.
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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