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Mapping subjective inputs onto mathematical expressions allows us to bring to bear the toolbox of mathematics on unobservable subjective entities (see the General Discussion section for examples of other recent applications).
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These expressions allow us to compare patient welfare with fee discrimination (FD) and without fee discrimination (NFD) under balance billing.
The developed expressions allow us to obtain an equivalent viscous model which dynamic matrices explicitly depend on the viscoelastic damping parameters.
These expressions allow us to implement efficient statistical analysis, avoiding the time-consuming Monte Carlo techniques for estimating the confidence interval of the fluxes.
The rate expressions allow us to assess the rate loss as compared to the optimal receiver for varying channel parameters such as channel length and spatial correlation.
Both the numerical results and the closed-form expressions allow us to conclude that in the simulated scenarios, multi-tap precoding and equalization based on the frequency sampling approach do not boost the power.
The analytical expressions allow us to separate the roles of the dynamic restraints imposed by the protein on the binding site and the temperature-independent chemical effects in metal-ligand coordination.
These expressions allow us to interpret the cancellation of the pure and mixed non-abelian anomalies geometrically as a result of the general form of the matter surfaces, without reference to a specific type of gauge flux.
Such simple expressions allow us to connect with others, ease our hearts with a gentle touch of shared humanity.
The morphed nature of these stimuli provides ambiguous expressions, allowing us to determine the tendency to read fear in the morphed expressions, rather than scoring the responses as correct/incorrect.
Tight temporal control over protein expression allows us to perform in-cell biochemistry, such as phosphorylation, by expressing a kinase domain capable of post-translationally modifying the interactor protein, off an inducible plasmid (Fig. 1ab).
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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