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Figure 4 and Supplementary Figure 3 show theoretical examples for different center-surround configurations.
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In our theoretical example, for instance, it was possible to optimize a process so that all of the X's were moved close to or below the diagonal.
Lest one think this warning is purely theoretical, examples of lawyers being prosecuted for insider trading are many.
These physicians also indicated a need for 'watching': getting theoretical examples (e.g. theory on communication techniques or how to communicate conclusions) and practical communication examples (e.g. from role models or peers).
For the theoretical example, the value for Condition 1 was set to a minimum trough effect value of 0.35 (units) and the value for Condition 2 was 0.9 such that at least 90% of doses (from dose 11) within an individual must have an effect at the trough greater than 0.35 (units).
The reaction-diffusion mechanism presented by A. M. Turing more than 60 years ago is the most common theoretical model for explaining various examples of biological pattern formation, including pigment patterning (Kondo and Miura, 2010; Meinhardt, 1982; Murray, 2002; Turing, 1952).
However the patterns of sequence variation make it logically impossible to use DNA barcodes for species circumscription as originally proposed [see 8 for an empirical example, see 10 for a theoretical example].
In this study, we have proposed a criterion to quantify forgiveness; illustrated the criterion for a theoretical example and evaluated the forgiveness of a motivating example, namely warfarin.
In this study, we have developed a criterion to quantify forgiveness and then: (1) illustrate the criterion for a theoretical example and (2) apply the criterion to warfarin as a motivating example.
More significant examples require theoretical advances, for example with respect to the Metropolis filter.
The latter was revealed through the various theoretical (for example, some relatively modern researches in [2 5]) and experimental investigations (see starting, for example, from [6, 7] to the modern applications like described in [8] and impressively effective experimental realizations as in [1]).
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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