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The phrase "a much smaller instance" is correct and usable in written English.
It can be used when comparing the size or scale of one instance to another, indicating that the instance in question is significantly smaller.
Example: "In this study, we will analyze a much smaller instance of the phenomenon to understand its basic principles."
Alternatives: "a significantly smaller example" or "a considerably smaller case".
Exact(1)
The 282 node Cray XE6, Tödi (Swiss National Supercomputing Center), is useful for development and testing of large scale applications for Titan, being a much smaller instance of this system.
Similar(58)
If these data are split according to possible ontogeny, the numbers remain comparable: potentially ritualized, 5.5 ± 1.7 functions per individual per zoo, with 50.7 ± 28.9 instances per zoo examined; species-typical, 3.6 ± 1.1 functions per individual per zoo, with a much smaller number of instances to examine per zoo, 18.6 ± 13.3.
Private companies can use similar technology on a much smaller scale using their own cameras - for instance, if a supermarket or car park chain wants to enforce parking restrictions or ensure customers do not leave without paying.
The approach was validated by first using an equal proportion of training and test instances (1 1) and second using a much smaller training set (1 9).
This can for instance be seen in fig 3A where a much smaller shift in mean probe intensity is observed for those populations of probes that carry motifs from related, nearly identical T7 primers.
For instance, if only teachers are included, it may be a much smaller number than if all employees are included, because many districts are trying to cut everywhere except in the classroom.
Images taken from dynamic systems (a coalescence cell and laboratory-scale bubble columns) show that in some instances the coalescence of two bubbles is accompanied by the formation of a much smaller daughter bubble.
A "much smaller boat"?
His is a much smaller outfit.
"There's a much smaller field.
Rolls-Royce is a much smaller challenge.
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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