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The phrase "an increase in complexity" is correct and usable in written English.
It can be used when discussing situations, processes, or systems that are becoming more complicated or intricate over time.
Example: "The project faced challenges due to an increase in complexity as new requirements were added."
Alternatives: "a rise in complexity" or "a growth in complexity".
Exact(57)
Neither serial nor parallel direct evolution necessarily leads to an increase in complexity, and in terms of highly complex organs, the most important contribution made by direct adaptive evolution probably relates to refinements of particular functions through the modification of a few components.
In her view, conception marks not the beginning of life, since both egg and sperm are alive, but merely an increase in complexity.
Indexing, which need not involve an increase in complexity, increases the equity of the tax system, but it reduces the tax's countercyclical influence.
These advantages have been obtained by an increase in complexity as explained in Remark 7.
These examples clearly demonstrate that evolution does not always result in an increase in complexity.
As the distribution involves an increase in complexity, new approaches are needed that address this problem.
Third, multi-antenna NOMA comes with an increase in complexity at both the transmitter and the receivers.
In MDPs, non-linear objectives can be treated by state-space extensions, with an increase in complexity.
Similar(3)
Positive values correspond to a decreasing in complexity, meanwhile negative values correspond to a an increasing in complexity.
Table 8 shows an increasing in complexity in terms of arithmetic operations (−38.3%), meanwhile positive ratios are seen for read/write access memory.
Thus Earth's evolution from ancestral prokaryotes to Homo sapiens is accompanied by the reduction of cellular chemical complexity and an increase in structural complexity (eukaryotic organelles, multicellularity).
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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