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The phrase "a higher order level" is correct and usable in written English.
It can be used in contexts discussing concepts, classifications, or hierarchies, particularly in academic or technical writing.
Example: "In this study, we aim to analyze the effects of a higher order level of cognitive processing on learning outcomes."
Alternatives: "an elevated level" or "a more advanced level".
Exact(3)
An assembled transcription unit represents a module again, albeit one of a higher order (level 1 module), which can be directionally assembled into a multigene construct (level 2) (Fig. 1A).
The families were then grouped into P450 clans, a higher order level of nomenclature that represents a cluster of P450 families across species, grouped based on relationships that are beyond the family designations [ 57].
The aromatase family offers an example where a combination of phylogenetic analysis, molecular evolutionary analysis, and chemical analysis set within the context of the paleontological and geological records, and supported by contemporary bioinformatics and molecular modeling tools, permits a higher order level of hypothesis generation concerning the function of proteins.
Similar(57)
On Frankfurt's account, autonomy requires "wholehearted identification" at a higher-order level with lower-order motives, preferences, or desires (Frankfurt 1988).
In fact, amplicons can display a higher-order level of architectural organization: they can be organized in symmetrical arrays of contiguous units.
Furthermore, the hypergraph-based model more flexibly represents miRNA-RNA interactions than other methods (which assume that the expression states of miRNAs and mRNAs are linearly proportional to each other), because it isolates significant modules from the statistical co-expressed pattern among genes at a higher-order level.
The method has to be slightly modified if one of the output variables is a higher order occurrence level which is not contained in any of the submodels.
This conclusion may underestimate the linkage, as whether or not the supercontigs themselves that contain these SDMA genes are part of a higher order linkage at the chromosomal level awaits a better assembly of the A. aegypti genome.
By desiring at a hierarchically higher-order level of reflection that one's will be a certain way (or not be a certain way), one reveals her deeper self, not merely at the surface of her conduct, but in terms of how she herself regards her very own motives issuing in her conduct.
A still higher-order level of regulation consists of chemical and physical PTMs, and influences the physiological aspects of function and determines the half-life of proteins and their interactions with other proteins, ligands and DNA.
At a higher-order level both factors capture the same underlying mechanism the fear of anxiety related sensations.
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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