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The phrase "by the higher level" is correct and usable in written English.
You can use it to describe an action as being conducted at a higher level than usual, or to refer to something being governed or organized by a higher level of authority. For example: "This complex operation is being managed by the higher level of command."
Exact(33)
Expanding only slightly on his philosophy, he said later in the conversation, "My role is to follow the rules as established by the higher level courts".
"The market will now do its own analysis, aided by the higher level of detail provided, and apply more severe stresses to the various institutions," Mr. Whitfield of RBC said.
Only those drives, in which the expected pattern or keywords were detected, are analyzed by the higher level host.
The RESOURCE_RELEASE procedure releases the excess time slots to its parent for use by the higher level clusters.
Their jobs are distinguished by the higher level of theoretical expertise and innovation they apply to complex problems and to the creation or application of new technology.
The actual operation time allowed by the higher level for processing an operation at the lower level is subsequently determined by a scheduling algorithm at the higher level.
Similar(27)
The increased dispersion of these suspensions is proposed to be caused by the higher levels of turbulence.
This proposal is further supported by the higher levels of reduced thioredoxin.
This was indicated by the higher levels of osteocalcin and OPG in their conditioned media.
These results can be justified by the higher levels of bacillus exposure among the contacts of multibacillary cases.
Most seemed surprised as well as encouraged by the high level of compliance among the subjects.
More suggestions(18)
by the higher proportions
by the upper level
by the rising level
by the higher qualifications
by the above
by the senior level
by the higher degrees
by the higher layers
by the higher price
by the higher security
by the higher court
by the higher income
by the higher interest
by the higher wage
by the higher altitude
by the higher temperature
by the higher presale
by the higher caste
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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