The phrase "with respect to the patterns" is correct and usable in written English.
It can be used when discussing or analyzing specific patterns in a particular context.
Example: "The researchers conducted a thorough analysis with respect to the patterns observed in the data."
Alternatives: "regarding the patterns" or "concerning the patterns."
This project, she said, will not only provide crucial perspectives about the past but also be instrumental in giving insights about the future, especially with respect to the patterns of migration.
Hence, it is crucial to validate the correctness and compliance of the final customized business process with respect to the patterns and business constraints that are specified in the reference model.
The T. thermophila ten strains hence differed also with respect to the patterns of their investment along different trait axes.
However, the third group of isolates identified as C. subterminale was intermediate to the other two populations with respect to the patterns obtained with both the REs - AluI and DpnII.
Analyses of neutral population genetic variation offers a window to these processes, at least with respect to the patterns imprinted in the genome, and here we apply this approach to a weedy annual plant, Ipomoea hederacea, to better understand its population history in North America.
Tribological experiments (polyimide substrate versus steel ball) under dry sliding conditions were performed using ball-on-disk tribometer in linear reciprocating sliding mode as a function of the relative alignment of the sliding direction with respect to the pattern orientation.
Hildreth15 and Sherrod and Smith14 both provide volume estimates for Quaternary extrusive volcanism along the entire length of the Cascades Arc and were examined for use in our calculations (Figured S1 and S2), and both sets of volume estimates produces broadly comparable results with respect to the pattern of variations in erupted volume and Quaternary heat budgets.
Wolsterstorff complains that Wollheim's thesis about the sharing of properties among types and their tokens gives us "no illumination" with respect to the pattern of such sharing (1975, 239).
On the other hand, the real/complex field implementation of error correction codes has stability problems with respect to the pattern of impulsive, quantization and additive noise [52, 59, 74, 106 109].
Furthermore, in this vicinity A x) must yield high positive values (because 1 / σ n 2 ≫ 1 / ( a 2 ( x ) σ ε 2 ( x ) + σ n 2 ) ), peaking in an isolated maximum where the covariance factor gets closest to 1, i.e., when the pattern candidate is aligned with respect to the pattern guess p0.
With respect to the pattern of inflammation with disease involving the ileum there was no significant difference between patients with and without SIBO.
