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The phrase "assumption existed" is correct and usable in written English.
It can be used when discussing a belief or idea that was held to be true in a particular context or situation.
Example: "In the early stages of the project, the assumption existed that all team members would be available for the meeting."
Alternatives: "belief was present" or "premise was held".
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There are some documented cases, however, where exceptions to this assumption exist.
Yet with continued pricing pressures in server processors, a high margin product, "this recovery is delayed by at least one quarter and risk to this assumption exists".
But merely noting that this symmetrical assumption exists does not go far enough.
13 Approaches to estimating efficacy without making this key assumption exist, and are becoming increasingly popular.
Statistical tests of this assumption exist but tend to have low power and therefore not commonly conducted in practice.
However, there are cases that no gene satisfying this assumption exists, and it is important to consider structural control via external stimuli.
Given that some visual suggestion of potential violations of the linear model assumptions existed, we also produced bootstrapped confidence intervals for the between group differences for each outcome measure.
However, little or even conflicting assumptions exist about their putative import and functionality inside the cells.
Particularly when violations of the underlying theoretical assumptions exist, consideration of demographic processes (i.e. vital rates, species specific life history strategies and dispersal) and genetic structuring will allow for more appropriate conservation recommendations.
I guess I am still not sure as to why, truly, these assumptions exist, but I have no doubt that our fetish with money and the dangerous idea that "net-worth = self-worth" is tied to them.
In a cryobiological context, this is much less of a concern but in case it is, special techniques (with their own sets of assumptions) exist to correct for some types of motion artefacts [86], [87] or to quantifiy motion directly (e.g. [88], [89]).
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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