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The phrase "as a function of session number" is correct and usable in written English.
It is typically used in mathematical, scientific, or technical contexts to describe how one variable depends on another, in this case, session number.
Example: "The results were analyzed as a function of session number to determine trends over time."
Alternatives: "in relation to session number" or "depending on session number".
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Figure 7D shows average endpoint error as a function of session number.
In contrast, response times improved strongly as a function of session number (r = −0.70, p = 0.012, prep = 0.95, d = 1.96) for the Sn subjects, presumably because they learned to hit as many LEDs as they could, as fast as they could, and increasingly used both hands for the task.
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Figure 5 plots the Laplace d-prime range as a function of the number of sessions in each of the conditions of the experiment.
To detect more subtle changes over rapid timescales, we plotted average Purkinje cell firing during the first 100 ms of each trial of a given training session as a function of trial number (typically, 30 40 individual vestibular stimuli, or trials, in a given direction made up a single session) (see examples in Figure 4A).
Results of the 25 real-time feedback sessions are provided in Figure 7. Panels A C indicate hit rate, mean movement time, and mean endpoint error (measured as the difference between the formant space position at the end of the trial and the target formant position for that trial) as a function of block number, averaged across all 25 sessions.
The time between tasting activities varied as a function of the number of people participating during each testing session.
The chart shows the location of all nuclei as a function of their neutron number (N) and proton number (Z).
(b) Directivity of the designed antenna as a function of the number of directors.
(b) Programmable non-reciprocal states as a function of the number of ports.
(b) Recognition rate as a function of the number of presented images for different noise levels.
Supplementary Figure 13 CRISPR off-target activity as a function of mismatch number and mismatch position.
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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