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Binocular rivalry is quantified over the distorted stereo pairs, and the scene quality is quantified over the disparity map.
This visualization is extremely useful in optimizing waterfloods/gas floods because the benefits of injection can be easily quantified over the time as can be seen in Fig. 4.
Finally, the decrease of NO oxidation activity in DOC due to PtOx formation and its impact on NOx conversion in SCR is quantified over the repeated driving cycles, showing 2 10% difference between the deNOx performance with the pre-reduced DOC and after few hours of operation under oxidizing conditions.
The effects of PTIO and L-NAME were quantified over the last 100 msec of the pulse (Fig. 5A), by subtracting currents in the presence of the NO blockers from those in ASW (Fig. 5C).
Similarly, inflammation in the meninges was quantified over the entire cortex per slide.
Unlike conventional microscopy, this technique enables gametocyte densities to be quantified over the entire epidemiologically relevant range.
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Also, out-of-pocket expenses of patients will be quantified (over-the-counter medication, private help at home, etc).
In either case, in order to refer to, and quantify over, the possible histories passing through the current instant, an additional modal operator \(\diamondsuit\) and its dual \ \Box\) are introduced, with \(\diamondsuit \varphi\) declared true at (\({h},{t}\)) if there is some history \(h'\) through \(t\) such that \(\varphi\) is true at (\({h'},{t}\)).
Given that when the Quinean says that we should believe in what the best theory quantifies over, this must be understood to mean "literally quantifies over".
Counterfactual attitude verbs update S with the set of worlds they quantify over, S', which is the attitude holder x's doxastic worlds, DOXx,w,t.
The binders bind nominals to points in two different ways: The ∀ binder quantifies over points analogous to the standard first-order universal quantifier, that is, ∀aφ is true relative to w if and only if whatever point the nominal a refers to, it is the case that φ is true relative to w.
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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