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It is worth mentioning that the theoretical contrast that can be achieved on semitransparent gold substrates is between half and three halves of the contrast that can be achieved on SiO2 substrates[2, 3], in which single mica layers can be detected.
For the 4-mm acquisition, theoretical contrast calculations suggest that PA imaging would have still outperformed US imaging had the seed been imaged in the short-axis orientation, with a slightly reduced contrast improvement (i.e., PA imaging over US imaging) of 24.4 dB (compared to a 27.9-dB improvement) being realized in this case.
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For Feyerabend, the theoretical contrasts with nothing at all.
In Table 1, the theoretical contrasts of the phantom are given including the attenuation of the PMMA and excluding the partial volume effect.
For a spatial distribution of these graph theoretical contrasts (hits vs. misses, normalized change), see Figures 4 A and 5. Node degree and betweenness centrality show a strong spatial overlap regarding the left auditory cortex (Figs 4 A and 5).
Such a signal reduction -which also occurs but to a lesser extent for US imaging - would have resulted in US imaging slightly outperforming PA imaging (i.e., with theoretical contrasts of 24.3 dB and 22.9 dB, respectively) for the 13-mm acquisition had the seed been imaged in the short-axis orientation.
Kuhn (1962) in The Structure of Scientific Revolutions, clearly explains how in the early stages of scientific revolutions when major disciplinary paradigms are in crisis and are about to change, it is possible that two extreme theoretical positions contrast each other.
Unfortunately, for the social aspect, there is a lack of theoretical underpinnings, in contrast to the environmental dimension, for which the theoretical underpinnings were studied twenty years ago.
The performances of the 3-UPU mechanism concur with the theoretical observations in contrast to what is presented in previous works.
However, the two-stage design reached a methane yield equal to 95% of the theoretical value, in contrast with the single stage configuration, which reached a maximum of 33% of the theoretical methane yield.
In contrast, theoretical geometrical analysis for a spherical contact yields a depth independent strain gradient proportional to 1/R and continuum calculations suggest a slight increase of a strain gradient proportional to δ1/4/R3/4.
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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