I have skipped quite a lot and am just skimming really for info on infinitives specifically, but found some text that intrigued two friends who are maths orientated. This is from chapter 7
“Next, I counted the distribution of the different complementizers over each of these extra-linguistic factors, yielding a 14x51 dimensional table. Obviously such a large-di-mensional table is difficult to interpret. To better understand patterns in the data, I used correspondence analysis (CA: see Glynn 2014 for more detail), an exploratory statistical technique to identify patterns of association and disassociation in a given dataset.84 CA plots high-dimensional data on a lower-dimensional (e.g. two-dimensional) plot in such a way that items that show similar distributions are plotted closely together. In our case, this means that when complement constructions are plotted closely together on the cor-respondence analysis plot, they tend to occur in similar texts, while, conversely, when extra-linguistic factors are plotted closely together, these text types tend to have the same complementizers. Points that are removed further from the origin are more dis-criminative. Finally, the association between extra-linguistic factors and complementiz-ers can be interpreted by the angle between the two points and the origin: acute angles indicate positive association, while obtuse angles indicate negative association (i.e. dis-association). In other words, when there is a long, acute angle between an extra-linguis-tic factor and a complementizer, there is a strong, positive association, while if there is a long, obtuse angle, there is a strong disassociation.”
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The second dimension is quite straightforward to interpret: it corresponds to register differences, with very formal, carefully written texts at the top (declarations, petitions, official letters etc.) and informal, less carefully written texts at the bottom (texts written on pottery, private letters etc. – similarly, all texts written in Mons Claudianus and most in the Eastern desert are on pottery, and most of them are private letters). This is not particularly surprising: it is well known that in the post-classical period, especially in the papyri, register is an important variable in complementizer choice – Bentein has shown that this is true for both major complementation patterns such as ὅτι and the infinitive (Bentein 2017) and for minor complementation patterns such as ὡς, ὅπως and ἵνα (Bentein 2015, see also James 2008). The variants at the bottom of the plot, i.e. ἵνα with the subjunctive, ὅτι with the sub-junctive, indicative and imperative, πῶς with the indicative and μή with the subjunctive are particularly associated with informal text genres (ὅπως with the indicative as well to a very small extent, although we only have 20 examples of this construction, of which 10 appear in private letters, so this might be due to chance). This corroborates the find-ings of Bentein (2015, 2017) as for ἵνα, ὅτι and πῶς (the number of examples for μή in Bentein 2015 are too small to say anything about its genre distribution).
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The horizontal dimension roughly corresponds to diachrony, with constructions that are associated more with the Ptolemaic period (e.g. διότι, ὅπως, the participle) on the top left hand side of the plot, and constructions more associated with later periods (ὡς, ὥστε, μή, ὅτι, πῶς) on the right hand side of the plot; ἵνα with the subjunctive and the infinitive are quite neutral with regard to this dimension. It is well known that participial complementation declined in usage in the course of the post-classical period (James 2001/2005; James 2008), which is also confirmed by these data (see also the absolute numbers in Table 47 as compared to e.g. ὅτι). As for ὅπως and διότι, there has been no diachronic study so far, as far as I know, covering these constructions in the whole papyrus corpus, but the CA plot suggest that these constructions (which were already pre-sent in classical literary texts) are reduced in usage in time as well
There is a lot here to get stuck into including work on complementizer classes