Happy to help! It is a common enough error :)

When changing variables for multiple variables integral, the scaling factor is the absolute value of the Jacobian. See en.wikipedia.org/wiki/Integra...

This is another graph from the same study, which is not super easy to read, but presents the trends for the whole population.

This study (in French) seems to support the idea that in the last 20 years young French men are indeed turning more to the right, while young French women are staying consistently on the left. See, e.g., this graph.

www.cepremap.fr/2025/03/un-f...

📌

Letting x be the argument of the non linearity in (1), you recover (3). Hence the dynamics (3) is more “general”. If this procedure is invertible, the two are equivalent.

As others said, biologically, (1) and (3) come from modeling the dynamics of either membrane potentials or rate of fire.

This seems a variation on a very old argument (quite flawed indeed!). Gödel even formalized it:

en.m.wikipedia.org/wiki/G%C3%B6...