The diagram below shows a sagittal section of the human brain with regions labelled $P$, $Q$, $R$, and $S$.

A patient suffers a localized stroke that results in two key neurological deficits:

1. An inability to regulate blood water potential, leading to the excretion of abnormally large volumes of highly dilute urine.
2. A severe impairment in the coordination of smooth, precise skeletal muscle movements and balance, resulting in uncoordinated, jerky motion.

Which of the labelled regions are responsible for managing these two physiological functions respectively?