Can an Arcanist that selects the School Understanding Exploit choose one of the focused arcane schools available to Wizards? For instance the Teleportation school of Conjuration or the Foresight school of Divination?
The text of the Arcanist's ability specifies (emphasis mine):
The arcanist can select one arcane school from any of the schools available to a character with the arcane school wizard class feature
There is no caveat that limits the choices; it says any school a wizard could choose, the Arcanist can choose. Additionally, the Arcanist was published well after other materials that introduced most of these variant arcane school choices, so it is not a situation where the ability was written and the options it provides were expanded later; these were available choices when the Arcanist ability was written and the text specifies "any" rather than providing a list. Taken together, there's no rules-as-written reason that the Arcanist should not be able to choose these variant schools, nor does it appear that such a restriction was intended (quite the opposite).
The arcanist exploit school understanding says that an arcanist picks "one arcane school from any of the schools available to a character with the arcane school wizard class feature." So, in addition to being able to pick from the traditional schools like abjuration, an arcanist should also be able to pick from focused arcane schools like foresight or even elemental schools like void. However, the exploit school understanding is vague as to how it works with some school special abilities like the divination school supernatural ability forewarned, so ask the GM if picking something exceptionally wacky.
A really strict GM could forbid an arcanist from picking a focused arcane school or an elemental school by ruling that these are not, technically, arcane schools, in the same way that cover is different from partial, total, and improved cover. But, seeing as how the arcanist is already Pathfinder's most powerful class, that seems a particularly unusual ruling to make.