The sign for "institute is an "initialized" sign, but it
is well accepted.
The dominant hand lowers and touches the base hand, raises back up, and then
comes down again. It is most commonly recognized in the Deaf world
as the sign for "
Deaf School" (meaning, a
state-run residential school for the Deaf). Whether this sign means
"institute" or not will depend on the context in which it is used. If you are
talking about "mental patients" then it is going to mean "institutionalized."
I saw it used in Northern Utah to refer to an "institute" of religion.
In this variation the base hand is a fist. This sign is also commonly
recognized in the Deaf world as meaning "Deaf School."
Remember, ASL isn't English and thus in many cases it is perfectly fine to just
sign SCHOOL (as shown below) when the English word "institute" is being used to
refer to a general "school."