Minority Report (film) composed and conducted by John Williams and orchestrated by John Neufeld, with vocals by Deborah Dietrich. Williams normally enters Spielberg productions at an early stage, well before the movie starts shooting. For "Minority Report" however, his entry was delayed due to his work on "", and he joined the film when it was nearly completed, leaving him scant production time. The soundtrack takes inspiration from Bernard Herrmann's work. Williams decided not to focus on the science fiction elements, and made a score suitable for film noir. He included traditional noir elements such as a female singer in the Anne Lively
Directed set Directed set In mathematics, a directed set (or a directed preorder or a filtered set) is a nonempty set "A" together with a reflexive and transitive binary relation ≤ (that is, a preorder), with the additional property that every pair of elements has an upper bound. In other words, for any "a" and "b" in "A" there must exist "c" in "A" with "a" ≤ "c" and "b" ≤ "c". The notion defined above is sometimes called an upward directed set. A downward directed set is defined analogously, meaning when every pair of elements is bounded below. Some authors (and