Example of histogram intersection. The expression hist(S1..i) ∩ hist(T1..i) denotes the histogram intersection of two string prefixes. Depicts the histogram intersection of two UMLS terms, ammonium and ammonium ion. The histogram of ammonium is in a, the histogram of ammonium ion is in b. The intersection (c) is computed as the minimum for each pair of argument values of the same character, with missing values in one argument omitted from the result. For example, ammonium contains one “o” while there are two letters “o” in ammonium ion. As min (1, 2) = 1, the resulting histogram in c contains the entry “1” for the letter “o.” As there is no blank in ammonium, there is also no entry for the blank character in the resulting histogram. In order to compute the size (the “absolute value” ||) of the histogram intersection in c, the sum of all the numbers in the result matrix is calculated. For c, the size of the histogram intersection is (1 + 1 + 3 + 1 + 1 + 1) = 8.