Conversely, every bounded sequence in a Hilbert space admits weakly convergent subsequences (Alaoglu's theorem). In bioinformatics, "k"-mers are subsequences of length formula 1 contained within a biological sequence. Other applications include assembling contiguous subsequences in DNA mapping, and temporal reasoning. While a sequence is a net, a sequence has subnets that are not subsequences. Finally, alternative splicing in higher eukaryotes can result in many identical protein subsequences. The table also shows the longest common subsequences for every possible pair of prefixes. Other subsequences of the fifths-circle chord-progression are used in music. Citation patterns represent subsequences non-exclusively containing citations shared by the documents compared. So (ABD) and (ACD) are their longest common subsequences. "k"-mers are simply length formula 1 subsequences. This was reduced to 3 subsequences in Block II. The result is that "LCS"("R", "C") also contains the two subsequences, (A) and (G). The result is that "LCS"("R", "C") contains the two subsequences, (A) and (G). Define the function "LCS"("X", "Y") as the longest subsequences common to "X" and "Y".