# Subsequence

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## subsequence

[′səb·sə·kwəns]
(mathematics)
A subsequence of a given sequence is any sequence all of whose entries appear in the original sequence and in the same manner of succession.

## Subsequence

in mathematics, the sequence

xn1, xn2,…., xnk

derived from the given sequence x1, x2,…, xn with observation of the order, that is, provided that n1 <n2 < … <nk….

References in periodicals archive ?
The homogenized equation has a unique solution in [H.sup.2.sub.0] ([OMEGA]), so every subsequence of ([u.sub.n]) converges to the same limit u and this implies that the entire sequence ([u.sub.n]) converges to u.
(1) If y and z are limit points of ([x.sub.n]), then there exist subsequences [mathematical expression not reproducible].
(b) [P'.sub.i] holds for some boundedly spaced subsequence [mathematical expression not reproducible] of {[T.sup.n]}
Moreover, the DTW algorithm-based approach provides the advantage of searching all matched subsequences automatically from a long sequence.
If {[[??].sub.n]} is a sequence in a bounded soft closed set S, then there exists a subsequence [mathematical expression not reproducible] of {[[??].sub.n]} converging to some [??] [member of] S.
Section 3 introduces our approach for completing large missing subsequences in low/uncorrelated multivariate time series.
Assume, up to a subsequence, that [mathematical expression not reproducible].
Setting [v.sup.[k]] = [u.sup.[k]] / [parallel] [u.sup.[k]] [parallel] and arguing as in the proof of Claim 1, we conclude that, possibly passing to a subsequence,
We utilize LSTM network itself without additional model to complete subsequence selection.
The traditionally LCS method measures the similarity by calculating the length of the longest common subsequence. Given two strings [S.sub.1] and [S.sub.2] with length I and J respectively, [S.sub.1](i) and [S.sub.2](j) are the [i.sup.th] member of the string [S.sub.1] and the [j.sup.th] member of [S.sub.2] respectively, and L(i, j) represents the value of the LCS matrix at the location of (i, j).
A traversal sequence S' is said to be a subsequence of sequence S if it is a subset of S.

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