The phrase "as initial subsequences" is correct and usable in written English.
It can be used in contexts related to sequences, mathematics, or computer science, particularly when discussing parts of a sequence that come at the beginning.
Example: "The algorithm processes the data by examining the strings as initial subsequences to determine their relevance."
Alternatives: "as leading subsequences" or "as starting subsequences".
The general idea is to show that for a sequence ω which is not ML-random, and fails some sequential test, then there is a way of constructing a Turing machine that will compress initial subsequences of ω arbitrarily much as the length of the initial subsequence increases (i.e., the difference between n and the prefix-free complexity of the length n initial subsequence of ω is positively unbounded).
Only if: The set Uk consists of those sequences which have finite initial subsequences which are compressible by k bits.
Any sequence which violates the property of large numbers, or the law of symmetric oscillations, etc., will do so on increasingly long initial subsequences.
So it can be that, uniformly, when x is an infinite sequence, for any of its initial subsequences σ, K ≥ |σ|.
This dip in complexity of an initial subsequence will occur infinitely often in even a random infinite sequence, a phenomenon known as complexity oscillation (Li and Vitányi 2008: §20081).
This suggests that we can extend prefix-free Kolmogorov complexity to the infinite case in the straightforward way: an infinite sequence x is prefix-free Kolmogorov random iff every finite initial subsequence is prefix-free Kolmogorov random.
A sequence σ is λ-incompressible iff for each n, the Kolmogorov complexity of the length n initial subsequence of σ (denoted σn) is greater than or equal to − log2 (λ(σn)).
Subsequences that had higher counts than any of their neighbors at Huddinge distance of one were identified as local maxima, and used as initial seeds for the generation of the binding profiles.
In BLASTX, the length of the subsequence for seed is three and neighborhood words are identified, as well as exact subsequences (Altschul et al., 1997).
However, delineating subsequences by forcing all their residues to share a common set of match partners may be too restrictive, as short subsequences were frequently defined at subsequence boundaries owing e.g. to alignment artifacts.
