Given a weighted string x and a cumulative weight threshold 1/ z∈ 0,1], any valid factor of x occurs in at least one extended factor.
Given a weighted string x and a cumulative weight threshold 1/ z∈ 0,1], any valid factor of x occurs in at most z ℓ (2 ℓ+1) extended factors of x, where ℓ = log z / log z z − 1.
Given a weighted string x and a cumulative weight threshold 1/ z∈ 0,1], any valid factor of x contains at most log z / log z z − 1 black positions. Consider a valid factor u of x containing ℓ black positions and no grey positions. Any letter at a black position has occurrence probability at most 1−1/ z.
Given a weighted string x and a cumulative weight threshold 1/ z∈ 0,1], any valid repetition in x occurs in at least one extended factor. By Lemma 2, any valid factor of x occurs in at least one extended factor. By the definition of valid repetitions, any valid repetition is a valid factor.
However, some of the opinions and data revealed in this article show that HBCUs are still a valid factor in American higher education and should be maintained.
As far as I'm concerned, the age of the man who wants to have his finger on the nuclear button is a valid factor in the campaign.
The intuition behind extended factors is to generate a set of strings such that all the valid factors of the weighted string occur in at least one extended factor.
Nonomura et al. concluded that the number of MCs infiltrating around cancer foci in prostate biopsy specimens is a valid prognostic factor of prostate cancer.
Although, at shorter wavelengths, the big difference between pellet and bulk measurements is definitely valid (a factor of about 3 at λ = 70 μ m, also with the Imai et al. data), a steep decrease beyond this wavelength is not excluded.
The fact that the absolute β-actin expression trend was identical to that of the proliferation assay implied that the expression of this housekeeping gene could be used as a valid normalization factor in assessing the expression of osteogenic marker genes.
