In the last section, we defined HS scheme over a non-commutative ring R. Here, we can take a non-commutative ring over a finite field K or a ring (mathbb {Z}/Nmathbb {Z}).
Using snapshots from the last 1-ns, we defined persistent native contacts as contacting residues that appeared in >70% of the snapshots.
Because of the flanking regions before the first nicking site and after the last nicking site, we defined a thorough alignment if mapping length ratio ≥ 0.95.
As the transfer rate dropped to 2.4% in the last flushing step, we defined a maximum of three flushing steps to be useful.
The last measure we define is (spatial) coverage.
In the last chapter we define Haagerup-like tensor products of the first kind and of the second kind and we use them to study functions of noncommuting self-adjoint operators under perturbation.
In the first case, the E sparse(d) is obtained using the fixed DCT bases, in the second case, it is learned using the K-SVD dictionary learning method, and in the last case, we define the E sparse(d) using the proposed sparse autoencoder.
To prove the last property, we define a function F = αfi,j p) − fi,j αp), whose first-order partial derivative with respect to α is: ∂ F α ∂ α = α α − 1 α + 1 p + 2 γ p γ p + γ 2 α p + γ 2 a i, j Γ i, j + ln a i, j g i, j b i, j g 0, j (23).
Because HSPs only deviate from true exons by a few nucleotides (due to ambiguity in the alignment at the splice site), we defined the last exon as the 3'-most HSP.
We defined full length last exons as those derived from mRNA sequences that were complete on the 3' end.
