The heuristic is based on protein domain annotations provided through the Pfam-A collection of sequence-based protein domains (Punta et al., 2012).
Algorithms were validated with a collection of sequences with positive results.
Proposition 2 A collection of sequences ( X m ) m ≥ 1 is asymptotically μ-binary if and only if there exists a μ-binary collection ( Z m ) m ≥ 1 such that ∥ X m − Z m ∥ → 0 as m → ∞.
The potentials are used to estimate the cost of deforming a collection of sequences known to bind or resist uptake in nucleosomes along various left-handed superhelical pathways and to deduce the features of sequence contributing to a particular structural form.
A collection of sequences of vectors (v={left { v_{1}^{x},dots,v^{x}_{N^{x}})right }}_{xin mathcal {X}}) with (v_{k}^{x}in mathcal {I}_{T}cap mathbb {R}_{geqslant 0}^{d}), such that begin{aligned} v_{k}^{x} ge u_{k}^{x} quad text{for all}~ kinmathcal{K}^{x},xinmathcal{X}.
A collection of sequences ( X m ) m ≥ 1 is called μ-binary -binary) if X m is μ-binary -binary) for all large enough m; ( X m ) m ≥ 1 is called asymptotically μ-binary if for arbitrary ε > 0 it is -binary.
Additional confidence was achieved when putative novel hairpins assembled a collection of sequences highly similar to the putative mature miRNA but with heterogeneous 3'-ends.
In the next step of our analysis, we screened for putative novel hairpins that captured a collection of sequences (strong signal) mapping to a specific region of 15 25 nt within the reference hairpin on one side of the stem.
