Plant miRNAs are usually perfectly complementary to their targets and cause the cleavage of their targets by RNA-induced silencing complex (RISC), whereas in animals targets with weaker complementarities appear to have decreased translational efficacy [ 9].
Nevertheless, these computational approaches often provide numerous target candidates with a large number of false positives because of the weak complementarity between miRNAs and 3'-UTRs [ 20].
Indeed, the signal resulting from heterologous hybridization is low and difficult to interpret because of the weak complementarity between probe and target sequences, especially when no microarray dedicated to a genetically close species is available.
Binding occurs with either perfect complementarity or, more often, imperfect complementarity [5].
Furthermore, weak electrostatic complementarity between Asp77 on the alpha1 helix of Kb and 2C is enhanced in the allogeneic complex by closer proximity of QL9 peptide residue AspP8 to the 2C HV4 loop.
(Weak) vector complementarity problem (VCP): finding such that (1.1).
Next two definitions extend the domain of games with weak general complementarities (see Calciano [11]) to CPOs.
Theorem 6 Let T be a partially ordered set, and ( Γ t ) t ∈ T be a collection of games with extended weak general complementarities such that the joint best reply correspondence F ( ⋅, t ) is lower increasing in ( x, t ) on X × T and has a bottom element for every ( x, t ) ∈ X × T. Then the least Nash equilibrium is increasing in t.
Definition 3 A game Γ has extended weak general complementarities on CPOs (hence, is a GEWGC) if (i) each strategy set X i (a subset of a complete lattice Y) is a CPO; (ii) ∀ x ∈ X : the joint best reply correspondence F is nonempty and has a least element; and (iii) F is lower increasing.
(Weak) generalized vector complementarity problem (GVCP): finding and such that (1.4).
