For each (Ktrans, fV) pair there existed one unique (α, P) pair and one unique (μG, Δ V) pair.
For example, when aligning the network of yeast and fruit fly, setting parameter l and r to 2 and 3 respectively means that UEDAMAlign locally extends a pair of homologous proteins if there exists one path of length not larger than 2 to connect the yeast node in the homologous protein pair or one path of length not larger than 3 to connect the fruit fly node in the homologous protein pair.
We show that for every pair (v,λ) for which a triple system, TS v,λ), exists, there exists one which has a zero-sum 3-flow, except when (v,λ)∈{ 3,1),(4,2),(6,2),(7,1)}.
If the condition (H1) holds, then there exists one positive root (v_{0}) of Eq. (6) such that Eq. (3) has a pair of purely imaginary roots (pm iomega _{0} =pm isqrt{v_{0}}).
there exists one such that that is,.
If there exist real numbers, such that for all there exists one has and then.
We first transformed the original SNP-SNP interaction network into a gene-gene interaction network by setting each vertex as a gene and connecting two genes if there existed at least one pair of SNPs, each from one of the two genes, that had a significant and strong pairwise interaction in the original SEN.
(varepsilon^{2}=frac{b-b^{c}}{b^{c}}) is small enough so that the positive constant steady state ((u_{ast},v_{ast})) of system (1.3) is unstable to modes corresponding only to the eigenvalue (hat{k}_{c}^{2}), which is defined in (4.17); there exists only one pair of integers ((l,n)) in (4.17); the Landau coefficient L in equation (4.22) is positive.
Assume that (i) (varepsilon^{2}=frac{b-b^{c}}{b^{c}}) is small enough so that the positive constant steady state ((u_{ast},v_{ast})) of system (1.3) is unstable to modes corresponding only to the eigenvalue (hat{k}_{c}^{2}), which is defined in (4.17); (ii) there exists only one pair of integers ((l,n)) in (4.17); (iii) the Landau coefficient L in equation (4.22) is positive.
A machine is deterministic if for each pair (s,i) ∈ S × I there exists at most one pair (o, s′)∈O × S such that (s, i, o, s′) ∈ h S ; otherwise, the machine is non-deterministic.
Since p 1 conflicts with p 2, there exists at least one pair of unconnected vertices in (mathcal {G}_{g}) that represents p 1 and p 2. This pair is not included in (mathcal {M}_{g}), and thus is kept after removing (mathcal {M}_{g}) from (mathcal {G}_{g}).
