Sentence examples for linked with respect to from inspiring English sources
We define two genes to be "synergistically linked with respect to a phenotype" if their corresponding synergy is positive.
Thus, ethylene, jasmonic acid and salicylic acid are frequently linked with respect to biotic stress and all of them have been linked to NO, in one way or another (Nurnberger and Scheel 2001).
All remaining pairs among the 8416 training genes were considered not to be functionally linked (with respect to the current GO term category) and were scored as "0" in the training network.
One of our main conclusions from the analysis of these data is that RBP1 (cellular retinol-binding protein-1, also known as CRBP-1) is synergistically linked with respect to prostate cancer with many other "partner" genes, many of which are ribosomal genes.
We note here that under the framework of Proposition 2.3, S ρ and ∂Q homotopically link with respect to the direct sum decomposition E = X ⊕ Y. S ρ and ∂Q are also homologically linked.
Theorem 3.4 includes the case that for λ close to λ k + 1 A from the right-hand side, the linking with respect to E k + 1 ⊕ E k + 1 ⊥ is constructed provided the negative values of F are small.
This implies that B m and ∂ Q m homologically link with respect to the direct sum decomposition E = E m ⊕ E m ⊥ (see Example 3 of Chapter II in [16]).
Now we construct a linking with respect to the decomposition E = E m ⊕ E m ⊥ or E = E m − 1 ⊥ ⊕ E m − 1. Lemma 3.2 Suppose that f satisfies ( f 0 ) and (f).
Now, we construct a homological linking with respect to the direct sum decomposition of E for k ⩾ 1 : E = E k + 1 ⊕ E k + 1 ⊥, dim E k + 1 = ℓ k + 1.
Since S k + 1 and ∂Q homotopically link with respect to the decomposition E = E k + 1 ⊕ E k + 1 ⊥, and dim V k + 1 = ℓ k + 1 + 1, it follows from Proposition 2.3 that Φ has a critical point z ∗ ∈ E with positive energy Φ ( z ∗ ) ⩾ α > 0 and its critical group satisfying (3.13).
If F ⩾ 0, then for any fixed λ ∈ [ λ k A, λ k + 1 A ), a linking with respect to E k ⊕ E k ⊥ can be constructed. Proposition 2.3 is applied again to get a nontrivial solution z ∗ satisfying C ℓ k + 1 ( Φ, z ∗ ) ≇ 0. (3.15).
