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Five taxa showed significant negative multiplicative interactions identified by an interaction term with p ≤ 0·05.
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Corollary 3 Let h : ( 0, ∞ ) → R be a non-negative super-multiplicative function.
If h is a non-negative sub-multiplicative function and f ∈ g h v ( h, p, I ), then the inequality sign in (4.2) is reversed.
Theorem 1 Let h : J → R be a non-negative super-multiplicative function and let f : I → R be a function such that f ∈ g h x ( h, p, I ).
Theorem 2 Let w 1, …, w n be positive real numbers with n ≥ 2. If h is a non-negative super-multiplicative function and if f ∈ g h x ( h, p, I ) and x 1, …, x n ∈ I, then we have the inequality f ( [ 1 W n ∑ i = 1 n w i x i p ] 1 p ) ≤ ∑ i = 1 n h ( w i W n ) f ( x i ), where W n = ∑ i = 1 n w i. (4.1).
If h : ( 0, ∞ ) → R is a non-negative super-multiplicative function and f ∈ g h x ( h, p, I ), then for all x 1, …, x n ∈ ( m, M ) we have the inequality ∑ i = 1 n h ( w i W n ) f ( x i ) ≤ f ( m ) ∑ i = 1 n h ( w i W n ) h ( M p − x i p M p − m p ) + f ( M ) ∑ i = 1 n h ( w i W n ) h ( x i p − m p M p − m p ). (4.2).
There was strong evidence for a multiplicative negative interaction between infection status and Hb levels, highlighting the health impacts of parasitic infections in school-aged children.
A case-only analysis among all cases from the case-control and family materials (ESM Table 5) supported a significant negative deviation from multiplicative effects, with weaker ORs conferred by PTPN22 in the HLA risk categories (3 df test for interaction; p = 0.028).
Chaining multiple negative feedback loops together should lead to a multiplicative improvement.
The ORs were smaller for the risk-conferring HLA genotypes, indicating negative deviation from a multiplicative model.
This curvature implies negative epistasis on a multiplicative fitness scale, the deleterious effects of mutations together being stronger than when alone.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com