We investigate the functional equation ∑n i=1 aif(bix + ciy) = 0, where ai, bi, ci ∈ C, and the unknown function f is defined on the field K = Q(b1, . . . , bn, c1, . . . , cn). (It is easy to see that every solution on K can be extended to C as a solution.) Let S1 denote the set of additive solutions defined on K. We prove that S1 is spanned by S1 ∩ D, where D is the set of the functions φ ◦ D...

Background—There is increasing interest in the predictive value of C-reactive protein (CRP) and fibrin D-dimer in the prediction of ischemic heart disease (IHD). We assessed their joint and independent associations with IHD in a large combined analysis of 2 population cohorts. Methods and Results—Men aged 49 to 66 years from the general populations of Caerphilly and Speedwell were studied betwe...

In bread wheat (Triticum aestivum L.), crop height is an important determinant of agronomic performance. To map QTLs with additive effects and additive×additive epistatic interactions, 148 recombinant inbred lines and their parents, (‘YecoraRojo’ and Iranian landrace (No. #49)) were evaluated under normal and water deficit conditions. The experiments were carried out on research farms of Mahaba...

Let X1 t1 , X 2 t2 , · · · ,X N tN be N independent Lévy processes in IR d with their respective Lévy exponents Ψj, j = 1, 2, · · · , N . The random field Xt = X 1 t1 +X 2 t2 + · · ·+X N tN , t = (t1, t2, · · · , tN ) ∈ IR N + is called the additive Lévy process. Let λd denote Lebesgue measure in IR . Define E1 + E2 = {x+ y : x ∈ E1, y ∈ E2} for any two sets E1, E2 of IR . The following theorem...

Spanners, emulators, and approximate distance oracles can be viewed as lossy compression schemes that represent an unweighted graph metric in small space, say Õ(n) bits. There is an inherent tradeoff between the sparsity parameter δ and the stretch function f of the compression scheme, but the qualitative nature of this tradeoff has remained a persistent open problem. It has been known for some...

A function f : R → R is referred to as a SparseAdditive Model (SPAM), if it is of the formf(x) =∑l∈S φl(xl), where S ⊂ [d], |S| d.Assuming φl’s and S to be unknown, the prob-lem of estimating f from its samples has beenstudied extensively. In this work, we consider ageneralized SPAM, allowing for second order in-teraction terms. For someS1 ⊂ [d],S2 ⊂<...

The covariance of inbred relatives from a population in linkage and identity equilibrium in the presence of dominance and epistasis is formulated using a similar procedure to that which B. S. WEIR and C. C. COCKERHAM used to derive a general expression for the genotypic variance. An alternative model based on the description of a genotype in terms of the homozygotes of its constituent alleles i...

(A1) a+ b = b+ a (commutativity of addition); (A2) (a+ b) + c = a+ (b+ c) (associativity of addition); (A3) There exists an element, called 0, such that 0 + a = a. (additive identity) (A4) For x ∈ R, there is a y ∈ R such that x+y = 0 (existence of additive inverses). (M1) (a · b) · c = a · (b · c) (associativity of multiplication). (M2) There exists an element, called 1, such that 1 · a = a · ...

The paper addresses the problem of reconstructing a highresolution image from a set of observation images sampled at a lower rate and subject to additive noise and distortion. The method introduced here is based on our work in multirate optimal filtering, extended to two dimensions. The linear filters used for the reconstruction are periodically spatially-varying (in 2-D) and chosen so that the...

This paper is devoted to the stability and convergence analysis of the additive Runge-Kutta methods with the Lagrangian interpolation ARKLMs for the numerical solution of a delay differential equation with many delays. GDN stability and D-Convergence are introduced and proved. It is shown that strongly algebraically stability gives D-Convergence DA, DAS, and ASI stability give GDN stability. So...