The traditional quantitative genetics model was used as the unifying approach to derive six existing and new definitions of genomic additive and dominance relationships. The theoretical differences of these definitions were in the assumptions of equal SNP effects (equivalent to across-SNP standardization), equal SNP variances (equivalent to within-SNP standardization), and expected or sample SN...

Let X be a Banach space and (Ω,Σ) be a measure space. We provide a characterization of sequences in the space of X-valued countably additive measures on (Ω,Σ) of bounded variation that generates complemented copies of l1. As application, we prove that if a dual Banach space E∗ has Pe lczyński’s property (V*) then so does the space of E∗-valued countably additive measures with the variation norm...

Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-l...

----------------------------In this paper we justify the use of the between-groups S-convex relative inequality to measure interregional convergence, within an axiomatic normative context. In addition, the use of additive decomposable inequality indices makes the additive multidimensional (and multilevel) inequality decomposition possible, and help us better understand the evolution of the betw...

We address the distinction between dynamical and additive noise in time series analysis by making a joint evaluation of both the statistical continuity of the series and the statistical differentiability of the reconstructed measure. Low levels of the latter and high levels of the former indicate the presence of dynamical noise only, while low values of the two are observed as soon as additive ...

In this contribution we discuss weight selection which allows additive neural networks to represent certain periodic patterns. Given a periodic set of vectors V(l) whose components are v(i)(l)=+/-1 we measure correlation between i-th and j-th components of V(l) in time l. We show that in the additive neural net with weights chosen based on this correlation, almost all trajectories converge to a...

The Ostrowski theorem in question is that an additive function bounded (above, say) on a set T of positive measure is continuous. In the converse direction, recall that a topological space T is pseudocompact if every function continuous on T is bounded. Thus theorems of ‘converse Ostrowski’type relate to ‘additive (pseudo)compactness’. We give a di¤erent characterization of such sets, in terms ...

Set functions are widely used in many domains of Operations Research (cooperative game theory, decision under risk and uncertainty, combinatorial optimization) under different names (TU-game, capacity, nonadditive measure, pseudo-Boolean function, etc.). Remarkable families of set functions form polyhedra, e.g., the polytope of capacities, the polytope of p-additive capacities, the cone of supe...

A fuzzy approach is proposed here for restoring color images that are corrupted with additive noise. The proposed fuzzy approach consists of two sub-filters, where the first fuzzy sub-filter computes the fuzzy distances between the color components of the central pixel and its neighborhood using Gaussian combination membership function, and the second sub-filter corrects the pixels where color ...

C. Shannon revolutionized the design of information systems by showing that the logarithm of independent probabilities were additive and constituted a unit of measure for information. Because ln p  is additive, basic analytics could be applied to information, such as the average which forms entropy and the average difference which forms divergence. Unnecessarily neglected in this formative fra...