This way, we shall make use of the star-sphere intersection-proportion function (ipf) of a given set.
denotes the intersection proportion function (ipf) of the set B. If K is the Euclidean unit ball then K ∗=K and O S is the Euclidean surface content measure.
The star sphere intersection-proportion function (ipf) of the set B ∈ B n is defined as F S ( B, r ) = O S 1 r B ∩ S / O S ( S ), r > 0. The ipf was first introduced in (Richter [1985], [1987], [1991]) for Gaussian and spherical distributions, respectively, i.e. for cases where S is the Euclidean unit sphere, and generalized later in ([Richter 2007]) to the case that S is an ln,p−sphere.
However, there may be some other models for different species groups by using different proportion functions.
The proportion functions below (10) derived from the formula for volume of a sphere and the thickness of the different layers are plotted in Figure 4b.
Cord blood mercury was inversely correlated with the proportion of naive helper T cells and plasma IgM levels in cord blood but unrelated to multiple other measures of T-, B-, and natural killer cell proportions and function.
For each functional category, the proportions of function-related pathway pairs (FRPs) in intra- and inter-categories were compared.
These signatures include: 1) high proportion of function altering mutations; 2) reduction in genetic diversity; 3) high-frequency of derived alleles; 4) high genetic differentiation between populations; 5) long range haplotypes and strong linkage disequilibrium [16].
The proportion and function of phagocytosing granulocytes, and the production of reactive oxygen species (ROS) by peritoneal lavage cells were decreased in HFD-fed compared with LFD-fed mice.
In addition, both the proportion and function of granulocytes were decreased in uninfected HFD-fed mice, and the ROS production by phagocytosing cells was greatly decreased in infected HFD-fed mice.
