Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). A finitely additive probability P on A such that P ∼ P0 and EP (X) = 0 for each X ∈ L is called EMFA (equivalent martingale finitely additive probability). In this note, EMFA’s are investigated in case P0 is atomic. Existence of EMFA’s is characterized and various examples are given. Given y ∈ R and a b...

It is shown that a threshold network of width w and depth d cannot be constructed from balancers of width p0; p1; : : : ; pm 1, if w does not divide P , where P is the least common multiple of p0; p1; : : : ; pm 1. This holds regardless of the size of the network, as long as it is nite, and it implies a lower bound of logP w on the depth of the network. More strongly, a lower bound of logpmax w...

Specific antibodies have been developed against P1, P2, and P0 myelin proteins and were used to study the localization of these proteins in the rat peripheral nervous system. Both peripheral and central nervous system myelin sheaths contain P1 protein. P0 and P2 proteins are found exclusively in peripheral nervous system myelin sheaths. Antisera to P1 and P0 proteins stain all peripheral nervou...

Activity of users on Internet discussion forums is analyzed. The rank of users is shown to be approximated better by stretched-exponential function than by Zipfs law. Cumulative distribution function is found as an excellent tool in analysis of the dynamics of the collective social phenomena. We are able to approximate the number of blog comments with time by simple functions that resemble Ferm...

Recently, p-wave cold collisions were shown to dominate the density-dependent shift of the clock transition frequency in a 171Yb optical lattice clock. Here we demonstrate that by operating such a system at the proper excitation fraction, the cold-collision shift is canceled below the 5 × 10−18 fractional frequency level. We report inelastic two-body loss rates for P0 -P0 and S0 -P0 scattering....

For example, a woman who is described as 'gravida 2, para 2 (sometimes abbreviated to G2 P2) has had two pregnancies and two deliveries after 24 weeks, and a woman who is described as 'gravida 2, para 0' (G2 P0) has had two pregnancies, neither of which survived to a gestational age of 24 weeks. If they are both currently pregnant again, these women would have the obstetric résumé of G3 P2 and ...

i=1 each of which is presumed to be randomly drawn independently from some probability distribution with density p(x). The goal is to test the hypothesis that p(x) = p0(x), where p0(x) is some specified reference probability density. Ideally, the test should have power against all alternatives. That is as the sample size N becomes arbitrarily large, N → ∞, the test will reject the hypothesis fo...

Given M ∈ <n×n and q ∈ <, the linear complementarity problem (LCP) is to find (x, s) ∈ < × < such that (x, s) ≥ 0, s = Mx + q, x s = 0. By using the ChenHarker-Kanzow-Smale (CHKS) smoothing function, the LCP is reformulated as a system of parameterized smooth-nonsmooth equations. As a result, a smoothing Newton algorithm, which is a modified version of the Qi-Sun-Zhou algorithm [Mathematical Pr...

The characteristics of eukaryotic ribosomal proteins P0, P1, and P2 (P proteins) and their antigenic determinants were studied using the sera of patients with systemic lupus erythematosus (SLE). P0, P1, and P2 were isolated as a macromolecular complex by preparative isoelectric focusing and anion-exchange chromatography in the presence of 6 M urea. The apparent molecular size of the complex was...