We review the current status of calculations of the two pion decays of the kaon using the firstprinciples methods of lattice gauge theory and the significant challenges that these calculations pose. While a calculation with controlled errors at even the 10-20% level has not yet been performed, present results suggest that such a calculation of the real and imaginary parts of the ∆I = 3/2 amplit...

vspace{0.2cm}In this paper, we design a data structure for the following problem. Let $pi$ be an $x$-monotone trajectory with $n$ vertices in the plane and $epsilon >0$. We show how to preprocess $pi$ and $epsilon$ into a data structure such that for any horizontal query segment $Q$ in the plane, one can quickly determine the minimal continuous fraction of $pi$ whose Fr{'e}chet and Hausdo...

The use of random samples to approximate properties of geometric configurations has been an influential idea for both combinatorial and algorithmic purposes. This chapter considers two related notions— -approximations and -nets—that capture the most important quantitative properties that one would expect from a random sample with respect to an underlying geometric configuration. An example prob...

A population of cells that express mast cell markers, including the membrane protein p161, but that lack expression of the high affinity IgE receptor, Fc epsilon RI, can be routinely grown from bone marrow. Ionomycin, but not IgE immune complexes, causes these cells to release serotonin and to express IL-3 and IL-13 mRNA, consistent with their being FC epsilon RI-deficient mast cells. These p16...

We present extensive molecular dynamics simulation results for the structure and the static and dynamical responses of a droplet of 1000 soft spheres carrying extended dipoles and confined to spherical cavities of radii R=2.5, 3, and 4 nm embedded in a dielectric continuum of permittivity epsilon(')>or=1. The polarization of the external medium by the charge distribution inside the cavity is ac...

Protein kinase C (PKC) plays a prominent role in immune signaling, and the paradigms for isoform selective signaling are beginning to be elucidated. Real-time microscopy was combined with molecular and biochemical approaches to demonstrate a role for PKC- epsilon in Fc gamma receptor (Fc gammaR)-dependent phagocytosis. RAW 264.7 macrophages were transfected with GFP-conjugated PKC isoforms, and...

We studied the relationship of apolipoprotein E (apoE) isoforms and coronary artery disease (CAD) in 224 African Americans and 326 Caucasians undergoing diagnostic coronary angiography. The presence of CAD was defined as >50% stenosis in at least one artery. ApoE allele frequencies were 0.12, 0.62, and 0.26 for epsilon 2, epsilon 3, and epsilon 4, respectively, in African Americans and 0.08, 0....

The Poisson-Boltzmann equation gives the electrostatic free energy of a solute molecule (with dielectric constant epsilon(l)) solvated in a continuum solvent (with dielectric constant epsilon(s)). Here a simple formula is presented that accurately predicts the electrostatic free energy for all combinations of epsilon(l) and epsilon(s) from the calculation on a single set of epsilon(l) and epsil...

The molar absorption coefficient, epsilon, of a protein is usually based on concentrations measured by dry weight, nitrogen, or amino acid analysis. The studies reported here suggest that the Edelhoch method is the best method for measuring epsilon for a protein. (This method is described by Gill and von Hippel [1989, Anal Biochem 182:319-326] and is based on data from Edelhoch [1967, Biochemis...