Asymptotic behavior of an intrinsic rank-based estimator of the Pickands dependence function constructed from B-splines

A bivariate extreme-value copula is characterized by its Pickands dependence function, i.e., a convex function defined on the unit interval satisfying boundary conditions. This paper investigates the large-sample behavior of a nonparametric estimator of this function due to Cormier et al. (Extremes 17:633-659, 2014). These authors showed how to construct this estimator through constrained quadratic median B-spline smoothing of pairs of pseudo-observations derived from a random sample. Their estimator is shown here to exist whatever the order m ≥ 3 of the B-spline basis, and its consistency is established under minimal conditions. The large-sample distribution of this estimator is also determined under the additional assumption that the underlying Pickands dependence function is a B-spline of given order with a known set of knots.

All-at-once multigrid approaches for one-dimensional space-fractional diffusion equations

We focus on a time-dependent one-dimensional space-fractional diffusion equation with constant diffusion coefficients. An all-at-once rephrasing of the discretized problem, obtained by considering the time as an additional dimension, yields a large block linear system and paves the way for parallelization. In particular, in case of uniform space-time meshes, the coefficient matrix shows a two-level Toeplitz structure, and such structure can be leveraged to build ad-hoc iterative solvers that aim at ensuring an overall computational cost independent of time. In this direction, we study the behavior of certain multigrid strategies with both semi- and full-coarsening that properly take into account the sources of anisotropy of the problem caused by the grid choice and the diffusion coefficients. The performances of the aforementioned multigrid methods reveal sensitive to the choice of the time discretization scheme. Many tests show that Crank-Nicolson prevents the multigrid to yield good convergence results, while second-order backward-difference scheme is shown to be unconditionally stable and that it allows good convergence under certain conditions on the grid and the diffusion coefficients. The effectiveness of our proposal is numerically confirmed in the case of variable coefficients too and a two-dimensional example is given.

Effects of the Serber first step in 3DHZETRN-v2.1

3DHZETRN-v2 includes a detailed three dimensional (3D) treatment of neutron/light-ion transport based on a quasi-elastic/multiple production assumption allowing improved agreement of the neutron/light-ion fluence compared with results of three Monte Carlo (MC) codes in the sense that the variance with respect to the individual MC results is less than the variance among the MC code results. The current numerical methods are no longer the main limitation to HZETRN code development and further changes in the nuclear model are required. In a prior study, an improved quasi-elastic spectrum based on a solution of the transport approximation to nuclear media effects showed promise, but the remaining multiple-production spectrum was based on a database derived from the Ranft model that used Bertini multiplicities. In the present paper, we will implement a more complete Serber first step into the 3DHZETRN-v2 code, but we retain the Bertini-Ranft branching ratios and evaporation multiplicities. It is shown that the new Serber model in the 3HZETRN-v2 code reduces the variance with individual MC codes, which are largely due to nuclear cross section model differences. The code will be available through the software system, OLTARIS, for shield design and validation and provides a basis for personal computer software capable of space shield analysis and optimization.

Impact of location, type, and number of glycosidic substitutions on the color expression of o-dihydroxylated anthocyanidins

Anthocyanins express many hues depending on environmental factors and structural aspects, of which aglycone structure and acylation have been considered most impactful. Effects of different glycosylations on anthocyanins' colors are less known. Twelve cyanidin and 3-deoxy-cyanidin (luteolinidin) derivatives were isolated from red cabbage and black carrot hydrolysates and from black sorghum, diluted in pH 1-9, and analyzed by spectrophotometry and colorimetry. Location, number, and structure of glycosylations affected λ_max and spectral shape of o-dihydroxylated anthocyanins, playing important roles on color expression. Generally, glycosylation of cyanidin decreased its λ_max (≤27 nm), greatest decreases by 3-monoglycosylation. All cyanidin-glycosides appeared red in pH 1-3 and paled in pH 4-6. However, cyanidin-3-glycosides did not decolor completely like 3,5-glycosides. In alkaline pH, glycosylation patterns affected color more greatly: Cy-3-glycosides expressed maroon-purple hues (300-20°), 5-glycosides were green (100-115°), and only 3,5-glycosides expressed blue (240-250°). Luteolinidin derivatives shifted from yellow to red-purple hues with increasing pH.