A note on uniform approximation to distributions of extreme order statistics

Summary The error bound of an approximation to the distribution of thekth largest order statistic as established by Reiss (1981,Adv. Appl. Prob.,13, 533–547) is improved by making use of an asymptotic expansion of length two in Reiss (the same as above).     

Asymptotic independence of distributions of normalized order statistics of the underlying probability measure

Let n denote the sample size, and let r_i ∈ {1,…,n} fulfill the conditions r_i ? r_i?1 ≥ 5 for i = 1,…,k. It is proved that the joint normalized distribution of the order statistics Z_ri:n, i = 1,…,k, is independent of the underlying probability measure up to a remainder term of order $\text{O((}\text{k}\text{n}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$. A counterexample shows that, as far as central order statistics are concerned, this remainder term is not of the order $\text{O((}\text{k}\text{n}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ if r_i ? r_i?1 = 1 for i = 2,…,k.     

Investigation of the level schemes of 73,75,77As via the (3He,d) reaction

The reactions ^{72, 74, 76}Ge(³He, d) were investigated at E_lab = 23 MeV with a multigap and a Q3D magnetic spectrograph. Some 30 new levels up to $\text{E}{}^1\text{≈ 4}\text{MeV}$ have been found. The level schemes of the odd As isotopes ^{73, 75, 77}As up to $\text{E}{}^1\text{≈ 4}\text{MeV}$ seem to be rather independent of the neutron number. The good agreement of the low-lying level structure with the Coriolis-coupling model including a pairing force was verified and the vacancies of low-lying shell model states were extracted and compared with the simple pairing theory.     

Improving solid-state NMR dipolar recoupling by optimal control

We present the first solid-state NMR experiments developed using optimal control theory. Taking heteronuclear dipolar recoupling in magic-angle-spinning NMR as an example, it proves possible to significantly improve the efficiency of the experiments while introducing robustness toward instrumental imperfections such as radio frequency inhomogeneity. The improvements are demonstrated by numerical simulations as well as practical experiments on a 13Calpha,15N-labeled powder of glycine. The experiments demonstrate a gain of 53% in the efficiency for 15N to 13Calpha coherence transfer relative to the typically double-cross-polarization experiments.     

Massively Parallel Nonparametric Regression,With an Application to Developmental Brain Mapping

A penalized approach is proposed for performing large numbers of parallel nonparametric analyses of either of two types: restricted likelihood ratio tests of a parametric regression model versus a general smooth alternative, and nonparametric regression. Compared with naïvely performing each analysis in turn, our techniques reduce computation time dramatically. Viewing the large collection of scatterplot smooths produced by our methods as functional data, we develop a clustering approach to summarize and visualize these results. Our approach is applicable to ultra-high-dimensional data, particularly data acquired by neuroimaging; we illustrate it with an analysis of developmental trajectories of functional connectivity at each of approximately 70,000 brain locations. Supplementary materials, including an appendix and an R package, are available online.     

The double salt tris(diisopropylammonium) tetrachloridoferrate(III) dichloride: Synthesis, crystal structure, and vibrational spectra

Tris(diisopropylammonium)tetrachloridoferrate(III) dichloride crystallizes in the monoclinic space group P2₁/c (a = 7.6685(2) ?, b = 17.6079(3) ?, c = 23.3217(4) ?, β = 91.396(2)°, V = 3148.1(1) ?³, Z = 4, T = 113 K) with three diisopropylammonium cations (dip), one tetrachloridoferrate(III) anion, and two chloride anions in the asymmetric unit. The dip cations and the chloride anions form hydrogen bonded one-dimensional polymers along [010]. The tetrachloridoferrate(III) anion, habituated in between these chains, is not involved in any hydrogen bonding. The structural characterization is supported by infrared and Raman spectroscopic data.