Rearranging Edgeworth-Cornish-Fisher Expansions

This paper applies a regularization procedure called increasing rearrangement to monotonize Edgeworth and Cornish-Fisher expansions and any other related approximations of distribution and quantile functions of sample statistics. Besides satisfying the logical monotonicity, required of distribution and quantile functions, the procedure often delivers strikingly better approximations to the distribution and quantile functions of the sample mean than the original Edgeworth-Cornish-Fisher expansions.Comment: 17 pages, 3 figure

Life and Liesegang: Outcrop-Scale Microbially Induced Diagenetic Structures and Geochemical Self-Organization Phenomena Produced by Oxidation of Reduced Iron

The Kanab Wonderstone is sandstone (Shinarump Member, Chinle Formation) that is cemented and stained with iron oxide. The iron-oxide cementation and staining in these rocks have been considered examples of the Liesegang phenomenon, but we will show that they comprise a microbially induced structure. The spacing of bands of iron-oxide stain follow the Jablczynski spacing law (wherein the spacing between bands of iron-oxide stain increases as one traverses a series of bands) characteristic of Liesegang. Bands of iron-oxide cement exhibit more variable spacing and exhibit a weak but significant correlation between band thickness and distance between bands of cement. The pore-filling cement contains morphotypes that are similar in size and habit to those exhibited by microaerophilic iron-oxidizing bacteria. Other disseminated iron-oxide mineralization occurs as rhombohedra interpreted to be pseudomorphs after siderite. We interpret the cement to be produced by microbially mediated oxidation of siderite (a typical early diagenetic mineral in fluvial sandstones). Iron-oxidizing bacteria colonized the redox interface between siderite-cemented sand and porous sandstone. Microbes oxidized aqueous Fe(II), generating acid that caused siderite dissolution. The iron-oxide cement is the microbial product of a geochemical drive for organization; whereas the iron-oxide stain is true Liesegang. Together, they comprise a distinctive microbially induced structure with high preservation potential. Key Words: Biosignatures—Iron oxides—Diagenesis—Iron-oxidizing bacteria—Shinarump

Single Spin Asymmetry ANA_N in Polarized Proton-Proton Elastic Scattering at s=200\sqrt{s}=200 GeV

We report a high precision measurement of the transverse single spin asymmetry $A_N$ at the center of mass energy $\sqrt{s}=200$ GeV in elastic proton-proton scattering by the STAR experiment at RHIC. The $A_N$ was measured in the four-momentum transfer squared $t$ range $0.003 \leqslant |t| \leqslant 0.035$ \GeVcSq, the region of a significant interference between the electromagnetic and hadronic scattering amplitudes. The measured values of $A_N$ and its $t$-dependence are consistent with a vanishing hadronic spin-flip amplitude, thus providing strong constraints on the ratio of the single spin-flip to the non-flip amplitudes. Since the hadronic amplitude is dominated by the Pomeron amplitude at this $\sqrt{s}$, we conclude that this measurement addresses the question about the presence of a hadronic spin flip due to the Pomeron exchange in polarized proton-proton elastic scattering.Comment: 12 pages, 6 figure