Evaluating the Anderson-Darling Distribution

Except for n = 1, only the limit as n approaches infinity for the distribution of the Anderson-Darling test for uniformity has been found, and that in so complicated a form that published values for a few percentiles had to be determined by numerical integration, saddlepoint or other approximation methods. We give here our method for evaluating that asymptotic distribution to great accuracy--directly, via series with two-term recursions. We also give, for any particular n, a procedure for evaluating the distribution to the fourth digit, based on empirical CDF's from samples of size 10^10 .

The Transformation of Sediment Into Rock : Insights From IODP Site U1352, Canterbury Basin, New Zealand

ACKNOWLEDGMENTS We thank the crew of the RV JOIDES Resolution for professional seamanship, excellent drilling, and the scientific support on board. GHB and SCG thank the Australia–New Zealand IODP Consortium (ANZIC), and KMM thanks the Consortium for Ocean Leadership U.S. Science Support Program for partly funding this work. Thanks also to funding agencies of the respective authors, and Mark Lawrence (GNS Science) and Cam Nelson (University of Waikato) for their thoughtful comments on an earlier draft. Karsten Kroeger (GNS Science) helped by providing compaction data for New Zealand basins, and Michelle Kominz (Western Michigan University) provided data on which Figure 8 was developed. Further improvements were the result of thoughtful detailed reviews by Gemma Barrie, Bill Heins, Stan Paxton, Associate Editor Joe Macquaker, and Editor Leslie Melim.Peer reviewedPostprin

Commutativity of the adiabatic elimination limit of fast oscillatory components and the instantaneous feedback limit in quantum feedback networks

We show that, for arbitrary quantum feedback networks consisting of several quantum mechanical components connected by quantum fields, the limit of adiabatic elimination of fast oscillator modes in the components and the limit of instantaneous transmission along internal quantum field connections commute. The underlying technique is to show that both limits involve a Schur complement procedure. The result shows that the frequently used approximations, for instance to eliminate strongly coupled optical cavities, are mathematically consistent.Comment: 38 pages, 10 figures, minor typos corrected and minor editorial changes. Published in Journal of Mathematical Physic

Evaluating the Anderson-Darling Distribution

Except for n = 1, only the limit as n approaches infinity for the distribution of the Anderson-Darling test for uniformity has been found, and that in so complicated a form that published values for a few percentiles had to be determined by numerical integration, saddlepoint or other approximation methods. We give here our method for evaluating that asymptotic distribution to great accuracy--directly, via series with two-term recursions. We also give, for any particular n, a procedure for evaluating the distribution to the fourth digit, based on empirical CDF's from samples of size 1010

Rapid evaluation of the inverse of the normal distribution function

Here is a method for very fast evaluation of the inverse of the normal distribution--in two versions. The first, given u, rapidly produces the solution x to 2 , to within the accuracy available in single precision arithmetic. The second is faster. Using one less term in an expansion, it provides accuracy to within 0.000002--suitable for generating a normal random variable by direct inversion of its distribution function.

The Transformation of Sediment Into Rock: Insights From IODP Site U1352, Canterbury Basin, New Zealand

At Integrated Ocean Drilling Program (IODP) Expedition 317 Site U1352, east of the South Island New Zealand, we continuously cored a 1927-m-thick Holocene-to-Eocene section where we can uniquely document downhole changes in induration and lithification in siliciclastic to calcareous fine-grained sediment using a wide range of petrological, physical-property, and geochemical data sets. Porosity decreases from around 50% at the surface to 5–10% at the base of the deepest hole, with a corresponding increase in density from ∼ 2 to ∼ 2.5 g cm3. There are progressive bulk mineral changes with depth, including an increase in carbonate and decrease in quartz and clay content. Grain compaction is first seen in thin section at 347 m below sea floor and intensifies downhole. Pressure solution (chemical compaction) begins at 380 m and is common below 1440 m, with stylolite development below 1600 m, and sediment injection features below 1680 m. Porewater geochemistry and petrographic observations document two active zones of cementation, one shallow (eogenetic) down to ∼ 50 m, as evidenced by micritic nodules and pore-water geochemistry driven by methane oxidation by sulfate, and another burial-related cementation zone (mesogenetic) starting at ∼ 300 m. A transitional zone occurs between 50 and 300 m. Our results quantify downhole diagenetic changes and verify depth estimates for these processes inferred from outcrop studies, and provide an actualistic example of cementation and compaction trends in a slope setting.Published272–2875A. Paleoclima e ricerche polariJCR Journa