Optimal Confidence Bands for Shape-Restricted Curves

Let Y be a stochastic process on [0,1] satisfying dY(t)=n 1/2 f(t)dt+dW(t) , where n≥1 is a given scale parameter (`sample size'), W is standard Brownian motion and f is an unknown function. Utilizing suitable multiscale tests, we construct confidence bands for f with guaranteed given coverage probability, assuming that f is isotonic or convex. These confidence bands are computationally feasible and shown to be asymptotically sharp optimal in an appropriate sense.

Volcanostratigraphic Controls on the Occurrence of Massive Sulfide (VMS) Deposits in the Semail Ophiolite, Oman

The Semail ophiolite in Oman is capped by up to 2 km of basaltic-andesitic lavas that host copper-dominant, Cyprus-type, volcanogenic massive sulfide (VMS) deposits. This study identifies multiple volcanostratigraphic horizons on which the deposits are situated, based on characterization of footwall and hanging-wall lavas from 16 deposits or deposit clusters. Comparison of field and petrographic features, compositions of igneous clinopyroxenes, and whole-rock geochemical signatures permits classification of the lavas within a modified version of the established regional volcanostratigraphy. Four extrusive units host deposits: Geotimes (earliest), Lasail, Alley, and Boninitic Alley (latest). The latter was previously known only at few localities, but this study reveals its regional extent and significance as a host for VMS deposits. The Geotimes and Lasail units represent Late Cretaceous, ocean spreading ridge and related off-axis volcanic environments, respectively. The Alley and Boninitic Alley units represent younger, subduction-related volcanism prior to Coniacian-Santonian obduction of the ophiolite. Our results show that VMS deposits occur on or near the Geotimes/Lasail and Geotimes/Alley contacts as well as entirely within the Geotimes, Lasail, Alley, and Boninitic Alley units. Highest Cu grades tend to occur in deposits lying on or within the Geotimes, whereas highest Au grades occur in deposits within the Boninitic Alley. In contrast to earlier studies, we conclude that essentially every horizon marking a hiatus in lava deposition in the Semail ophiolite, i.e., contacts between the four major eruptive units, and umbers and sedimentary chert layers within the units, has exploration potential for Cu-Au VMS deposits.

Confidence Bands for Isotonic Median Curves using Sign-Tests

Suppose that one observes independent random variables (X1, Y1), (X2, Y2), …, (Xn, Yn) in R2 with unknown distributions, except that Median(Yi | Xi = M(x) for some unknown isotonic function M. We describe an explicit algorithm for the computation of confidence bands for the median function M whose running time is of order O(n2). The bands rely on multiscale sign tests and are shown to have desirable asymptotic properties.

Influence of quantized massive matter fields on the Casimir effect

Charged massive matter fields of spin-0 and spin- 1/2 are quantized in the presence of an external uniform magnetic field in a spatial region bounded by two parallel plates. The most general set of boundary conditions at the plates, that is required by mathematical consistency and the self-adjointness of the Hamiltonian operator, is employed. The vacuum fluctuations of the matter field in the case of the magnetic field orthogonal to the plates are analyzed, and it is shown that the pressure from the vacuum onto the plates is positive and independent of the boundary condition, as well as of the distance between the plates. Possibilities of the detection of this new-type Casimir effect are discussed. Read More: http://www.worldscientific.com/doi/10.1142/S0217732315500996