Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds

For data given on a nonlinear space, like angles, symmetric positive matrices, the sphere, or the hyperbolic space, there is often enough structure to form a Riemannian manifold. We present the Julia package Manifolds.jl, providing a fast and easy to use library of Riemannian manifolds and Lie groups. We introduce a common interface, available in ManifoldsBase.jl, with which new manifolds, applications, and algorithms can be implemented. We demonstrate the utility of Manifolds.jl using B\'ezier splines, an optimization task on manifolds, and a principal component analysis on nonlinear data. In a benchmark, Manifolds.jl outperforms existing packages in Matlab or Python by several orders of magnitude and is about twice as fast as a comparable package implemented in C++

pi-NN Coupling Constants from NN Elastic Data between 210 and 800 Mev

High partial waves for $pp$ and $np$ elastic scattering are examined critically from 210 to 800 MeV. Non-OPE contributions are compared with predictions from theory. There are some discrepancies, but sufficient agreement that values of the $\pi NN$ coupling constants $g_0^2$ for $\pi ^0$ exchange and $g^2_{c}$ for charged $\pi$ exchange can be derived. Results are $g^2_0 = 13.91 \pm 0.13 \pm 0.07$ and $g^2_c = 13.69 \pm 0.15 \pm 0.24$, where the first error is statistical and the second is an estimate of the likely systematic error, arising mostly from uncertainties in the normalisation of total cross sections and $d\sigma/d\Omega$.Comment: 21 pages of LaTeX, UI-NTH-940

Seismic structure of the southern Gulf of California from Los Cabos block to the East Pacific Rise

Multichannel reflection and coincident wide-angle seismic data collected during the 2002 Premier Experiment, Sea of Cortez, Addressing the Development of Oblique Rifting (PESCADOR) experiment provide the most detailed seismic structure to date of the southern Gulf of California. Multichannel seismic (MCS) data were recorded with a 6-km-long streamer, 480-channel, aboard the R/V Maurice Ewing, and wide-angle data was recorded by 19 instruments spaced every similar to 12 km along the transect. The MCS and wide-angle data reveal the seismic structure across the continent-ocean transition of the rifted margin. Typical continental and oceanic crust are separated by a similar to 75-km-wide zone of extended continental crust dominated by block-faulted basement. Little lateral variation in crustal thicknesses and seismic velocities is observed in the oceanic crust, suggesting a constant rate of magmatic productivity since seafloor spreading began. Oceanic crustal thickness and mean crustal velocities suggest normal mantle temperature (1300 degrees C) and passive mantle upwelling at the early stages of seafloor spreading. The crustal thickness, width of extended continental crust, and predicted temperature conditions all indicate a narrow rift mode of extension. On the basis of upper and lower crust stretching factors, an excess of lower crust was found in the extended continental crust. Total extension along transect 5W is estimated to be similar to 35 km. Following crustal extension, new oceanic crust similar to 6.4-km-thick was formed at a rate of similar to 48 mm a(-1) to accommodate plate separation

Timing of detachment faulting in the Bullfrog Hills and Bare Mountain area, southwest Nevada: Inferences from 40Ar/39Ar, K-Ar, U-Pb and fission track thermochronology

Crustal extension in the Bullfrog Hills and Bare Mountain area of southwest Nevada is associated with movement along a regional detachment fault. Normal faulting in the upper plate and rapid cooling (denudation) of the lower plate were coeval with Miocene silicic volcanism and with west-northwest transport along the detachment fault. A west-northwest progression of tilting along upper plate normal faults is indicated by ages of the volcanic rocks in relation to angular unconformities. Near the breakaway, tilting in the upper plate occurred between 12.7 and 11.6 Ma, continued less strongly past 10.7 Ma, and was over by 8.2 Ma. Ten to 20 km west of the breakaway, tilting occurred between 10.7 and 10.33 Ma, continued less strongly after 10.33 Ma, and was over by 8.1 Ma. The cooling histories of the lower plate metamorphic rocks were determined by thermochronologic dating methods: K-Ar and Ar-40/(39)A on muscovite, biotite, and hornblende, Ar-40/(39)A on K-feldspar, U-Pb on apatite, zircon, and sphene, and fission track on apatite, zircon, and sphene. Lower plate rocks 10 km west of the breakaway cooled slowly from Early Cretaceous lower-amphibolite facies conditions through 350+/-50 degrees to 300+/-50 degrees C between 57 and 38 Ma, then cooled rapidly from 205+/-50 degrees to 120+/-5O degrees C between 12.6+/-1.6 and 11.1+/-1.9 Ma. Lower plate rocks 20 km west of the breakaway cooled slowly from Early Cretaceous upper-amphibolite facies conditions through 500+/-50 degrees C at 78-67 Ma, passed through 350+/-50 degrees to 300+/-50 degrees C between 16.3+/-0.4 and 10.5+/-0.3 Ma, then cooled rapidly from 285+/-50 degrees to 120+/-50 degrees C between 10.2 and 8.6 Ma. Upper plate tilting and rapid cooling (denudation) of the lower plate occurred simultaneously in the respective areas. The early slow-cooling part of the lower plate thermal histories was probably related to erosion at the Earth's surface, which stripped off about 9 km of material in 50 to 100 m.y. The results indicate an initial fault dip greater than or equal to 30 degrees and a 12 mm yr(-1) west-northwest migration of the locus of rapid tilting in the upper plate

Search for scalar top and scalar bottom quarks at LEP

Searches for a scalar top quark and a scalar bottom quark have been performed using a data sample of 438 pb^(−1) at centre-of-mass energies of sqrt(s) = –209 GeV collected with the OPAL detector at LEP. No evidence for a signal was found. The 95% confidence level lower limit on the scalar top quark mass is 97.6 GeV if the mixing angle between the supersymmetric partners of the left- and right-handed states of the top quark is zero. When the scalar top quark decouples from the Z0 boson, the lower limit is 95.7 GeV. These limits were obtained assuming that the scalar top quark decays into a charm quark and the lightest neutralino, and that the mass difference between the scalar top quark and the lightest neutralino is larger than 10 GeV. The complementary decay mode of the scalar top quark decaying into a bottom quark, a charged lepton and a scalar neutrino has also been studied. The lower limit on the scalar top quark mass is 96.0 GeV for this decay mode, if the mass difference between the scalar top quark and the scalar neutrino is greater than 10 GeV and if the mixing angle of the scalar top quark is zero. From a search for the scalar bottom quark, a mass limit of 96.9 GeV was obtained if the mass difference between the scalar bottom quark and the lightest neutralino is larger than 10 GeV

Bose–Einstein correlations of π^0 pairs from hadronic Z^0 decays

We observe Bose–Einstein correlations in π^0 pairs using back-to-back two jet hadronic events from Z^0 decays in the data sample collected by the OPAL detector at LEP 1 from 1991 to 1995. Using a static Gaussian picture for the pion emitter source, we obtain the chaoticity parameter λ=0.55±0.10±0.10 and the source radius R=(0.59±0.08±0.05) fm. According to the JETSET and HERWIG Monte Carlo models, the Bose–Einstein correlations in our data sample largely connect π^0s originating from the decays of different hadrons. Prompt pions formed at string break-ups or cluster decays only form a small fraction of the sample

Inclusive production of charged hadrons in photon–photon collisions

The inclusive production of charged hadrons in the collisions of quasi-real photons (e+e−→e+e−+Xe+e−→e+e−+X) has been measured using the OPAL detector at LEP. The data were taken at e+e−e+e− centre-of-mass energies from 183 to 209 GeV209 GeV. The differential cross-sections as a function of the transverse momentum and the pseudorapidity of the hadrons are compared to theoretical calculations of up to next-to-leading order (NLO) in the strong coupling constant αsαs. The data are also compared to a measurement by the L3 Collaboration, in which a large deviation from the NLO predictions is observed

Search for new physics in rare B decays

A search for the decay B^±→K^±K^±π^∓ was performed using data collected by the OPAL detector at LEP. These decays are strongly suppressed in the Standard Model but could occur with a higher branching ratio in supersymmetric models, especially in those with R-parity violating couplings. No evidence for a signal was observed and a 90% confidence level upper limit of 1.29×10^(−4) was set for the branching ratio