Transcendental numbers and the topology of three-loop bubbles

We present a proof that all transcendental numbers that are needed for the calculation of the master integrals for three-loop vacuum Feynman diagrams can be obtained by calculating diagrams with an even simpler topology, the topology of spectacles.Comment: 4 pages in REVTeX, 1 PostScript figure included, submitted to Phys. Rev. Let

Analytical on-shell QED results: 3-loop vacuum polarization, 4-loop beta-function and the muon anomaly

We present the results of analytical calculations of the 3-loop contributions to the asymptotic photon vacuum polarization function, in the on shell scheme, and of the 4-loop contributions to the on shell QED beta-function. These are used to evaluate various 4-loop and 5-loop contributions to the muon anomaly. Our analytical contributions to (g-2)_\mu differ significantly from previous numerical results. A very recent numerical re-evaluation of 4-loop muon-anomaly contributions has yielded results much closer to ours.Comment: LaTex, 11 pages, figures available from O.V.T. CERN--TH. 6602/92, OUT--4102--39, BI--TP--92/3

Two-loop two-point functions with masses: asymptotic expansions and Taylor series, in any dimension

In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small $q^2$, in $d$ dimensions, using identities derived from integration by parts. Expansions are given, in terms of hypergeometric series, for all gluon diagrams and for all but one of the quark diagrams; expansions of the latter are obtained from differential equations. Pad\'{e} approximants to truncations of the expansions are shown to be of great utility. As an application, we obtain the two-loop photon self-energy, for all $d$, and achieve highly accelerated convergence of its expansions in powers of $q^2/m^2$ or $m^2/q^2$, for $d=4$.Comment: 25 pages, OUT--4102--43, BI--TP/92--5

Perturbative Part of the Non-Singlet Structure Function F_2 in the Large-N_F Limit

We have calculated $\bar{MS}$ Wilson coefficients and anomalous dimensions for the non-singlet part of the structure function F_2 in the large-N_F limit. Our result agrees with exact two and three loop calculations and gives the leading N_F dependence of the perturbative non-singlet Wilson coefficients to all orders in $\alpha_S$.Comment: 11 pages, including one figur

Growth and Metal Accumulation of an Alyssum murale Nickel Hyperaccumulator Ecotype Co-cropped with Alyssum montanum and Perennial Ryegrass in Serpentine Soil

The genus Alyssum (Brassicaceae) contains Ni hyperaccumulators (50), many of which can achieve 30 g kg-1 Ni in dry leaf. Some Alyssum hyperaccumulators are viable candidates for commercial Ni phytoremediation and phytomining technologies. It is not known whether these species secrete organic and/or amino acids into the rhizosphere to solubilize Ni, or can make use of such acids within the soil to facilitate uptake. It has been hypothesized that in fields with mixed plant species, mobilization of metals by phytosiderophores secreted by Graminaceae plants could affect Alyssum Ni, Fe, Cu and Mn uptake.We co-cropped the Ni hyperaccumulator Alyssum murale, non-hyperaccumulator A. montanum and perennial ryegrass in a natural serpentine soil. All treatments had standard inorganic fertilization required for ryegrass growth and one treatment was compost amended. After 4 months A. murale leaves and stems contained 3600 mg kg-1 Ni which did not differ significantly with co-cropping. Overall Ni and Mn concentrations were significantly higher in A. murale than in A. montanum or L. perenne. Copper was not accumulated by either Alyssum species, but L. perenne accumulated up to 10 mg kg-1. A. montanum could not compete with either A. murale or ryegrass, and neither Alyssum species survived in the compost-amended soil. Co-cropping with ryegrass reduced Fe and Mn concentrations in A. murale but not to the extent of either increasing Ni uptake or affecting plant nutrition. The hypothesized Alyssum Ni accumulation in response to phytosiderophores secreted by co-cropped grass did not occur. Our data do not support increased mobilization of Mn by a phytosiderophore mechanism either, but the converse: mobilization of Mn by the Alyssum hyperaccumulator species significantly increased Mn levels in L. perenne. Tilling soil to maximize root penetration, adequate inorganic fertilization and appropriate plant densities are more important for developing efficient phytoremediation and phytomining approaches

Probing the Cluster Mass Distribution using Subaru Weak Lensing Data

We present results from a weak lensing analysis of the galaxy cluster A1689 (z=0.183) based on deep wide-field imaging data taken with Suprime-Cam on Subaru telescope. A maximum entropy method has been used to reconstruct directly the projected mass distribution of A1689 from combined lensing distortion and magnification measurements of red background galaxies.The resulting mass distribution is clearly concentrated around the cD galaxy, and mass and light in the cluster are similarly distributed in terms of shape and orientation. The azimuthally-averaged mass profile from the two-dimensional reconstruction is in good agreement with the earlier results from the Subaru one-dimensional analysis of the weak lensing data, supporting the assumption of quasi-circular symmetry in the projected mass distribution of the cluster.Comment: To appear in Mod. Phys. Lett. A, 8pages, 5 figures, minor typo errors corrected, Fig.5 modifie

Signaling local non-credibility in an automatic segmentation pipeline

The advancing technology for automatic segmentation of medical images should be accompanied by techniques to inform the user of the local credibility of results. To the extent that this technology produces clinically acceptable segmentations for a significant fraction of cases, there is a risk that the clinician will assume every result is acceptable. In the less frequent case where segmentation fails, we are concerned that unless the user is alerted by the computer, she would still put the result to clinical use. By alerting the user to the location of a likely segmentation failure, we allow her to apply limited validation and editing resources where they are most needed. We propose an automated method to signal suspected non-credible regions of the segmentation, triggered by statistical outliers of the local image match function. We apply this test to m-rep segmentations of the bladder and prostate in CT images using a local image match computed by PCA on regional intensity quantile functions. We validate these results by correlating the non-credible regions with regions that have surface distance greater than 5.5mm to a reference segmentation for the bladder. A 6mm surface distance was used to validate the prostate results. Varying the outlier threshold level produced a receiver operating characteristic with area under the curve of 0.89 for the bladder and 0.92 for the prostate. Based on this preliminary result, our method has been able to predict local segmentation failures and shows potential for validation in an automatic segmentation pipeline

Using Weak Lensing Dilution to Improve Measurements of the Luminous and Dark Matter in A1689

The E/SO sequence of a cluster defines a boundary redward of which a reliable weak lensing signal can be obtained from background galaxies, uncontaminated by cluster members. For bluer colors, both background and cluster members are present, reducing the distortion signal by the proportion of unlensed cluster members. In deep Subaru and HST/ACS images of A1689 the tangential distortion of galaxies with bluer colors falls rapidly toward the cluster center relative to the lensing signal of the red background. We use this dilution effect to derive the cluster light profile and luminosity function to large radius, with the advantage that no subtraction of far-field background counts is required. The light profile declines smoothly to the limit of the data, r<2Mpc/h, with a constant slope, dlog(L)/dlog(r)=-1.12+-0.06, unlike the lensing mass profile which steepens continuously with radius, so that M/L peaks at an intermediate radius, ~100kpc/h. A flatter behavior is found for the more physically meaningful ratio of dark-matter to stellar-matter, when accounting for the color-mass relation of cluster members. The cluster luminosity function has a flat slope, alpha=-1.05+-0.07, independent of radius and with no faint upturn to M_i'<-12. We establish that the very bluest objects are negligibly contaminated by the cluster V-i'<0.2, because their distortion profile rises towards the center following the red background, but offset higher by ~20%. This larger amplitude is consistent with the greater estimated depth of the faint blue galaxies, z~=2.0 compared to z~=0.85 for the red background, a purely geometric effect related to cosmological parameters. Finally, we improve upon our earlier mass profile by combining both the red and blue background populations, clearly excluding low concentration CDM profiles.Comment: 17 pages, 21 figures, revised version in response to referee comments,(added some discussion, references), conclusions unchanged. Accepted for publication in Ap

Young Red Spheroidal Galaxies in the Hubble Deep Fields: Evidence for a Truncated IMF at ~2M_solar and a Constant Space Density to z~2

The optical-IR images of the Northern and Southern Hubble Deep Fields are used to measure the spectral and density evolution of early-type galaxies. The mean optical SED is found to evolve passively towards a mid F-star dominated spectrum by z ~ 2. We demonstrate with realistic simulations that hotter ellipticals would be readily visible if evolution progressed blueward and brightward at z > 2, following a standard IMF. The colour distributions are best fitted by a `red' IMF, deficient above ~2 M_solar and with a spread of formation in the range 1.5 < z_f < 2.5. Traditional age dating is spurious in this context, a distant elliptical can be young but appear red, with an apparent age >3 Gyrs independent of its formation redshift. Regarding density evolution, we demonstrate that the sharp decline in numbers claimed at z > 1 results from a selection bias against distant red galaxies in the optical, where the flux is too weak for morphological classification, but is remedied with relatively modest IR exposures revealing a roughly constant space density to z ~ 2. We point out that the lack of high mass star-formation inferred here and the requirement of metals implicates cooling-flows of pre-enriched gas in the creation of the stellar content of spheroidal galaxies. Deep-field X-ray images will be very helpful to examine this possibility.Comment: 6 pages, 3 figures, submitted to Astrophysical Journal Letters, typographical errors corrected, simulated images with different IMFs illustrated at http://astro.berkeley.edu/~bouwens/ellip.htm