Pade Approximants, Optimal Renormalization Scales, and Momentum Flow in Feynman Diagrams

We show that the Pade Approximant (PA) approach for resummation of perturbative series in QCD provides a systematic method for approximating the flow of momentum in Feynman diagrams. In the large-$\beta_0$ limit, diagonal PA's generalize the Brodsky-Lepage-Mackenzie (BLM) scale-setting method to higher orders in a renormalization scale- and scheme-invariant manner, using multiple scales that represent Neubert's concept of the distribution of momentum flow through a virtual gluon. If the distribution is non-negative, the PA's have only real roots, and approximate the distribution function by a sum of delta-functions, whose locations and weights are identical to the optimal choice provided by the Gaussian quadrature method for numerical integration. We show how the first few coefficients in a perturbative series can set rigorous bounds on the all-order momentum distribution function, if it is positive. We illustrate the method with the vacuum polarization function and the Bjorken sum rule computed in the large-$\beta_0$ limit.Comment: 28 pages, LaTeX, including 6 figures requires epsfig.st

Why Pad\'e Approximants reduce the Renormalization-Scale dependence in QFT?

We prove that in the limit where the beta function is dominated by the 1-loop contribution (``large beta_0 limit'') diagonal Pad\'e Approximants (PA's) of perturbative series become exactly renormalization scale (RS) independent. This symmetry suggest that diagonal PA's are resumming correctly contributions from higher order diagrams that are responsible for the renormalization of the coupling-constant. Non-diagonal PA's are not exactly invariant, but generally reduce the RS dependence as compared to partial-sums. In physical cases, higher-order corrections in the beta function break the symmetry softly, introducing a small scale and scheme dependence. We also compare the Pad\'e resummation with the BLM method. We find that in the large-N_f limit using the BLM scale is identical to resumming the series by a $x[0/n]$ non-diagonal PA.Comment: 25 pages, LateX. Replaced so that the figures would fit into the page siz

Assessing the Extent of Carbonate Deposition in Early Rift Settings

Select lacustrine and marine depositional settings show a spectrum of styles of carbonate deposition and illustrate the types of carbonates, with an emphasis on microbialites and tufa, to be expected in early rift settings. Early rift lake examples examined in this review article are all from East Africa: Lakes Turkana, Bogoria, Natron and Magadi, Manyara, and Tanganyika. Other lake examples include four from the western United States (Great Salt Lake and high lake level Lake Bonneville, Mono Lake and high lake level Russell Lake, Pyramid Lake and high lake level Lake Lahontan, and Searles Lake) and two from Australia (Lakes Clifton and Thetis). Marine basin examples are the Hamelin Pool part of Shark Bay from Australia (marginal marine) and the Red Sea (marine rift). Landsat images and digital elevation models for each example are used to delineate present and past lake-basin margins based on published lake-level elevations, and for some examples, the shorelines representing different lake levels can be compared to evaluate how changes in size, shape, and lake configuration might have impacted carbonate development. The early rift lakes show a range of characteristics to be expected in lacustrine settings during the earliest stages of continental extension and rifting, whereas the Red Sea shows well advanced rifting with marine incursion and reef–skeletal sand development. Collectively, the lacustrine examples show a wide range of sizes, with several of them being large enough that they could produce carbonate deposits of potential economic interest. Three of the areas—Great Salt Lake and high lake level Lake Bonneville, Pyramid Lake and high lake level Lake Lahontan, and the Red Sea—are exceedingly complex in that they illustrate a large degree of potential depositional facies heterogeneity because of their size, irregular pattern, and connectivity of subbasins within the overall basin outline

Beam alignment techniques based on the current multiplication effect in photoconductors Third summary technical progress report, 15 Nov. 1966 - 15 Oct. 1967

Beam alignment techniques developed for infrared sensitive single crystal germanium to study multiplication effect in photoconductor

Renormalization-Scale Invariance, Minimal Sensitivity, and the Inclusive Hadronic Decays of a 115 GeV Higgs Particle

Known perturbative expressions for the decay rates of 115 GeV Higgs particle into either two gluons or a $b\bar{b}$ pair are shown to exhibit renormalization-scale-($\mu$)-dependence that is largely removed via renormalization-group/Pade-approximant estimates of these rates' next order contributions. The extrema in $\mu$ characterizing both rates, as determined from fully-known orders of perturbation theory, are very nearly equal to corresponding $\mu$-insensitive rates obtained via estimation of their next order contributions, consistent with "minimal-sensitivity" expectations.Comment: 12 pages, 3 figures, LaTe

Identification and characterisation of enteroaggregative Escherichia coli subtypes associated with human disease

Enteroaggregative E. coli (EAEC) are a major cause of diarrhoea worldwide. Due to their heterogeneity and carriage in healthy individuals, identification of diagnostic virulence markers for pathogenic strains has been difficult. In this study, we have determined phenotypic and genotypic differences between EAEC strains of sequence types (STs) epidemiologically associated with asymptomatic carriage (ST31) and diarrhoeal disease (ST40). ST40 strains demonstrated significantly enhanced intestinal adherence, biofilm formation, and pro-inflammatory interleukin-8 secretion compared with ST31 isolates. This was independent of whether strains were derived from diarrhoea patients or healthy controls. Whole genome sequencing revealed differences in putative virulence genes encoding aggregative adherence fimbriae, E. coli common pilus, flagellin and EAEC heat-stable enterotoxin 1. Our results indicate that ST40 strains have a higher intrinsic potential of human pathogenesis due to a specific combination of virulence-related factors which promote host cell colonization and inflammation. These findings may contribute to the development of genotypic and/or phenotypic markers for EAEC strains of high virulence

Asymptotic Pade Approximant Predictions: up to Five Loops in QCD and SQCD

We use Asymptotic Pade Approximants (APAP's) to predict the four- and five-loop \beta-functions in QCD and N=1 supersymmetric QCD (SQCD), as well as the quark mass anomalous dimensions in Abelian and non-Abelian gauge theories. We show how the accuracy of our previous \beta-function predictions at the four-loop level may be further improved by using estimators weighted over negative numbers of flavours (WAPAP's). The accuracy of the improved four-loop results encourages confidence in the new five-loop \beta-function predictions that we present. However, the WAPAP approach does not provide improved results for the anomalous mass dimension, or for Abelian theories.Comment: Title page revised with deep regret following the untimely death of our friend and collaborator Mark Samuel; 25 pages, harvmac (b), including 3 figures; requires epsf.tex and tables.te

Digital fragment analysis of short tandem repeats by high‐throughput amplicon sequencing

High‐throughput sequencing has been proposed as a method to genotype microsatellites and overcome the four main technical drawbacks of capillary electrophoresis: amplification artifacts, imprecise sizing, length homoplasy, and limited multiplex capability. The objective of this project was to test a high‐throughput amplicon sequencing approach to fragment analysis of short tandem repeats and characterize its advantages and disadvantages against traditional capillary electrophoresis. We amplified and sequenced 12 muskrat microsatellite loci from 180 muskrat specimens and analyzed the sequencing data for precision of allele calling, propensity for amplification or sequencing artifacts, and for evidence of length homoplasy. Of the 294 total alleles, we detected by sequencing, only 164 alleles would have been detected by capillary electrophoresis as the remaining 130 alleles (44%) would have been hidden by length homoplasy. The ability to detect a greater number of unique alleles resulted in the ability to resolve greater population genetic structure. The primary advantages of fragment analysis by sequencing are the ability to precisely size fragments, resolve length homoplasy, multiplex many individuals and many loci into a single high‐throughput run, and compare data across projects and across laboratories (present and future) with minimal technical calibration. A significant disadvantage of fragment analysis by sequencing is that the method is only practical and cost‐effective when performed on batches of several hundred samples with multiple loci. Future work is needed to optimize throughput while minimizing costs and to update existing microsatellite allele calling and analysis programs to accommodate sequence‐aware microsatellite data