Parallel integer relation detection: techniques and applications

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Exponential suppression with four legs and an infinity of loops

The L-loop 4-point ladder diagram of massless phi^3 theory is finite when all 4 legs are off-shell and is given in terms of polylogarithms with orders ranging from L to 2L. We obtain the exact solution of the linear Dyson-Schwinger equation that sums these ladder diagrams and show that this sum vanishes exponentially fast at strong coupling.Comment: 5 pages, 1 figure, presented at "Loops and Legs in Quantum Field Theory 2010", Woerlitz, Germany, April 201

Special values of multiple polylogarithms

Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and high-energy physics. More recently, we have been forced to consider multidimensional extensions encompassing the classical polylogarithm, Euler sums, and the Riemann zeta function. Here, we provide a general framework within which previously isolated results can now be properly understood. Applying the theory developed herein, we prove several previously conjectured evaluations, including an intriguing conjecture of Don Zagier

Central Binomial Sums, Multiple Clausen Values and Zeta Values

We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Ap\'ery sums). The study of non-alternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio. In the non-alternating case, there is a strong connection to polylogarithms of the sixth root of unity, encountered in the 3-loop Feynman diagrams of {\tt hep-th/9803091} and subsequently in hep-ph/9910223, hep-ph/9910224, cond-mat/9911452 and hep-th/0004010.Comment: 17 pages, LaTeX, with use of amsmath and amssymb packages, to appear in Journal of Experimental Mathematic

Hopf Algebra Primitives in Perturbation Quantum Field Theory

The analysis of the combinatorics resulting from the perturbative expansion of the transition amplitude in quantum field theories, and the relation of this expansion to the Hausdorff series leads naturally to consider an infinite dimensional Lie subalgebra and the corresponding enveloping Hopf algebra, to which the elements of this series are associated. We show that in the context of these structures the power sum symmetric functionals of the perturbative expansion are Hopf primitives and that they are given by linear combinations of Hall polynomials, or diagrammatically by Hall trees. We show that each Hall tree corresponds to sums of Feynman diagrams each with the same number of vertices, external legs and loops. In addition, since the Lie subalgebra admits a derivation endomorphism, we also show that with respect to it these primitives are cyclic vectors generated by the free propagator, and thus provide a recursion relation by means of which the (n+1)-vertex connected Green functions can be derived systematically from the n-vertex ones.Comment: 21 pages, accepted for publication in J.Geom.and Phy

Metabolomics reveals mouse plasma metabolite responses to acute exercise and effects of disrupting AMPK-glycogen interactions

Introduction: The AMP-activated protein kinase (AMPK) is a master regulator of energy homeostasis that becomes activated by exercise and binds glycogen, an important energy store required to meet exercise-induced energy demands. Disruption of AMPK-glycogen interactions in mice reduces exercise capacity and impairs whole-body metabolism. However, the mechanisms underlying these phenotypic effects at rest and following exercise are unknown. Furthermore, the plasma metabolite responses to an acute exercise challenge in mice remain largely uncharacterized. Methods : Plasma samples were collected from wild type (WT) and AMPK double knock-in (DKI) mice with disrupted AMPK-glycogen binding at rest and following 30-min submaximal treadmill running. An untargeted metabolomics approach was utilized to determine the breadth of plasma metabolite changes occurring in response to acute exercise and the effects of disrupting AMPK-glycogen binding. Results: Relative to WT mice, DKI mice had reduced maximal running speed (p \u3c 0.0001) concomitant with increased body mass (p \u3c 0.01) and adiposity (p \u3c 0.001). A total of 83 plasma metabolites were identified/annotated, with 17 metabolites significantly different (p \u3c 0.05; FDR \u3c 0.1) in exercised (↑ 6; ↓ 11) versus rested mice, including amino acids, acylcarnitines and steroid hormones. Pantothenic acid was reduced in DKI mice versus WT. Distinct plasma metabolite profiles were observed between the rest and exercise conditions and between WT and DKI mice at rest, while metabolite profiles of both genotypes converged following exercise. These differences in metabolite profiles were primarily explained by exercise-associated increases in acylcarnitines and steroid hormones as well as decreases in amino acids and derivatives following exercise. DKI plasma showed greater decreases in amino acids following exercise versus WT. Conclusion : This is the first study to map mouse plasma metabolomic changes following a bout of acute exercise in WT mice and the effects of disrupting AMPK-glycogen interactions in DKI mice. Untargeted metabolomics revealed alterations in metabolite profiles between rested and exercised mice in both genotypes, and between genotypes at rest. This study has uncovered known and previously unreported plasma metabolite responses to acute exercise in WT mice, as well as greater decreases in amino acids following exercise in DKI plasma. Reduced pantothenic acid levels may contribute to differences in fuel utilization in DKI mice

The Sextet Arcs: a Strongly Lensed Lyman Break Galaxy in the ACS Spectroscopic Galaxy Survey towards Abell 1689

We present results of the HST Advanced Camera for Surveys spectroscopic ground-based redshift survey in the field of A1689. We measure 98 redshifts, increasing the number of spectroscopically confirmed objects by sixfold. We present two spectra from this catalog of the Sextet Arcs, images which arise from a strongly-lensed Lyman Break Galaxy (LBG) at a redshift of z=3.038. Gravitational lensing by the cluster magnifies its flux by a factor of ~16 and produces six separate images with a total r-band magnitude of r_625=21.7. The two spectra, each of which represents emission from different regions of the LBG, show H I and interstellar metal absorption lines at the systemic redshift. Significant variations are seen in Ly-alpha profile across a single galaxy, ranging from strong absorption to a combination of emission plus absorption. A spectrum of a third image close to the brightest arc shows Ly-alpha emission at the same redshift as the LBG, arising from either another spatially distinct region of the galaxy, or from a companion galaxy close to the LBG. Taken as a group, the Ly-alpha equivalent width in these three spectra decreases with increasing equivalent width of the strongest interstellar absorption lines. We discuss how these variations can be used to understand the physical conditions in the LBG. Intrinsically, this LBG is faint, ~0.1L*, and forming stars at a modest rate, ~4 solar masses per year. We also detect absorption line systems toward the Sextet Arcs at z=2.873 and z=2.534. The latter system is seen across two of our spectra.Comment: Accepted for publication in Ap

New Constraints on the Complex Mass Substructure in Abell 1689 from Gravitational Flexion

In a recent publication, the flexion aperture mass statistic was found to provide a robust and effective method by which substructure in galaxy clusters might be mapped. Moreover, we suggested that the masses and mass profile of structures might be constrained using this method. In this paper, we apply the flexion aperture mass technique to HST ACS images of Abell 1689. We demonstrate that the flexion aperture mass statistic is sensitive to small-scale structures in the central region of the cluster. While the central potential is not constrained by our method, due largely to missing data in the central 0.5$^\prime$ of the cluster, we are able to place constraints on the masses and mass profiles of prominent substructures. We identify 4 separate mass peaks, and use the peak aperture mass signal and zero signal radius in each case to constrain the masses and mass profiles of these substructures. The three most massive peaks exhibit complex small-scale structure, and the masses indicated by the flexion aperture mass statistic suggest that these three peaks represent the dominant substructure component of the cluster ($\sim 7\times 10^{14}h^{-1}M_\odot$). Their complex structure indicates that the cluster -- far from being relaxed -- may have recently undergone a merger. The smaller, subsidiary peak is located coincident with a group of galaxies within the cluster, with mass $\sim 1\times10^{14}h^{-1}M_\odot$. These results are in excellent agreement with previous substructure studies of this cluster.Comment: 18 pages, 10 figures, MNRAS accepted (7 Dec 2010