1,794 research outputs found
On one example and one counterexample in counting rational points on graph hypersurfaces
In this paper we present a concrete counterexample to the conjecture of
Kontsevich about the polynomial countability of graph hypersurfaces. In
contrast to this, we show that the "wheel with spokes" graphs are
polynomially countable
Higher loop renormalization of a supersymmetric field theory
Using Dyson--Schwinger equations within an approach developed by Broadhurst
and Kreimer and the renormalization group, we show how high loop order of the
renormalization group coefficients can be efficiently computed in a
supersymmetric model.Comment: 8 pages, 2 figure
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 , in 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
, and achieve highly accelerated convergence of its expansions in powers of
or , for .Comment: 25 pages, OUT--4102--43, BI--TP/92--5
An Efficient Method for the Solution of Schwinger--Dyson equations for propagators
Efficient computation methods are devised for the perturbative solution of
Schwinger--Dyson equations for propagators. We show how a simple computation
allows to obtain the dominant contribution in the sum of many parts of previous
computations. This allows for an easy study of the asymptotic behavior of the
perturbative series. In the cases of the four-dimensional supersymmetric
Wess--Zumino model and the complex scalar field, the singularities
of the Borel transform for both positive and negative values of the parameter
are obtained and compared.Comment: 9 pages, no figures. Match of the published version, with the
corrections in proo
On Motives Associated to Graph Polynomials
The appearance of multiple zeta values in anomalous dimensions and
-functions of renormalizable quantum field theories has given evidence
towards a motivic interpretation of these renormalization group functions. In
this paper we start to hunt the motive, restricting our attention to a subclass
of graphs in four dimensional scalar field theory which give scheme independent
contributions to the above functions.Comment: 54
The massless higher-loop two-point function
We introduce a new method for computing massless Feynman integrals
analytically in parametric form. An analysis of the method yields a criterion
for a primitive Feynman graph to evaluate to multiple zeta values. The
criterion depends only on the topology of , and can be checked
algorithmically. As a corollary, we reprove the result, due to Bierenbaum and
Weinzierl, that the massless 2-loop 2-point function is expressible in terms of
multiple zeta values, and generalize this to the 3, 4, and 5-loop cases. We
find that the coefficients in the Taylor expansion of planar graphs in this
range evaluate to multiple zeta values, but the non-planar graphs with crossing
number 1 may evaluate to multiple sums with roots of unity. Our
method fails for the five loop graphs with crossing number 2 obtained by
breaking open the bipartite graph at one edge
Can the Steep Mass Profile of A1689 Be Explained by a Triaxial Dark Halo?
The steep mass profile of A1689 derived from recent detailed lensing
observations is not readily reconciled with the low concentration halos
predicted by the standard CDM model. However, halo triaxiality may act to bias
the profile constraints derived assuming a spherically symmetric mass
distribution, since lensing relates only to the projected mass distribution. A
degree of halo triaxiality is inherent to the CDM structure formation, arising
from the collision-less nature of the dark matter. Here we compare the
CDM-based model predictions of triaxial halo with the precise lensing
measurements of A1689 based on the ACS/HST and Subaru data, over a wide range
of 10kpc<r<2Mpc. The model lensing profiles cover the intrinsic spread of halo
mass and shape, and are projected over all inclinations when comparing with the
data. We show that the model parameters are only weakly constrained and
strongly degenerate mainly because of the lack of information along the line of
sight. In particular, the limits on the concentration parameter become less
restrictive with increasing triaxiality. Yet, by comparing the obtained
constraints with expected probability distributions for the axis ratio and
concentration parameters computed from numerical simulations, we find that ~6%
of cluster-size halos in the CDM model can match the A1689 lensing observations
at the 2-sigma level, corresponding to cases where the major-axis of the halo
is aligned with the line of sight. Thus halo triaxiality could reduce the
apparent discrepancy between theory and observation. This hypothesis needs to
be further explored by a statistical lensing study for other clusters as well
as by complementary three-dimensional information derived using X-ray,
kinematics, and SZ effect observations.Comment: 7 pages, 6 figures, accepted for publication in Ap
Modified sorting technique to mitigate the collateral mortality of trawled school prawns (Metapenaeus macleayi)
The potential for changes to onboard handling practices in order to improve the fate of juvenile school prawns (Metapenaeus macleayi) discarded during trawling were investigated in two Australian rivers (Clarence and Hunter) by comparing a purpose-built, water-filled sorting tray against a conventional dry tray across various conditions, including the range of typical delays before the start of sorting the catch (2 min vs. 15 min). Juvenile school prawns
(n= 5760), caught during 32 and 16 deployments in each river, were caged and sacrificed at four times: immediately
(T0), and at 24 (T24), 72 (T72), and 120 (T12 0) hours after having been discarded. In both rivers, most
mortalities occurred between T0 and T24 and, after adjusting for control deaths (<12%), were greatest for the
15-min conventional treatment (up to 41% at T120). Mixed-effects logistic models revealed that in addition to the sampling time, method of sorting, and delay in sorting, the weight of the catch, salinity, and percentage cloud cover were significant predictors of mortality. Although trawling
caused some mortalities and comparable stress (measured as L -lactate) in all school prawns, use of the water tray lessened the negative impacts of some of the above factors across both the 2-min and 15-min delays in sorting so that the overall discard mortality was reduced by more than a
third. When used in conjunction with selective trawls, widespread application of the water tray should help to
improve the sustainability of trawling for school prawns
Non-parametric mass reconstruction of A1689 from strong lensing data with SLAP
We present the mass distribution in the central area of the cluster A1689 by
fitting over 100 multiply lensed images with the non-parametric Strong Lensing
Analysis Package (SLAP, Diego et al. 2004). The surface mass distribution is
obtained in a robust way finding a total mass of 0.25E15 M_sun/h within a 70''
circle radius from the central peak. Our reconstructed density profile fits
well an NFW profile with small perturbations due to substructure and is
compatible with the more model dependent analysis of Broadhurst et al. (2004a)
based on the same data. Our estimated mass does not rely on any prior
information about the distribution of dark matter in the cluster. The peak of
the mass distribution falls very close to the central cD and there is
substructure near the center suggesting that the cluster is not fully relaxed.
We also examine the effect on the recovered mass when we include the
uncertainties in the redshift of the sources and in the original shape of the
sources. Using simulations designed to mimic the data, we identify some biases
in our reconstructed mass distribution. We find that the recovered mass is
biased toward lower masses beyond 1 arcmin (150 kpc) from the central cD and
that in the very center we may be affected by degeneracy problems. On the other
hand, we confirm that the reconstructed mass between 25'' and 70'' is a robust,
unbiased estimate of the true mass distribution and is compatible with an NFW
profile.Comment: 11 pages, 12 figures. MNRAS submitted. A full resolution of the paper
can be found in http://darwin.physics.upenn.edu/SLAP
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
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