28,126 research outputs found
A-infinity algebra of an elliptic curve and Eisenstein series
We compute explicitly the A-infinity structure on the Ext-algebra of the
collection , where is a line bundle of degree 1 on an
elliptic curve . The answer involves higher derivatives of Eisenstein
series.Comment: 13 pages, 3 figures; v3: added remark on the limit at the cus
Superpotentials from variational derivatives rather than Lagrangians in relativistic theories of gravity
The prescription of Silva to derive superpotential equations from variational
derivatives rather than from Lagrangian densities is applied to theories of
gravity derived from Lovelock Lagrangians in the Palatini representation.
Spacetimes are without torsion and isolated sources of gravity are minimally
coupled. On a closed boundary of spacetime, the metric is given and the
connection coefficients are those of Christoffel. We derive equations for the
superpotentials in these conditions. The equations are easily integrated and we
give the general expression for all superpotentials associated with Lovelock
Lagrangians. We find, in particular, that in Einstein's theory, in any number
of dimensions, the superpotential, valid at spatial and at null infinity, is
that of Katz, Bicak and Lynden-Bell, the KBL superpotential. We also give
explicitly the superpotential for Gauss-Bonnet theories of gravity. Finally, we
find a simple expression for the superpotential of Einstein-Gauss-Bonnet
theories with an anti-de Sitter background: it is minus the KBL superpotential,
confirming, as it should, the calculation of the total mass-energy of spacetime
at spatial infinity by Deser and Tekin.Comment: Scheduled to appear in Class. Quantum Grav. August 200
Unequal Intra-layer Coupling in a Bilayer Driven Lattice Gas
The system under study is a twin-layered square lattice gas at half-filling,
being driven to non-equilibrium steady states by a large, finite `electric'
field. By making intra-layer couplings unequal we were able to extend the phase
diagram obtained by Hill, Zia and Schmittmann (1996) and found that the
tri-critical point, which separates the phase regions of the stripped (S) phase
(stable at positive interlayer interactions J_3), the filled-empty (FE) phase
(stable at negative J_3) and disorder (D), is shifted even further into the
negative J_3 region as the coupling traverse to the driving field increases.
Many transient phases to the S phase at the S-FE boundary were found to be
long-lived. We also attempted to test whether the universality class of D-FE
transitions under a drive is still Ising. Simulation results suggest a value of
1.75 for the exponent gamma but a value close to 2.0 for the ratio gamma/nu. We
speculate that the D-FE second order transition is different from Ising near
criticality, where observed first-order-like transitions between FE and its
"local minimum" cousin occur during each simulation run.Comment: 29 pages, 19 figure
Reciprocity relations between ordinary temperature and the Frieden-Soffer's Fisher-temperature
Frieden and Soffer conjectured some years ago the existence of a ``Fisher
temperature" T_F that would play, with regards to Fisher's information measure
I, the same role that the ordinary temperature T plays vis-a-vis Shannon's
logarithmic measure. Here we exhibit the existence of reciprocity relations
between T_F and T and provide an interpretation with reference to the meaning
of T_F for the canonical ensemble.Comment: 3 pages, no figure
Investigation of light scattering in high reflecting pigmented coatings quarterly report, 1 may - 1 aug. 1965
Application of light scattering theories to highly pigmented coating
Gravitational energy
Observers at rest in a stationary spacetime flat at infinity can measure
small amounts of rest-mass+internal energies+kinetic energies+pressure energy
in a small volume of fluid attached to a local inertial frame. The sum of these
small amounts is the total "matter energy" for those observers. The total
mass-energy minus the matter energy is the binding gravitational energy.
Misner, Thorne and Wheeler evaluated the gravitational energy of a
spherically symmetric static spacetime. Here we show how to calculate
gravitational energy in any static and stationary spacetime for isolated
sources with a set of observers at rest.
The result of MTW is recovered and we find that electromagnetic and
gravitational 3-covariant energy densities in conformastatic spacetimes are of
opposite signs. Various examples suggest that gravitational energy is negative
in spacetimes with special symmetries or when the energy-momentum tensor
satisfies usual energy conditions.Comment: 12 pages. Accepted for publication in Class. Quantum Gra
Prioritising the care of critically ill children: a pilot study using SCREEN reduces clinic waiting times
Objective In low-resource settings, childhood mortality secondary to delays in triage and treatment remains high. This paper seeks to evaluate the impact of the novel Sick Children Require Emergency Evaluation Now (SCREEN) tool on the waiting times of critically ill children who present for care to primary healthcare clinics in Cape Town, South Africa. Methods We used a pre/postevaluation study design to calculate the median waiting times of all children who presented to four randomly chosen clinics for 5 days before, and 5 days after, the implementation of SCREEN. Findings The SCREEN programme resulted in statistical and clinically significant reductions in waiting times for children with critical illness to see a professional nurse (2 hours 45 min to 1 hour 12 min; p<0.001). There was also a statistically significant reduction in the proportion of children who left without being seen by a professional nurse (25.8% to 18.48%; p<0.001). Conclusions SCREEN is a novel programme that uses readily available laypersons, trained to make a subjective assessment of children arriving at primary healthcare centres, and provides a low cost, simple methodology to prioritise children and reduce waiting times in low-resource healthcare clinics
Random matrix theory, the exceptional Lie groups, and L-functions
There has recently been interest in relating properties of matrices drawn at
random from the classical compact groups to statistical characteristics of
number-theoretical L-functions. One example is the relationship conjectured to
hold between the value distributions of the characteristic polynomials of such
matrices and value distributions within families of L-functions. These
connections are here extended to non-classical groups. We focus on an explicit
example: the exceptional Lie group G_2. The value distributions for
characteristic polynomials associated with the 7- and 14-dimensional
representations of G_2, defined with respect to the uniform invariant (Haar)
measure, are calculated using two of the Macdonald constant term identities. A
one parameter family of L-functions over a finite field is described whose
value distribution in the limit as the size of the finite field grows is
related to that of the characteristic polynomials associated with the
7-dimensional representation of G_2. The random matrix calculations extend to
all exceptional Lie groupsComment: 14 page
Lattice Gas Dynamics; Application to Driven Vortices in Two Dimensional Superconductors
A continuous time Monte Carlo lattice gas dynamics is developed to model
driven steady states of vortices in two dimensional superconducting networks.
Dramatic differences are found when compared to a simpler Metropolis dynamics.
Subtle finite size effects are found at low temperature, with a moving smectic
that becomes unstable to an anisotropic liquid on sufficiently large length
scales.Comment: 5 pages, 4 figure
Reionization history constraints from neural network based predictions of high-redshift quasar continua
Observations of the early Universe suggest that reionization was complete by
, however, the exact history of this process is still unknown. One
method for measuring the evolution of the neutral fraction throughout this
epoch is via observing the Ly damping wings of high-redshift quasars.
In order to constrain the neutral fraction from quasar observations, one needs
an accurate model of the quasar spectrum around Ly, after the spectrum
has been processed by its host galaxy but before it is altered by absorption
and damping in the intervening IGM. In this paper, we present a novel machine
learning approach, using artificial neural networks, to reconstruct quasar
continua around Ly. Our QSANNdRA algorithm improves the error in this
reconstruction compared to the state-of-the-art PCA-based model in the
literature by 14.2% on average, and provides an improvement of 6.1% on average
when compared to an extension thereof. In comparison with the extended PCA
model, QSANNdRA further achieves an improvement of 22.1% and 16.8% when
evaluated on low-redshift quasars most similar to the two high-redshift quasars
under consideration, ULAS J1120+0641 at and ULAS J1342+0928 at
, respectively. Using our more accurate reconstructions of these two
quasars, we estimate the neutral fraction of the IGM using a homogeneous
reionization model and find at
and at . Our
results are consistent with the literature and favour a rapid end to
reionization
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