6,015 research outputs found
Generalised Fermat Hypermaps and Galois Orbits
We consider families of quasiplatonic Riemann surfaces characterised by the
fact that -- as in the case of Fermat curves of exponent -- their
underlying regular (Walsh) hypermap is the complete bipartite graph , where is an odd prime power. We will show that all these surfaces,
regarded as algebraic curves, are defined over abelian number fields. We will
determine the orbits under the action of the absolute Galois group, their
minimal fields of definition, and in some easier cases also their defining
equations. The paper relies on group-- and graph--theoretic results by G. A.
Jones, R. Nedela and M.\v{S}koviera about regular embeddings of the graphs
[JN\v{S}] and generalises the analogous question for maps treated in
[JStW], partly using different methods.Comment: 14 pages, new version with extended introduction, minor corrections
and updated reference
Symmetry Representations in the Rigged Hilbert Space Formulation of Quantum Mechanics
We discuss some basic properties of Lie group representations in rigged
Hilbert spaces. In particular, we show that a differentiable representation in
a rigged Hilbert space may be obtained as the projective limit of a family of
continuous representations in a nested scale of Hilbert spaces. We also
construct a couple of examples illustrative of the key features of group
representations in rigged Hilbert spaces. Finally, we establish a simple
criterion for the integrability of an operator Lie algebra in a rigged Hilbert
space
Measuring the one-particle excitations of ultracold fermionic atoms by stimulated Raman spectroscopy
We propose a Raman spectroscopy technique which is able to probe the
one-particle Green's function, the Fermi surface, and the quasiparticles of a
gas of strongly interacting ultracold atoms. We give quantitative examples of
experimentally accessible spectra. The efficiency of the method is validated by
means of simulated images for the case of a usual Fermi liquid as well as for
more exotic states: specific signatures of e.g. a d-wave pseudo-gap are clearly
visible.Comment: 5 pages, 3 figures accepted for publication at Phys. Rev. Letter
Simulating full-sky interferometric observations
Aperture array interferometers, such as that proposed for the Square
Kilometre Array (SKA), will see the entire sky, hence the standard approach to
simulating visibilities will not be applicable since it relies on a tangent
plane approximation that is valid only for small fields of view. We derive
interferometric formulations in real, spherical harmonic and wavelet space that
include contributions over the entire sky and do not rely on any tangent plane
approximations. A fast wavelet method is developed to simulate the visibilities
observed by an interferometer in the full-sky setting. Computing visibilities
using the fast wavelet method adapts to the sparse representation of the
primary beam and sky intensity in the wavelet basis. Consequently, the fast
wavelet method exhibits superior computational complexity to the real and
spherical harmonic space methods and may be performed at substantially lower
computational cost, while introducing only negligible error to simulated
visibilities. Low-resolution interferometric observations are simulated using
all of the methods to compare their performance, demonstrating that the fast
wavelet method is approximately three times faster that the other methods for
these low-resolution simulations. The computational burden of the real and
spherical harmonic space methods renders these techniques computationally
infeasible for higher resolution simulations. High-resolution interferometric
observations are simulated using the fast wavelet method only, demonstrating
and validating the application of this method to realistic simulations. The
fast wavelet method is estimated to provide a greater than ten-fold reduction
in execution time compared to the other methods for these high-resolution
simulations.Comment: 16 pages, 9 figures, replaced to match version accepted by MNRAS
(major additions to previous version including new fast wavelet method
Linearly bounded infinite graphs
Linearly bounded Turing machines have been mainly studied as acceptors for
context-sensitive languages. We define a natural class of infinite automata
representing their observable computational behavior, called linearly bounded
graphs. These automata naturally accept the same languages as the linearly
bounded machines defining them. We present some of their structural properties
as well as alternative characterizations in terms of rewriting systems and
context-sensitive transductions. Finally, we compare these graphs to rational
graphs, which are another class of automata accepting the context-sensitive
languages, and prove that in the bounded-degree case, rational graphs are a
strict sub-class of linearly bounded graphs
Non-Gaussianity detections in the Bianchi VIIh corrected WMAP 1-year data made with directional spherical wavelets
Many of the current anomalies reported in the Wilkinson Microwave Anisotropy
Probe (WMAP) 1-year data disappear after `correcting' for the best-fit embedded
Bianchi type VII_h component (Jaffe et al. 2005), albeit assuming no dark
energy component. We investigate the effect of this Bianchi correction on the
detections of non-Gaussianity in the WMAP data that we previously made using
directional spherical wavelets (McEwen et al. 2005a). As previously discovered
by Jaffe et al. (2005), the deviations from Gaussianity in the kurtosis of
spherical Mexican hat wavelet coefficients are eliminated once the data is
corrected for the Bianchi component. This is due to the reduction of the cold
spot at Galactic coordinates (l,b)=(209^\circ,-57\circ), which Cruz et al.
(2005) claim to be the source of non-Gaussianity introduced in the kurtosis.
Our previous detections of non-Gaussianity observed in the skewness of
spherical wavelet coefficients are not reduced by the Bianchi correction.
Indeed, the most significant detection of non-Gaussianity made with the
spherical real Morlet wavelet at a significant level of 98.4% remains (using a
very conservative method to estimate the significance). We make our code to
simulate Bianchi induced temperature fluctuations publicly available.Comment: 11 pages, 8 figures, replaced to match version accepted by MNRA
Higher-order thoughts in action : Consciousness as an unconscious re-description process
Peer reviewedPostprin
Extended envelopes around Galactic Cepheids III. Y Oph and alpha Per from near-infrared interferometry with CHARA/FLUOR
Unbiased angular diameter measurements are required for accurate distances to
Cepheids using the interferometric Baade Wesselink method (IBWM). The precision
of this technique is currently limited by interferometric measurements at the
1.5% level. At this level, the center-to-limb darkening (CLD) and the presence
of circumstellar envelopes (CSE) seem to be the two main sources of bias. The
observations we performed aim at improving our knowledge of the interferometric
visibility profile of Cepheids. In particular, we assess the systematic
presence of CSE around Cepheids in order determine accurate distances with the
IBWM free from CSE biased angular diameters. We observed a Cepheid (Y Oph) for
which the pulsation is well resolved and a non-pulsating yellow supergiant
(alpha Per) using long-baseline near-infrared interferometry. We interpreted
these data using a simple CSE model we previously developed. We found that our
observations of alpha Per do not provide evidence for a CSE. The measured CLD
is explained by an hydrostatic photospheric model. Our observations of Y Oph,
when compared to smaller baseline measurements, suggest that it is surrounded
by a CSE with similar characteristics to CSE found previously around other
Cepheids. We have determined the distance to Y Oph to be d=491+/-18 pc.
Additional evidence points toward the conclusion that most Cepheids are
surrounded by faint CSE, detected by near infrared interferometry: after
observing four Cepheids, all show evidence for a CSE. Our CSE non-detection
around a non-pulsating supergiant in the instability strip, alpha Per, provides
confidence in the detection technique and suggests a pulsation driven mass-loss
mechanism for the Cepheids.Comment: accepted for publication in Ap
Kalman Filter Track Fits and Track Breakpoint Analysis
We give an overview of track fitting using the Kalman filter method in the
NOMAD detector at CERN, and emphasize how the wealth of by-product information
can be used to analyze track breakpoints (discontinuities in track parameters
caused by scattering, decay, etc.). After reviewing how this information has
been previously exploited by others, we describe extensions which add power to
breakpoint detection and characterization. We show how complete fits to the
entire track, with breakpoint parameters added, can be easily obtained from the
information from unbroken fits. Tests inspired by the Fisher F-test can then be
used to judge breakpoints. Signed quantities (such as change in momentum at the
breakpoint) can supplement unsigned quantities such as the various chisquares.
We illustrate the method with electrons from real data, and with Monte Carlo
simulations of pion decays.Comment: 27 pages including 10 figures. To appear in NI
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