8,366 research outputs found
Weight enumerators of Reed-Muller codes from cubic curves and their duals
Let be a finite field of characteristic not equal to or
. We compute the weight enumerators of some projective and affine
Reed-Muller codes of order over . These weight enumerators
answer enumerative questions about plane cubic curves. We apply the MacWilliams
theorem to give formulas for coefficients of the weight enumerator of the duals
of these codes. We see how traces of Hecke operators acting on spaces of cusp
forms for play a role in these formulas.Comment: 19 pages. To appear in "Arithmetic, Geometry, Cryptography, and
Coding Theory" (Y. Aubry, E. W. Howe, C. Ritzenthaler, eds.), Contemp. Math.,
201
Morphing the CMB: a technique for interpolating power spectra
The confrontation of the Cosmic Microwave Background (CMB) theoretical
angular power spectrum with available data often requires the calculation of
large numbers of power spectra. The standard practice is to use a fast code to
compute the CMB power spectra over some large parameter space, in order to
estimate likelihoods and constrain these parameters. But as the dimensionality
of the space under study increases, then even with relatively fast anisotropy
codes, the computation can become prohibitive. This paper describes the
employment of a "morphing" strategy to interpolate new power spectra based on
previously calculated ones. We simply present the basic idea here, and
illustrate with a few examples; optimization of interpolation schemes will
depend on the specific application. In addition to facilitating the exploration
of large parameter spaces, this morphing technique may be helpful for Fisher
matrix calculations involving derivatives.Comment: 18 pages, including 6 figures, uses elsart.cls, accepted for
publication in New Astronomy, changes to match published versio
Slow-light and evanescent modes at interfaces in photonic crystal waveguides: optimal extraction from experimental near-field measurements
We develop a systematic approach for simultaneous extraction of the dispersion relations and profiles of multiple modes in periodic waveguides though a special global optimization procedure applied to near-field electric field measurements in the waveguide plane. We apply this method to perform in-depth analysis of experimental data on wave propagation close to an interface between waveguide sections with different dispersion characteristics, and we successfully identify several modes contributing to the experimentally measured fields. We find clear evidence that when the group velocity is reduced across the interface, evanescent modes that facilitate the excitation of propagating slow-light waves appear, confirming previous theoretical predictions. (C) 2011 Optical Society of AmericaPublisher PDFPeer reviewe
Entropy-difference based stereo error detection
Stereo depth estimation is error-prone; hence, effective error detection
methods are desirable. Most such existing methods depend on characteristics of
the stereo matching cost curve, making them unduly dependent on functional
details of the matching algorithm. As a remedy, we propose a novel error
detection approach based solely on the input image and its depth map. Our
assumption is that, entropy of any point on an image will be significantly
higher than the entropy of its corresponding point on the image's depth map. In
this paper, we propose a confidence measure, Entropy-Difference (ED) for stereo
depth estimates and a binary classification method to identify incorrect
depths. Experiments on the Middlebury dataset show the effectiveness of our
method. Our proposed stereo confidence measure outperforms 17 existing measures
in all aspects except occlusion detection. Established metrics such as
precision, accuracy, recall, and area-under-curve are used to demonstrate the
effectiveness of our method
Thermodynamic investigations in the precursor region of FeGe
High-resolution DC magnetization and AC-specific heat data of the cubic
helimagnet FeGe have been measured as function of temperature and magnetic
field. The magnetization data as well as the isothermal susceptibility data
confirm the complexity of the magnetic phase diagram in the vicinity of the
onset of long-rang magnetic order (Tc = 278.5 K) and the existence of a
segmented A-phase region. Moreover, these data revealed independent and clear
indications of phase boundaries and crossovers within the A-phase region.
Together with the anomalies in the specific-heat data around Tc and at small
magnetic fields (H < 600 Oe) a complex magnetic phase diagram of FeGe is
obtained.Comment: Presented at the QCNP conference in Dreden, Germany, August 201
Study of the spatial and temporal coherence of high order harmonics
We apply the theory of high-order harmonic generation by low-frequency laser
fields in the strong field approximation to the study of the spatial and
temporal coherence properties of the harmonics. We discuss the role of
dynamically induced phases of the atomic polarization in determining the
optimal phase matching conditions and angular distributions of harmonics. We
demonstrate that the phase matching and the spatial coherence can be controlled
by changing the focusing parameters of the fundamental laser beam. Then we
present a detailed study of the temporal and spectral properties of harmonics.
We discuss how the focusing conditions influence the individual harmonic
spectra and time profiles, and how the intensity dependence of the dynamically
induced phase leads to a chirp of the harmonic frequency. This phase modulation
can be used to control the temporal and spectral properties of the harmonic
radiation. Temporally, the harmonic chirped pulse can be recompressed to very
small durations. Spectrally, chirping of the fundamental beam may be employed
to compensate for the dynamically induced chirp and to control the individual
harmonic spectrum. Finally, we discuss the short pulse effects, in particular
nonadiabatic phenomena and the possibility of generating attosecond pulses.Comment: Latex file with 37 pages, 25 postscript figures. to appear in
Advances in Atomic, Molecular and Optical Physic
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