32,732 research outputs found
A computability theoretic equivalent to Vaught's conjecture
We prove that, for every theory which is given by an sentence, has less than many countable
models if and only if we have that, for every on a cone of
Turing degrees, every -hyperarithmetic model of has an -computable
copy. We also find a concrete description, relative to some oracle, of the
Turing-degree spectra of all the models of a counterexample to Vaught's
conjecture
High frequency and high wavenumber solar oscillations
We determine the frequencies of solar oscillations covering a wide range of
degree (100< l <4000) and frequency (1.5 <\nu<10 mHz) using the ring diagram
technique applied to power spectra obtained from MDI (Michelson Doppler Imager)
data. The f-mode ridge extends up to degree of approximately 3000, where the
line width becomes very large, implying a damping time which is comparable to
the time period. The frequencies of high degree f-modes are significantly
different from those given by the simple dispersion relation \omega^2=gk. The
f-mode peaks in power spectra are distinctly asymmetric and use of asymmetric
profile increases the fitted frequency bringing them closer to the frequencies
computed for a solar model.Comment: Revised version. 1.2 mHz features identified as artifacts of data
analysis. Accepted for publication in Ap
Why Not Consider Closed Universes?
We consider structure formation and CMB anisotropies in a closed universe,
both with and without a cosmological constant. The CMB angular power spectrum
and the matter transfer function are presented, along with a discussion of
their relative normalization. This represents the first full numerical
evolution of density perturbations and anisotropies in a spherical geometry. We
extend the likelihood function vs. Omega from the COBE 2-year data to Omega>=1.
For large Omega the presence of a very steep rise in the spectrum towards low
ell allows us to put an upper limit of Omega<=1.5 (95%CL) for primordial
spectra with n<=1. This compares favorably with existing limits on Omega. We
show that there are a range of closed models which are consistent with
observational constraints while being even older than the currently popular
flat models with a cosmological constant. Future constraints from degree scale
CMB data may soon probe this region of parameter space. A derivation of the
perturbed Einstein, fluid and Boltzmann equations for open and closed
geometries is presented in an appendix.Comment: 24 pages, including 13 figures in a uuencoded self-unpacking shell
script. Submitted to Ap
Implementation strategies for hyperspectral unmixing using Bayesian source separation
Bayesian Positive Source Separation (BPSS) is a useful unsupervised approach
for hyperspectral data unmixing, where numerical non-negativity of spectra and
abundances has to be ensured, such in remote sensing. Moreover, it is sensible
to impose a sum-to-one (full additivity) constraint to the estimated source
abundances in each pixel. Even though non-negativity and full additivity are
two necessary properties to get physically interpretable results, the use of
BPSS algorithms has been so far limited by high computation time and large
memory requirements due to the Markov chain Monte Carlo calculations. An
implementation strategy which allows one to apply these algorithms on a full
hyperspectral image, as typical in Earth and Planetary Science, is introduced.
Effects of pixel selection, the impact of such sampling on the relevance of the
estimated component spectra and abundance maps, as well as on the computation
times, are discussed. For that purpose, two different dataset have been used: a
synthetic one and a real hyperspectral image from Mars.Comment: 10 pages, 6 figures, submitted to IEEE Transactions on Geoscience and
Remote Sensing in the special issue on Hyperspectral Image and Signal
Processing (WHISPERS
- …