Overcomplete steerable pyramid filters and rotation invariance

A given (overcomplete) discrete oriented pyramid may be converted into a steerable pyramid by interpolation. We present a technique for deriving the optimal interpolation functions (otherwise called 'steering coefficients'). The proposed scheme is demonstrated on a computationally efficient oriented pyramid, which is a variation on the Burt and Adelson (1983) pyramid. We apply the generated steerable pyramid to orientation-invariant texture analysis in order to demonstrate its excellent rotational isotropy. High classification rates and precise rotation identification are demonstrated

Broadband, radio spectro-polarimetric study of 100 radiative-mode and jet-mode AGN

We present the results from a broadband (1 to 3 GHz), spectro-polarimetry study of the integrated emission from 100 extragalactic radio sources with the ATCA, selected to be highly linearly polarized at 1.4 GHz. We use a general purpose, polarization model-fitting procedure that describes the Faraday rotation measure (RM) and intrinsic polarization structure of up to three distinct polarized emission regions or 'RM components' of a source. Overall, 37%/52%/11% of sources are best fit by one/two/three RM components. However, these fractions are dependent on the signal-to-noise ratio (S/N) in polarization (more RM components more likely at higher S/N). In general, our analysis shows that sources with high integrated degrees of polarization at 1.4 GHz have low Faraday depolarization, are typically dominated by a single RM component, have a steep spectral index, and a high intrinsic degree of polarization. After classifying our sample into radiative-mode and jet-mode AGN, we find no significant difference between the Faraday rotation or Faraday depolarization properties of jet-mode and radiative-mode AGN. However, there is a statistically significant difference in the intrinsic degree of polarization between the two types, with the jet-mode sources having more intrinsically ordered magnetic field structures than the radiative-mode sources. We also find a preferred perpendicular orientation of the intrinsic magnetic field structure of jet-mode AGN with respect to the jet direction, while no clear preference is found for the radiative-mode sources.Comment: 29 pages (including Appendix), 28 figures, 7 tables. Accepted for publication in MNRA

Multiresolution pattern recognition of small volcanos in Magellan data

The Magellan data is a treasure-trove for scientific analysis of venusian geology, providing far more detail than was previously available from Pioneer Venus, Venera 15/16, or ground-based radar observations. However, at this point, planetary scientists are being overwhelmed by the sheer quantities of data collected--data analysis technology has not kept pace with our ability to collect and store it. In particular, 'small-shield' volcanos (less than 20 km in diameter) are the most abundant visible geologic feature on the planet. It is estimated, based on extrapolating from previous studies and knowledge of the underlying geologic processes, that there should be on the order of 10(exp 5) to 10(exp 6) of these volcanos visible in the Magellan data. Identifying and studying these volcanos is fundamental to a proper understanding of the geologic evolution of Venus. However, locating and parameterizing them in a manual manner is very time-consuming. Hence, we have undertaken the development of techniques to partially automate this task. The goal is not the unrealistic one of total automation, but rather the development of a useful tool to aid the project scientists. The primary constraints for this particular problem are as follows: (1) the method must be reasonably robust; and (2) the method must be reasonably fast. Unlike most geological features, the small volcanos of Venus can be ascribed to a basic process that produces features with a short list of readily defined characteristics differing significantly from other surface features on Venus. For pattern recognition purposes the relevant criteria include the following: (1) a circular planimetric outline; (2) known diameter frequency distribution from preliminary studies; (3) a limited number of basic morphological shapes; and (4) the common occurrence of a single, circular summit pit at the center of the edifice

Increasing d-wave superconductivity by on site repulsion

We study by Variational Monte Carlo an extended Hubbard model away from half filled band density which contains two competing nearest-neighbor interactions: a superexchange $J$ favoring d-wave superconductivity and a repulsion $V$ opposing against it. We find that the on-site repulsion $U$ effectively enhances the strength of $J$ meanwhile suppressing that of $V$, thus favoring superconductivity. This result shows that attractions which do not involve charge fluctuations are very well equipped against strong electron-electron repulsion so much to get advantage from it.Comment: 4 pages, 3 figure

Generalized tt-jj Model

By parameterizing the t-j model we present a new electron correlation model with one free parameter for high-temperature superconductivity. This model is of $SU_{q}(1,2)$ symmetry. The energy spectrums are shown to be modulated by the free parameter in the model. The solution and symmetric structures of the Hilbert space, as well as the Bethe ansatz approach are discussed for special cases.Comment: 13 page, Latex, to appear in J. Phys.

Superconducting correlations in ultra-small metallic grains

To describe the crossover from the bulk BCS superconductivity to a fluctuation-dominated regime in ultrasmall metallic grains, new order parameters and correlation functions, such as ``parity gap'' and ``pair-mixing correlation function'', have been recently introduced. In this paper, we discuss the small-grain behaviour of the Penrose-Onsager-Yang off-diagonal long-range order (ODLRO) parameter in a pseudo-spin representation. Relations between the ODLRO parameter and those mentioned above are established through analytical and numerical calculations.Comment: 7 pages, 1 figur

Application of Monte Carlo Algorithms to the Bayesian Analysis of the Cosmic Microwave Background

Power spectrum estimation and evaluation of associated errors in the presence of incomplete sky coverage; non-homogeneous, correlated instrumental noise; and foreground emission is a problem of central importance for the extraction of cosmological information from the cosmic microwave background. We develop a Monte Carlo approach for the maximum likelihood estimation of the power spectrum. The method is based on an identity for the Bayesian posterior as a marginalization over unknowns. Maximization of the posterior involves the computation of expectation values as a sample average from maps of the cosmic microwave background and foregrounds given some current estimate of the power spectrum or cosmological model, and some assumed statistical characterization of the foregrounds. Maps of the CMB are sampled by a linear transform of a Gaussian white noise process, implemented numerically with conjugate gradient descent. For time series data with N_{t} samples, and N pixels on the sphere, the method has a computational expense $KO[N^{2} +- N_{t} +AFw-log N_{t}], where K is a prefactor determined by the convergence rate of conjugate gradient descent. Preconditioners for conjugate gradient descent are given for scans close to great circle paths, and the method allows partial sky coverage for these cases by numerically marginalizing over the unobserved, or removed, region.Comment: submitted to Ap

Remarks on evolution of space-times in 3+1 and 4+1 dimensions

A large class of vacuum space-times is constructed in dimension 4+1 from hyperboloidal initial data sets which are not small perturbations of empty space data. These space-times are future geodesically complete, smooth up to their future null infinity, and extend as vacuum space-times through their Cauchy horizon. Dimensional reduction gives non-vacuum space-times with the same properties in 3+1 dimensions.Comment: 10pp, exposition improved; final versio