The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: II. Numerical Treatment

A procedure is described for efficiently finding the ground state energy and configuration for a Frenkel-Kontorova model in a periodic potential, consisting of N parabolic segments of identical curvature in each period, through a numerical solution of the convex minimization problem described in the preceding paper. The key elements are the use of subdifferentials to describe the structure of the minimization problem; an intuitive picture of how to solve it, based on motion of quasiparticles; and a fast linear optimization method with a reduced memory requirement. The procedure has been tested for N up to 200.Comment: 9 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 3 Postscript figures, accepted by Phys.Rev.B to be published together with cond-mat/970722

Full Sky Study of Diffuse Galactic Emission at Decimeter Wavelengths

A detailed knowledge of the Galactic radio continuum is of high interest for studies of the dynamics and structure of the Galaxy as well as for the problem of foreground removal in Cosmic Microwave Background measurements. In this work we present a full-sky study of the diffuse Galactic emission at frequencies of few GHz, where synchrotron radiation is by far the dominant component. We perform a detailed combined analysis of the extended surveys at 408, 1420 and 2326 MHz (by Haslam et al. 1982, Reich 1982, Reich & Reich, 1986 and Jonas et al. 1998, respectively). Using the technique applied by Schlegel et al. (1998) to the IRAS data, we produce destriped versions of the three maps. This allows us to construct a nearly-full-sky map of the spectral index and of the normalization factor with sub-degree angular resolution. The resulting distribution of the spectral indices has an average of beta = 2.695 and dispersion sigma_{beta} = 0.120. This is representative for the Galactic diffuse synchrotron emission, with only minor effects from free-free emission and point sources.Comment: 10 pages, 16 jpeg figures, accepted to Astronomy & Astrophysics, Comments and figure adde

A Compact Linear Programming Relaxation for Binary Sub-modular MRF

We propose a novel compact linear programming (LP) relaxation for binary sub-modular MRF in the context of object segmentation. Our model is obtained by linearizing an $l_1^+$-norm derived from the quadratic programming (QP) form of the MRF energy. The resultant LP model contains significantly fewer variables and constraints compared to the conventional LP relaxation of the MRF energy. In addition, unlike QP which can produce ambiguous labels, our model can be viewed as a quasi-total-variation minimization problem, and it can therefore preserve the discontinuities in the labels. We further establish a relaxation bound between our LP model and the conventional LP model. In the experiments, we demonstrate our method for the task of interactive object segmentation. Our LP model outperforms QP when converting the continuous labels to binary labels using different threshold values on the entire Oxford interactive segmentation dataset. The computational complexity of our LP is of the same order as that of the QP, and it is significantly lower than the conventional LP relaxation

Isotropic inverse-problem approach for two-dimensional phase unwrapping

In this paper, we propose a new technique for two-dimensional phase unwrapping. The unwrapped phase is found as the solution of an inverse problem that consists in the minimization of an energy functional. The latter includes a weighted data-fidelity term that favors sparsity in the error between the true and wrapped phase differences, as well as a regularizer based on higher-order total-variation. One desirable feature of our method is its rotation invariance, which allows it to unwrap a much larger class of images compared to the state of the art. We demonstrate the effectiveness of our method through several experiments on simulated and real data obtained through the tomographic phase microscope. The proposed method can enhance the applicability and outreach of techniques that rely on quantitative phase evaluation

An hybrid Tykhonov method for neutron spectrum unfolding

An hybrid iterative Tykhonov regularization approach with an accelerating algorithm is considered. This method is illustrated by two neutron spectrum unfoldings measured with a Bonner Sphere system.Comment: 19 pages, work done at IRS