Classical Integrable N=1 and N=2N= 2 Super Sinh-Gordon Models with Jump Defects

The structure of integrable field theories in the presence of jump defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the boundary functions for the N=1 and N=2 super sinh-Gordon models are constructed and shown to generate the Backlund transformations for its soliton solutions. As a new and interesting example, a solution with an incoming boson and an outgoing fermion for the N=1 case is presented. The resulting integrable models are shown to be invariant under supersymmetric transformation.Comment: talk presented at the V International Symposium on Quantum Theory and Symmetries, Valladolid, Spain, July 22-28,200

Dressing approach to the nonvanishing boundary value problem for the AKNS hierarchy

We propose an approach to the nonvanishing boundary value problem for integrable hierarchies based on the dressing method. Then we apply the method to the AKNS hierarchy. The solutions are found by introducing appropriate vertex operators that takes into account the boundary conditions.Comment: Published version Proc. Quantum Theory and Symmetries 7 (QTS7)(Prague, Czech Republic, 2011

Integrable Field Theories with Defects

The structure of integrable field theories in the presence of defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the boundary functions for the super sinh-Gordon model is constructed and shown to generate the Backlund transformations for its soliton solutions.Comment: talk presented at the XVth International Colloquium on Integrable Systems and Quantum Symmetries, to appear in Czechoslovak Journal of Physics (2006

On the properties of the interstellar medium in extremely metal-poor blue compact dwarf galaxies: GMOS-IFU spectroscopy and SDSS photometry of the double-knot galaxy HS 2236+1344

The main goal of this study is to carry out a spatially resolved investigation of the warm interstellar medium (ISM) in the extremely metal-poor Blue Compact Dwarf (BCD) galaxy HS 2236+1344. Special emphasis is laid on the analysis of the spatial distribution of chemical abundances, emission-line ratios and kinematics of the ISM, and to the recent star-forming activity in this galaxy. This study is based on optical integral field unit spectroscopy data from Gemini Multi-Object Spectrograph at the Gemini North telescope and archival Sloan Digital Sky Survey images. The data were obtained in two different positions across the galaxy, obtaining a total 4 arcsec X 8 arcsec field which encompasses most of its ISM. Emission-line maps and broad-band images obtained in this study indicate that HS 2236+1344 hosts three Giant HII regions. Our data also reveal some faint curved features in the BCD periphery that might be due to tidal perturbations or expanding ionized-gas shells. The ISM velocity field shows systematic gradients along the major axis of the BCD, with its south-eastern and north-western half differing by ~80 km/s in their recessional velocity. The Ha and Hb equivalent width distribution in the central part of HS 2236+1344 is consistent with a very young (~3 Myr) burst. Our surface photometry analysis indicates that the ongoing starburst provides ~50% of the total optical emission, similar to other BCDs. It also reveals an underlying lower-surface brightness component with moderately red colors, which suggest that the galaxy has undergone previous star formation. We derive an integrated oxygen abundance of 12+log(O/H)=7.53\pm0.06 and a nitrogen-to-oxygen ratio of log(N/O)=-1.57\pm0.19. Our results are consistent, within the uncertainties, with a homogeneous distribution of oxygen and nitrogen within the ISM of the galaxy. (abridged)Comment: 15 pages, 16 figures, accepted for publication in A&

Counting solutions from finite samplings

We formulate the solution counting problem within the framework of inverse Ising problem and use fast belief propagation equations to estimate the entropy whose value provides an estimate on the true one. We test this idea on both diluted models (random 2-SAT and 3-SAT problems) and fully-connected model (binary perceptron), and show that when the constraint density is small, this estimate can be very close to the true value. The information stored by the salamander retina under the natural movie stimuli can also be estimated and our result is consistent with that obtained by Monte Carlo method. Of particular significance is sizes of other metastable states for this real neuronal network are predicted.Comment: 9 pages, 4 figures and 1 table, further discussions adde