The Darboux-Backlund transformation for the static 2-dimensional continuum Heisenberg chain

We construct the Darboux-Backlund transformation for the sigma model describing static configurations of the 2-dimensional classical continuum Heisenberg chain. The transformation is characterized by a non-trivial normalization matrix depending on the background solution. In order to obtain the transformation we use a new, more general, spectral problem.Comment: 12 page

On analytic descriptions of two-dimensional surfaces associated with the CP^(N-1) sigma model

We study analytic descriptions of conformal immersions of the Riemann sphere S^2 into the CP^(N-1) sigma model. In particular, an explicit expression for two-dimensional (2-D) surfaces, obtained from the generalized Weierstrass formula, is given. It is also demonstrated that these surfaces coincide with the ones obtained from the Sym-Tafel formula. These two approaches correspond to parametrizations of one and the same surface in R^(N^2-1).Comment: 6 page

The geometric sense of R. Sasaki connection

For the Riemannian manifold $M^{n}$ two special connections on the sum of the tangent bundle $TM^{n}$ and the trivial one-dimensional bundle are constructed. These connections are flat if and only if the space $M^{n}$ has a constant sectional curvature $\pm 1$. The geometric explanation of this property is given. This construction gives a coordinate free many-dimensional generalization of the connection from the paper: R. Sasaki 1979 Soliton equations and pseudospherical surfaces, Nuclear Phys., {\bf 154 B}, pp. 343-357. It is shown that these connections are in close relation with the imbedding of $M^{n}$ into Euclidean or pseudoeuclidean $(n+1)$-dimension spaces.Comment: 7 pages, the key reference to the paper of Min-Oo is included in the second versio

Pseudospherical surfaces on time scales: a geometric definition and the spectral approach

We define and discuss the notion of pseudospherical surfaces in asymptotic coordinates on time scales. Thus we extend well known notions of discrete pseudospherical surfaces and smooth pseudosperical surfaces on more exotic domains (e.g, the Cantor set). In particular, we present a new expression for the discrete Gaussian curvature which turns out to be valid for asymptotic nets on any time scale. We show that asymptotic Chebyshev nets on an arbitrary time scale have constant negative Gaussian curvature. We present also the quaternion-valued spectral problem (the Lax pair) and the Darboux-Backlund transformation for pseudospherical surfaces (in asymptotic coordinates) on arbitrary time scales.Comment: 20 page

Comparing Computational Architectures for Automated Journalism

The majority of NLG systems have been designed following either a template-based or a pipeline-based architecture. Recent neural models for data-to-text generation have been proposed with an end-to-end deep learning flavor, which handles non-linguistic input in natural language without explicit intermediary representations. This study compares the most often employed methods for generating Brazilian Portuguese texts from structured data. Results suggest that explicit intermediate steps in the generation process produce better texts than the ones generated by neural end-to-end architectures, avoiding data hallucination while better generalizing to unseen inputs. Code and corpus are publicly available.Comment: Accepted at the 19th National Meeting on Artificial and Computational Intelligence (ENIAC 2022

Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations

We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is "unpinched" to produce a new pair of branch points and therefore a solution of higher genus. We prove that every step in this process corresponds to a cabling operation on the previous curve, and we provide a labelling scheme that matches the deformation data with the knot type of the resulting filament.Comment: 33 pages, 5 figures; submitted to Journal of Nonlinear Scienc

The ISO SWS on-line system

The software which is currently being developed for the Short Wavelength Spectrometer (SWS) of the Infrared Space Observatory (ISO) is described. The spectrometer has a wide range of capabilities in the 2-45 micron infrared band. SWS contains two independent gratings, one for the long and one for the short wavelength section of the band. With the gratings a spectral resolution of approximately 1000 to approximately 2500 can be obtained. The instrument also contains two Fabry-Perault's yielding a resolution between approximately 1000 and approximately 20000. Software is currently being developed for the acquisition, calibration, and analysis of SWS data. The software is firstly required to run in a pipeline mode without human interaction, to process data as they are received from the telescope. However, both for testing and calibration of the instrument as well as for evaluation of the planned operating procedures the software should also be suitable for interactive use. Thirdly the same software will be used for long term characterization of the instrument. The software must work properly within the environment designed by the European Space Agency (ESA) for the spacecraft operations. As a result strict constraints are put on I/O devices, throughput etc

Potential medicinal value of some South African seaweeds

Eleven macroalgae were collected from the KwaZulu-Natal coast and nineteen species from the cooler Western Cape coast in March and April 2000. Ethanolic and aqueous extracts were made and tested for biological activity in the Cox-1 anti-inflammatory assay, in a nematode mortality bioassay for anthelminthic activity, an IC50 anticancer assay and a MIC antimicrobial assay. The ethanolic extracts were very active in the Cox-1 anti-inflammatory assay for almost all of the species tested. The aqueous extracts were not active. No anthelminthic mortality was detected in extracts from any of the species tested. Many of the extracts had cytotoxic activity against three cancer cell lines tested, with those from representative species of the Chlorophyta and Rhodophyta being the most effective. The extracts had much lower cytotoxic activity when tested on normal mouse fibroblasts (NIH3T3). Extracts from only a few species had antimicrobial activity with those of the Chlorophyta tested being the most effective against both the Gram-positive and Gram-negative bacteria

Scalar second order evolution equations possessing an irreducible sl2_2-valued zero curvature representation

We find all scalar second order evolution equations possessing an sl$_2$-valued zero curvature representation that is not reducible to a proper subalgebra of sl$_2$. None of these zero-curvature representations admits a parameter.Comment: 10 pages, requires nath.st

Generalized isothermic lattices

We study multidimensional quadrilateral lattices satisfying simultaneously two integrable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Moebius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constraint imposed on the (complex) cross-ratio of the circular lattice. We derive the analogous condition for our generalized isthermic lattices using Steiner's projective structure of conics and we present basic geometric constructions which encode integrability of the lattice. In particular, we introduce the Darboux transformation of the generalized isothermic lattice and we derive the corresponding Bianchi permutability principle. Finally, we study two dimensional generalized isothermic lattices, in particular geometry of their initial boundary value problem.Comment: 19 pages, 11 figures; v2. some typos corrected; v3. new references added, higlighted similarities and differences with recent papers on the subjec