Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric RR-Matrix

We study quantum integrable models with GL(3) trigonometric $R$-matrix and solvable by the nested algebraic Bethe ansatz. Using the presentation of the universal Bethe vectors in terms of projections of products of the currents of the quantum affine algebra $U_q(\hat{\mathfrak{gl}}_3)$ onto intersections of different types of Borel subalgebras, we prove that the set of the nested Bethe vectors is closed under the action of the elements of the monodromy matrix

Towards an Efficient Evaluation of General Queries

Database applications often require to evaluate queries containing quantifiers or disjunctions, e.g., for handling general integrity constraints. Existing efficient methods for processing quantifiers depart from the relational model as they rely on non-algebraic procedures. Looking at quantified query evaluation from a new angle, we propose an approach to process quantifiers that makes use of relational algebra operators only. Our approach performs in two phases. The first phase normalizes the queries producing a canonical form. This form permits to improve the translation into relational algebra performed during the second phase. The improved translation relies on a new operator - the complement-join - that generalizes the set difference, on algebraic expressions of universal quantifiers that avoid the expensive division operator in many cases, and on a special processing of disjunctions by means of constrained outer-joins. Our method achieves an efficiency at least comparable with that of previous proposals, better in most cases. Furthermore, it is considerably simpler to implement as it completely relies on relational data structures and operators

Reachability analysis of first-order definable pushdown systems

We study pushdown systems where control states, stack alphabet, and transition relation, instead of being finite, are first-order definable in a fixed countably-infinite structure. We show that the reachability analysis can be addressed with the well-known saturation technique for the wide class of oligomorphic structures. Moreover, for the more restrictive homogeneous structures, we are able to give concrete complexity upper bounds. We show ample applicability of our technique by presenting several concrete examples of homogeneous structures, subsuming, with optimal complexity, known results from the literature. We show that infinitely many such examples of homogeneous structures can be obtained with the classical wreath product construction.Comment: to appear in CSL'1

Knowledge formalization in experience feedback processes : an ontology-based approach

Because of the current trend of integration and interoperability of industrial systems, their size and complexity continue to grow making it more difficult to analyze, to understand and to solve the problems that happen in their organizations. Continuous improvement methodologies are powerful tools in order to understand and to solve problems, to control the effects of changes and finally to capitalize knowledge about changes and improvements. These tools involve suitably represent knowledge relating to the concerned system. Consequently, knowledge management (KM) is an increasingly important source of competitive advantage for organizations. Particularly, the capitalization and sharing of knowledge resulting from experience feedback are elements which play an essential role in the continuous improvement of industrial activities. In this paper, the contribution deals with semantic interoperability and relates to the structuring and the formalization of an experience feedback (EF) process aiming at transforming information or understanding gained by experience into explicit knowledge. The reuse of such knowledge has proved to have significant impact on achieving themissions of companies. However, the means of describing the knowledge objects of an experience generally remain informal. Based on an experience feedback process model and conceptual graphs, this paper takes domain ontology as a framework for the clarification of explicit knowledge and know-how, the aim of which is to get lessons learned descriptions that are significant, correct and applicable

Nested Bethe ansatz for Y(gl(n)) open spin chains with diagonal boundary conditions

In this proceeding we present the nested Bethe ansatz for open spin chains of XXX-type, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices $(K^+(u),K^-(u))$. The nested Bethe anstaz applies for a general $K^-(u)$, but a particular form of the $K^+(u)$ matrix. We give the eigenvalues, Bethe equations and the form of the Bethe vectors for the corresponding models. The Bethe vectors are expressed using a trace formula.Comment: 15 pages, proceeding for Dubna International SQS 09 Worksho

The revenge of geopolitics: the space as a metaphor of fear in the clash of civilizations

Una de las obras que más ha contribuido a forjar el imaginario geopolítico del mundo occidental es el libro de S. P. Huntington El choque de civilizaciones. En este artículo pretendo evidenciar que este libro y su tesis son estrictamente geopolíticas, es decir, que entran en el marco de los análisis que adoptan un enfoque de ciencia geográfica aplicada, útil para los políticos y para orientar y movilizar a los lectores. De acuerdo con mi lectura, la interpretación de Huntington se encuentra alineada con el imperialismo de Estados Unidos y tiene un impacto insospechado en la política interna de los países occidentales; Por otra parte, la tesis del choque de civilizaciones se basa en una ceguera consciente de la naturaleza de la sociedad contemporánea y los efectos de la globalización. Esta “zona oscura” de la teoría de Huntington revela la preocupación principal del trabajo, a saber, la defensa de Occidente frente a la des-occidentalización. El objetivo de este artículo, por lo tanto, es demostrar en primer lugar que el modelo geopolítico de Huntington se deriva de una fuerte tradición de la historia de la hegemonía estadounidense; en segundo lugar, que su principal objetivo es reconstruir un orden y homogeneidad estables dentro de la civilización occidental; por último, que el incremento reciente en el uso de este modelo puede dar lugar a un aumento de las tensiones entre grupos y los individuos.One of the works that forged the Western geopolitical imagination was The Clash of Civilizations by Samuel P. Huntington. This book, which has been dealt with primarily as a political, sociological work, is imbued by schemes and categories coming from the geographical and geopolitical. My contribution shows that Huntington’s geopolitical approach, that enjoyed a huge success in the world, has an origin in USA imperialism and that it has a much stronger impact than usually noticed. Here I will argue that the Clash of civilizations thesis is based on a conscious blindness with regard to the nature of contemporary societies and by a strong internal contradiction between its description of the world market and its interpretation of culture. These blind spots reveal the main focus of Huntington’s approach: the celebration of homogeneity inside each civilization – and in particular the protection of the West against any de-westernization

On Spatial Conjunction as Second-Order Logic

Spatial conjunction is a powerful construct for reasoning about dynamically allocated data structures, as well as concurrent, distributed and mobile computation. While researchers have identified many uses of spatial conjunction, its precise expressive power compared to traditional logical constructs was not previously known. In this paper we establish the expressive power of spatial conjunction. We construct an embedding from first-order logic with spatial conjunction into second-order logic, and more surprisingly, an embedding from full second order logic into first-order logic with spatial conjunction. These embeddings show that the satisfiability of formulas in first-order logic with spatial conjunction is equivalent to the satisfiability of formulas in second-order logic. These results explain the great expressive power of spatial conjunction and can be used to show that adding unrestricted spatial conjunction to a decidable logic leads to an undecidable logic. As one example, we show that adding unrestricted spatial conjunction to two-variable logic leads to undecidability. On the side of decidability, the embedding into second-order logic immediately implies the decidability of first-order logic with a form of spatial conjunction over trees. The embedding into spatial conjunction also has useful consequences: because a restricted form of spatial conjunction in two-variable logic preserves decidability, we obtain that a correspondingly restricted form of second-order quantification in two-variable logic is decidable. The resulting language generalizes the first-order theory of boolean algebra over sets and is useful in reasoning about the contents of data structures in object-oriented languages.Comment: 16 page