Designers of statistical machine translation (SMT) systems have begun to employ tree-structured translation models. Systems involving tree-structured translation models tend to be complex. This article aims to reduce the conceptual complexity of such systems, in order to make them easier to design, implement, debug, use, study, understand, explain, modify, and improve. In service of this goal, ...

We present a formal framework that generalizes a variety of monolingual and synchronous grammar formalisms for parsing and translation. Our framework is based on regular tree grammars that describe derivation trees, which are interpreted in arbitrary algebras. We obtain generic parsing algorithms by exploiting closure properties of regular tree languages.

Hierarchical-phrase based machine translation model is a popular translation model which combines advantages of phrase-based translation models and syntax-based translation models. However, since there are no linguistic constraints in the procedure of current hierarchical phrase extraction, there are a large number of redundant generalized rules extracted. In this paper, we propose two strategi...

We introduce an algebra H consisting of difference-reflection operators and multiplication operators that can be considered as a q = 1 analogue of Sahi's double affine Hecke algebra related to the affine root system of type (C ∨ 1 , C1). We study eigenfunctions of a Dunkl-Cherednik-type operator in the algebra H, and the corresponding Fourier transforms. These eigenfunctions are non-symmetric v...

Abstract. Integrability, algebraic structures and orthogonal basis of the Calogero model are studied by the quantum Lax and Dunkl operator formulations. The commutator algebra among operators including conserved operators and creation-annihilation operators has the structure of the W-algebra. Through an algebraic construction of the simultaneous eigenfunctions of all the commuting conserved ope...

We generalize a construction of Dunkl, obtaining a wide class intertwining functions on the symmetric group and a related family of multidimensional Hahn polynomials. Following a suggestion of Vilenkin and Klymik, we develop a tree-method approach for those intertwining functions. We also give a group theoretic proof of the relation between Hahn polynomials and Clebesh-Gordan coefficients, give...

Abstract Recently, deformed quantum systems have received lots of attention in the literature. Dunkl formalism differs from others by containing difference-differential and reflection operator. It is one most interesting deformations since it let us discuss solutions according to even odd solutions. In this work, we studied ideal Bose gas blackbody radiation via formalism. To end, made a liaiso...

We introduce a novel framework for the expression, rapid-prototyping, and evaluation of statistical machine-translation (MT) systems using graphical models. The framework extends dynamic Bayesian networks with multiple connected different-length streams, switching variable existence and dependence mechanisms, and constraint factors. We have implemented a new general-purpose MT training/decoding...

Generalized n-gons were introduced by Tits in a famous work on triality [20] of 1959, in order to propose an axiomatic and combinatorial treatment for semisimple algebraic groups (including Chevalley groups and groups of Lie type) of relative rank 2. They are the central rank 2 incidence geometries, and the atoms of the more general “Tits-buildings.” If the number of elements of a generalized n...