Free profinite R-trivial, locally idempotent and locally commutative semigroups

This paper is concerned with the structure of implicit operations on R intersection with LJ1, the pseudovariety of all R-trivial, locally idempotent and locally commutative semigroups. We give a unique factorization statement, in terms of component projections and idempotent elements, for the implicit operations on R intersection with LJ1. As an application we give a combinatorial description of the languages that are both R-trivial and locally testable. A similar study is conducted for the pseudovariety DA intersection with LJ1 of locally idempotent and locally commutative semigroups in which each regular D-class is a rectangular band.INVOTAN, grant 4/ A/94/PO.PRC-GdR AM

Classifying melodies using tree grammars

Similarity computation is a difficult issue in music information retrieval, because it tries to emulate the special ability that humans show for pattern recognition in general, and particularly in the presence of noisy data. A number of works have addressed the problem of what is the best representation for symbolic music in this context. The tree representation, using rhythm for defining the tree structure and pitch information for leaf and node labeling has proven to be effective in melodic similarity computation. In this paper we propose a solution when we have melodies represented by trees for the training but the duration information is not available for the input data. For that, we infer a probabilistic context-free grammar using the information in the trees (duration and pitch) and classify new melodies represented by strings using only the pitch. The case study in this paper is to identify a snippet query among a set of songs stored in symbolic format. For it, the utilized method must be able to deal with inexact queries and efficient for scalability issues.This work is supported by the Spanish Ministry project TIN2009-14247-C02-02, TIN2009-14205-C04-C1, the Pascal Network of Excellence, and the program Consolider Ingenio 2010 (CSD2007-00018)