The Hopf algebra of diagonal rectangulations

We define and study a combinatorial Hopf algebra dRec with basis elements indexed by diagonal rectangulations of a square. This Hopf algebra provides an intrinsic combinatorial realization of the Hopf algebra tBax of twisted Baxter permutations, which previously had only been described extrinsically as a sub Hopf algebra of the Malvenuto-Reutenauer Hopf algebra of permutations. We describe the natural lattice structure on diagonal rectangulations, analogous to the Tamari lattice on triangulations, and observe that diagonal rectangulations index the vertices of a polytope analogous to the associahedron. We give an explicit bijection between twisted Baxter permutations and the better-known Baxter permutations, and describe the resulting Hopf algebra structure on Baxter permutations.Comment: Very minor changes from version 1, in response to comments by referees. This is the final version, to appear in JCTA. 43 pages, 17 figure

Information structure and the referential status of linguistic expression : workshop as part of the 23th annual meetings of the Deutsche Gesellschaft für Sprachwissenschaft in Leipzig, Leipzig, February 28 - March 2, 2001

This volume comprises papers that were given at the workshop Information Structure and the Referential Status of Linguistic Expressions, which we organized during the Deutsche Gesellschaft für Sprachwissenschaft (DGfS) Conference in Leipzig in February 2001. At this workshop we discussed the connection between information structure and the referential interpretation of linguistic expressions, a topic mostly neglected in current linguistics research. One common aim of the papers is to find out to what extent the focus-background as well as the topic-comment structuring determine the referential interpretation of simple arguments like definite and indefinite NPs on the one hand and sentences on the other

Second Language Transfer During Third Language Acquisition

A recent focus in the study of cross-linguistic influence is the role of transfer during third language acquisition. How do the learner’s first and second languages influence the acquisition of a third language? Current research suggests that the multilingual dynamic differs from L1 effects during second language acquisition. This literature review will examine L2 transfer during third language acquisition within the general context of cross-linguistic influence. An overview of the study of language transfer will be presented, followed by a discussion of the variables that operate and interact when two or more languages come into contact. The variables are categorized as learner-based or language-based, and each is discussed in the contexts of L2 and L3 acquisition. A particular area of focus will be hybrid lexical forms and the unintentional intrusion of L2 items during L3 production

04241 Abstracts Collection -- Graph Transformations and Process Algebras for Modeling Distributed and Mobile Systems

Recently there has been a lot of research, combining concepts of process algebra with those of the theory of graph grammars and graph transformation systems. Both can be viewed as general frameworks in which one can specify and reason about concurrent and distributed systems. There are many areas where both theories overlap and this reaches much further than just using graphs to give a graphic representation to processes. Processes in a communication network can be seen in two different ways: as terms in an algebraic theory, emphasizing their behaviour and their interaction with the environment, and as nodes (or edges) in a graph, emphasizing their topology and their connectedness. Especially topology, mobility and dynamic reconfigurations at runtime can be modelled in a very intuitive way using graph transformation. On the other hand the definition and proof of behavioural equivalences is often easier in the process algebra setting. Also standard techniques of algebraic semantics for universal constructions, refinement and compositionality can take better advantage of the process algebra representation. An important example where the combined theory is more convenient than both alternatives is for defining the concurrent (noninterleaving), abstract semantics of distributed systems. Here graph transformations lack abstraction and process algebras lack expressiveness. Another important example is the work on bigraphical reactive systems with the aim of deriving a labelled transitions system from an unlabelled reactive system such that the resulting bisimilarity is a congruence. Here, graphs seem to be a convenient framework, in which this theory can be stated and developed. So, although it is the central aim of both frameworks to model and reason about concurrent systems, the semantics of processes can have a very different flavour in these theories. Research in this area aims at combining the advantages of both frameworks and translating concepts of one theory into the other. The Dagsuthl Seminar, which took place from 06.06. to 11.06.2004, was aimed at bringing together researchers of the two communities in order to share their ideas and develop new concepts. These proceedings4 of the do not only contain abstracts of the talks given at the seminar, but also summaries of topics of central interest. We would like to thank all participants of the seminar for coming and sharing their ideas and everybody who has contributed to the proceedings

Paving the Road to Business Process Administration

Event-driven Process Chains (EPCs) have been helped to achieve an important role in business process modeling by the commercial success of SAP and ARIS. Both users and IT experts may describe the process to be modelled from their individual perspectives. Event-driven Process Chains, therefore, create a common platform for communication and the analysis of ideas beyond the boundaries of both application and information-system domains. This is accomplished by a semiformal semantics, which gives the participants greater freedom of expression but leads to unintended ambiguities clearly undesirable in later stages of development such as design and implementation. In the literature, several approaches to this problem have been suggested including definitions of a formal semantics for EPCs. We investigate difficulties with such approaches and suggest two solutions: the introduction of a new logical connector (XORAND) and a slight modification of the OR join. This facilitates the design of correct EPCs while continuing to allow freedom of expression, thus enabling a smoother transition into the more formal phases of software development such as design and implementation. A comparative experiment validates these results