Properties of linear integral equations related to the six-vertex model with disorder parameter

One of the key steps in recent work on the correlation functions of the XXZ chain was to regularize the underlying six-vertex model by a disorder parameter $\alpha$. For the regularized model it was shown that all static correlation functions are polynomials in only two functions. It was further shown that these two functions can be written as contour integrals involving the solutions of a certain type of linear and non-linear integral equations. The linear integral equations depend parametrically on $\alpha$ and generalize linear integral equations known from the study of the bulk thermodynamic properties of the model. In this note we consider the generalized dressed charge and a generalized magnetization density. We express the generalized dressed charge as a linear combination of two quotients of $Q$-functions, the solutions of Baxter's $t$-$Q$-equation. With this result we give a new proof of a lemma on the asymptotics of the generalized magnetization density as a function of the spectral parameter.Comment: 10 pages, latex, needs ws-procs9x6.cls, dedicated to Prof. Tetsuji Miwa on the occasion of his 60th birthday; v2 minor correction

Simulating Multigraph Transformations Using Simple Graphs

Application of graph transformations for software verification and model transformation is an emergent field of research. In particular, graph transformation approaches provide a natural way of modelling object oriented systems and semantics of object-oriented languages.\ud \ud There exist a number of tools for graph transformations that are often specialised in a particular kind of graphs and/or graph transformation approaches, depending on the desired application domain. The main drawback of this diversity is the lack of interoperability.\ud \ud In this paper we show how (typed) multigraph production systems can be translated into (typed) simple-graph production systems. The presented construction enables the use of multigraphs with DPO transformation approach in tools that only support simple graphs with SPO transformation approach, e.g. the GROOVE tool

Process Denition of Adhesive HLR Systems (Long Version)

Process models of graph transformation systems are based on the concept of occurrence grammars, which are a generalization of Petri net processes given by occurrence nets. Recently, subobject transformation systems were proposed as an abstract framework for occurrence grammars in adhesive categories, but they are restricted to monomorphic matches for transformation steps. In this paper we review the construction of STSs as processes for plain graph grammars and present an extension to weak adhesive HLR categories with non-monomorphic matching, such that e.g. attributed graph grammars are included

Towards Translating Graph Transformation Approaches by Model Transformations

Recently, many researchers are working on semantics preserving model transformation. In the field of graph transformation one can think of translating graph grammars written in one approach to a behaviourally equivalent graph grammar in another approach. In this paper we translate graph grammars developed with the GROOVE tool to AGG graph grammars by first investigating the set of core graph transformation concepts supported by both tools. Then, we define what it means for two graph grammars to be behaviourally equivalent, and for the regarded approaches we actually show how to handle different definitions of both - application conditions and graph structures. The translation itself is explained by means of intuitive examples

Satisfaction, Restriction and Amalgamation of Constraints in the Framework of M-Adhesive Categories

Application conditions for rules and constraints for graphs are well-known in the theory of graph transformation and have been extended already to M-adhesive transformation systems. According to the literature we distinguish between two kinds of satisfaction for constraints, called general and initial satisfaction of constraints, where initial satisfaction is defined for constraints over an initial object of the base category. Unfortunately, the standard definition of general satisfaction is not compatible with negation in contrast to initial satisfaction. Based on the well-known restriction of objects along type morphisms, we study in this paper restriction and amalgamation of application conditions and constraints together with their solutions. In our main result, we show compatibility of initial satisfaction for positive constraints with restriction and amalgamation, while general satisfaction fails in general. Our main result is based on the compatibility of composition via pushouts with restriction, which is ensured by the horizontal van Kampen property in addition to the vertical one that is generally satisfied in M-adhesive categories.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

Conformance Analysis of Organizational Models in a new Enterprise Modeling Framework using Algebraic Graph Transformation - Extended Version

Organizational models play a key role in today's enterprise modeling. These models often show up as partial models produced by people with different conceptual understandings in a usually decentralized organization, where they are modeled in a distributed and non-synchronized fashion. For this reason, there is a first major need to organize partial organizational models within a suitable modeling framework, and there is a second major need to check their mutual conformance. This builds the basis to integrate the partial organizational models later on into one holistic model of the organization. Moreover, the partial models can be used for model checking certain security, risk, and compliance constraints. In order to satisfy the two major needs, this paper presents two mutually aligned contributions. The first one is a new enterprise modeling framework the EM-Cube. The second contribution is a new approach for checking conformance of models that are developed based on the suggested formal modeling technique associated with the proposed framework. In addition to that, we evaluate our potential solution against concrete requirements derived from a real-world scenario coming out of the finance industry