Dense graph limits under respondent-driven sampling

We consider certain respondent-driven sampling procedures on dense graphs. We show that if the sequence of the vertex-sets is ergodic then the limiting graph can be expressed in terms of the original dense graph via a transformation related to the invariant measure of the ergodic sequence. For specific sampling procedures, we describe the transformation explicitly.Comment: Published at http://dx.doi.org/10.1214/15-AAP1144 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Sampling and Reconstruction of Sparse Signals on Circulant Graphs - An Introduction to Graph-FRI

With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate of Innovation (FRI) theory to the graph domain, and can be applied to arbitrary graphs via suitable approximation schemes. At its core, the introduced Graph-FRI-framework states that any K-sparse signal on the vertices of a circulant graph can be perfectly reconstructed from its dimensionality-reduced representation in the graph spectral domain, the Graph Fourier Transform (GFT), of minimum size 2K. By leveraging the recently developed theory of e-splines and e-spline wavelets on graphs, one can decompose this graph spectral transformation into the multiresolution low-pass filtering operation with a graph e-spline filter, and subsequent transformation to the spectral graph domain; this allows to infer a distinct sampling pattern, and, ultimately, the structure of an associated coarsened graph, which preserves essential properties of the original, including circularity and, where applicable, the graph generating set.Comment: To appear in Appl. Comput. Harmon. Anal. (2017

Parallel Graph Transformation for Model Simulation applied to Timed Transition Petri Nets

Proceedings of the Workshop on Graph Transformation and Visual Modelling Techniques (GT-VMT 2004)This work discusses the use of parallel graph transformation systems for (multi-formalism) modeling and simulation and their implementation in the meta-modeling tool AToM3. As an example, a simulator for Timed Transition Petri Nets (TTPN) is modeled using parallel graph transformation.This work has been partially sponsored by the SEGRAVIS network and the Spanish Ministry of Science and Technology (TIC2002-01948)

Confluence Detection for Transformations of Labelled Transition Systems

The development of complex component software systems can be made more manageable by first creating an abstract model and then incrementally adding details. Model transformation is an approach to add such details in a controlled way. In order for model transformation systems to be useful, it is crucial that they are confluent, i.e. that when applied on a given model, they will always produce a unique output model, independent of the order in which rules of the system are applied on the input. In this work, we consider Labelled Transition Systems (LTSs) to reason about the semantics of models, and LTS transformation systems to reason about model transformations. In related work, the problem of confluence detection has been investigated for general graph structures. We observe, however, that confluence can be detected more efficiently in special cases where the graphs have particular structural properties. In this paper, we present a number of observations to detect confluence of LTS transformation systems, and propose both a new confluence detection algorithm and a conflict resolution algorithm based on them.Comment: In Proceedings GaM 2015, arXiv:1504.0244

Co-Transformation of Type and Instance Graphs Supporting Merging of Types and Retyping

Algebraic graph transformation is a well-known rule-based approach to manipulate graphs that can be applied in several contexts. In this paper we use it in the context of model-driven engineering. Graph transformation rules usually specify changes to only one graph per application, however there are use cases such as model co-evolution where not only a single graph should be manipulated but also related ones. The co-transformation of type graphs together with their instance graphs has shown to be a promising approach to formalize model and meta-model co-evolution. In this paper, we extend our earlier work on co-evolution by allowing transformation rules that have less restrictions so that graph manipulations such as merging of types and retyping of graph elements are allowed

EMF Model Refactoring based on Graph Transformation Concepts

The Eclipse Modeling Framework (EMF) provides a modeling and code generation framework for Eclipse applications based on structured data models. Within model driven software development based on EMF, refactoring of EMF models become a key activity. In this paper, we present an approach to define EMF model refactoring methods as transformation rules being applied in place on EMF models. Performing an EMF model refactoring, EMF transformation rules are applied and can be translated to corresponding graph transformation rules, as in the graph transformation environment AGG. If the resulting EMF model is consistent, the corresponding result graph is equivalent and can be used for validating EMF model refactoring. Results on conflicts and dependencies of refactorings for example, can help the developer to decide which refactoring is most suitable for a given model and why