Curvature-controlled defect dynamics in active systems

We have studied the collective motion of polar active particles confined to ellipsoidal surfaces. The geometric constraints lead to the formation of vortices that encircle surface points of constant curvature (umbilics). We have found that collective motion patterns are particularly rich on ellipsoids, with four umbilics where vortices tend to be located near pairs of umbilical points to minimize their interaction energy. Our results provide a new perspective on the migration of living cells, which most likely use the information provided from the curved substrate geometry to guide their collective motion.Comment: Accepted manuscript. 8 pages, 7 Figures. Movies of the motion patterns can be found at https://www.youtube.com/playlist?list=PLEsE7_tnqXZ_U258VwxES8KAJTV_eO43

Representing First-Order Logic Using Graphs

Abstract. We show how edge-labelled graphs can be used to represent first-order logic formulae. This gives rise to recursively nested structures, in which each level of nesting corresponds to the negation of a set of existentials. The model is a direct generalisation of the negative application conditions used in graph rewriting, which count a single level of nesting and are thereby shown to correspond to the fragment ∃¬∃ of first-order logic. Vice versa, this generalisation may be used to strengthen the notion of application conditions. We then proceed to show how these nested models may be flattened to (sets of) plain graphs, by allowing some structure on the labels. The resulting formulae-as-graphs may form the basis of a unification of the theories of graph transformation and predicate transformation

Pattern-based model-to-model transformation: Handling attribute conditions

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-02408-5_7Proceedings of Second International Conference, ICMT 2009, Zurich, Switzerland, June 29-30, 2009Pattern-based model-to-model transformation is a new approach for specifying transformations in a declarative, relational and formal style. The language relies on patterns describing allowed or forbidden relations between two models, which are compiled into operational mechanisms to perform forward and backward transformations. In this paper, we extend the approach for handling attribute conditions expressed in some suitable logic, adapt the operational mechanisms based on graph transformation to relax attribute handling by constraint solving, and discuss heuristics for the compilation of patterns into rules.Work supported by the Spanish Ministry of Science and Innovation, projects METEORIC (TIN2008-02081),MODUWEB (TIN2006-09678) and FORMALISM (TIN2007-66523).Moreover, part of this work was done during a sabbatical leave of the third author at TU Berlin, with financial support from the Ministerio de Ciencia e Innovaci´on (grant ref. PR2008-0185). We thank the referees for their useful comment

On insertion-deletion systems over relational words

We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation between their labels. We define the operations of insertion and deletion on relational words generalizing corresponding operations on strings. We prove that the transitive and reflexive closure of these operations has a decidable membership problem for the case of short insertion-deletion rules (of size two/three and three/two). At the same time, we show that in the general case such systems can produce a coding of any recursively enumerable language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure

The EMF Model Transformation Framework

We present the EMF Model Transformation framework (EMT), which supports the rule-based modification of EMF models. Model transformation rules are defined graphically and compiled into Java code to be used in model transformation applications

Integrated Structure and Semantics for Reo Connectors and Petri Nets

In this paper, we present an integrated structural and behavioral model of Reo connectors and Petri nets, allowing a direct comparison of the two concurrency models. For this purpose, we introduce a notion of connectors which consist of a number of interconnected, user-defined primitives with fixed behavior. While the structure of connectors resembles hypergraphs, their semantics is given in terms of so-called port automata. We define both models in a categorical setting where composition operations can be elegantly defined and integrated. Specifically, we formalize structural gluings of connectors as pushouts, and joins of port automata as pullbacks. We then define a semantical functor from the connector to the port automata category which preserves this composition. We further show how to encode Reo connectors and Petri nets into this model and indicate applications to dynamic reconfigurations modeled using double pushout graph transformation