Handbook of graph grammars and computing by graph transformation: vol. 2: applications, languages, and tools
A Logical Characterization of Individual-Based Models
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Electronic Notes in Theoretical Computer Science (ENTCS)
Agile Modelling of Cellular Signalling (Invited Paper)
Electronic Notes in Theoretical Computer Science (ENTCS)
A rule-based approach for automated generation of kinetic chemical mechanisms
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Scalable simulation of cellular signaling networks
APLAS'07 Proceedings of the 5th Asian conference on Programming languages and systems
DPO transformation with open maps
ICGT'12 Proceedings of the 6th international conference on Graph Transformations
Pattern graphs and rule-based models: the semantics of kappa
FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
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We develop a new 'thermodynamic' approach to stochastic graph-rewriting. The ingredients are a finite set of reversible graph-rewriting rules ${\mathcal{G}}$ (called generating rules), a finite set of connected graphs ${\mathcal{P}}$ (called energy patterns), and an energy cost function $\epsilon:{\mathcal{P}}\to{\mathbb{R}}$. The idea is that ${\mathcal{G}}$ defines the qualitative dynamics by showing which transformations are possible, while ${\mathcal{P}}$ and ε specify the long-term probability π of any graph reachable under ${\mathcal{G}}$. Given ${\mathcal{G}}, {\mathcal{P}}$, we construct a finite set of rules ${\mathcal{G}}_{\mathcal{P}}$ which (i) has the same qualitative transition system as ${\mathcal{G}}$, and (ii) when equipped with suitable rates, defines a continuous-time Markov chain of which π is the unique fixed point. The construction relies on the use of site graphs and a technique of 'growth policy' for quantitative rule refinement which is of independent interest. The 'division of labour' between the qualitative and the long-term quantitative aspects of the dynamics leads to intuitive and concise descriptions for realistic models (see the example in §4). It also guarantees thermodynamical consistency (aka detailed balance), otherwise known to be undecidable, which is important for some applications. Finally, it leads to parsimonious parameterizations of models, again an important point in some applications.