Graph grammars as an analytical tool in physics and biology

Gernert, Dieter

doi:10.1016/s0303-2647(97)00037-3

Cited by 10 publications

(6 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…But the reciprocal phenomenon has also happened, usually at a lower level, and it is called "the phenomenon of the earlier tool" in sociology of science [4]. When some branch of mathematics reaches a high standard then it will be surely used in many other sciences, specially in those that are fashionable a that moment, be it because of pure scientific reasons, or because of funding reasons; many methods of algebraic geometry have entered physics in this way in the 1980s, but also the surge of applications of physics in biology after the World War II has a certain component of this effect.…”

Section: Resultsmentioning

confidence: 99%

“…According to D. Gernert [4], as soon as patterns are represented as graphs, graph grammars are a natural tool to describe the fundamental operations related to patterns: pattern generation, pattern transfer (the duplication of a certain subpattern and its insertion in a different location), pattern recognition, pattern interpretation (the influence of certain subpatterns on the behavior of whole system) and pattern application (the transmission of a certain pattern to another location). A type of graph grammars specifically tailored to handle patterns was proposed in [5].…”

Section: Introductionmentioning

confidence: 99%

“…Molecular biology is no exception: the inner structure of chemical compounds [6], the tridimensional structure of nucleic acids and proteins [7], the chemical reactions [8], the biochemical and metabolical pathways [9], most formal components of molecular biology can be represented as graphs. This fact must be added to what is called in sociology of science "the phenomenon of the earlier tool" [4]: when some branch of mathematics reaches a high standard or it becomes fashionable, then it will be surely used in many other sciences.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Graph Transformation in Molecular Biology

Rosselló

Valiente

2005

Formal Methods in Software and Systems Modeling

View full text Add to dashboard Cite

Abstract. In the beginning, one of the main fields of application of graph transformation was biology, and more specifically morphology. Later, however, it was like if the biological applications had been left aside by the graph transformation community, just to be moved back into the mainstream these very last years with a new interest in molecular biology. In this paper, we review several fields of application of graph grammars in molecular biology, including: the modeling higherdimensional structures of biomolecules, the description of biochemical reactions, the analysis of metabolic pathways, and their potential use in computational systems biology.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Graph Transformation in Molecular Biology

Rosselló

Valiente

2005

Formal Methods in Software and Systems Modeling

View full text Add to dashboard Cite

show abstract

“…(These were defined in 1969 and since have proved their usefulness in a great variety of application fields (Drewes 2007); for details see Gernert (1997), with diagrams and references.) In the simplest case, each object is represented by a finite connected graph, possibly with vertex labels.…”

Section: Graph Grammarsmentioning

confidence: 99%

Distance and Similarity Measures in Generalised Quantum Theory

Gernert

2010

Axiomathes

Self Cite

View full text Add to dashboard Cite

A summary of recent experimental results shows that entanglement can be generated more easily than before, and that there are improved chances for its persistence. An eminent finding of Generalised Quantum Theory is the insight that the notion of entanglement can be extended, such that, e.g., psychological or psychophysical problem areas can be included, too. First, a general condition for entanglement to occur is given by the term 'common prearranged context'. A formalised treatment requires a quantitative definition of the similarity or dissimilarity between two complex structures which takes their internal structures into account. After some specific remarks on distance, metrics, and semi-metrics in mathematics, a procedure is described for setting up a similarity function with the required properties. This procedure is in analogy with the two-step character of measurement and with the well-known properties of perspective notions. A general methodology can be derived for handling perspective notions. Finally, these concepts supply heuristic clues towards a formalised treatment of the notions of 'meaning' and 'interpretation'.

show abstract

“…Graph grammars can represent hierarchical structures in data and generalize knowledge in graph domains. They have been applied as analytical tools in physics, biology, and engineering [7,15]. Our objective with this research is to develop algorithms for graph grammar inference capable of learning recursive productions.…”

Section: Introductionmentioning

confidence: 99%

Inference of node replacement graph grammars

Kukluk

Holder

Cook

2007

IDA

View full text Add to dashboard Cite

Graph grammars combine the relational aspect of graphs with the iterative and recursive aspects of string grammars, and thus represent an important next step in our ability to discover knowledge from data. In this paper we describe an approach to learning node replacement graph grammars. This approach is based on previous research in frequent isomorphic subgraphs discovery. We extend the search for frequent subgraphs by checking for overlap among the instances of the subgraphs in the input graph. If subgraphs overlap by one node we propose a node replacement grammar production. We also can infer a hierarchy of productions by compressing portions of a graph described by a production and then infer new productions on the compressed graph. We validate this approach in experiments where we generate graphs from known grammars and measure how well our system infers the original grammar from the generated graph. We also describe results on several real-world tasks from chemical mining to XML schema induction. We briefly discuss other grammar inference systems indicating that our study extends classes of learnable graph grammars.

show abstract

Graph grammars as an analytical tool in physics and biology

Cited by 10 publications

References 26 publications

Graph Transformation in Molecular Biology

Graph Transformation in Molecular Biology

Distance and Similarity Measures in Generalised Quantum Theory

Inference of node replacement graph grammars

Contact Info

Product

Resources

About