“What Is a Petri Net?” Informal Answers for the Informed Reader

Desel, Jörg; Juhás, Gabriel

doi:10.1007/3-540-45541-8_1

Cited by 74 publications

(22 citation statements)

References 25 publications

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“…This process is iterated to yield a Petri net model that is consistent with the genetic model. Desel and Juhas [2001], Petri nets are a type of directed graph that can be used to model discrete dynamical systems. Goss and Peccoud [1998] demonstrated that Petri nets could be used to model molecular interactions in biochemical systems.…”

Section: Biological Systems Modeling Of Epistasismentioning

confidence: 99%

The Ubiquitous Nature of Epistasis in Determining Susceptibility to Common Human Diseases

Moore¹

2003

Hum Hered

643

484

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There is increasing awareness that epistasis or gene-gene interaction plays a role in susceptibility to common human diseases. In this paper, we formulate a working hypothesis that epistasis is a ubiquitous component of the genetic architecture of common human diseases and that complex interactions are more important than the independent main effects of any one susceptibility gene. This working hypothesis is based on several bodies of evidence. First, the idea that epistasis is important is not new. In fact, the recognition that deviations from Mendelian ratios are due to interactions between genes has been around for nearly 100 years. Second, the ubiquity of biomolecular interactions in gene regulation and biochemical and metabolic systems suggest that relationship between DNA sequence variations and clinical endpoints is likely to involve gene-gene interactions. Third, positive results from studies of single polymorphisms typically do not replicate across independent samples. This is true for both linkage and association studies. Fourth, gene-gene interactions are commonly found when properly investigated. We review each of these points and then review an analytical strategy called multifactor dimensionality reduction for detecting epistasis. We end with ideas of how hypotheses about biological epistasis can be generated from statistical evidence using biochemical systems models. If this working hypothesis is true, it suggests that we need a research strategy for identifying common disease susceptibility genes that embraces, rather than ignores, the complexity of the genotype to phenotype relationship.

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Section: Biological Systems Modeling Of Epistasismentioning

confidence: 99%

The Ubiquitous Nature of Epistasis in Determining Susceptibility to Common Human Diseases

Moore¹

2003

Hum Hered

643

484

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“…Hyperedge h must only leave and enter BASIC nodes that are in its source and target set; otherwise, the configuration reached after taking h in C does not correspond to the marking reached by firing isomorphic transition f −1 (h) in M . This implies that in the statechart no additional BASIC nodes are left or entered by taking h. This corresponds to the Petri net locality principle [DJ01] that states that each transition can only consume tokens from places in its preset and only produce tokens for places in its postset.…”

Section: Statecharts Corresponding To Statechartable Netsmentioning

confidence: 99%

Statechartable Petri nets

Eshuis

2013

Form. Asp. Comput.

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Abstract. Petri nets and statecharts can model concurrent systems in a succinct way. While translations from statecharts to Petri nets exist, a well-defined translation from Petri nets to statecharts is lacking. Such a translation should map an input net to a corresponding statechart, having a structure and behaviour similar to that of the input net. Since statecharts can only model a restricted form of concurrency, not every Petri net has a corresponding statechart. We identify a class of Petri nets, called statechartable nets, that can be translated to corresponding statecharts. Statechartable Petri nets are structurally defined using the novel notion of an area. We also define a structural translation that maps each statechartable Petri net to a corresponding statechart. The translation is proven sound and complete for statechartable Petri nets.

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“…So BASIC node n4 is left even though it was not a source of h5. In Petri nets, such behaviour is impossible due the locality principle [3], which states that each transition can only consume tokens from places that are in its preset. Thus, mapping a transition to a hyperedge with an in- complete source set does not preserve behaviour.…”

Section: Processing Of Transitionsmentioning

confidence: 99%

Translating Safe Petri Nets to Statecharts in a Structure-Preserving Way

Eshuis

2009

FM 2009: Formal Methods

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Abstract. Statecharts and Petri nets are two popular visual formalisms for modelling complex systems that exhibit concurrency. Both formalisms are supported by various design tools. To enable the automated exchange of models between Petri net and statechart tools, we present a structural, polynomial algorithm that translates safe Petri nets into statecharts. The translation algorithm preserves both the structure and the behaviour of the input net. The algorithm can fail, since not every safe net has a statechart translation that preserves both its structure and behaviour. The algorithm is proven correct and the class of safe nets for which the algorithm succeeds is formally characterised. We show that the algorithm can also fail for some nets that do have a structure-and behaviour-preserving statechart translation, but this incompleteness does not appear to be a severe limitation in practice.

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“What Is a Petri Net?” Informal Answers for the Informed Reader

Cited by 74 publications

References 25 publications

The Ubiquitous Nature of Epistasis in Determining Susceptibility to Common Human Diseases

The Ubiquitous Nature of Epistasis in Determining Susceptibility to Common Human Diseases

Statechartable Petri nets

Translating Safe Petri Nets to Statecharts in a Structure-Preserving Way

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