Generating basis siphons and traps of Petri nets using the sign incidence matrix

AbstractMathematical frameworks circumventing the need of mechanistic detail to build models of signal transduction networks include graphs, hypergraphs, Boolean Networks, and Petri Nets. Predicting how a signal transduces in a signaling network is essential to understand cellular functions and disease. Different formalisms exist to describe how a signal transduces in a given intracellular signaling network represented in the aforementioned modeling frameworks: elementary signaling modes, T-invariants, extreme pathway analysis, elementary flux modes, and simple paths. How do these formalisms compare?We present an overview of how signal transduction networks have been modelled using graphs, hypergraphs, Boolean Networks, and Petri Nets in the literature. We provide a review of the different formalisms for capturing signal transduction in a given model of an intracellular signaling network. We also discuss the existing translations between the different modeling frameworks, and the relationships between their corresponding signal transduction representations that have been described in the literature. Furthermore, as a new formalism of signal transduction, we show how minimal functional routes proposed for signaling networks modeled as Boolean Networks can be captured by computing topological factories, a methodology found in the metabolic networks literature. We further show that in the case of signaling networks represented with an acyclic B-hypergraph structure, the definitions are equivalent. In signaling networks represented as directed graphs, it has been shown that computations of elementary modes via its incidence matrix correspond to computations of simple paths and feedback loops. We show that computing elementary modes based on the incidence matrix of a B-hypergraph fails to capture minimal functional routes.

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How to find Invariants for Coloured Petri Nets

DAIMI Report Series ◽

10.7146/dpb.v9i120.6538 ◽

1983 ◽

Vol 9 (120) ◽

Author(s):

Kurt Jensen

Keyword(s):

Petri Nets ◽

Incidence Matrix ◽

Coloured Petri Nets ◽

Transformation Rules

This paper shows how invariants can be found for coloured Petri nets. We define a set of transformation rules, which can be used to transform the incidence-matrix, without changing the set of invariants.

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Reachability analysis of logic Petri nets using incidence matrix

Enterprise Information Systems ◽

10.1080/17517575.2012.759280 ◽

2013 ◽

Vol 8 (6) ◽

pp. 630-647 ◽

Cited By ~ 8

Author(s):

Yu Yue Du ◽

Yu Hui Ning ◽

Liang Qi

Keyword(s):

Petri Nets ◽

Incidence Matrix ◽

Reachability Analysis

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A Method to Compute Siphons Based on Matrix Manipulation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.88-89.486 ◽

2011 ◽

Vol 88-89 ◽

pp. 486-490

Author(s):

Xue Peng Chen ◽

Liang Xu Zhao ◽

Shan Fa Lin ◽

Wen Hui Wu

Keyword(s):

Petri Nets ◽

Petri Net ◽

Flexible Manufacturing ◽

Flexible Manufacturing Systems ◽

Manufacturing Systems ◽

Incidence Matrix ◽

Sequential Processes ◽

Matrix Manipulation ◽

Structural Object ◽

And Control

As a structural object of Petri nets, siphons are significant in the analysis and control of deadlocks in a Petri net. However, some existing siphon computation methods are quite time-consuming. In this paper, based on incidence matrix manipulation, a new method is proposed to compute a set of siphons in a class of Petri nets called systems of simple sequential processes with resources (S3PR). The proposed method consists of two algorithms: 1) computation of an unmarked maximal siphon and 2) obtain minimal siphons from an unmarked maximal siphon. A flexible manufacturing systems (FMS) example is used to illustrate the proposed method.

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