Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

Mining structured Petri nets for the visualization of process behavior

Visualization is essential for understanding the models obtained by process mining. Clear and efficient visual representations make the embedded information more accessible and analyzable. This work presents a novel approach for generating process models with structural properties that induce visually friendly layouts. Rather than generating a single model that captures all behaviors, a set of Petri net models is delivered, each one covering a subset of traces of the log. The models are mined by extracting slices of labelled transition systems with specific properties from the complete state space produced by the process logs. In most cases, few Petri nets are sufficient to cover a significant part of the behavior produced by the log.Peer ReviewedPostprint (author's final draft

Analysis of Petri Nets and Transition Systems

This paper describes a stand-alone, no-frills tool supporting the analysis of (labelled) place/transition Petri nets and the synthesis of labelled transition systems into Petri nets. It is implemented as a collection of independent, dedicated algorithms which have been designed to operate modularly, portably, extensibly, and efficiently.Comment: In Proceedings ICE 2015, arXiv:1508.0459

Performance evaluation of an emergency call center: tropical polynomial systems applied to timed Petri nets

We analyze a timed Petri net model of an emergency call center which processes calls with different levels of priority. The counter variables of the Petri net represent the cumulated number of events as a function of time. We show that these variables are determined by a piecewise linear dynamical system. We also prove that computing the stationary regimes of the associated fluid dynamics reduces to solving a polynomial system over a tropical (min-plus) semifield of germs. This leads to explicit formul{\ae} expressing the throughput of the fluid system as a piecewise linear function of the resources, revealing the existence of different congestion phases. Numerical experiments show that the analysis of the fluid dynamics yields a good approximation of the real throughput.Comment: 21 pages, 4 figures. A shorter version can be found in the proceedings of the conference FORMATS 201

An Operational Petri Net Semantics for the Join-Calculus

We present a concurrent operational Petri net semantics for the join-calculus, a process calculus for specifying concurrent and distributed systems. There often is a gap between system specifications and the actual implementations caused by synchrony assumptions on the specification side and asynchronously interacting components in implementations. The join-calculus is promising to reduce this gap by providing an abstract specification language which is asynchronously distributable. Classical process semantics establish an implicit order of actually independent actions, by means of an interleaving. So does the semantics of the join-calculus. To capture such independent actions, step-based semantics, e.g., as defined on Petri nets, are employed. Our Petri net semantics for the join-calculus induces step-behavior in a natural way. We prove our semantics behaviorally equivalent to the original join-calculus semantics by means of a bisimulation. We discuss how join specific assumptions influence an existing notion of distributability based on Petri nets.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244

An Approach to the Category of Net Computations

We introduce the notion of strongly concatenable process as a refinement of concatenable processes [DMM89] which can be expressed axiomatically via a functor $Q[-]$ from the category of Petri nets to an appropriate category of symmetric strict monoidal categories, in the precise sense that, for each net $N$, the strongly concatenable processes of $N$ are isomorphic to the arrows of $Q[N]$. In addition, we identify a coreflection right adjoint to $Q[-]$ and characterize its replete image, thus yielding an axiomatization of the category of net computations

On the Category of Petri Net Computations

We introduce the notion of strongly concatenable process as a refinement of concatenable processes [DMM89] which can be expressed axiomatically via a functor $Q[-]$ from the category of Petri nets to an appropriate category of symmetric strict monoidal categories, in the precise sense that, for each net $N$, the strongly concatenable processes of $N$ are isomorphic to the arrows of $Q[-]$. In addition, we identify a coreflection right adjoint to $Q[-]$ and characterize its replete image, thus yielding an axiomatization of the category of net computations