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Petri nets for systems and synthetic biology.
 Formal Methods for Computational Systems Biology, Lecture Notes in Computer Science,
, 2008
"... Abstract. We give a description of a Petri netbased framework for modelling and analysing biochemical pathways, which unifies the qualitative, stochastic and continuous paradigms. Each perspective adds its contribution to the understanding of the system, thus the three approaches do not compete, b ..."
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Cited by 80 (23 self)
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Abstract. We give a description of a Petri netbased framework for modelling and analysing biochemical pathways, which unifies the qualitative, stochastic and continuous paradigms. Each perspective adds its contribution 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 qualitative descriptions are abstractions over stochastic or continuous descriptions, 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. Motivation Biochemical reaction systems have by their very nature three distinctive characteristics. (1) They are inherently bipartite, i.e. they consist of two types of game players, the species and their interactions. (2) They are inherently concurrent, i.e. several interactions can usually happen independently and in parallel. (3) They are inherently stochastic, i.e. the timing behaviour of the interactions is governed by stochastic laws. So it seems to be a natural choice to model and analyse them with a formal method, which shares exactly these distinctive characteristics: stochastic Petri nets. However, due to the computational efforts required to analyse stochastic models, two abstractions are more popular: qualitative models, abstracting away from any time dependencies, and continuous models, commonly used to approximate stochastic behaviour by a deterministic one. We describe an overall framework to unify these three paradigms, providing a family of related models with high analytical power. The advantages of using Petri nets as a kind of umbrella formalism are seen in the following: M. Bernardo, P. Degano, and G. Zavattaro (Eds.): SFM
Biopathways Representation and Simulation on Hybrid Functional Petri Net
 SOFTWARE TOOLS FOR TECHNOLOGY TRANSFER
"... The following two matters should be resolved for biosimulation tools in order to be accepted by users in biology/medicine; (1) Remove issues which are irrelevant to biological importance, and (2) Allow users to represent biopathways intuitively and understand/manage easily the details of representa ..."
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Cited by 62 (9 self)
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The following two matters should be resolved for biosimulation tools in order to be accepted by users in biology/medicine; (1) Remove issues which are irrelevant to biological importance, and (2) Allow users to represent biopathways intuitively and understand/manage easily the details of representation and simulation mechanism. From these criteria, we firstly define a novel notion of Petri net called hybrid functional Petri net (HFPN). Then, we introduce a software tool, Genomic Object Net, for representing and simulating biopathways, which we have developed by employing the architecture of HFPN. In order to show the effectiveness of Genomic Object Net for representing and simulating biopathways, we show some typical biopathway modelings related to gene regulation (switching mechanism of λ phage, circadian rhythm of Drosophila, lacoperon regulatory mechanism of E. coli), metabolic pathway (glycolitic pathway), and signal transduction (Fas ligand induced apoptosis)), which cover the basic aspects in biopathways. The software is available to academic users from
Firstorder hybrid Petri nets: A model for optimization and control
 IEEE Trans. on Robotics and Automation
, 2000
"... Abstract—We consider in this paper firstorder hybrid Petri Nets, a model that consists of continuous places holding fluid, discrete places containing a nonnegative integer number of tokens, and transitions, either discrete or continuous. We set up a linear algebraic formalism to study the firstor ..."
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Cited by 39 (2 self)
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Abstract—We consider in this paper firstorder hybrid Petri Nets, a model that consists of continuous places holding fluid, discrete places containing a nonnegative integer number of tokens, and transitions, either discrete or continuous. We set up a linear algebraic formalism to study the firstorder continuous behavior of this model and show how its control can be framed as a conflict resolution policy that aims at optimizing a given objective function. The use of linear algebra leads to sensitivity analysis that allows one to study of how changes in the structure of the model influence the optimal behavior. As an example of application, we show how the proposed formalism can be applied to flexible manufacturing systems with arbitrary layout and different classes of products. Index Terms—Flexible manufacturing systems, hybrid Petri nets, optimization, performance evaluation, sensitivity analysis.
Fluid stochastic Petri nets augmented with flushout arcs: modelling and analysis
 Discrete Event Dynamic Systems, 11(1
, 2001
"... Abstract. Fluid (or Hybrid) Petri Nets are Petri net based models with two classes of places: discrete places that carry a natural number of distinct objects (tokens), and fluid places that hold a positive amount of fluid, represented by a real number. With respect to previous formulations, the FSPN ..."
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Cited by 37 (20 self)
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Abstract. Fluid (or Hybrid) Petri Nets are Petri net based models with two classes of places: discrete places that carry a natural number of distinct objects (tokens), and fluid places that hold a positive amount of fluid, represented by a real number. With respect to previous formulations, the FSPN model presented in this paper, is augmented with a new primitive, called flushout arc. A flushout arc connects a fluid place to a timed transition, and has the effect of instantaneously emptying the fluid place when the transition fires. The paper discusses the modeling power of the augmented formalism, and shows how the dynamics of the underlying stochastic process can be analytically described by a set of integrodifferential equations. A procedure is presented to automatically derive the solution equations from the model specifications. The whole methodology is illustrated by means of various examples.
Recent Developments in NonMarkovian Stochastic Petri Nets
, 1998
"... Analytical modeling plays a crucial role in the analysis and design of computer systems. Stochastic Petri Nets represent a powerful paradigm, widely used for such modeling in the context of dependability, performance and performability. Many structural and stochastic extensions have been proposed in ..."
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Cited by 22 (4 self)
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Analytical modeling plays a crucial role in the analysis and design of computer systems. Stochastic Petri Nets represent a powerful paradigm, widely used for such modeling in the context of dependability, performance and performability. Many structural and stochastic extensions have been proposed in recent years to increase their modeling power, or their capability to handle large systems. This paper reviews recent developments by providing the theoretical background and the possible areas of application. Markovian Petri nets are first considered together with very well established extensions known as Generalized Stochastic Petri nets and Stochastic Reward Nets. Key ideas for coping with large state spaces are then discussed. The challenging area of nonMarkovian Petri nets is considered, and the related analysis techniques are surveyed together with the detailed elaboration of an example. Finally new models based on Continuous or Fluid Stochastic Petri Nets are briefly discussed.
Asymptotic Throughput of Continuous Timed Petri Nets
, 1995
"... We set up a connection between Continuous Timed Petri Nets (the fluid version of usual Timed Petri Nets) and Markov decision processes. We characterize the subclass of Continuous Timed Petri Nets corresponding to undiscounted average cost structure. This subclass satisfies consetration laws and show ..."
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Cited by 19 (6 self)
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We set up a connection between Continuous Timed Petri Nets (the fluid version of usual Timed Petri Nets) and Markov decision processes. We characterize the subclass of Continuous Timed Petri Nets corresponding to undiscounted average cost structure. This subclass satisfies consetration laws and shows a linear growth: one obtains as mere application of existing results for Dynamic Programming the existence of an asymptotic throughput. This rate can be computed using Howardtype 'algorithms, or by an extension of the well known cycle time formula for timed event graphs. We present an illustrating example and briefly sketch the relation with the discrete case.
Hybrid Systems in Process Control
"... Modeling and control of hybrid systems, with particular emphasis on process control applications, are considered in this article. Based on a number of observations on typical mixed discrete and continuous features for such applications, a fairly general model structure for hybrid systems is prop ..."
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Cited by 19 (4 self)
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Modeling and control of hybrid systems, with particular emphasis on process control applications, are considered in this article. Based on a number of observations on typical mixed discrete and continuous features for such applications, a fairly general model structure for hybrid systems is proposed. This model structure, which clearly separates the open loop plant from the closed loop system, is suitable for analysis and synthesis of hybrid control systems. To illustrate this, three different approaches for controllaw synthesis based on continuous and discrete specifications are discussed. In the first one, the hybrid plant model is replaced by a purely discrete event model, related to the continuous specification, and a supervisor is synthesized applying supervisory control theory suggested by WonhamRamadge. The other two methods directly utilize the continuous specification for determination of a control event generator, where timeoptimal aspects are introduced as an ...
PN: Modeling and simulation of molecular biology systems using petri nets: modeling goals of various approaches
 J Bioinform Comput Biol
, 2004
"... Petri nets are a discrete event simulation approach developed for system representation, in particular for their concurrency and synchronization properties. Various extensions to the original theory of Petri nets have been used for modeling molecular biology systems and metabolic networks. These ext ..."
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Cited by 18 (2 self)
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Petri nets are a discrete event simulation approach developed for system representation, in particular for their concurrency and synchronization properties. Various extensions to the original theory of Petri nets have been used for modeling molecular biology systems and metabolic networks. These extensions are stochastic, colored, hybrid and functional. This paper carries out an initial review of the various modeling approaches based on Petri net found in the literature, and of the biological systems that have been successfully modeled with these approaches. Moreover, the modeling goals and possibilities of qualitative analysis and system simulation of each approach are discussed.
Formal modeling and analysis of organizations
 in Proceedings ofthe International Workshop on Organizations in MultiAgent Systems (OOOP
, 2005
"... Abstract. A new, formal, rolebased, framework for modeling and analyzing both real world and artificial organizations is introduced. It exploits static and dynamic properties of the organizational model and includes the (frequently ignored) environment. The transition is described from a generic fr ..."
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Cited by 18 (9 self)
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Abstract. A new, formal, rolebased, framework for modeling and analyzing both real world and artificial organizations is introduced. It exploits static and dynamic properties of the organizational model and includes the (frequently ignored) environment. The transition is described from a generic framework of an organization to its deployed model and to the actual agent allocation. For verification and validation purposes, a set of dedicated techniques is introduced. Moreover, where most models can handle only two or three layered organizational structures, our framework can handle any arbitrary number of organizational layers. Henceforth, realworld organizations can be modeled and analyzed, as illustrated by a case study, within the DEAL project line. 1
Creating Metabolic and Regulatory Network Models using Fuzzy Cognitive Maps. http://www.botany.iastate.edu/~mash/metnetex/NAFIPS01v3a.p df
"... Abstract This paper describes a model of metabolic networks that uses fuzzy cognitive maps. Nodes of the map represent specific biochemicals such as proteins, RNA, and small molecules, or stimuli, such as light, heat, or nutrients. Edges of the map capture regulatory and metabolic relationships fou ..."
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Cited by 17 (4 self)
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Abstract This paper describes a model of metabolic networks that uses fuzzy cognitive maps. Nodes of the map represent specific biochemicals such as proteins, RNA, and small molecules, or stimuli, such as light, heat, or nutrients. Edges of the map capture regulatory and metabolic relationships found in biological systems. These relationships are established by a domain expert, the biological literature, and extracted from RNA microarray data. This work is part of the development of a software tool, FCModeler, which models and visualizes metabolic networks. A model of the metabolism of the plant hormone gibberellin in Arabidopsis is used to show the capabilities of the fuzzy model.