生化网络的随机Petri网建模与分析

细胞的行为是随机性的,学习细胞中的随机性有助于理解细胞的组织,设计和进化。建立、确认和分析随机的生化网络模型是当前计算系统生物学领域的一个重要研究主题。当前,标准的Petri网模型已经成为生化网络模拟和定性分析的有力工具。尝试使用随机Petri网对生化网络进行建模与分析,简单描述了随机Petri网理论对标准Petri网的扩充,通过对二聚作用和肌动蛋白这两个典型例子的建模与演化模拟,介绍、论证了随机Petri网理论的新应用。     

Petri网在代谢网络模块化分析中的应用

代谢网络的模块化分析有助于理解网络的结构和功能。然而,当前众多的模块化分析方法大多将代谢网络考虑为普通的复杂网络,所得模块的生物学意义较低。对枯草芽孢杆菌的核黄素代谢进行Petri网建模分析,研究结果表明：Petri网的T不变量可用于识别代谢网络中的功能模块,具备较好的生物学意义。     

一种基于Petri网的代谢流分析方法

基于Petri网理论构建生物代谢网络模型,提出一种新的采用不等式的代谢流分析方法。以克鲁斯假丝酵母分批发酵,生产甘油的代谢网络为例,验证这种分析方法。结果表明,新分析方法,在前提假设和分析性能两方面均比采用方程式的传统方法明显优越。首先,方法允许实验数据有一定误差,使模型更加接近真实的实验系统。其次,新方法还可以做代谢模型更详细的分析:代谢流分裂比分析、敏感性分析。实际上,分析结果还可直接用于校正代谢物浓度、酶活力的边界值,为进一步研究代谢途径优化提供约束条件。     

流体随机Petri网与混合Petri网的比较分析

流体随机Petri网和混合Petri网作为传统Petri网的拓展,可以建模离散成分和连续成分并存的混合系统,也可用于解决离散模型的状态空间爆炸问题.由于这两种建模机制远未发展成熟,分析比较它们的异同点有助于机制本身的进一步发展完善,有助于为特定的应用选择合适的建模方法.本文讨论了流体随机Petri网和混合Petri网的定义、连续标识、分析方法、以及相互转换的可能性.结论是这两种建模机制是互补的,各自适合于特定的应用场合.     

基于XML的生物代谢Petri网模型的标准化

针对分析生物代谢网络的需要，构建了生物代谢Petri网模型建模环境，并采用基于XML的Petri网标记语言PNML为标准，利用DOM实现XML解析，完成Petri网模型的标准化，通过对代谢网络Petri网模型实例的仿真，验证了标准化模型的正确性。     

混合Petri网的流体随机Petri网模型

混合Petri网和流体随机Petri网作为混合系统的建模方法,其内在的建模机制和分析方法不尽相同,而且这两种机制远未发展成熟.分析并建立它们之间相互转换的方法有助于机制本身的发展完善,并利用对方的建模原语和分析方法对系统进行多角度的分析.提出了一阶混合Petri网转换成流体随机Petri网的形式化方法及转换后变迁合并的方法,并给出了转换和合并方法的正确性证明,最后结合实例简要阐述了这两种方法的实现过程.     

基于Petri网的软件测试分析

软件测试是发现软件中错误而检查文档、运行程序的一个过程。对软件文档和代码进行测试,是贯穿于整个开发生命周期的,尤其在开发早期,其作用更为重要。Petri网是一种好的分析工具,它能够动态运行程序模型,分析模型中存在的死锁、并发、冲突等问题,对程序正确性进行验证和分析。     

基于Petri网的软件测试分析

软件测试是发现软件中错误而检查文档、运行程序的一个过程。对软件文档和代码进行测试，是贯穿于整个开发生命周期的，尤其在开发早期，其作用更为重要。Petri网是一种好的分析工具，它能够动态运行程序模型，分析模型中存在的死锁、并发、冲突等问题，对程序正确性进行验证和分析。     

基于Petri网方法的红血球代谢系统研究

随着生物网络数据的迅速增长,对这些数据进行模拟分析的工具也随之发展。由于组合了图形化和数学化的特征,Petri网成为这一领域的重要模拟分析工具之一。但是,通过Petri网模拟分析的生物系统大多是一些孤立的生化途径。本文采用Petri网技术对红血球细胞的新陈代谢系统进行建模分析。首先介绍了基本的Petri网概念和分析方法,然后采用Petri网技术研究红血球的新陈代谢系统,建立了红血球新陈代谢系统的Petri网模型,最后计算了该模型中的P、T不变量,并讨论了它们的功能意义。     

Petri网死锁的分析与检测

本文在讨论Petri网静态结构和动态运行特性的基础上,给出了死锁的定义,描述了死锁的物理意义,并且给出了死锁的分析方法和检测算法.本文的研究对Petri网的工程应用具有基础性的重要作用.     

Performance analysis using Petri nets

The purpose of this paper is to focus on the implementation issues associated with using Petri nets for the performance analysis of discrete event dynamic systems while demonstrating several applications in manufacturing systems. Practical modeling issues will be discussed and several applications will be presented that illustrate the advantages and limitations of this methodology. These issues lead to the definition of several research problems in Petri nets for performance analysis.     

Timing and liveness in continuous Petri nets

Fluidification constitutes a relaxation technique for studying discrete event systems through fluidified approximated models, thus avoiding the state explosion problem. Moreover, the class of continuous models thus obtained may be interesting in itself. In Petri nets, fluidification leads to the so-called continuous Petri nets, which are technically hybrid models. Under infinite server semantics, timing a continuous Petri net model preserves the liveness property, but the converse is not necessarily true, and if the autonomous net model is not live, the timing may transform it into a live model. In this paper, we investigate the conditions on the firing rates of timed continuous models that make a given continuous system live.     

Partial order behaviour and structure of Petri nets

This paper argues that partial order semantics can be used profitably in the proofs of some nontrivial results in Petri net theory. We show that most of Commoner's and Hack's structure theory of free choice nets can be phrased and proved in terms of partial order behaviour. The new proofs are considerably shorter (and, arguably, more lucid) than the old ones; they also generalise the results from (safe) free choice nets to (bounded) extended free choice nets.Work partly done while both authors were with the Institut für Methodische Grundlagen, Gesellschaft für Mathematik und Datenverarbeitung, D-520S Sankt Augustin, and supported in part by Esprit Basic Research Action No. 3148: DEMON.     

Gradient-based controllers for timed continuous Petri nets

This paper is about control design for timed continuous Petri nets that are described as piecewise affine systems. In this context, the marking vector is considered as the state space vector, weighted marking of place subsets are defined as the model outputs and the model inputs correspond to multiplicative control actions that slow down the firing rate of some controllable transitions. Structural and functional sensitivity of the outputs with respect to the inputs are discussed in terms of Petri nets. Then, gradient-based controllers (GBC) are developed in order to adapt the control actions of the controllable transitions according to desired trajectories of the outputs.     

基于精炼操作的Petri网建模及其分析方法

针对复杂系统的Petri网建模及其分析问题,定义了Petri网的精炼操作及其相关的Petri网模型.基于序列投影,建立精炼Petri网与原网、子网间的动态行为关联关系,并分析了该精炼操作的相关动态性质,得到一组性质保持判据.最后,基于该方法实现了一个顺序资源共享系统的应用案例的建模及其分析.所提出的方法不仅为复杂系统的Petri建模提供了新的思路,而且有助于复杂Petri网模型的分析和验证.     

一类受控Petri网的控制器设计

通过挖掘Petri网的内在的结构特性, 获得了一种新的解决禁止状态避免问题的控制器设计方法. 这种设计方法适用于一类具有特殊结构的受控Petri网 (即所有前向路径子网是状态机 )的状态反馈控制器设计. 在非并发的假设条件下, 所综合的控制器是最大允许.     

Discrete event diagnosis using labeled Petri nets. An application to manufacturing systems

In this paper an approach to on-line diagnosis of discrete event systems based on labeled Petri nets is presented. The approach is based on the notion of basis markings and justifications and it can be applied both to bounded and unbounded Petri nets whose unobservable subnet is acyclic. Moreover it is shown that, in the case of bounded Petri nets, the most burdensome part of the procedure may be moved off-line, computing a particular graph called Basis Reachability Graph.Finally, the effectiveness of the proposed procedure is analyzed applying a MATLAB diagnosis toolbox we developed to a manufacturing example taken from the literature.     

Robustness analysis of non-ordinary Petri nets for flexible assembly systems

Non-ordinary controlled Petri nets (NCPNs) have the advantages to model flexible assembly systems in which multiple identical resources may be required to perform an operation. However, existing studies on NCPNs are still limited. For example, the robustness properties of NCPNs have not been studied. This motivates us to develop an analysis method for NCPNs. Robustness analysis concerns the ability for a system to maintain operation in the presence of uncertainties. It provides an alternative way to analyse a perturbed system without reanalysis. In our previous research, we have analysed the robustness properties of several subclasses of ordinary controlled Petri nets. To study the robustness properties of NCPNs, we augment NCPNs with an uncertainty model, which specifies an upper bound on the uncertainties for each reachable marking. The resulting PN models are called non-ordinary controlled Petri nets with uncertainties (NCPNU). Based on NCPNU, the problem is to characterise the maximal tolerable uncertainties for each reachable marking. The computational complexities to characterise maximal tolerable uncertainties for each reachable marking grow exponentially with the size of the nets. Instead of considering general NCPNU, we limit our scope to a subclass of PN models called non-ordinary controlled flexible assembly Petri net with uncertainties (NCFAPNU) for assembly systems and study its robustness. We will extend the robustness analysis to NCFAPNU. We identify two types of uncertainties under which the liveness of NCFAPNU can be maintained.     

基于分层模糊有色Petri网的防空C~3I系统建模研究

通过分析某防空C~3I系统的组成和运行方式,针对系统结构复杂、多种资源、资源多种模糊属性等特点,定义了一种分层模糊有色Petri网HFCPN,并给出具体的推理算法。在此基础上建立该防空C~3I系统模型,从而提出了一种建立防空C~3I系统分析模型的新方法。最后通过应用实例验证了该方法在描述系统分布、并发、异步等特性的同时,分析系统资源多种模糊属性问题的能力。