Petri net models for the semi-automatic construction of large scale biological networks

For the implementation of the virtual cell, the fundamental question is how to model and simulate complex biological networks. During the last 15 years, Petri nets have attracted more and more attention to help to solve this key problem. Regarding the published papers, it seems clear that hybrid functional Petri nets are the adequate method to model complex biological networks. Today, a Petri net model of biological networks is built manually by drawing places, transitions and arcs with mouse events. Therefore, based on relevant molecular database and information systems biological data integration is an essential step in constructing biological networks. In this paper, we will motivate the application of Petri nets for modeling and simulation of biological networks. Furthermore, we will present a type of access to relevant metabolic databases such as KEGG, BRENDA, etc. Based on this integration process, the system supports semi-automatic generation of the correlated hybrid Petri net model. A case study of the cardio-disease related gene-regulated biological network is also presented. MoVisPP is available at .     

Petri nets as a framework for the reconstruction and analysis of signal transduction pathways and regulatory networks

Petri nets are directed, weighted bipartite graphs that have successfully been applied to the systems biology of metabolic and signal transduction pathways in modeling both stochastic (discrete) and deterministic (continuous) processes. Here we exemplify how molecular mechanisms, biochemical or genetic, can be consistently respresented in the form of place/transition Petri nets. We then describe the application of Petri nets to the reconstruction of molecular and genetic networks from experimental data and their power to represent biological processes with arbitrary degree of resolution of the subprocesses at the cellular and the molecular level. Petri nets are executable formal language models that permit the unambiguous visualization of regulatory mechanisms, and they can be used to encode the results of mathematical algorithms for the reconstruction of causal interaction networks from experimental time series data.     

一种自适应模糊Petri网及其应用*

模糊Petri网(fuzzy Petri nets, FPN)是基于模糊产生式规则的知识库系统的有力建模工具,但其缺乏较强的自学习能力。在FPN的基础上引入神经网络技术,给出了一种自适应模糊Petri网(adapt fuzzy Petri nets, AFPN)模型。该模型将神经网络中的BP网络算法引入到FPN模型中,对FPN中的权值进行反复的学习训练,避免了依靠人工经验设置带来的不确定性。AFPN具有很强的推理能力和自适应能力,对知识库系统的建立、更新和维护有着重要的意义。     

Modeling temporal processes via belief networks and Petri nets,with application to expert systems

We show how Bayesian belief networks (BNs) can be used to model common temporal knowledge. Two approaches to their structuring are proposed. The first leads to BNs with nodes representing states of a process and times spent in such states, and with a graphical structure reflecting the conditional independence assumptions of a Markovian process. A second approach leads to BNs whose topology represents a conditional independence structure between event-times. Once required distributional specifications are stored within the nodes of a BN, this becomes a powerful inference machine capable, for example, of reasoning backwards in time. We discuss computational difficulties associated with propagation algorithms necessary to perform these inferences, and the reasons why we chose to adopt Monte Carlo-based propagation algorithms. Two improvements to existing Monte Carlo algorithms are proposed; an enhancement based on the principle of importance sampling, and a combined technique that exploits both forward and Markov sampling. Finally, we consider Petri nets, a very interesting and general representation of temporal knowledge. A combined approach is proposed, in which the user structures temporal knowledge in Petri net formalism. The obtained Petri net is then automatically translated into an equivalent BN for probability propagation. Inferred conclusions may finally be explained with the aid of Petri nets again.     

Petri网在生物信息学中的应用

生物信息学是一门正在快速发展的使用数学和计算机技术来构造和分析生物学模型的学科.Petri网是近来被用于生物信息学的有效工具,但是应用的深度和广度还有待深入研究.文中综述了Petri网在生物信息学领域应用的最新研究进展,主要包括三个方面:应用位置/变迁网定性分析生物学对象的结构性质;应用随机Petri网将随机性加入到生物学建模和分析中;应用混合Petri网描述和分析同时具有离散特性和连续特性的生物系统.最后对Petri网在生物信息学领域的应用情况进行总结并展望了未来的研究方向.     

Methods of constructing Bayesian networks based on scoring functions

Available methods of constructing Bayesian networks with the use of scoring functions are analyzed. The Cooper-Herskovits and MDL functions are described in detail and used to compare algorithms of constructing Bayesian networks. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 81–88, March–April 2008.     

基于Petri网的Web服务流语言(WSFL)建模与分析

描述了Web服务流语言(WSFL)的Petri网建模方法，利用网结构描述商业流程基本结构。在对WSFL的语法元素进行分析的基础上，有效地对WSFL所描述的商业流程进行了Petri网建模。在此基础上，结合Petri网的可达图分析技术，分析和验证了商业流程的可达性和活性等性质。     

Learning Bayesian networks using various datasources and applications to financial analysis

 This paper illustrates opportunities of using Bayesian networks in fundamental financial analysis. In it, we will present an application based on construction of a Bayesian network from a database of financial reports collected for the years 1993–97. We will focus on one sector of the Czech economy – engineering – presenting an example that use the constructed Bayesian network in the sector financial analysis. In addition, we will deal with the rating analysis and show how to perform this kind of analysis by means of neural and Bayesian networks. This work was supported by the grant VS96008 of the Ministry of Education of the Czech Republic.     

Construction and Methods of Learning of Bayesian Networks

Methods of learning Bayesian networks from databases, basic concepts of Bayesian networks, basic methods of learning, methods of learning parameters, and the structures of a network and hidden parameters are considered. Basic definitions and key concepts with illustrative examples are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 133–147, July–August 2005.     

基于模糊神经Petri网的故障诊断模型

Petri网是对具有产生式规则的故障诊断系统的有力建模工具，但其缺乏较强的学习能力．本文以Petri网的基本定义为基础，结合模糊逻辑和Petri网模型，定义了模糊Petri网模型，在此基础上引入人工神经网络技术，给出了人工神经网络的模糊Petri网表示方法，并针对工程机械故障诊断异步、离散等特点，提出并建立了故障诊断的模糊神经Petri网模型及其改进模型．基于模糊神经Petri网的故障诊断系统结合了Petri网和人工神经网络的优点，经过自学习后同时具有很强的推理能力和自适应能力．     

Discovering excitatory relationships using dynamic Bayesian networks

Mining temporal network models from discrete event streams is an important problem with applications in computational neuroscience, physical plant diagnostics, and human–computer interaction modeling. In this paper, we introduce the notion of excitatory networks which are essentially temporal models where all connections are stimulative, rather than inhibitive. The emphasis on excitatory connections facilitates learning of network models by creating bridges to frequent episode mining. Specifically, we show that frequent episodes help identify nodes with high mutual information relationships and that such relationships can be summarized into a dynamic Bayesian network (DBN). This leads to an algorithm that is significantly faster than state-of-the-art methods for inferring DBNs, while simultaneously providing theoretical guarantees on network optimality. We demonstrate the advantages of our approach through an application in neuroscience, where we show how strong excitatory networks can be efficiently inferred from both mathematical models of spiking neurons and several real neuroscience datasets.     

Method of probabilistic inference from learning data in Bayesian networks

Bayesian networks (BN) are a powerful tool for various data-mining systems. The available methods of probabilistic inference from learning data have shortcomings such as high computation complexity and cumulative error. This is due to a partial loss of information in transition from empiric information to conditional probability tables. The paper presents a new simple and exact algorithm for probabilistic inference in BN from learning data. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 93–99, May–June 2007.     

Modeling and synthesis of supervisory control based on Petri nets for distributed objects. I. Interaction mechanism and the basic method

We describe a methodology of discrete event modeling for a class of distributed objects and their required behavior (specifications) for the design of real time automation systems. In our methodology, we use the structured discrete event system (SDES2) model: on the first stage, it is used to analyze the functionality and coherence of the object and its specification; on the second, we propose for SDES2 a basic synthesis method that works for the models of object and supervisor based on Petri nets (both modeling and controlling). At the same time, we propose to synthesize the supervisor as a Petri net embedded in SDES2 with a feedback circuit in order to restrict the object’s operation according to specification requirements. We propose an interaction mechanism for the modeling and controlling Petri nets with the object and the external environment. In essence, the interaction mechanism is an object control scheme based on the constructed net. This mechanism analyzes the current state of the object and computes the controls that should be passed on to the object’s actuators. Computations are done with a cyclic procedure looping over the matrix representation of the net.     

Modeling Incomplete Knowledge of Semantic Web Using Bayesian Networks

ABSTRACT

Interoperable ontologies already exist in the biomedical field, enabling scientists to communicate with minimum ambiguity. Unfortunately, ontology languages, in the semantic web, such as OWL and RDF(S), are based on crisp logic and thus they cannot handle uncertain knowledge about an application field, which is unsuitable for the medical domain. In this paper, we focus on modeling incomplete knowledge in the classical OWL ontologies, using Bayesian networks, all keeping the semantic of the first ontology, and applying algorithms dedicated to learn parameters of Bayesian networks in order to generate the Bayesian networks. We use EM algorithm for learning conditional probability tables of different nodes of Bayesian network automatically, contrary to different tools of Bayesian networks where probabilities are inserted manually. To validate our work, we have applied our model on the diagnosis of liver cancer using classical ontology containing incomplete instances, in order to handle medical uncertain knowledge, for predicting a liver cancer.     

Probability propagation in fuzzy Bayesian belief networks with nondeterministic states

The conceptual basis of fuzzy Bayesian belief networks with nondeterministic states is considered. The concept of a fuzzy probability estimate as a fuzzy relation of special type is introduced and its geometrical interpretation is given. Functional transformations of fuzzy probability estimates are defined and a multidimensional linear interpolation procedure is developed. Fundamental aspects of information distribution in fuzzy Bayesian belief networks with nondeterministic states are considered. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 153–169, November–December 2008.     

Compositional analysis of Petri nets

Foundations of compositional analysis of Petri nets are presented. This analysis consist of the determination of properties of a given Petri net from the properties of its functional subnets. Compositional analysis covers the investigation of behavioral and structural properties of Petri nets with the help of matrix methods that use fundamental equations and invariants. The exponential acceleration of computations as a function of the dimensionality of a net is obtained. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 143–154, January–February 2006.     

Sensitivity analysis on causal chains of Bayesian networks

To analyze the key path of Bayesian network in complex systems, this study proposes to analyze the sensitivity of causal chains of Bayesian networks using the Petri net structural analysis approach to obtain the key chain through which the cause influences the consequence. First, the Bayesian network is transformed into Petri net, the structural analysis approach of which is employed to analyze structural nature of the Bayesian network, ensuring correctness of the constructed Bayesian network structure. Then based on the above fact that the structure is correct, S‐invariants of a Petri net is used to search for simple causal chains of the Bayesian network. Finally, the causal effect is defined and sensitivity analysis is made on the causal chains. The said method is applied to MDS causal chain analysis. Results show that the proposed method is direct viewing and practical. This method has some reference value for decision making in complex systems. © 2011 Wiley Periodicals, Inc.     

On enumerating minimal siphons in Petri nets using CLP and SAT solvers: theoretical and practical complexity

Petri nets are a simple formalism for modeling concurrent computation. They are also an interesting tool for modeling and analysing biochemical reaction systems, bridging the gap between purely qualitative and quantitative models. Biological networks can indeed be complex, large, and with many unknown kinetic parameters, which makes the development of quantitative models difficult. In this paper, we focus on the Petri net representation of biochemical reactions and on two structural properties of Petri nets, siphons and traps, that bring us information about the persistence of some molecular species, independently of the kinetics. We first study the theoretical time complexity of minimal siphon decision problems in general Petri nets, and present three new complexity results: first, we show that the existence of a siphon of a given cardinality is NP-complete; second, we prove that deciding the Siphon-Trap property is co-NP-complete; third, we prove that deciding the existence of a minimal siphon containing a given set of places, deciding the existence of a siphon of a given cardinality and deciding the Siphon-Trap property can be done in linear time in Petri nets of bounded tree-width. Then, we present a Boolean model of siphons and traps, and two method for enumerating all minimal siphons and traps of a Petri net, by using a SAT solver and a Constraint Logic Program (CLP) respectively. On a benchmark of 345 Petri nets of hundreds of places and transitions, extracted from biological models from the BioModels repository, as well as on a benchmark composed of 80 Petri nets from the Petriweb database of industrial processes, we show that both the SAT and CLP methods are overall faster by one or two orders of magnitude compared to the state-of-the-art algorithm from the Petri net community, and are in fact able to solve all the enumeration problems of our practical benchmarks. We investigate why these programs perform so well in practice, and provide some elements of explanation related to our theoretical complexity results.     

代谢网络结构与功能的Petri网分析

发展基因组尺度代谢网络模型的模拟和分析方法有助于学习这些网络的结构与功能关系,是当前计算系统生物学领域的一个重要研究主题。由于具备严格的数学描述,直观的图形表达,外加存在众多的算法和工具,Petri网可能成为代谢网络模拟和分析的有力工具。应用位置/变迁网来分析代谢网络的结构与功能特征,首先建立了巴斯德毕赤酵母代谢的Petri网模型,随后计算了该模型中的P、T不变量,并讨论了它们的生物学意义。