8,352 research outputs found

    Using the probabilistic evaluation tool for the analytical solution of large Markov models

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    Stochastic Petri net-based Markov modeling is a potentially very powerful and generic approach for evaluating the performance and dependability of many different systems, such as computer systems, communication networks, manufacturing systems, etc. As a consequence of their general applicability, SPN-based Markov models form the basic solution approach for several software packages that have been developed for the analytic solution of performance and dependability models. In these tools, stochastic Petri nets are used to conveniently specify complicated models, after which an automatic mapping can be carried out to an underlying Markov reward model. Subsequently, this Markov reward model is solved by specialized solution algorithms, appropriately selected for the measure of interest. One of the major aspects that hampers the use of SPN-based Markov models for the analytic solution of performance and dependability results is the size of the state space. Although typically models of up to a few hundred thousand states can conveniently be solved on modern-day work-stations, often even larger models are required to represent all the desired detail of the system. Our tool PET (probabilistic evaluation tool) circumvents problems of large state spaces when the desired performance and dependability measure are transient measures. It does so by an approach named probabilistic evaluatio

    Modelling bacterial regulatory networks with Petri nets

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    To exploit the vast data obtained from high throughput molecular biology, a variety of modelling and analysis techniques must be fully utilised. In this thesis, Petri nets are investigated within the context of computational systems biology, with the specific focus of facilitating the creation and analysis of models of biological pathways. The analysis of qualitative models of genetic networks using safe Petri net techniques was investigated with particular reference to model checking. To exploit existing model repositories a mapping was presented for the automatic translation of models encoded in the Systems Biology Markup Language (SBML) into the Petri Net framework. The mapping is demonstrated via the conversion and invariant analysis of two published models of the glycolysis pathway. Dynamic stochastic simulations of biological systems suffer from two problems: computational cost; and lack of kinetic parameters. A new stochastic Petri net simulation tool, NASTY was developed which addresses the prohibitive real-time computational costs of simulations by using distributed job scheduling. In order to manage and maximise the usefulness of simulation results a new data standard, TSML was presented. The computational power of NASTY provided the basis for the development of a genetic algorithm for the automatic parameterisation of stochastic models. This parameter estimation technique was evaluated on a published model of the general stress response of E. coli. An attempt to enhance the parameter estimation process using sensitivity analysis was then investigated. To explore the scope and limits of applying the Petri net techniques presented, a realistic case study investigated how the Pho and aB regulons interact to mitigate phosphate stress in Bacillus subtilis. This study made use of a combination of qualitative and quantitative Petri net techniques and was able to confirm an existing experimental hypothesis.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

    The Formal Language and Design Principles of Autonomous DNA Walker Circuits.

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    Simple computation can be performed using the interactions between single-stranded molecules of DNA. These interactions are typically toehold-mediated strand displacement reactions in a well-mixed solution. We demonstrate that a DNA circuit with tethered reactants is a distributed system and show how it can be described as a stochastic Petri net. The system can be verified by mapping the Petri net onto a continuous-time Markov chain, which can also be used to find an optimal design for the circuit. This theoretical machinery can be applied to create software that automatically designs a DNA circuit, linking an abstract propositional formula to a physical DNA computation system that is capable of evaluating it. We conclude by introducing example mechanisms that can implement such circuits experimentally and discuss their individual strengths and weaknesses

    Modelling bacterial regulatory networks with Petri nets

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    To exploit the vast data obtained from high throughput molecular biology, a variety of modelling and analysis techniques must be fully utilised. In this thesis, Petri nets are investigated within the context of computational systems biology, with the specific focus of facilitating the creation and analysis of models of biological pathways. The analysis of qualitative models of genetic networks using safe Petri net techniques was investigated with particular reference to model checking. To exploit existing model repositories a mapping was presented for the automatic translation of models encoded in the Systems Biology Markup Language (SBML) into the Petri Net framework. The mapping is demonstrated via the conversion and invariant analysis of two published models of the glycolysis pathway. Dynamic stochastic simulations of biological systems suffer from two problems: computational cost; and lack of kinetic parameters. A new stochastic Petri net simulation tool, NASTY was developed which addresses the prohibitive real-time computational costs of simulations by using distributed job scheduling. In order to manage and maximise the usefulness of simulation results a new data standard, TSML was presented. The computational power of NASTY provided the basis for the development of a genetic algorithm for the automatic parameterisation of stochastic models. This parameter estimation technique was evaluated on a published model of the general stress response of E. coli. An attempt to enhance the parameter estimation process using sensitivity analysis was then investigated. To explore the scope and limits of applying the Petri net techniques presented, a realistic case study investigated how the Pho and aB regulons interact to mitigate phosphate stress in Bacillus subtilis. This study made use of a combination of qualitative and quantitative Petri net techniques and was able to confirm an existing experimental hypothesis.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

    Mathematical Formula Recognition and Automatic Detection and Translation of Algorithmic Components into Stochastic Petri Nets in Scientific Documents

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    A great percentage of documents in scientific and engineering disciplines include mathematical formulas and/or algorithms. Exploring the mathematical formulas in the technical documents, we focused on the mathematical operations associations, their syntactical correctness, and the association of these components into attributed graphs and Stochastic Petri Nets (SPN). We also introduce a formal language to generate mathematical formulas and evaluate their syntactical correctness. The main contribution of this work focuses on the automatic segmentation of mathematical documents for the parsing and analysis of detected algorithmic components. To achieve this, we present a synergy of methods, such as string parsing according to mathematical rules, Formal Language Modeling, optical analysis of technical documents in forms of images, structural analysis of text in images, and graph and Stochastic Petri Net mapping. Finally, for the recognition of the algorithms, we enriched our rule based model with machine learning techniques to acquire better results

    Quantitative evaluation of Pandora Temporal Fault Trees via Petri Nets

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    © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Using classical combinatorial fault trees, analysts are able to assess the effects of combinations of failures on system behaviour but are unable to capture sequence dependent dynamic behaviour. Pandora introduces temporal gates and temporal laws to fault trees to allow sequence-dependent dynamic analysis of events. Pandora can be easily integrated in model-based design and analysis techniques; however, the combinatorial quantification techniques used to solve classical fault trees cannot be applied to temporal fault trees. Temporal fault trees capture state and therefore require a state space solution for quantification of probability. In this paper, we identify Petri Nets as a possible framework for quantifying temporal trees. We describe how Pandora fault trees can be mapped to Petri Nets for dynamic dependability analysis and demonstrate the process on a fault tolerant fuel distribution system model

    Compositional modelling using Petri nets with the analysis power of stochastic hybrid processes

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    A general stochastic hybrid process (GSHP) is a mathematical formalism that covers most of the requirements posed by the modelling of complex operations, such as time dependencies, multi-dimensional continuous as well as discrete processes, discontinuities, randomness and model uncertainties. In addition, it is possible to study GSHP by using stochastic analysis methodologies, thereby empowering it with powerful mathematical properties. This guarantees unambiguous simulation possibility of the model and allows speeding up this simulation while keeping the model properties intact. However, using GSHP to construct a model of a complex operation is not easy. To support the modelling and the subsequent verification both by mathematical and by multiple operational domain experts, a supporting graphical modelling formalism is desired. Petri nets have shown to be useful for developing models of various complex applications. Typical Petri net features are concurrency and synchronisation mechanism, hierarchical and modular construction, and natural expression of causal dependencies, in combination with graphical and analytical representations.\ud \ud The aim of this thesis is to combine the strengths of Petri net modelling formalisms and those of GSHP. First, dynamically coloured Petri nets (DCPN) are developed, and proof of equivalence is provided with piecewise deterministic Markov processes, which is a particular class of GSHP. Next, DCPN are extended to stochastically and dynamically coloured Petri nets (SDCPN), and proof of equivalence is provided with GSHP. Subsequently, SDCPN are extended to SDCPN with interconnection mapping types (SDCPNimt) and proof of equivalence is provided with both SDCPN and GSHP. It is shown with illustrative air transport examples that these three classes of Petri net are very effective when it comes to the compositional modelling of operations consisting of many distributed components that behave and interact in a dynamic way with many uncertainties. With the equivalence relations between these formalisms, the properties and strengths of the various approaches are combined. The many applications of the approach developed in this thesis, executed at NLR and beyond, show that both the approach and its combined strengths are acknowledged and supported by practice

    Bisimulation Relations Between Automata, Stochastic Differential Equations and Petri Nets

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    Two formal stochastic models are said to be bisimilar if their solutions as a stochastic process are probabilistically equivalent. Bisimilarity between two stochastic model formalisms means that the strengths of one stochastic model formalism can be used by the other stochastic model formalism. The aim of this paper is to explain bisimilarity relations between stochastic hybrid automata, stochastic differential equations on hybrid space and stochastic hybrid Petri nets. These bisimilarity relations make it possible to combine the formal verification power of automata with the analysis power of stochastic differential equations and the compositional specification power of Petri nets. The relations and their combined strengths are illustrated for an air traffic example.Comment: 15 pages, 4 figures, Workshop on Formal Methods for Aerospace (FMA), EPTCS 20m 201
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