ACM Transactions on Computer Systems (TOCS)
A petri net application to model metabolic processes
Systems Analysis Modelling Simulation
The Operational Analysis of Queueing Network Models
ACM Computing Surveys (CSUR)
Primer in Petri Net Design
Petri Net Representations in Metabolic Pathways
Proceedings of the 1st International Conference on Intelligent Systems for Molecular Biology
Conservation analysis of large biochemical networks
Bioinformatics
Complexity reduction of biochemical networks
Proceedings of the 38th conference on Winter simulation
Performance Analysis Using Stochastic Petri Nets
IEEE Transactions on Computers
The GreatSPN tool: recent enhancements
ACM SIGMETRICS Performance Evaluation Review
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
Parametric analysis of queuing networks
IBM Journal of Research and Development
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
Petri nets for systems and synthetic biology
SFM'08 Proceedings of the Formal methods for the design of computer, communication, and software systems 8th international conference on Formal methods for computational systems biology
A numerical aggregation algorithm for the enzyme-catalyzed substrate conversion
CMSB'06 Proceedings of the 2006 international conference on Computational Methods in Systems Biology
Analysis of signalling pathways using continuous time markov chains
Transactions on Computational Systems Biology VI
GreatSPN enhanced with decision diagram data structures
PETRI NETS'10 Proceedings of the 31st international conference on Applications and Theory of Petri Nets
Analysis of stochastic reaction networks with Markov reward models
Proceedings of the 9th International Conference on Computational Methods in Systems Biology
Product Form Approximation of Transient Probabilities in Stochastic Reaction Networks
Electronic Notes in Theoretical Computer Science (ENTCS)
Quasi product form approximation for markov models of reaction networks
Transactions on Computational Systems Biology XIV
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In this paper we consider the modeling of a portion of the signal transduction pathway involved in the angiogenic process. The detailed model of this process is affected by a high level of complexity due to the functional properties that are represented and the size of its state space. To overcome these problems, we suggest approaches to simplify the detailed representation that result in models with a lower computational and structural complexity, while still capturing the overall behavior of the detailed one. The simplification process must take into account both the structural aspects and the quantitative behavior of the original model. To control the simplification from a structural point of view, we propose a set of reduction steps that maintain the invariants of the original model. To ensure the correspondence between the simplified and the original models from a quantitative point of view we use the flow equivalent method that provides a way of obtaining the parameters of the simplified model on the basis of those of the original one. To support the proposed methodology we show that a good agreement exists among the temporal evolutions of the relevant biological products in the simplified and detailed model evaluated with a large set of input parameters.