Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Bisimulation through probabilistic testing (preliminary report)
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A compositional approach to performance modelling
A compositional approach to performance modelling
Weak Bisimulation for Fully Probabilistic Processes
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Bisimulation for labelled Markov processes
Information and Computation - Special issue: LICS'97
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Backward Stochastic Bisimulation in CSL Model Checking
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Theoretical Computer Science - Special issue: Computational systems biology
Inexact Uniformization Method for Computing Transient Distributions of Markov Chains
SIAM Journal on Scientific Computing
Bisimulation relations for weighted automata
Theoretical Computer Science
Rule-Based Modelling, Symmetries, Refinements
FMSB '08 Proceedings of the 1st international workshop on Formal Methods in Systems Biology
Sliding Window Abstraction for Infinite Markov Chains
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Scalable simulation of cellular signaling networks
APLAS'07 Proceedings of the 5th Asian conference on Programming languages and systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Fragments-based Model Reduction: Some Case Studies
Electronic Notes in Theoretical Computer Science (ENTCS)
Reconstructing species-based dynamics from reduced stochastic rule-based models
Proceedings of the Winter Simulation Conference
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The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a mathematical model is an important challenge in systems biology. Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the combinatorial complexity by quotienting the reachable set of molecular species into species aggregates while preserving the deterministic semantics of the thermodynamic limit. Recently, we proposed a quotienting that also preserves the stochastic semantics and that is complete in the sense that the semantics of individual species can be recovered from the aggregate semantics. In this paper, we prove that this quotienting yields a sufficient condition for weak lumpability (that is to say that the quotient system is still Markovian for a given set of initial distributions) and that it gives rise to a backward Markov bisimulation between the original and aggregated transition system (which means that the conditional probability of being in a given state in the original system knowing that we are in its equivalence class is an invariant of the system). We illustrate the framework on a case study of the epidermal growth factor (EGF)/insulin receptor crosstalk.