Adaptive Aggregation of Markov Chains: Quantitative Analysis of Chemical Reaction Networks

Abate, Alessandro; Brim, Luboš; Češka, Milan; Kwiatkowska, Marta

doi:10.1007/978-3-319-21690-4_12

Cited by 18 publications

(42 citation statements)

References 29 publications

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“…Other techniques can also be integrated to speed up the synthesis process, including fast adaptive uniformisation [16,34], state aggregation [1,44], and abstraction [33]. Finally, we plan to include the synthesis algorithms in the param module of the PRISM model checker [14,32], and to extend the method to general non-linear rate functions.…”

Section: Conclusion and Discussionmentioning

confidence: 97%

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Precise parameter synthesis for stochastic biochemical systems

et al. 2016

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We consider the problem of synthesising rate parameters for stochastic biochemical networks so that a given time-bounded CSL property is guaranteed to hold, or, in the case of quantitative properties, the probability of satisfying the property is maximised or minimised. Our method is based on extending CSL model checking and standard uniformisation to parametric models, in order to compute safe bounds on the satisfaction probability of the property. We develop synthesis algorithms that yield answers that are precise to within an arbitrarily small tolerance value. The algorithms combine the computation of probability bounds with the refinement and sampling of the parameter space. Our methods are precise and efficient, and improve on existing approximate techniques that employ discretisation and refinement. We evaluate the usefulness of the methods by synthesising rates for three biologically motivated case studies: infection control for a SIR epidemic model; reliability

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Section: Conclusion and Discussionmentioning

confidence: 97%

“…1 [φ ] partitions the parameter space into a single undecided region. In the second step, the parameter space refinement yields a refinement of the satisfaction sets.…”

Section: Parameter Synthesis For Nested Csl Formulasmentioning

confidence: 99%

Precise parameter synthesis for stochastic biochemical systems

et al. 2016

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“…Thus, SMB may give a reduced model that exactly preserves the dynamics of interest. Since the CRN syntax is often combinatorially smaller than the underlying CTMC, we envisage SMB to be used as a pre-processing stage for CTMC analyses or for further reduction techniques on the semantics, either in exact or approximate form (e.g., [1]). Indeed, it would be interesting to conduct further experiments in order to understand how tight the lumping is with respect to the coarsest one obtained by applying Markov chain minimization algorithms on the fully enumerated state space; for this, we plan to develop fully integrated support for SMB into our software tool for model reduction techniques, ERODE [12] (http://sysma.imtlucca.it/tools/erode/).…”

Section: Resultsmentioning

confidence: 99%

Syntactic Markovian Bisimulation for Chemical Reaction Networks

Cardelli

Tribastone

Tschaikowski

et al. 2017

Lecture Notes in Computer Science

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In chemical reaction networks (CRNs) with stochastic semantics based on continuous-time Markov chains (CTMCs), the typically large populations of species cause combinatorially large state spaces. This makes the analysis very difficult in practice and represents the major bottleneck for the applicability of minimization techniques based, for instance, on lumpability. In this paper we present syntactic Markovian bisimulation (SMB), a notion of bisimulation developed in the Larsen-Skou style of probabilistic bisimulation, defined over the structure of a CRN rather than over its underlying CTMC. SMB identifies a lumpable partition of the CTMC state space a priori, in the sense that it is an equivalence relation over species implying that two CTMC states are lumpable when they are invariant with respect to the total population of species within the same equivalence class. We develop an efficient partition-refinement algorithm which computes the largest SMB of a CRN in polynomial time in the number of species and reactions. We also provide an algorithm for obtaining a quotient network from an SMB that induces the lumped CTMC directly, thus avoiding the generation of the state space of the original CRN altogether. In practice, we show that SMB allows significant reductions in a number of models from the literature. Finally, we study SMB with respect to the deterministic semantics of CRNs based on ordinary differential equations (ODEs), where each equation gives the time-course evolution of the concentration of a species. SMB implies forward CRN bisimulation, a recently developed behavioral notion of equivalence for the ODE semantics, in an analogous sense: it yields a smaller ODE system that keeps track of the sums of the solutions for equivalent species.

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“…Example 3. Let us consider our running example (1). Then, the partition {x 1 }, {x 2 , x 3 } is a 0.02-BDE partition, as can be easily seen from Example 2.…”

Section: Approximate Differential Equivalencesmentioning

confidence: 99%

“…This allows relating ODE variables that would be distinct otherwise. Like in other established approaches such as behavioral pseudometrics (e.g., [1,9]), ε = 0 corresponds to an exact differential equivalence of [11]. In addition to defining criteria for approximate differential equivalences, we provide an algorithm for obtaining the largest one.…”

Section: Introductionmentioning

confidence: 99%

Guaranteed Error Bounds on Approximate Model Abstractions Through Reachability Analysis

Cardelli

Tribastone

Tschaikowski

et al. 2018

Quantitative Evaluation of Systems

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It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem for nonlinear ordinary differential equations (ODEs) with polynomial derivatives. We introduce approximate differential equivalence as a more permissive variant of a recently developed exact counterpart, allowing ODE variables to be related even when they are governed by nearby derivatives. We develop algorithms to (i) compute the largest approximate differential equivalence; (ii) construct an approximate quotient model from the original one via an appropriate parameter perturbation; and (iii) provide a formal certificate on the quality of the approximation as an error bound, computed as an over-approximation of the reachable set of the perturbed model. Finally, we apply approximate differential equivalences to study the effect of parametric tolerances in models of symmetric electric circuits.

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Adaptive Aggregation of Markov Chains: Quantitative Analysis of Chemical Reaction Networks

Cited by 18 publications

References 29 publications

Precise parameter synthesis for stochastic biochemical systems

Precise parameter synthesis for stochastic biochemical systems

Syntactic Markovian Bisimulation for Chemical Reaction Networks

Guaranteed Error Bounds on Approximate Model Abstractions Through Reachability Analysis

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