Guaranteed Error Bounds on Approximate Model Abstractions Through Reachability Analysis

Cardelli, Luca; Tribastone, Mirco; Tschaikowski, Max; Vandin, Andrea

doi:10.1007/978-3-319-99154-2_7

Cited by 9 publications

(5 citation statements)

References 36 publications

(63 reference statements)

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“…For the future, it might be interesting to consider extensions of our importer or of the ERODE input language so to be able to import a higher percentage of models from the BioModels repository. The availability of ready-to-use model conversions in a simple CRN format such as ERODE's might stimulate similar assessments with other model reduction techniques (e.g., [7,16]), or with techniques for bifurcation analysis based on temporal logic as in [6].…”

Section: Discussionmentioning

confidence: 99%

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A large-scale assessment of exact lumping of quantitative models in the BioModels repository

Pérez-Verona

Tribastone

Vandin

2021

Theoretical Computer Science

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Chemical reaction networks are a popular formalism for modeling biological processes which supports both a deterministic and a stochastic interpretation based on ordinary differential equations and continuous-time Markov chains, respectively. In most cases, these models do not enjoy analytical solution, thus typically requiring expensive computational methods based on numerical solvers or stochastic simulations. Exact model reduction techniques can be used as an aid to lower the analysis cost by providing reduced networks that preserve the dynamics of interest to the modeler without incurring any approximation error. We hereby consider a family of techniques for both deterministic and stochastic networks which are based on equivalence relations over the species in the network, leading to a coarse graining which provides the exact aggregate time-course evolution for each equivalence class. We present a largescale empirical assessment on the BioModels repository by measuring their compression capability over 579 models. Through a number of selected case studies, we also show their ability in yielding physically interpretable reductions that can reveal dynamical patterns of the bio-molecular processes under consideration, independently of the values of the kinetic parameters used in the models.

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Section: Discussionmentioning

confidence: 99%

“…• models with non integer stoichiometries (multiplicities) in the reagents or products of reactions (16).…”

Section: Repository Preprocessingmentioning

confidence: 99%

A large-scale assessment of exact lumping of quantitative models in the BioModels repository

Pérez-Verona

Tribastone

Vandin

2021

Theoretical Computer Science

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“…This motivates the development of our ERODE translator into a more mature tool to be further integrated with BioModels/SBML. The availability of ready-to-use model conversions in a simple CRN format such as ERODE's might stimulate similar assessments with other model reduction techniques (e.g., [3,12]).…”

Section: Discussionmentioning

confidence: 99%

A Large-Scale Assessment of Exact Model Reduction in the BioModels Repository

Pérez-Verona

Tribastone

Vandin

2019

Computational Methods in Systems Biology

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Chemical reaction networks are a popular formalism for modeling biological processes which supports both a deterministic and a stochastic interpretation based on ordinary differential equations and continuous-time Markov chains, respectively. In most cases, these models do not enjoy analytical solution, thus typically requiring expensive computational methods based on numerical solvers or stochastic simulations. Exact model reduction techniques can be used as an aid to lower the analysis cost by providing reduced networks that preserve the dynamics of interest to the modeler. We hereby consider a family of techniques for both deterministic and stochastic networks which are based on equivalence relations over the species in the network, leading to a coarse graining which provides the exact aggregate time-course evolution for each equivalence class. We present a large-scale empirical assessment on the BioModels repository by measuring their compression capability over 667 models. Through a number of selected case studies, we also show their ability in yielding physically interpretable reductions that can reveal dynamical patterns of the bio-molecular processes under consideration.

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“…The models include Fluid Process Algebra (FPA) [78,79], Fluid Extended Process Algebra (FEPA) [80,57], heterogenous systems specified by ordinary differential equations (ODEs) [81], chemical reaction networks (CRNs) [30], Intermediate Drift Oriented Language (IDOL) [31] and product form queueing networks (QNs) [3]. The most recent results on this subject are forward and backward equivalences (FE and BE) on the polynomial ODE systems [32] and polynomial dynamical systems (PDSs) [77], approximate back and forth differential equivalences (ε-BDE and ε-FDE) for polynomial initial value problem (PIVP) over the ODE variables [34], syntactic Markovian bisimulation (SMB) equivalence on CRNs with stochastic CTMC-based semantics [33,77], and also L-bisimulation equivalence on the polynomials in the variables for systems of polynomial ODEs [27]. Again, all the mentioned relations are not traditional behavioural equivalences, since FE, BE, ε-BDE, ε-FDE and L-bisimulation are defined for the ODE system specifications that include no action symbols while SMB considers species instead of actions.…”

Section: Introductionmentioning

confidence: 99%

Logical characterization of fluid equivalences

Tarasyuk¹,

Buchholz²

2019

Sib. Elektron. Mat. Izv.

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We investigate fluid equivalences that allow one to compare and reduce behaviour of labeled fluid stochastic Petri nets (LFSPNs) with a single continuous place while preserving their discrete and continuous properties. We propose a linear-time relation of fluid trace equivalence and its branching-time counterpart, fluid bisimulation equivalence. Both fluid relations take into account the essential features of the LFSPNs behaviour, such as functional activity, stochastic timing and fluid flow. We consider the LFSPNs whose continuous markings have no influence to the discrete ones, i.e. every discrete marking determines completely both the set of enabled transitions, their firing rates and the fluid flow rates of the incoming and outgoing arcs for each continuous place. Moreover, we require that the discrete part of the LFSPNs should be continuous time stochastic Petri nets. The underlying stochastic model for the discrete part of the LFSPNs is continuous time Markov chains (CTMCs). The performance analysis of the continuous part of LFSPNs is accomplished via the associated stochastic fluid models (SFMs). We characterize logically fluid trace and bisimulation equivalences with two novel fluid modal logics HM L f lt and HM L f lb , constructed on the basis of the well-known Hennessy-Milner Logic (HML). These characterizations guarantee that two LFSPNs are fluid (trace or bisimulation) equivalent iff they satisfy the same formulas of the respective logic, i.e. they are logically equivalent. The results imply operational characterizations of the logical equivalences.

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Guaranteed Error Bounds on Approximate Model Abstractions Through Reachability Analysis

Cited by 9 publications

References 36 publications

A large-scale assessment of exact lumping of quantitative models in the BioModels repository

A large-scale assessment of exact lumping of quantitative models in the BioModels repository

A Large-Scale Assessment of Exact Model Reduction in the BioModels Repository

Logical characterization of fluid equivalences

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