ERODE: A Tool for the Evaluation and Reduction of Ordinary Differential Equations

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

doi:10.1007/978-3-662-54580-5_19

Cited by 49 publications

(47 citation statements)

References 44 publications

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“…The latter result compares with ours, but the resulting method appears to be not (relatively) complete in the sense of our double chain algorithm. Moreover, the computational prerequisites of [23] (symbolic linear programming, 9 Which are x6 = x7 and x8 = x9, as checked with the Erode tool by the same authors [17]. exponential size matrices, symbolic root extraction) are very different from ours, and much more demanding.…”

Section: Conclusion Further and Related Workmentioning

confidence: 90%

Algebra, Coalgebra, and Minimization in Polynomial Differential Equations

Boreale

2017

Lecture Notes in Computer Science

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We consider reasoning and minimization in systems of polynomial ordinary differential equations (ode's). The ring of multivariate polynomials is employed as a syntax for denoting system behaviours. We endow this set with a transition system structure based on the concept of Lie derivative, thus inducing a notion of L-bisimulation. We prove that two states (variables) are L-bisimilar if and only if they correspond to the same solution in the ode's system. We then characterize L-bisimilarity algebraically, in terms of certain ideals in the polynomial ring that are invariant under Lie-derivation. This characterization allows us to develop a complete algorithm, based on building an ascending chain of ideals, for computing the largest L-bisimulation containing all valid identities that are instances of a user-specified template. A specific largest L-bisimulation can be used to build a reduced system of ode's, equivalent to the original one, but minimal among all those obtainable by linear aggregation of the original equations. A computationally less demanding approximate reduction and linearization technique is also proposed.

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Section: Conclusion Further and Related Workmentioning

confidence: 90%

Algebra, Coalgebra, and Minimization in Polynomial Differential Equations

Boreale

2017

Lecture Notes in Computer Science

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“…A prototype of EGAC was implemented in Python, using the DEAP package for genetic algorithms [12]. EGAC relies on the Eclipse-based tool ERODE [9], in order to execute the refineBDE function of Algorithm 4. ERODE implements a recently proposed polynomial-time algorithm to compute the coarsest BDE refinement of a partition of species for CRNs with mass action kinetics [8,10].…”

Section: Resultsmentioning

confidence: 99%

Egac

Tognazzi

Tribastone

Tschaikowski

et al. 2017

Proceedings of the Genetic and Evolutionary Computation Conference

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Discovering relations between chemical reaction networks (CRNs) is a relevant problem in computational systems biology for model reduction, to explain if a given system can be seen as an abstraction of another one; and for model comparison, useful to establish an evolutionary path from simpler networks to more complex ones. This is also related to foundational issues in computer science regarding program equivalence, in light of the established interpretation of a CRN as a kernel programming language for concurrency. Criteria for deciding if two CRNs can be formally related have been recently developed, but these require that a candidate mapping be provided. Automatically finding candidate mappings is very hard in general since the search space essentially consists of all possible partitions of a set. In this paper we tackle this problem by developing a genetic algorithm for a class of CRNs called influence networks, which can be used to model a variety of biological systems including cell-cycle switches and gene networks. An extensive numerical evaluation shows that our approach can successfully establish relations between influence networks from the literature which cannot be found by exact algorithms due to their large computational requirements.

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“…Enhancing scalability is the main improvement of alternative methods of performance analysis for very large systems, e.g., based on fluid approximation techniques [83,138] and on solving systems of ordinary differential equations (ODEs) [35], which is an approach allowing for producing approximated transient measures for models of 10 100 states and beyond, even thanks to (approximate) reductions [141] and aggregations [139] of ODE systems. These methods are supported by automated analysers, like, e.g., GPA [134], the specification language of which is inspired by a version of the process algebra PEPA, and ERODE [42,141]. Approximation methods [15] and scalable reachability analysis techniques [125] are proposed also for mixed models like probabilistic hybrid automata.…”

Section: Analysis Techniques and Tools: Program Analysis Model Checkmentioning

confidence: 99%

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

Aldini

2020

Electron. Proc. Theor. Comput. Sci.

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Quantitative aspects of computation are related to the use of both physical and mathematical quantities, including time, performance metrics, probability, and measures for reliability and security. They are essential in characterizing the behaviour of many critical systems and in estimating their properties. Hence, they need to be integrated both at the level of system modeling and within the verification methodologies and tools. Along the last two decades a variety of theoretical achievements and automated techniques have contributed to make quantitative modeling and verification mainstream in the research community. In the same period, they represented the central theme of the series of workshops entitled Quantitative Aspects of Programming Languages and Systems (QAPL) and born in 2001. The aim of this survey is to revisit such achievements and results from the standpoint of QAPL and its community.

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ERODE: A Tool for the Evaluation and Reduction of Ordinary Differential Equations

Cited by 49 publications

References 44 publications

Algebra, Coalgebra, and Minimization in Polynomial Differential Equations

Algebra, Coalgebra, and Minimization in Polynomial Differential Equations

Egac

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

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