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Forward and Backward Bisimulations for Chemical Reaction Networks [article]

Luca Cardelli, Mirco Tribastone, Max Tschaikowski, Andrea Vandin
2015 arXiv   pre-print
We present two quantitative behavioral equivalences over species of a chemical reaction network (CRN) with semantics based on ordinary differential equations.  ...  Backward CRN bisimulation relates species that have the identical solutions at all time points when starting from the same initial conditions.  ...  Krivine and J. Feret for helpful discussions, and the anonymous referees for suggestions that improved the paper. This work was partially supported by the EU project QUANTICOL, 600708. L.  ... 
arXiv:1507.00163v5 fatcat:t4h3b2kcp5dohaunfm5k3zname

Language-based Abstractions for Dynamical Systems

Andrea Vandin
2017 Electronic Proceedings in Theoretical Computer Science  
Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences.  ...  The author is indebted to Luca Cardelli, Mirco Tribastone, and Max Tschaikowski for the collaboration on the development of the presented framework, and for many fruitful discussions.  ...  , forward and backward RN bisimulations.  ... 
doi:10.4204/eptcs.250.2 fatcat:vwujzl2gendq3dsfe5s5ohduly

Challenges in Quantitative Abstractions for Collective Adaptive Systems

Mirco Tribastone
2016 Electronic Proceedings in Theoretical Computer Science  
the art and setting out challenges for future research.  ...  This calls for the development of appropriate quantitative abstraction techniques that preserve most of the system's dynamical behaviour using a more compact representation.  ...  The author is indebted to Luca Cardelli, Max Tschaikowski, and Andrea Vandin for their collaboration in [7, 9, 8] and the numerous fruitful discussions.  ... 
doi:10.4204/eptcs.217.8 fatcat:3cep4abwk5bfnphytxtrcrid54

Symbolic computation of differential equivalences

Luca Cardelli, Mirco Tribastone, Max Tschaikowski, Andrea Vandin
2016 SIGPLAN notices  
for chemical reaction networks recently proposed by Cardelli et al., and (iii) behavioral relations for process algebra with ODE semantics.  ...  The first variant is forward differential equivalence (FDE). This is such that an ODE system can be written for the variables that represent the equivalence classes.  ...  Acknowledgement The authors thank Michele Loreti for helpful discussions. This work was partially supported by the EU project QUANTICOL, 600708.  ... 
doi:10.1145/2914770.2837649 fatcat:ysxlmtlh5rhmhmdul6rb5aityy

Symbolic computation of differential equivalences

Luca Cardelli, Mirco Tribastone, Max Tschaikowski, Andrea Vandin
2016 Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL 2016  
for chemical reaction networks recently proposed by Cardelli et al., and (iii) behavioral relations for process algebra with ODE semantics.  ...  Chemical reaction networks (CRNs) express interactions between chemical species or molecular compounds.  ...  For instance, using the nonlinear ODEẋ 1 = −x 2 1 in (1) we would equate x 2 and x 3 in the forward as well as in backward sense. Chemical reaction networks and their extensions.  ... 
doi:10.1145/2837614.2837649 dblp:conf/popl/CardelliTTV16 fatcat:r53ffzkzyzaf3njsmgmgrfnr24

Efficient Syntax-Driven Lumping of Differential Equations [chapter]

Luca Cardelli, Mirco Tribastone, Max Tschaikowski, Andrea Vandin
2016 Lecture Notes in Computer Science  
In particular, we consider a simple extension of the syntax of elementary chemical reaction networks because i) it can express ODEs with derivatives given by polynomials of degree at most two, which are  ...  relevant in many applications in natural sciences and engineering; and ii) we can build on two recently introduced bisimulations, which yield two complementary notions of ODE lumping.  ...  Headers |R| and |S| give the number of reactions and species of the original and reduced RNs. Headers "Red.  ... 
doi:10.1007/978-3-662-49674-9_6 fatcat:eaqgjxy3urhkzmbiclxx6hdcve

Lumpability abstractions of rule-based systems

Jerome Feret, Thomas Henzinger, Heinz Koeppl, Tatjana Petrov
2012 Theoretical Computer Science  
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  ...  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  ...  We would also like to thank Ferdinanda Camporesi for her careful reading and the useful insights that she gave us about the paper.  ... 
doi:10.1016/j.tcs.2011.12.059 fatcat:c5hevmo5a5aqfn3sa5bvwirxxu

Lumpability Abstractions of Rule-based Systems

Jerome Feret, Thomas Henzinger, Heinz Koeppl, Tatjana Petrov
2010 Electronic Proceedings in Theoretical Computer Science  
In this paper we prove that this quotienting yields a sufficient condition for weak lumpability and that it gives rise to a backward Markov bisimulation between the original and aggregated transition system  ...  The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins.  ...  We would also like to thank Ferdinanda Camporesi for her careful reading and the useful insights that she gave us about the paper.  ... 
doi:10.4204/eptcs.40.10 fatcat:2ncd5hb6izbolf3r52jheinkta

Simplifying Chemical Reaction Network Implementations with Two-Stranded DNA Building Blocks

Robert F. Johnson, Lulu Qian, Matthew J. Patitz, Cody Geary
2020 International Meeting on DNA Computing  
This allows us to treat the Chemical Reaction Network model as a programming language and the implementation schemes as its compiler.  ...  In molecular programming, the Chemical Reaction Network model is often used to describe real or hypothetical systems.  ...  Acknowledgements We would like to thank Chris Thachuk and Erik Winfree for helpful discussions on new DNA strand displacement motifs and optimization thereof.  ... 
doi:10.4230/lipics.dna.2020.2 dblp:conf/dna/JohnsonQ20 fatcat:bjfq5x7gxrbkjoek6ineiiwice

Front Matter, Table of Contents, Preface, Committees, External Reviewers

Luca Aceto, David De Frutos Escrig, Marc Herbstritt
2015 International Conference on Concurrency Theory  
., they are available online and free of charge.  ...  Forward and Backward Bisimulations for Chemical Reaction Networks Luca Cardelli, Mirco Tribastone, Max Tschaikowski, and Andrea Vandin . . . . . . . . .  ...  Lax Bialgebras and Up-To Techniques for Weak Bisimulations Filippo Bonchi, Daniela Petrişan, Damien Pous, and Jurriaan Rot . . . . . . . . . . . . . .  ... 
doi:10.4230/lipics.concur.2015.i dblp:conf/concur/X15 fatcat:xk6gbzxaynbpbcgklezhf2zn6m

Specification, construction, and exact reduction of state transition system models of biochemical processes

Scott M. Bugenhagen, Daniel A. Beard
2012 Journal of Chemical Physics  
Biochemical reaction systems may be viewed as discrete event processes characterized by a number of states and state transitions.  ...  Here, we describe methods for the high-level specification of a system using hypergraphs, for the automated generation of a state-level model from a high-level model, and for the exact reduction of a state-level  ...  (a) can be reduced by forward, but not backward bisimulation, (b) can be reduced by backward, but not forward bisimulation, and (c) can be reduced by both forward and backward bisimulation.  ... 
doi:10.1063/1.4758074 pmid:23083149 pmcid:PMC3487925 fatcat:7yhkxkr2qndifer62hsa7zease

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

Luca Cardelli, Mirco Tribastone, Max Tschaikowski, Andrea Vandin
2017 Lecture Notes in Computer Science  
In the special case of ODEs with polynomial derivatives of degree at most two (covering affine systems and elementary chemical reaction networks), it implements a more efficient partition-refinement algorithm  ...  We present ERODE , a multi-platform tool for the solution and exact reduction of systems of ordinary differential equations (ODEs).  ...  For this class, in [9] we presented the notions of forward bisimulation (FB) and backward bisimulation (BB).  ... 
doi:10.1007/978-3-662-54580-5_19 fatcat:cqsdi6x2zrbg3gamfkmj65cpuy

Weakly linear systems of fuzzy relation inequalities and their applications: A brief survey

Jelena Ignjatovic, Miroslav Ciric
2012 Filomat  
and equivalence of fuzzy automata, and in the social network analysis.  ...  Especially, we present algorithms for computing the greatest solutions to weakly linear systems.  ...  of chemical reactions, and in other fields.  ... 
doi:10.2298/fil1202207i fatcat:4ypn6ph435eqhck4sfynwdlili

Verifying Chemical Reaction Network Implementations: A Bisimulation Approach [chapter]

Robert F. Johnson, Qing Dong, Erik Winfree
2016 Lecture Notes in Computer Science  
The chemical reaction network model We work within the Chemical Reaction Network (CRN) model. A CRN is a pair (S, R), where S is a finite set of species and R a finite set of reactions.  ...  Efforts in programming DNA and other biological molecules have recently focused on general schemes to physically implement arbitrary Chemical Reaction Networks.  ...  We would also like to thank the anonymous reviewers for many helpful suggestions. RFJ and EW were supported by NSF grants 1317694, 1213127, and 0832824.  ... 
doi:10.1007/978-3-319-43994-5_8 fatcat:4gqys43izrbc3cejln7hioqana

Modular verification of chemical reaction network encodings via serializability analysis

Matthew R. Lakin, Darko Stefanovic, Andrew Phillips
2016 Theoretical Computer Science  
as a chemical reaction network.  ...  As an example, we show how this approach may be used to verify two-and four-domain DNA strand displacement encodings of chemical reaction networks, and we generalize our result to the limit where the populations  ...  Nanoscience and Microsystems Training Center (NIH/NCI grant 5R25CA153825).  ... 
doi:10.1016/j.tcs.2015.06.033 pmid:27325906 pmcid:PMC4911709 fatcat:4etq6rus7jfunpcrqwjzlvdybi
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