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;
ns1:author ( ) ;
ns1:datePublished "2015-09-02" ;
ns1:datePublishedReg "2015-09-02" ;
ns1:description "Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analysed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is complex and/or it cannot be ensured that initial populations are small. We develop a probabilistic logic for CRNs that enables stochastic analysis of the evolution of populations of molecular species. We present an approximate model checking algorithm based on the Linear Noise Approximation (LNA) of the CME, whose computational complexity is independent of the population size of each species and polynomial in the number of different species. The algorithm requires the solution of first order polynomial differential equations. We prove that our approach is valid for any CRN close enough to the thermodynamical limit. However, we show on three case studies that it can still provide good approximation even for low molecule counts. Our approach enables rigorous analysis of CRNs that are not analyzable by solving the CME, but are far from the deterministic limit. Moreover, it can be used for a fast approximate stochastic characterization of a CRN." ;
ns1:editor ( [ a ns1:Person ;
ns1:familyName "Roux" ;
ns1:givenName "Olivier" ] [ a ns1:Person ;
ns1:familyName "Bourdon" ;
ns1:givenName "Jérémie" ] ) ;
ns1:genre "chapter" ;
ns1:inLanguage "en" ;
ns1:isAccessibleForFree true ;
ns1:isPartOf [ a ns1:Book ;
ns1:isbn "978-3-319-23400-7",
"978-3-319-23401-4" ;
ns1:name "Computational Methods in Systems Biology" ] ;
ns1:keywords "algorithm",
"analysis",
"approach",
"approximate model",
"approximate stochastic characterization",
"approximation",
"case study",
"characterization",
"chemical master equation",
"chemical reaction networks",
"complexity",
"computational complexity",
"counts",
"deterministic limit",
"different species",
"differential equations",
"equations",
"evolution",
"evolution of populations",
"extensive simulations",
"fast approximate stochastic characterization",
"first order polynomial differential equations",
"good approximation",
"initial population",
"limit",
"linear noise approximation",
"logic",
"low molecule counts",
"low number",
"master equation",
"model",
"molecular species",
"molecule counts",
"molecules",
"network",
"noise approximation",
"number",
"order polynomial differential equations",
"polynomial differential equations",
"polynomials",
"population",
"population size",
"probabilistic logic",
"reaction networks",
"rigorous analysis",
"simulations",
"size",
"solution",
"species",
"stochastic analysis",
"stochastic characterization",
"stochastic evolution",
"stochasticity",
"study",
"system",
"thermodynamical limit",
"time" ;
ns1:name "Stochastic Analysis of Chemical Reaction Networks Using Linear Noise Approximation" ;
ns1:pagination "64-76" ;
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ns1:value "pub.1007406060" ],
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ns1:name "doi" ;
ns1:value "10.1007/978-3-319-23401-4_7" ] ;
ns1:publisher [ a ns1:Organisation ;
ns1:name "Springer Nature" ] ;
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ns1:sdDatePublished "2022-01-01T19:22" ;
ns1:sdLicense "https://scigraph.springernature.com/explorer/license/" ;
ns1:sdPublisher [ a ns1:Organization ;
ns1:name "Springer Nature - SN SciGraph project" ] ;
ns1:url "https://doi.org/10.1007/978-3-319-23401-4_7" ;
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ns2:sdDataset "chapters" .
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ns1:name "Mathematical Sciences" .
a ns1:DefinedTerm ;
ns1:inDefinedTermSet ;
ns1:name "Statistics" .
a ns1:Person ;
ns1:affiliation ;
ns1:familyName "Kwiatkowska" ;
ns1:givenName "Marta" ;
ns1:sameAs .
a ns1:Person ;
ns1:affiliation ;
ns1:familyName "Laurenti" ;
ns1:givenName "Luca" ;
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a ns1:Person ;
ns1:affiliation ;
ns1:familyName "Cardelli" ;
ns1:givenName "Luca" ;
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a ns1:Organization ;
ns1:alternateName "Department of Computer Science, University of Oxford, Oxford, UK" ;
ns1:name "Department of Computer Science, University of Oxford, Oxford, UK",
"Microsoft Research, Cambridge, UK" .