_:Nc2823ee6e26a4c5f8f684723d36e2945 .
_:N2ccae6bb1d5e4cfc90d2724a760aee20 _:Nc605e80be0664639869ddcfcb72afdc7 .
"stochastic characterization" .
"approximation" .
.
"algorithm" .
_:N23c0cf7a30e84bca9b6f2d06400a52eb .
"number" .
_:N1b1b1f25dd084cbe864610c39050c788 "Computational Methods in Systems Biology" .
.
"probabilistic logic" .
"extensive simulations" .
"polynomial differential equations" .
_:N1b1b1f25dd084cbe864610c39050c788 .
"64-76" .
.
"evolution" .
"population size" .
_:Nb87e2ab3085e414dae9261c348b74fe3 .
"population" .
"model" .
"network" .
"low molecule counts" .
.
_:Nc6e57d7efae24f51b96ede561bd3c0d4 .
"differential equations" .
"simulations" .
"Department of Computer Science, University of Oxford, Oxford, UK" .
"fast approximate stochastic characterization" .
"approximate model" .
_:N5b082ca3ee424c5cb326bfe15b550b01 .
_:N5b082ca3ee424c5cb326bfe15b550b01 "pub.1007406060" .
_:N2ccae6bb1d5e4cfc90d2724a760aee20 _:N23c0cf7a30e84bca9b6f2d06400a52eb .
_:N12ed9c48280644c3859810aa4880aecf _:N7ac105ed707b463b9d09f319cb7c176e .
"good approximation" .
"true"^^ .
"Microsoft Research, Cambridge, UK" .
_:Nc6e57d7efae24f51b96ede561bd3c0d4 "Bourdon" .
.
"Marta" .
.
"Mathematical Sciences" .
_:N7ac105ed707b463b9d09f319cb7c176e .
"chemical reaction networks" .
"size" .
_:Nb87e2ab3085e414dae9261c348b74fe3 "Springer Nature - SN SciGraph project" .
"stochasticity" .
"Statistics" .
_:Nc605e80be0664639869ddcfcb72afdc7 "Roux" .
"approximate stochastic characterization" .
"Luca" .
"polynomials" .
"stochastic evolution" .
"Kwiatkowska" .
_:N5b082ca3ee424c5cb326bfe15b550b01 "dimensions_id" .
.
.
.
"equations" .
"characterization" .
"thermodynamical limit" .
"low number" .
_:Nc605e80be0664639869ddcfcb72afdc7 "Olivier" .
"first order polynomial differential equations" .
_:N5b082ca3ee424c5cb326bfe15b550b01 .
"molecules" .
"order polynomial differential equations" .
_:N1b1b1f25dd084cbe864610c39050c788 "978-3-319-23401-4" .
"Luca" .
"en" .
"Stochastic Analysis of Chemical Reaction Networks Using Linear Noise Approximation" .
"stochastic analysis" .
"molecular species" .
"Cardelli" .
"reaction networks" .
.
"computational complexity" .
_:Nc2823ee6e26a4c5f8f684723d36e2945 .
_:Nc2823ee6e26a4c5f8f684723d36e2945 _:N12ed9c48280644c3859810aa4880aecf .
_:N2ccae6bb1d5e4cfc90d2724a760aee20 .
_:N23c0cf7a30e84bca9b6f2d06400a52eb _:Nc6e57d7efae24f51b96ede561bd3c0d4 .
"study" .
.
"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." .
"chapter" .
"Laurenti" .
"time" .
"complexity" .
.
.
"chemical master equation" .
"linear noise approximation" .
.
"2015-09-02" .
"approach" .
"solution" .
"initial population" .
.
"2015-09-02" .
_:Nc6e57d7efae24f51b96ede561bd3c0d4 "J\u00E9r\u00E9mie" .
_:Ncad8a7f704f2469daf6a76b91393b474 "doi" .
"2022-01-01T19:22" .
"system" .
"master equation" .
.
_:Ncad8a7f704f2469daf6a76b91393b474 .
_:N6277f08e40964434a91bf344146def60 "Springer Nature" .
.
"https://scigraph.springernature.com/explorer/license/" .
_:Ncad8a7f704f2469daf6a76b91393b474 "10.1007/978-3-319-23401-4_7" .
_:Nb87e2ab3085e414dae9261c348b74fe3 .
"case study" .
"limit" .
"noise approximation" .
"deterministic limit" .
_:Ncad8a7f704f2469daf6a76b91393b474 .
"Department of Computer Science, University of Oxford, Oxford, UK" .
"evolution of populations" .
"chapters" .
"https://doi.org/10.1007/978-3-319-23401-4_7" .
"analysis" .
_:N1b1b1f25dd084cbe864610c39050c788 "978-3-319-23400-7" .
"different species" .
_:N12ed9c48280644c3859810aa4880aecf .
"logic" .
_:N1b1b1f25dd084cbe864610c39050c788 .
_:Nc605e80be0664639869ddcfcb72afdc7 .