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dc.contributor.author
Kazeev, Vladimir
dc.contributor.author
Schwab, Christoph
dc.date.accessioned
2022-09-19T09:19:14Z
dc.date.available
2022-09-19T09:19:14Z
dc.date.issued
2013-06
dc.identifier.uri
http://hdl.handle.net/20.500.11850/571347
dc.identifier.doi
10.3929/ethz-a-010386335
dc.description.abstract
We prove that the stationary distribution of a system of reacting species with a weakly- reversible reaction network of zero deficiency in the sense of Feinberg admits tensor- structured approximation of complexity which scales linearly with respect to the number of species and logarithmically in the maximum copy numbers as well as in the desired accuracy. Our results cover the classical mass-action and also Michaelis-Menten kinetics which correspond to two widely used classes of propensity functions, and also to arbitrary combinations of those. New rank bounds for tensor-structured approximations of the PDF of a truncated one-dimensional Poisson distribution are an auxiliary result of the present paper, which might be of independent interest. The present work complements recent results obtained by the authors jointly with M. Khammash and M. Nip on the tensor-structured numerical simulation of the evolution of system states distributions, driven by the Kolmogorov forward equation of the system, known also as the chemical master equation, or CME for short. For the two kinetics mentioned above we also analyze the low-rank tensor structure of the CME operator.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Seminar for Applied Mathematics, ETH Zurich
en_US
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.subject
chemical master equation
en_US
dc.subject
stochastic models
en_US
dc.subject
low rank
en_US
dc.subject
tensor approximation
en_US
dc.subject
tensor train
en_US
dc.subject
quantized tensor train
en_US
dc.subject
multilinear algebra
en_US
dc.subject
mass-action kinetics
en_US
dc.subject
Michaelis–Menten kinetics
en_US
dc.subject
stationary distribution
en_US
dc.subject
deficiency zero
en_US
dc.subject
chemical reaction network
en_US
dc.subject
Poisson distribution
en_US
dc.title
Tensor approximation of stationary distributions of chemical reaction networks
en_US
dc.type
Report
dc.rights.license
In Copyright - Non-Commercial Use Permitted
ethz.journal.title
SAM Research Report
ethz.journal.volume
2013-18
en_US
ethz.size
31 p.
en_US
ethz.code.ddc
DDC - DDC::5 - Science::510 - Mathematics
en_US
ethz.grant
Automated Urban Parking and Driving
en_US
ethz.publication.place
Zurich
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
ethz.identifier.url
https://math.ethz.ch/sam/research/reports.html?id=514
ethz.grant.agreementno
247277
ethz.grant.fundername
EC
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
FP7
ethz.date.deposited
2017-06-11T03:57:52Z
ethz.source
ECOL
ethz.source
ECIT
ethz.identifier.importid
imp59366b6f2f8c945462
ethz.identifier.importid
imp593651892c7ed44665
ethz.ecolpid
eth:47366
ethz.ecitpid
pub:124469
ethz.eth
yes
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ethz.availability
Open access
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ethz.rosetta.installDate
2022-09-19T09:19:24Z
ethz.rosetta.lastUpdated
2022-09-19T09:19:24Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/154921
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/79180
ethz.COinS
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