Efficient approximation of the stationary solution to the chemical master equation

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dc.contributor Sidje, Roger B.
dc.contributor Ames, Brendan
dc.contributor Sun, Min
dc.contributor Halpern, David
dc.contributor Knowles, Ian W.
dc.contributor.advisor Sidje, Roger B.
dc.contributor.author Reid, Brandon M.
dc.date.accessioned 2019-08-01T14:23:44Z
dc.date.available 2019-08-01T14:23:44Z
dc.date.issued 2019
dc.identifier.other u0015_0000001_0003272
dc.identifier.other Reid_alatus_0004D_13815
dc.identifier.uri http://ir.ua.edu/handle/123456789/6085
dc.description Electronic Thesis or Dissertation
dc.description.abstract When studying chemical reactions on the cellular level, it is often helpful to model the system using the continuous-time Markov chain (CTMC) that results from the chemical master equation (CME). It is frequently instructive to compute the probability distribution of this CTMC at statistical equilibrium, thereby gaining insight into the stationary, or long-term, behavior of the system. Computing such a distribution directly is problematic when the state space of the system is large. To alleviate this difficulty, it has become popular to constrain the computational burden by using a finite state projection (FSP), which aims only to capture the most likely states of the system, rather than every possible state. We propose efficient methods to further narrow these states to those that remain highly probable in the long run, after the transient behavior of the system has dissipated. Our strategy is to quickly estimate the local maxima of the stationary distribution using the reaction rate formulation, which is of considerably smaller size than the full-blown chemical master equation, and from there develop adaptive schemes to profile the distribution around the maxima. The primary focus is on constructing an efficient FSP; however, we also examine how some of our initial estimates perform on their own and discuss how they might be applied to tensor-based methods. We include numerical tests that show the efficiency of our approaches.
dc.format.extent 119 p.
dc.format.medium electronic
dc.format.mimetype application/pdf
dc.language English
dc.language.iso en_US
dc.publisher University of Alabama Libraries
dc.relation.ispartof The University of Alabama Electronic Theses and Dissertations
dc.relation.ispartof The University of Alabama Libraries Digital Collections
dc.relation.hasversion born digital
dc.rights All rights reserved by the author unless otherwise indicated.
dc.subject.other Mathematics
dc.subject.other Applied mathematics
dc.subject.other Computational chemistry
dc.title Efficient approximation of the stationary solution to the chemical master equation
dc.type thesis
dc.type text
etdms.degree.department University of Alabama. Department of Mathematics
etdms.degree.discipline Mathematics
etdms.degree.grantor The University of Alabama
etdms.degree.level doctoral
etdms.degree.name Ph.D.


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