Efficient approximation of the stationary solution to the chemical master equation

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dc.contributorSidje, Roger B.
dc.contributorAmes, Brendan
dc.contributorSun, Min
dc.contributorHalpern, David
dc.contributorKnowles, Ian W.
dc.contributor.advisorSidje, Roger B.
dc.contributor.authorReid, Brandon M.
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2019-08-01T14:23:44Z
dc.date.available2019-08-01T14:23:44Z
dc.date.issued2019
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractWhen 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.en_US
dc.format.extent119 p.
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otheru0015_0000001_0003272
dc.identifier.otherReid_alatus_0004D_13815
dc.identifier.urihttp://ir.ua.edu/handle/123456789/6085
dc.languageEnglish
dc.language.isoen_US
dc.publisherUniversity of Alabama Libraries
dc.relation.hasversionborn digital
dc.relation.ispartofThe University of Alabama Electronic Theses and Dissertations
dc.relation.ispartofThe University of Alabama Libraries Digital Collections
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.subjectMathematics
dc.subjectApplied mathematics
dc.subjectComputational chemistry
dc.titleEfficient approximation of the stationary solution to the chemical master equationen_US
dc.typethesis
dc.typetext
etdms.degree.departmentUniversity of Alabama. Department of Mathematics
etdms.degree.disciplineMathematics
etdms.degree.grantorThe University of Alabama
etdms.degree.leveldoctoral
etdms.degree.namePh.D.
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