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dc.contributor.authorZhang, Jingweien
dc.date.accessioned2014-03-14T20:20:05Zen
dc.date.available2014-03-14T20:20:05Zen
dc.date.issued2009-12-02en
dc.identifier.otheretd-12092009-143340en
dc.identifier.urihttp://hdl.handle.net/10919/30018en
dc.description.abstractThe chemical master equation, formulated on the Markov assumption of underlying chemical kinetics, offers an accurate stochastic description of general chemical reaction systems on the mesoscopic scale. The chemical master equation is especially useful when formulating mathematical models of gene regulatory networks and protein-protein interaction networks, where the numbers of molecules of most species are around tens or hundreds. However, solving the master equation directly suffers from the so called "curse of dimensionality" issue. This thesis first tries to study the numerical properties of the master equation using existing numerical methods and parallel machines. Next, approximation algorithms, namely the adaptive aggregation method and the radial basis function collocation method, are proposed as new paths to resolve the "curse of dimensionality". Several numerical results are presented to illustrate the promises and potential problems of these new algorithms. Comparisons with other numerical methods like Monte Carlo methods are also included. Development and analysis of the linear Shepard algorithm and its variants, all of which could be used for high dimensional scattered data interpolation problems, are also included here, as a candidate to help solve the master equation by building surrogate models in high dimensions.en
dc.publisherVirginia Techen
dc.relation.haspartthesis.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectCollocation Methoden
dc.subjectRadial Basis Functionen
dc.subjectShepard Algorithmen
dc.subjectM-estimationen
dc.subjectUniformization/Randomization Methoden
dc.subjectAggregation/Disaggregationen
dc.subjectUniformization/Randomization Methoden
dc.subjectStochastic Simulation Algorithmen
dc.subjectParallel Computingen
dc.subjectChemical Master Equationen
dc.subjectRadial Basis Functionen
dc.subjectStochastic Simulation Algorithmen
dc.subjectChemical Master Equationen
dc.subjectAggregation/Disaggregationen
dc.subjectParallel Computingen
dc.subjectCollocation Methoden
dc.titleNumerical Methods for the Chemical Master Equationen
dc.typeDissertationen
dc.contributor.departmentMathematicsen
dc.description.degreePh. D.en
thesis.degree.namePh. D.en
thesis.degree.leveldoctoralen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.disciplineMathematicsen
dc.contributor.committeechairWatson, Layne T.en
dc.contributor.committeememberLin, Taoen
dc.contributor.committeememberRibbens, Calvin J.en
dc.contributor.committeememberHerdman, Terry L.en
dc.contributor.committeememberBeattie, Christopher A.en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-12092009-143340/en
dc.date.sdate2009-12-09en
dc.date.rdate2010-01-20en
dc.date.adate2010-01-20en


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