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dc.contributor.authorZhang, Jingweien_US
dc.date.accessioned2014-03-14T20:20:05Z
dc.date.available2014-03-14T20:20:05Z
dc.date.issued2009-12-02en_US
dc.identifier.otheretd-12092009-143340en_US
dc.identifier.urihttp://hdl.handle.net/10919/30018
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_US
dc.publisherVirginia Techen_US
dc.relation.haspartthesis.pdfen_US
dc.rightsI hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Virginia Tech or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.en_US
dc.subjectCollocation Methoden_US
dc.subjectRadial Basis Functionen_US
dc.subjectShepard Algorithmen_US
dc.subjectM-estimationen_US
dc.subjectUniformization/Randomization Methoden_US
dc.subjectAggregation/Disaggregationen_US
dc.subjectUniformization/Randomization Methoden_US
dc.subjectStochastic Simulation Algorithmen_US
dc.subjectParallel Computingen_US
dc.subjectChemical Master Equationen_US
dc.subjectRadial Basis Functionen_US
dc.subjectStochastic Simulation Algorithmen_US
dc.subjectChemical Master Equationen_US
dc.subjectAggregation/Disaggregationen_US
dc.subjectParallel Computingen_US
dc.subjectCollocation Methoden_US
dc.titleNumerical Methods for the Chemical Master Equationen_US
dc.typeDissertationen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairWatson, Layne T.en_US
dc.contributor.committeememberLin, Taoen_US
dc.contributor.committeememberRibbens, Calvin J.en_US
dc.contributor.committeememberHerdman, Terry L.en_US
dc.contributor.committeememberBeattie, Christopher A.en_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-12092009-143340/en_US
dc.date.sdate2009-12-09en_US
dc.date.rdate2010-01-20
dc.date.adate2010-01-20en_US


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