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dc.contributor.advisorYi, Yengfei
dc.contributor.authorLi, Yao
dc.date.accessioned2013-09-20T12:00:15Z
dc.date.available2013-09-20T12:00:15Z
dc.date.issued2012-07-08
dc.identifier.urihttp://hdl.handle.net/1853/49013
dc.description.abstractThe primary objective of this thesis is to make a quantitative study of complex biological networks. Our fundamental motivation is to obtain the statistical dependency between modules by injecting external noise. To accomplish this, a deep study of stochastic dynamical systems would be essential. The first chapter is about the stochastic dynamical system theory. The classical estimation of invariant measures of Fokker-Planck equations is improved by the level set method. Further, we develop a discrete Fokker-Planck-type equation to study the discrete stochastic dynamical systems. In the second part, we quantify systematic measures including degeneracy, complexity and robustness. We also provide a series of results on their properties and the connection between them. Then we apply our theory to the JAK-STAT signaling pathway network.
dc.language.isoen_US
dc.publisherGeorgia Institute of Technology
dc.subjectStochastic dynamical system
dc.subjectFokker-Planck equation
dc.subjectSystematic measure
dc.subject.lcshSystems biology
dc.subject.lcshBioinformatics
dc.subject.lcshFokker-Planck equation Numerical solutions
dc.subject.lcshStochastic differential equations
dc.titleStochastic perturbation theory and its application to complex biological networks -- a quantification of systematic features of biological networks
dc.typeDissertation
dc.description.degreePh.D.
dc.contributor.departmentMathematics
dc.contributor.committeeMemberZhou, Hao-min
dc.contributor.committeeMemberKemp, Melissa Lambeth
dc.contributor.committeeMemberChow, Shui-Nee
dc.contributor.committeeMemberBakhtin, Yuri


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