Abstract
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.
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2009
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Zhang, Jingwei
- Chair dc:contributor.committeechair
-
- Watson, Layne T.
- Committee members dc:contributor.committeemember
-
- Lin, Tao
- Ribbens, Calvin J.
- Herdman, Terry L.
- Beattie, Christopher A.
Subjects
dc:subject × 9Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-12092009-143340
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/30018