Thesis (Ph. D.)--University of Hong Kong, 2008.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (Ph.D..(Mathematics and Applied Mathematics)) -- University of Pretoria, 2009. / Summary in English. Includes bibliographical references.

Thesis (M.S.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on August 12, 2009) Includes bibliographical references.

Thesis (Ph. D.)--University of Hong Kong, 2009. / Includes bibliographical references (leaves 136-158) Also available online.

Thesis--University of Florida. / Description based on print version record. Typescript. Vita. Bibliography: leaves 112-113.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Orientador: Roy E. Bruns / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Quimica / Made available in DSpace on 2018-08-12T00:57:18Z (GMT). No. of bitstreams: 1 Guadagnini_PauloHenrique_D.pdf: 1175328 bytes, checksum: 1d90b1cecc2001bf1f665148300c3852 (MD5) Previous issue date: 2000 / Doutorado

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). This thesis addresses such computational challenges by a tensor-structured computational framework. After a background introduction in Chapter 1, Chapter 2 derives the order of convergence in volume size between the stationary distributions of the exact chemical master equation (CME) and its continuous Fokker-Planck approximation (CFPE). It also proposes the multi-scale approaches to address the failure of the CFPE in capturing the noise-induced multi-stability of the CME distribution. Chapter 3 studies the numerical solution of the high-dimensional CFPE using the tensor train and the quantized-TT data formats. In Chapter 4, the tensor solutions are applied to study the parameter estimation, robustness, sensitivity and bifurcation structures of stochastic reaction networks. A Matlab implementation of the proposed methods/algorithms is available at http://www.stobifan.org.

No description available.