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High-dimensional problems in stochastic modelling of biological processes

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.

Identiferoai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:729087
Date January 2017
CreatorsLiao, Shuohao
ContributorsErban, Radek ; Maini, Philip K. ; Baker, Ruth E.
PublisherUniversity of Oxford
Source SetsEthos UK
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Sourcehttps://ora.ox.ac.uk/objects/uuid:2d710a16-e790-47eb-8670-a4dcdd86f143

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