Inexact methods for the chemical master equation with constant or time-varying propensities, and application to parameter inference

Complex reaction networks arise in molecular biology and many other different fields of science such as ecology and social study. A familiar approach to modeling such problems is to find their master equation. In systems biology, the equation is called the chemical master equation (CME), and solving the CME is a difficult task, because of the curse of dimensionality. The goal of this dissertation is to alleviate this curse via the use of the finite state projection (FSP), in both cases where the CME matrix is constant (if the reaction rates are time-independent) or time-varying (if the reaction rates change over time). The work includes a theoretical characterization of the FSP truncation technique by showing that it can be put in the framework of inexact Krylov methods that relax matrix-vector products and compute them expediently by trading accuracy for speed. We also examine practical applications of our work in delay CME and parameter inference through local and global optimization schemes.

Grantor dc:publisher

University of Alabama Libraries

Year dc:date.issued

2018

Author dc:creator

• Dinh, Khanh Ngoc

Advisor dc:contributor.advisor

• Sidje, Roger B.

Contributors dc:contributor

• Hadji, Layachi
• Halpern, David
• Marquez Lago, Tatiana T.
• Sun, Min

• Applied mathematics

Statement dc:rights

• All rights reserved by the author unless otherwise indicated.

Language dc:language.iso

en_US, English

Dc Identifier Other

u0015_0000001_0002943
Dinh_alatus_0004D_13456

OAI identifier oai:identifier

oai:ir.ua.edu:123456789/3628