{"id":{"repo_id":"alabama","oai_identifier":"oai:ir.ua.edu:123456789/3628"},"canonical_url":"https://search.dev.ndltd.org/etd/alabama/oai:ir.ua.edu:123456789/3628","repository":{"repo_id":"alabama","name":"University of Alabama","base_url":"https://ir-api.ua.edu/oai/request"},"display":{"title":"Inexact methods for the chemical master equation with constant or time-varying propensities, and application to parameter inference","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Dinh, Khanh Ngoc"],"institution":"University of Alabama Libraries","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Hadji, Layachi","Halpern, David","Marquez Lago, Tatiana T.","Sun, Min"],"advisors":["Sidje, Roger B."],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018","date_published":"2018","updated_at":"2026-07-27T18:44:20Z","subjects":["Applied mathematics"],"languages":["en_US","English"],"rights":["All rights reserved by the author unless otherwise indicated."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["u0015_0000001_0002943","Dinh_alatus_0004D_13456"],"render_values":[{"text":"u0015_0000001_0002943","href":null,"code":true},{"text":"Dinh_alatus_0004D_13456","href":null,"code":true}]}]},"links":{"outbound_url":"http://ir.ua.edu/handle/123456789/3628","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hadji, Layachi","Halpern, David","Marquez Lago, Tatiana T.","Sun, Min"]},{"key":"dc:contributor.advisor","label":"Advisor","values":["Sidje, Roger B."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["University of Alabama Tuscaloosa"]},{"key":"dc:creator","label":"Author","values":["Dinh, Khanh Ngoc"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-07-11T16:49:09Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-07-11T16:49:09Z"]},{"key":"dc:date.issued","label":"Date","values":["2018"]},{"key":"dc:publisher","label":"Institution","values":["University of Alabama Libraries"]},{"key":"dc:type","label":"Dc Type","values":["thesis","text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Applied mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["All rights reserved by the author unless otherwise indicated."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["u0015_0000001_0002943","Dinh_alatus_0004D_13456"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://ir.ua.edu/handle/123456789/3628"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Electronic Thesis or Dissertation"]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["electronic"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Inexact methods for the chemical master equation with constant or time-varying propensities, and application to parameter inference"]}]}],"canonical_facts":{"dc:contributor":["Hadji, Layachi","Halpern, David","Marquez Lago, Tatiana T.","Sun, Min"],"dc:contributor.advisor":["Sidje, Roger B."],"dc:contributor.other":["University of Alabama Tuscaloosa"],"dc:creator":["Dinh, Khanh Ngoc"],"dc:date.accessioned":["2018-07-11T16:49:09Z"],"dc:date.available":["2018-07-11T16:49:09Z"],"dc:date.issued":["2018"],"dc:description":["Electronic Thesis or Dissertation"],"dc:description.abstract":["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. 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