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On the Properties of the Reaction Counts Chemical Master Equation
The reaction counts chemical master equation (CME) is a high-dimensional variant of the classical population counts CME. In the reaction counts CME setting, we count the reactions which have fired over time rather than monitoring the population state over time. Since a reaction either fires or not,...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2019
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7515091/ https://www.ncbi.nlm.nih.gov/pubmed/33267321 http://dx.doi.org/10.3390/e21060607 |
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author | Sunkara, Vikram |
author_facet | Sunkara, Vikram |
author_sort | Sunkara, Vikram |
collection | PubMed |
description | The reaction counts chemical master equation (CME) is a high-dimensional variant of the classical population counts CME. In the reaction counts CME setting, we count the reactions which have fired over time rather than monitoring the population state over time. Since a reaction either fires or not, the reaction counts CME transitions are only forward stepping. Typically there are more reactions in a system than species, this results in the reaction counts CME being higher in dimension, but simpler in dynamics. In this work, we revisit the reaction counts CME framework and its key theoretical results. Then we will extend the theory by exploiting the reactions counts’ forward stepping feature, by decomposing the state space into independent continuous-time Markov chains (CTMC). We extend the reaction counts CME theory to derive analytical forms and estimates for the CTMC decomposition of the CME. This new theory gives new insights into solving hitting times-, rare events-, and a priori domain construction problems. |
format | Online Article Text |
id | pubmed-7515091 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75150912020-11-09 On the Properties of the Reaction Counts Chemical Master Equation Sunkara, Vikram Entropy (Basel) Article The reaction counts chemical master equation (CME) is a high-dimensional variant of the classical population counts CME. In the reaction counts CME setting, we count the reactions which have fired over time rather than monitoring the population state over time. Since a reaction either fires or not, the reaction counts CME transitions are only forward stepping. Typically there are more reactions in a system than species, this results in the reaction counts CME being higher in dimension, but simpler in dynamics. In this work, we revisit the reaction counts CME framework and its key theoretical results. Then we will extend the theory by exploiting the reactions counts’ forward stepping feature, by decomposing the state space into independent continuous-time Markov chains (CTMC). We extend the reaction counts CME theory to derive analytical forms and estimates for the CTMC decomposition of the CME. This new theory gives new insights into solving hitting times-, rare events-, and a priori domain construction problems. MDPI 2019-06-19 /pmc/articles/PMC7515091/ /pubmed/33267321 http://dx.doi.org/10.3390/e21060607 Text en © 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Sunkara, Vikram On the Properties of the Reaction Counts Chemical Master Equation |
title | On the Properties of the Reaction Counts Chemical Master Equation |
title_full | On the Properties of the Reaction Counts Chemical Master Equation |
title_fullStr | On the Properties of the Reaction Counts Chemical Master Equation |
title_full_unstemmed | On the Properties of the Reaction Counts Chemical Master Equation |
title_short | On the Properties of the Reaction Counts Chemical Master Equation |
title_sort | on the properties of the reaction counts chemical master equation |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7515091/ https://www.ncbi.nlm.nih.gov/pubmed/33267321 http://dx.doi.org/10.3390/e21060607 |
work_keys_str_mv | AT sunkaravikram onthepropertiesofthereactioncountschemicalmasterequation |