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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| Format: | Article |
| Language: | English |
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MDPI AG
2019-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/21/6/607 |
| _version_ | 1818016032728547328 |
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| author | Vikram Sunkara |
| author_facet | Vikram Sunkara |
| author_sort | Vikram Sunkara |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-14T07:06:16Z |
| format | Article |
| id | doaj.art-e20f33c3bc55413f89d889de578b4800 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T07:06:16Z |
| publishDate | 2019-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-e20f33c3bc55413f89d889de578b48002022-12-22T02:06:34ZengMDPI AGEntropy1099-43002019-06-0121660710.3390/e21060607e21060607On the Properties of the Reaction Counts Chemical Master EquationVikram Sunkara0Computational Medicine, Zuse Institute Berlin, 14195 Berlin, GermanyThe 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.https://www.mdpi.com/1099-4300/21/6/607chemical master equationjump continuous-time Markov chainsreaction counts |
| spellingShingle | Vikram Sunkara On the Properties of the Reaction Counts Chemical Master Equation Entropy chemical master equation jump continuous-time Markov chains reaction counts |
| 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 | chemical master equation jump continuous-time Markov chains reaction counts |
| url | https://www.mdpi.com/1099-4300/21/6/607 |
| work_keys_str_mv | AT vikramsunkara onthepropertiesofthereactioncountschemicalmasterequation |