--- res: bibo_abstract: - 'We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that of the aggregated one. We show how the applicability of de-aggregation depends on the initial distribution. The application section is devoted to illustrate how the developed theory aids in reducing CTMC models of biochemical systems particularly in connection to protein-protein interactions. We assume that the model is written by a biologist in form of site-graph-rewrite rules. Site-graph-rewrite rules compactly express that, often, only a local context of a protein (instead of a full molecular species) needs to be in a certain configuration in order to trigger a reaction event. This observation leads to suitable aggregate Markov chains with smaller state spaces, thereby providing sufficient reduction in computational complexity. This is further exemplified in two case studies: simple unbounded polymerization and early EGFR/insulin crosstalk.@eng' bibo_authorlist: - foaf_Person: foaf_givenName: Arnab foaf_name: Ganguly, Arnab foaf_surname: Ganguly - foaf_Person: foaf_givenName: Tatjana foaf_name: Petrov, Tatjana foaf_surname: Petrov foaf_workInfoHomepage: http://www.librecat.org/personId=3D5811FC-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-9041-0905 - foaf_Person: foaf_givenName: Heinz foaf_name: Koeppl, Heinz foaf_surname: Koeppl bibo_doi: 10.1007/s00285-013-0738-7 bibo_issue: '3' bibo_volume: 69 dct_date: 2014^xs_gYear dct_language: eng dct_publisher: Springer@ dct_title: Markov chain aggregation and its applications to combinatorial reaction networks@ ...