DocumentCode :
592517
Title :
Clustering-based ℌ2-state aggregation of positive networks and its application to reduction of chemical master equations
Author :
Ishizaki, Takayuki ; Kashima, Kenji ; Girard, Antoine ; Imura, Jun-ichi ; Luonan Chen ; Aihara, Kazuyuki
Author_Institution :
Dept. of Mech. & Environ. Inf., Tokyo Inst. of Technol., Tokyo, Japan
fYear :
2012
fDate :
10-13 Dec. 2012
Firstpage :
4175
Lastpage :
4180
Abstract :
In this paper, based on a notion of network clustering, we propose a state aggregation method for positive systems evolving over directed networks, which we call positive networks. In the proposed method, we construct a set of clusters (i.e., disjoint sets of state variables) according to a kind of local uncontrollability of systems. This method preserves interconnection topology among clusters as well as stability and some particular properties, such as system positivity and steady-state characteristic (steady-state distribution). In addition, we derive an ℌ2-error bound of the state discrepancy caused by the aggregation. The efficiency of the proposed method is shown through the reduction of a chemical master equation representing the time evolution of the Michaelis-Menten chemical reaction system.
Keywords :
Markov processes; biochemistry; catalysis; complex networks; enzymes; master equation; molecular biophysics; reaction kinetics theory; H2-error bound; Michaelis-Menten chemical reaction time evolution; chemical master equation reduction; clustering based H2-state aggregation; directed networks; interconnection topology preservaton; local system uncontrollability; positive networks; positive systems; state aggregation method; state discrepancy; state variable disjoint sets; steady state characteristic; steady state distribution; system positivity; Chemicals; Eigenvalues and eigenfunctions; Equations; Manganese; Mathematical model; Redundancy; Vectors;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control (CDC), 2012 IEEE 51st Annual Conference on
Conference_Location :
Maui, HI
ISSN :
0743-1546
Print_ISBN :
978-1-4673-2065-8
Electronic_ISBN :
0743-1546
Type :
conf
DOI :
10.1109/CDC.2012.6426793
Filename :
6426793
Link To Document :
بازگشت