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We investigate the propagation of random fluctuations through biochemical networks in which the concentrations of species are large enough so that the unperturbed problem is well-described by ordinary differential equation. We characterize the behavior of variance as fluctuations propagate down chains, study the effect of side chains and feedback loops, and investigate the asymptotic behavior as one rate constant gets large. We also describe how the ideas can be applied to the study of methionine metabolism.
The linear noise approximation is commonly used to obtain intrinsic noise statistics for biochemical networks. These estimates are accurate for networks with large numbers of molecules. However it is well known that many biochemical networks are char
This paper addresses the problem of model reduction for dynamical system models that describe biochemical reaction networks. Inherent in such models are properties such as stability, positivity and network structure. Ideally these properties should b
We consider a class of continuous-time stochastic growth models on $d$-dimensional lattice with non-negative real numbers as possible values per site. The class contains examples such as binary contact path process and potlatch process. We show the e
We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of the DebtRank
We consider a class of interacting particle systems with values in $[0,8)^{zd}$, of which the binary contact path process is an example. For $d ge 3$ and under a certain square integrability condition on the total number of the particles, we prove a