Stochastic Modeling and Control of Biological Systems: The Lactose Regulation System of Escherichia coli
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This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of ...
The important task of evaluating the impact of random parameters on the output of stochastic ordinary differential equations (SODE) can be computationally very demanding, in particular for problems with a high-dimensional parameter space. In this work we c ...
Background: A biological system's robustness to mutations and its evolution are influenced by the structure of its viable space, the region of its space of biochemical parameters where it can exert its function. In systems with a large number of biochemica ...
We investigate systems of ordinary differential equations with a parameter. We show that under suitable assumptions on the systems the solutions are computable in the sense of recursive analysis. As an application we give a complete characterization of the ...
Systems and synthetic biology are two emerging disciplines that hold promise to revolutionize our understanding of biological systems and to herald a new era of programmable hardware, respectively. Mathematical abstraction and today's abundance of quantita ...
In this paper, we propose a Markov chain modeling of complicated phenomena observed from coupled chaotic oscillators. Once we obtain the transition probability matrix from computer simulation results, various statistical quantities can be easily calculated ...
We apply the Metropolis-Hastings algorithm to efficiently sample from arbitrary paths distributions in a general network. Paths can be generalized into all-day travel plans through, e.g., an appropriate network expansion. The Metropolis-Hastings algorithm ...
We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is based on the const ...
We study the convergence of Markov Decision Processes made of a large number of objects to optimization problems on ordinary differential equations (ODE). We show that the optimal reward of such a Markov Decision Process, satisfying a Bellman equation, con ...
Within systems biology there is an increasing interest in the stochastic behaviour of biochemical reaction networks. An appropriate stochastic description is provided by the chemical master equation, which represents a continuous-time Markov chain (CTMC). ...