Solving the chemical master equation using sliding windows |
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Authors: | Verena Wolf Rushil Goel Maria Mateescu Thomas A Henzinger |
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Affiliation: | 1.Computer Science Department,Saarland University,Saarbrücken,Germany;2.Department of Computer Science and Engineering,IIT Bombay,Bombay,India;3.School of Computer and Communication Sciences,EPFL,Lausanne,Switzerland;4.Institute of Science and Technology,Klosterneuburg,Austria |
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Abstract: | Background The chemical master equation (CME) is a system of ordinary differential equations that describes the evolution of a network of chemical reactions as a stochastic process. Its solution yields the probability density vector of the system at each point in time. Solving the CME numerically is in many cases computationally expensive or even infeasible as the number of reachable states can be very large or infinite. We introduce the sliding window method, which computes an approximate solution of the CME by performing a sequence of local analysis steps. In each step, only a manageable subset of states is considered, representing a "window" into the state space. In subsequent steps, the window follows the direction in which the probability mass moves, until the time period of interest has elapsed. We construct the window based on a deterministic approximation of the future behavior of the system by estimating upper and lower bounds on the populations of the chemical species. |
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