Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Tal RotbartMichael Urbakh

Abstract

We study the effect of restart, and retry, on the mean completion time of a generic process. The need to do so arises in various branches of the sciences and we show that it can naturally be addressed by taking advantage of the classical reaction scheme of Michaelis and Menten. Stopping a process in its midst-only to start it all over again-may prolong, leave unchanged, or even shorten the time taken for its completion. Here we are interested in the optimal restart problem, i.e., in finding a restart rate which brings the mean completion time of a process to a minimum. We derive the governing equation for this problem and show that it is exactly solvable in cases of particular interest. We then continue to discover regimes at which solutions to the problem take on universal, details independent forms which further give rise to optimal scaling laws. The formalism we develop, and the results obtained, can be utilized when optimizing stochastic search processes and randomized computer algorithms. An immediate connection with kinetic proofreading is also noted and discussed.

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Citations

Jul 14, 2017·Physical Chemistry Chemical Physics : PCCP·G John Lapeyre, Marco Dentz
Feb 24, 2018·Nature Communications·Tal RobinMichael Urbakh
Feb 20, 2019·Physical Review. E·Jaume Masoliver
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