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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

The stretch to stray on time: Resonant length of random walks in a transient

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Author(s):
Falcke, Martin [1, 2] ; Friedhoff, Victor Nicolai [1, 2]
Total Authors: 2
Affiliation:
[1] Humboldt Univ, Dept Phys, Newtonstr 15, D-12489 Berlin - Germany
[2] Max Delbruck Ctr Mol Med, Robert Rossle Str 10, D-13125 Berlin - Germany
Total Affiliations: 2
Document type: Journal article
Source: Chaos; v. 28, n. 5 MAY 2018.
Web of Science Citations: 0
Abstract

First-passage times in random walks have a vast number of diverse applications in physics, chemistry, biology, and finance. In general, environmental conditions for a stochastic process are not constant on the time scale of the average first-passage time or control might be applied to reduce noise. We investigate moments of the first-passage time distribution under an exponential transient describing relaxation of environmental conditions. We solve the Laplace-transformed (generalized) master equation analytically using a novel method that is applicable to general state schemes. The first-passage time from one end to the other of a linear chain of states is our application for the solutions. The dependence of its average on the relaxation rate obeys a power law for slow transients. The exponent nu depends on the chain length N like nu= -N /(N+1) to leading order. Slow transients substantially reduce the noise of first-passage times expressed as the coefficient of variation (CV), even if the average first-passage time is much longer than the transient. The CV has a pronounced minimum for some lengths, which we call resonant lengths. These results also suggest a simple and efficient noise control strategy and are closely related to the timing of repetitive excitations, coherence resonance, and information transmission by noisy excitable systems. A resonant number of steps from the inhibited state to the excitation threshold and slow recovery from negative feedback provide optimal timing noise reduction and information transmission. (C) 2018 Author(s). (AU)

FAPESP's process: 11/50151-0 - Dynamical phenomena in complex networks: fundamentals and applications
Grantee:Elbert Einstein Nehrer Macau
Support type: Research Projects - Thematic Grants