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Optimal Non-Markovian Search Strategies with n-Step Memory

Hugues Meyer and Heiko Rieger
Phys. Rev. Lett. 127, 070601 – Published 10 August 2021
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Abstract

Stochastic search processes are ubiquitous in nature and are expected to become more efficient when equipped with a memory, where the searcher has been before. A natural realization of a search process with long-lasting memory is a migrating cell that is repelled from the diffusive chemotactic signal that it secretes on its way, denoted as an autochemotactic searcher. To analyze the efficiency of this class of non-Markovian search processes, we present a general formalism that allows one to compute the mean first-passage time (MFPT) for a given set of conditional transition probabilities for non-Markovian random walks on a lattice. We show that the optimal choice of the n-step transition probabilities decreases the MFPT systematically and substantially with an increasing number of steps. It turns out that the optimal search strategies can be reduced to simple cycles defined by a small parameter set and that mirror-asymmetric walks are more efficient. For the autochemotactic searcher, we show that an optimal coupling between the searcher and the chemical reduces the MFPT to 1/3 of the one for a Markovian random walk.

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  • Received 21 May 2021
  • Revised 19 July 2021
  • Accepted 22 July 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.070601

© 2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Hugues Meyer* and Heiko Rieger

  • Department of Theoretical Physics and Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany

  • *Corresponding author. hugues.meyer@uni-saarland.de

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Issue

Vol. 127, Iss. 7 — 13 August 2021

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