The inspection paradox in stochastic resetting

Pal, A.; Kostinski, Sarah; Reuveni, Shlomi

doi:10.1088/1751-8121/ac3cdf

Cited by 84 publications

(53 citation statements)

References 174 publications

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“…Our study reveals that resetting can indeed reduce the search time compared to that of the original search process. Secondly, we observe that resetting mechanism works in advantage when the fluctuations in the search time for the underlying active process is large -a robust feature that is observed quite ubiquitously (see also 62 ). We distill this core idea for the randomized/annealed initial conditions where resetting driven search always works efficiently.…”

Section: Introductionmentioning

confidence: 68%

Resetting mediated navigation of active Brownian searcher in a homogeneous topography

Sar¹,

Ray²,

Ghosh³

et al. 2022

Preprint

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Designing navigation strategies for search time optimization remains of interest in various interdisciplinary branches in science. In here, we focus on microscopic self-propelled searchers namely active Brownian walkers in noisy and confined environment which are mediated by one such autonomous strategy namely resetting. As such, resetting stops the motion and compels the walkers to restart from the initial configuration intermittently according to an external timer that do not require control by the walkers. In particular, the resetting coordinates are either quenched (fixed) or annealed (fluctuating) over the entire topography. Although the strategy relies upon simple rules, it shows a significant ramification on the search time statistics in contrast to the original search. We show that the resetting driven protocols mitigate the performance of these active searchers based, robustly, on the inherent search time fluctuations. Notably, for the annealed condition, resetting is always found to expedite the search process. These features, as well as their applicability to more general optimization problems starting from queuing systems, computer science to living systems, make resetting based strategies universally promising.

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Section: Introductionmentioning

confidence: 68%

Resetting mediated navigation of active Brownian searcher in a homogeneous topography

Sar¹,

Ray²,

Ghosh³

et al. 2022

Preprint

Self Cite

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“…B) The case of 'low-frequency resetting' which employs very large timers τ 1 -henceforth termed slow timers. As noted in the introduction, the case of low-frequency resetting attracted substantial scientific interest [38]- [48].…”

Section: Asymptotic Analysismentioning

confidence: 99%

“…This part continues with a comprehensive diversity analysis of sharp restart. Specifically, this paper shall establish a set of closed-form results that address sharp restart with: general timers; 'fast timers' that manifest high-frequency resetting; and 'slow timers' that manifest low-frequency resetting -a regime that attracted much scientific attention [38]- [48]. Moreover, this part shall further establish a set of closed-form results that determine the very existence of timers with which sharp restart either decreases or increases the diversity of task-completion durations.…”

Section: Introductionmentioning

confidence: 99%

Diversity of Sharp Restart

Eliazar¹,

Reuveni²

2022

Preprint

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When applied to a stochastic process of interest, a restart protocol alters the overall statistical distribution of the process' completion time; thus, the completion-time's mean and randomness change. The explicit effect of restart on the mean is well understood, and it is known that: from a mean perspective, deterministic restart protocols -termed sharp restartcan out-perform any other restart protocol. However, little is known on the explicit effect of restart on randomness. This paper is the second in a duo exploring the effect of sharp restart on randomness: via a Boltzmann-Gibbs-Shannon entropy analysis in the first part, and via a diversity analysis in this part. Specifically, gauging randomness via diversity -a measure that is intimately related to the Renyi entropy -this paper establishes a set of universal criteria that determine: A) precisely when a sharp-restart protocol decreases/increases the diversity of completion times; B) the very existence of sharp-restart protocols that decrease/increase the diversity of completion times. Moreover, addressing jointly mean-behavior and randomness, this paper asserts and demonstrates when sharp restart has an aligned effect on the two (decreasing/increasing both), and when the effect is antithetical (decreasing one while increasing the other). The joint mean-diversity results require remarkably little information regarding the (original) statistical distributions of completion times, and are remarkably practical and easy to implement.

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“…In the last years, resetting has been widely recognized as a simple yet effective mechanism to optimize diffusion and search processes. The effects of restart on stochastic dynamics have been considered in many branches of physics [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15], including quantum physics [16,17,18] and biophysics [19,20,21,22], but also in different fields such as computer science [23,24] and economics [25], to cite a few examples -see [26] for a review or [27] for a more recent introduction on the subject.…”

Section: Introductionmentioning

confidence: 99%

Diffusion processes with Gamma-distributed resetting and non-instantaneous returns

Radice

2022

Preprint

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We consider the dynamical evolution of a Brownian particle undergoing stochastic resetting, meaning that after random periods of time it is forced to return to the starting position. The intervals after which the random motion is stopped are drawn from a Gamma distribution of shape parameter α and scale parameter r, while the return motion is performed at constant velocity v, so that the time cost for a reset is correlated to the last position occupied during the stochastic phase. We show that for any value of α the process reaches a non-equilibrium steady state and unveil the dependence of the stationary distribution on v. Interestingly, there is a single value of α for which the steady state is unaffected by the return velocity. Furthermore, we consider the efficiency of the search process by computing explicitly the mean first passage time. All our findings are corroborated by numerical simulations.

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The inspection paradox in stochastic resetting

Cited by 84 publications

References 174 publications

Resetting mediated navigation of active Brownian searcher in a homogeneous topography

Resetting mediated navigation of active Brownian searcher in a homogeneous topography

Diversity of Sharp Restart

Diffusion processes with Gamma-distributed resetting and non-instantaneous returns

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