First passages for a search by a swarm of independent random searchers

Mejía‐Monasterio, Carlos; Oshanin, Gleb; Schehr, Grégory

doi:10.1088/1742-5468/2011/06/p06022

Cited by 132 publications

(188 citation statements)

References 93 publications

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“…In these settings basic goals are to maximize the probability that the target is actually found and to minimize the time and/or the cost required to find the target. In response to these challenges, a wide variety of search algorithms have been extensively investigated and rich dynamical behaviors have been uncovered [14,15].…”

Section: Introductionmentioning

confidence: 99%

Stochastic search with Poisson and deterministic resetting

Bhat¹,

Bacco²,

Redner³

2016

J. Stat. Mech.

140

136

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Abstract.We investigate a stochastic search process in one, two, and three dimensions in which N diffusing searchers that all start at x 0 seek a target at the origin. Each of the searchers is also reset to its starting point, either with rate r, or deterministically, with a reset time T . In one dimension and for a small number of searchers, the search time and the search cost are minimized at a non-zero optimal reset rate (or time), while for sufficiently large N , resetting always hinders the search. In general, a single searcher leads to the minimum search cost in one, two, and three dimensions. When the resetting is deterministic, several unexpected feature arise for N searchers, including the search time being independent of T for 1/T → 0 and the search cost being independent of N over a suitable range of N . Moreover, deterministic resetting typically leads to a lower search cost than in stochastic resetting.

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Section: Introductionmentioning

confidence: 99%

Stochastic search with Poisson and deterministic resetting

Bhat¹,

Bacco²,

Redner³

2016

J. Stat. Mech.

140

136

View full text Add to dashboard Cite

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“…In this case the random variable of interest, the first passage time τ to, e.g., a boundary, a target chemical group, a binding site on the surface of the domain or elsewhere within the domain, etc., has a distribution Ψ(τ ) of the generic, generalized inverse Gaussian form (see e.g., the discussion in Ref. [15] and references therein)…”

Section: Introductionmentioning

confidence: 99%

First passages in bounded domains: When is the mean first passage time meaningful?

et al. 2012

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We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we obtain the probability P (ω) distribution of the random variable ω = τ1/(τ1 +τ2), which is a measure for how similar the first passage times τ1 and τ2 are of two independent realisations of a Brownian walk starting at the same location. We construct a chart for each domain, determining whether P (ω) represents a unimodal, bell-shaped form, or a bimodal, M-shaped behavior. While in the former case the mean first passage time (MFPT) is a valid characteristic of the first passage behavior, in the latter case it is an insufficient measure for the process. Strikingly we find a distinct turnover between the two modes of P (ω), characteristic for the domain shape and the respective location of absorbing and reflective boundaries. Our results demonstrate that large fluctuations of the first passage times may occur frequently in twodimensional domains, rendering quite vague the general use of the MFPT as a robust measure of the actual behavior even in bounded domains, in which all moments of the first passage distribution exist.

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“…In contrast, research on foraging efficiency has focused largely on independent individuals [19][20][21][22][23][24][25], or on comparing foraging behavior across species [26]. In addition, recent theoretical work [27] has focused on the statistics of a population of independent random walkers, but an interaction mechanism, and its influence on search efficiency, has not been thoroughly studied.…”

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confidence: 99%

Optimizing the Search for Resources by Sharing Information: Mongolian Gazelles as a Case Study

et al. 2013

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We investigate the relationship between communication and search efficiency in a biological context by proposing a model of Brownian searchers with long-range pairwise interactions. After a general study of the properties of the model, we show an application to the particular case of acoustic communication among Mongolian gazelles, for which data are available, searching for good habitat areas. Using Monte Carlo simulations and density equations, our results point out that the search is optimal (i.e. the mean first hitting time among searchers is minimum) at intermediate scales of communication, showing that both an excess and a lack of information may worsen it. [7,8], and to pool information on resource locations when no single individual is sufficiently knowledgeable [9][10][11][12][13]. Communication among individuals frequently leads to group formation [14], which often has clear direct benefits such as reducing individual vulnerability to predators. Such strategies may, however, also have important incidental benefits. For example, an individual that has found a good foraging patch might try to attract conspecifics to reduce its risk of predation, but also provides its conspecifics with information on the location of good forage, thus increasing the foraging efficiency of those responding to the call.A variety of mammalian species are known to communicate acoustically over distances of up to several kilometers [3,15,16], but while group formation via vocalizations has been well studied [3,17,18], incidental benefits such as increased foraging efficiency have received little research attention. In contrast, research on foraging efficiency has focused largely on independent individuals [19][20][21][22][23][24][25], or on comparing foraging behavior across species [26]. In addition, recent theoretical work [27] has focused on the statistics of a population of independent random walkers, but an interaction mechanism, and its influence on search efficiency, has not been thoroughly studied. To date, very few models have examined the potential effect that long-distance communication [28]

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First passages for a search by a swarm of independent random searchers

Cited by 132 publications

References 93 publications

Stochastic search with Poisson and deterministic resetting

Stochastic search with Poisson and deterministic resetting

First passages in bounded domains: When is the mean first passage time meaningful?

Optimizing the Search for Resources by Sharing Information: Mongolian Gazelles as a Case Study

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