2021
DOI: 10.1088/1751-8121/ac16c5
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Mean-performance of sharp restart: II. Inequality roadmap

Abstract: Restarting a deterministic process always impedes its completion. However, it is known that restarting a random process can lead to an opposite outcome—expediting completion. Hence, the effect of restart is contingent on the underlying statistical heterogeneity of the process’ completion times. To quantify this heterogeneity we introduce a novel approach to restart research: the methodology of inequality indices, which is widely applied in economics and in the social sciences to measure income and wealth dispa… Show more

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Cited by 11 publications
(18 citation statements)
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“…In turn, various statistics of the output can be further calculated, e.g. : the output's mean (which was the focus of the studies [18]- [19]), as well as higher-order moments of the output; the output's Boltzmann-Gibbs-Shannon entropy (which was the focus of the first part of this duo [1]); and the output's diversity (which is the focus of this paper). So, why bother with the mean-performance analyses of [18]- [19], and with the randomness analyses of this duo?…”
Section: Raison D'êtrementioning
confidence: 99%
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“…In turn, various statistics of the output can be further calculated, e.g. : the output's mean (which was the focus of the studies [18]- [19]), as well as higher-order moments of the output; the output's Boltzmann-Gibbs-Shannon entropy (which was the focus of the first part of this duo [1]); and the output's diversity (which is the focus of this paper). So, why bother with the mean-performance analyses of [18]- [19], and with the randomness analyses of this duo?…”
Section: Raison D'êtrementioning
confidence: 99%
“…As established in the mean-performance analyses of [18]- [19] and in the entropy analysis of [1], and as shall be established here: 'standing on the shoulders' of Eq. ( 1), it is possible to construct highly insightful and highly implementable results that altogether circumvent the need to use Eq.…”
Section: Raison D'êtrementioning
confidence: 99%
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“…Among general restart protocols, sharp restart assumes center stage due to the following key fact: from a mean-performance perspective, sharp restart can out-perform any other restart protocol [2,3]. A comprehensive mean-performance analysis of sharp restart was established and presented in [18,19].…”
Section: Introductionmentioning
confidence: 99%
“…In essence, a similar situation holds with regard to sharp restart. Indeed, equipped only with a mean-performance analysis of sharp restart [18,19], we are completely 'in the dark' with regard to the effect of sharp restart on randomness. Namely, we do not know if the application of sharp restart decreases or increases the inherent randomness of task-completion durations.…”
Section: Introductionmentioning
confidence: 99%