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A Tactile Automated Passive-Finger Stimulator TAPS
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How target distributions shape optimal stochastic resetting.

Gregorio García-Valladares1, Antonio Prados1, Alessandro Manacorda2

  • 1Universidad de Sevilla, Física Teórica, Multidisciplinary Unit for Energy Science, Apartado de Correos 1065, E-41080 Seville, Spain.

Physical Review. E
|March 20, 2026
PubMed
Summary
This summary is machine-generated.

This study optimizes search strategies in a 1D domain with boundary and bulk resetting. The optimal strategy depends on the target distribution, showing a transition in bulk resetting.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Mathematical Biology

Background:

  • Search processes are fundamental in various scientific fields.
  • Optimizing search efficiency is crucial for many applications.
  • Brownian dynamics with resetting are common models for search behavior.

Purpose of the Study:

  • To determine the optimal bulk resetting strategy for a searcher in a 1D domain.
  • To minimize the average search time by finding the optimal spatially dependent bulk resetting rate.
  • To analyze how the target's spatial distribution influences the optimal search strategy.

Main Methods:

  • Modeling the searcher's movement using Brownian dynamics.
  • Incorporating boundary resetting and spatially dependent bulk resetting.
  • Analyzing the average search time and identifying conditions for optimal resetting rates.
  • Investigating a second-order phase transition in the optimal strategy.

Main Results:

  • The optimal bulk resetting strategy exhibits a second-order phase transition.
  • The transition occurs between vanishing and nonvanishing bulk resetting rates.
  • The target distribution critically influences the optimal search strategy.
  • Mathematical criteria for optimality were derived and analyzed for various distributions.

Conclusions:

  • The target distribution is a key factor in designing optimal search strategies.
  • A novel framework for studying search processes with resetting was established.
  • This research opens new avenues for understanding and optimizing search dynamics.