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Resetting can optimize complex processes by considering both the mean and coefficient of variation of conditional times. This helps determine when resetting expedites specific outcomes and influences outcome preference in diffusion processes.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Stochastic Processes

Background:

  • Resetting is crucial for optimizing completion times in complex first-passage processes.
  • A coefficient of variation greater than unity is generally needed for resetting to be beneficial across all outcomes.
  • The benefit of resetting for specific outcomes, however, requires a more nuanced condition.

Purpose of the Study:

  • To derive a universal condition for when resetting expedites a selective outcome.
  • To establish how mean and coefficient of variation of conditional times govern outcome biasing.
  • To demonstrate this universality in a one-dimensional diffusion process with two absorbing boundaries.

Main Methods:

  • Analysis of first-passage times in stochastic processes with resetting.
  • Derivation of conditional statistical metrics (mean and coefficient of variation).
  • Mathematical modeling of a one-dimensional diffusion process with resetting and two absorbing boundaries.

Main Results:

  • A universal condition for beneficial resetting on selective outcomes is derived.
  • The interplay between the mean and coefficient of variation of conditional times dictates resetting's efficacy.
  • Resetting can bias outcomes between preferential and non-preferential pathways.

Conclusions:

  • The study provides a universal framework for understanding resetting in first-passage processes.
  • Conditional statistical metrics are key to optimizing specific outcomes and managing outcome bias.
  • Findings are validated for a fundamental diffusion model, highlighting broad applicability.