Target search optimization by threshold resetting

ArXiv ID: 2504.13501 “View on arXiv”

Authors: Unknown

Abstract

We introduce a new class of first passage time optimization driven by threshold resetting, inspired by many natural processes where crossing a critical limit triggers failure, degradation or transition. In here, search agents are collectively reset when a threshold is reached, creating event-driven, system-coupled simultaneous resets that induce long-range interactions. We develop a unified framework to compute search times for these correlated stochastic processes, with ballistic- and diffusive- searchers as key examples uncovering diverse optimization behaviors. A cost function, akin to breakdown penalties, reveals that optimal resetting can forestall larger losses. This formalism generalizes to broader stochastic systems with multiple degrees of freedom.

Keywords: First Passage Time, Threshold Resetting, Stochastic Processes, Search Theory, Optimal Stopping, Abstract/Methodological

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats
  • Why: The paper is mathematically dense, featuring advanced stochastic processes, Laplace transforms, and detailed derivations for a generalized framework. It lacks empirical implementation details, backtesting, or data-driven validation, relying purely on theoretical analysis and simulation results.
  flowchart TD
    A["Research Goal<br>Optimize First Passage Time via<br>Threshold Resetting Mechanisms"] --> B["Methodology<br>Unified Framework for<br>Correlated Stochastic Processes"]
    
    B --> C["Key Inputs<br>Search Agent Type: Ballistic/Diffusive<br>Threshold Value H<br>Reset Rate Parameter r"]
    
    C --> D["Computational Process<br>1. Derive coupled reset dynamics<br>2. Compute mean first passage time<br>3. Analyze steady-state distribution<br>4. Apply cost function for penalties"]
    
    D --> E["Key Findings<br>• System-coupled simultaneous resets induce long-range interactions<br>• Optimal resetting prevents larger breakdown losses<br>• Unified theory generalizes to multi-degree systems<br>• Reveals diverse optimization behaviors"]