Optimal threshold resetting in collective diffusive search

Paper: arXiv 2603.25338

Authors: Arup Biswas, Satya N Majumdar, Arnab Pal

Abstract

Stochastic resetting has attracted significant attention in recent years due to its wide-ranging applications across physics, biology, and search processes. In most existing studies, however, resetting events are governed by an external timer and remain decoupled from the system’s intrinsic dynamics. In a recent Letter by Biswas et al, we introduced threshold resetting (TR) as an alternative, event-driven optimization strategy for target search problems. Under TR, the entire process is reset whenever any searcher reaches a prescribed threshold, thereby coupling the resetting mechanism directly to the internal dynamics. In this work, we study TR-enabled search by $N$ non-interacting diffusive searchers in a one-dimensional box $[0,L]$, with the target at the origin and the threshold at $L$. By optimally tuning the scaled threshold distance $u = x_0/L$, the mean first-passage time can be significantly reduced for $N \geq 2$. We identify a critical population size $N_c(u)$ below which TR outperforms reset-free dynamics. Furthermore, for fixed $u$, the mean first-passage time depends non-monotonically on $N$, attaining a minimum at $N_{\mathrm{opt}}(u)$. We also quantify the achievable speed-up and analyze the operational cost of TR, revealing a nontrivial optimization landscape. These findings highlight threshold resetting as an efficient and realistic optimization mechanism for complex stochastic search processes.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical and mathematical framework for event-driven threshold resetting in diffusive search processes using first-passage time analysis. However, as a purely theoretical statistical physics paper, it completely lacks empirical backtesting, financial datasets, or market-based verification required for high empirical rigor in quant finance.

Research Flowchart

  flowchart TD
    A["Research Goal: Optimize Target Search via Event-Driven Threshold Resetting (TR)"] --> B["System Model: N Non-interacting 1D Diffusive Searchers in Box [0,L]"]
    B --> C["Data & Inputs: Initial Position x₀, Target at 0, Threshold at L, Scaled Distance u = x₀/L"]
    C --> D["Computational Analysis: Calculate Mean First-Passage Time (MFPT) & Operational Costs"]
    D --> E["Key Finding 1: TR reduces MFPT for N ≥ 2 and outperforms reset-free search below N_c(u)"]
    D --> F["Key Finding 2: Non-monotonic MFPT dependence on N, achieving optimal speed-up at N_opt(u)"]

Cited References (344)

1. The Distribution and Frequency of Record Values (1952)
2. Broad distributions of sliding times are fingerprints of efficient target search on DNA (2026)
3. Record statistics of a strongly correlated time series: random walks and Lévy flights (2017)
4. Optimization in first-passage resetting (2020)
5. Random walks on complex networks with first-passage resetting (2021)
6. A first passage under resetting approach to income dynamics (2023)
7. First passage time approach to diffusion controlled reactions (1980)
8. Aviation automation: The search for a human-centered approach (2018)

1 of 344 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.