标题： 群体回避的通用重置理论 显示英文标题

标题： General Resetting Theory for Group Avoidance

摘要： 我们提出了一种用于多智能体系统在漂移势中的群体重置动力学的一般理论框架。 这种设置与典型的重置问题形成对比，后者涉及一个搜索者寻找目标，传统上研究重置是为了优化找到目标的搜索时间。 最近，重置也被用作一种调节机制，以避免不利结果，例如防止大坝中水位过高或减少金融投资组合的杠杆率。 在这里，我们将当前的重置理论扩展到群体动力学，应用范围从抗生素压力下的细菌进化到多搜索者优化算法。 我们的框架结合了极值统计和更新理论，从中推导出一组搜索者的质心分布的主方程。 这个主方程使我们能够解析地计算基本可观测量。 例如，群体的平均位置如何依赖于群体大小、重置速率、漂移势强度和扩散常数。 这种理论方法为通过重置优化群体搜索和调节机制提供了新的视角。 显示英文摘要

摘要： We present a general theoretical framework for group resetting dynamics in multi-agent systems in a drift potential. This setup contrasts with a typical resetting problem that involves a single searcher looking for a target, with resetting traditionally studied to optimize the search time to a target. More recently, resetting has also been used as a regulatory mechanism to avoid adverse outcomes, such as preventing critically high water levels in dams or deleveraging financial portfolios. Here, we extend current resetting theories to group dynamics, with applications ranging from bacterial evolution under antibiotic pressure to multiple-searcher optimization algorithms. Our framework incorporates extreme value statistics and renewal theory, from which we derive a master equation for the center of mass distribution of a group of searchers. This master equation allows us to calculate essential observables analytically. For example, how the group's average position depends on group size, resetting rates, drift potential strength, and diffusion constants. This theoretical approach offers a new perspective on optimizing group search and regulatory mechanisms through resetting.