论文标题
首先重置的优化
Optimization in First-Passage Resetting
论文作者
论文摘要
我们使用附加的特征研究经典扩散，即每次粒子达到指定的阈值时，扩散粒子都会重置为起点。在一个无限的域中，此过程是非平稳的，其概率分布具有丰富的特征。在有限的域中，我们定义了一个非平凡的优化，其中每当粒子重置并在粒子停留在复位点附近时获得奖励时，就会产生成本。我们得出了优化该系统净收益的条件，即奖励减去成本。
We investigate classic diffusion with the added feature that a diffusing particle is reset to its starting point each time the particle reaches a specified threshold. In an infinite domain, this process is non-stationary and its probability distribution exhibits rich features. In a finite domain, we define a non-trivial optimization in which a cost is incurred whenever the particle is reset and a reward is obtained while the particle stays near the reset point. We derive the condition to optimize the net gain in this system, namely, the reward minus the cost.
