首次通过程序和有针对性的资源积累
First-passage processes and the target-based accumulation of resources
摘要：
在有界域中随机搜索一个或多个目标在自然界中广泛存在，例子从动物觅食到细胞内囊泡的运输。大多数理论研究采取以搜索者为中心的观点，集中在第一通过时间（FTP）问题，以找到一个目标。这个单一的搜索和捕获事件然后触发一个下游过程，或提供一些资源，如食物。在本文中，我们采取以目标为中心的观点，通过考虑在一个或多个目标的资源积累，由于多轮的搜索和捕获事件相结合的资源退化，每当一个搜索引擎发现一个目标，它提供了一个资源包的目标，之后，它逃脱，并返回到其初始位置。然后，向该巡逻艇重新提供货物，并在随机延迟后启动新的搜索程序。它以前已经表明如何排队理论可以用来推导出一般表达式的稳态平均值和方差的资源分布。在这里，我们将理论应用到一些经典的FPT问题，涉及扩散在简单的几何形状与吸收边界，包括同心球，楔形域，和分支网络。在每种情况下，我们确定如何产生的Fano因子取决于退化率，延迟分布，和各种几何参数。因此，我们建立了Fano因子可以显着偏离泊松统计，并表现出非平凡的依赖模型参数，包括非单调性和交叉行为。这表明了资源积累的高阶统计量的非平凡性质。
英文摘要：
Random search for one or more targets in a bounded domain occurs widely in nature, with examples ranging from animal foraging to the transport of vesicles within cells. Most theoretical studies take a searcher-centric viewpoint, focusing on the first passage time (FTP) problem to find a target. This single search-and-capture event then triggers a downstream process or provides the searcher with some resource such as food. In this paper we take a target-centric viewpoint, by considering the accumulation of resources in one or more targets due to multiple rounds of search-and-capture events combined with resource degradation; whenever a searcher finds a target it delivers a resource packet to the target, after which it escapes and returns to its initial position. The searcher is then resupplied with cargo and a new search process is initiated after a random delay. It has previously been show how queuing theory can be used to derive general expressions for the steady-state mean and variance of the resulting resource distributions. Here we apply the theory to some classical FPT problems involving diffusion in simple geometries with absorbing boundaries, including concentric spheres, wedge domains, and branching networks. In each case, we determine how the resulting Fano factor depends on the degradation rate, the delay distribution, and various geometric parameters. We thus establish that the Fano factor can deviate significantly from Poisson statistics and exhibits a non-trivial dependence on model parameters, including non-monotonicity and crossover behavior. This indicates the non-trivial nature of the higher-order statistics of resource accumulation.
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