论文标题
间歇性逆方面的Lévy步道对于寻找各种尺寸的目标是最佳的
Intermittent Inverse-Square Lévy Walks are Optimal for Finding Targets of All Sizes
论文作者
论文摘要
Lévy步行是随机步行过程，其步长遵循长尾式幂律分布。由于它们作为生物生物的运动模式的丰富性，因此重要的理论努力致力于确定使这种模式有利的觅食情况。但是，尽管进行了广泛的研究，但目前尚无数学证据表明，在任何方面，莱维步行在更高的维度上都比一个更高的策略更可取。在这里，我们证明，在有限的二维地形中，逆向莱维步行策略在寻找任意大小和形状的稀疏目标方面非常有效。此外，这甚至在间歇性检测的弱模型下也存在。相反，任何其他间歇性的莱维步道都无法有效地找到大型目标或小目标。我们的结果为\ emph {lévy觅食假说}提供了新的启示，因此有望影响对行动lévy步行的动物的未来实验。
Lévy walks are random walk processes whose step-lengths follow a long-tailed power-law distribution. Due to their abundance as movement patterns of biological organisms, significant theoretical efforts have been devoted to identifying the foraging circumstances that would make such patterns advantageous. However, despite extensive research, there is currently no mathematical proof indicating that Lévy walks are, in any manner, preferable strategies in higher dimensions than one. Here we prove that in finite two-dimensional terrains, the inverse-square Lévy walk strategy is extremely efficient at finding sparse targets of arbitrary size and shape. Moreover, this holds even under the weak model of intermittent detection. Conversely, any other intermittent Lévy walk fails to efficiently find either large targets or small ones. Our results shed new light on the \emph{Lévy foraging hypothesis}, and are thus expected to impact future experiments on animals performing Lévy walks.
