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摘要翻译：
数值模型表明，集体动物行为可能来自个体间相互作用的简单局部规则。然而，人们对这种相互作用的本质知之甚少，因此模型和理论大多依赖于先验假设。通过重建几千人的空中鸟群中单个鸟类的三维位置，我们证明了这种相互作用并不像目前大多数模型和理论所假设的那样依赖于度量距离，而是依赖于拓扑距离。事实上，我们发现每只鸟平均与固定数量的邻居（6-7只）相互作用，而不是与固定度量距离内的所有邻居相互作用。我们认为，拓扑相互作用对于保持羊群的凝聚力抵抗外部扰动（通常是捕食）引起的大密度变化是必不可少的。我们通过数值模拟支持这一假设，表明与标准度量相比，拓扑交互赋予聚合显着更高的内聚性。
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英文标题：
《Interaction Ruling Animal Collective Behaviour Depends on Topological
rather than Metric Distance: Evidence from a Field Study》
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作者：
M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I.
Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale, V.
Zdravkovic
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最新提交年份：
2007
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分类信息：
一级分类：Quantitative Biology 数量生物学
二级分类：Populations and Evolution 种群与进化
分类描述：Population dynamics, spatio-temporal and epidemiological models, dynamic speciation, co-evolution, biodiversity, foodwebs, aging; molecular evolution and phylogeny; directed evolution; origin of life
种群动力学；时空和流行病学模型；动态物种形成；协同进化；生物多样性；食物网；老龄化；分子进化和系统发育；定向进化；生命起源
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
Numerical models indicate that collective animal behaviour may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely on aprioristic assumptions. By reconstructing the three-dimensional position of individual birds in airborne flocks of few thousands members, we prove that the interaction does not depend on the metric distance, as most current models and theories assume, but rather on the topological distance. In fact, we discover that each bird interacts on average with a fixed number of neighbours (six-seven), rather than with all neighbours within a fixed metric distance. We argue that a topological interaction is indispensable to maintain flock's cohesion against the large density changes caused by external perturbations, typically predation. We support this hypothesis by numerical simulations, showing that a topological interaction grants significantly higher cohesion of the aggregation compared to a standard metric one.
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PDF链接：
https://arxiv.org/pdf/709.1916
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