Cavagna Andrea, Del Castello Lorenzo, Dey Supravat, Giardina Irene, Melillo Stefania, Parisi Leonardo, Viale Massimiliano
Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy.
Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Jul;92(1):012705. doi: 10.1103/PhysRevE.92.012705. Epub 2015 Jul 6.
Bird flocks are a paradigmatic example of collective motion. One of the prominent traits of flocking is the presence of long range velocity correlations between individuals, which allow them to influence each other over the large scales, keeping a high level of group coordination. A crucial question is to understand what is the mutual interaction between birds generating such nontrivial correlations. Here we use the maximum entropy (ME) approach to infer from experimental data of natural flocks the effective interactions between individuals. Compared to previous studies, we make a significant step forward as we retrieve the full functional dependence of the interaction on distance, and find that it decays exponentially over a range of a few individuals. The fact that ME gives a short-range interaction even though its experimental input is the long-range correlation function, shows that the method is able to discriminate the relevant information encoded in such correlations and single out a minimal number of effective parameters. Finally, we show how the method can be used to capture the degree of anisotropy of mutual interactions.
鸟群是集体运动的一个典型例子。集群的一个突出特征是个体之间存在长程速度关联，这使它们能够在大尺度上相互影响，保持高度的群体协调性。一个关键问题是要理解产生这种非平凡关联的鸟类之间的相互作用是什么。在这里，我们使用最大熵（ME）方法从自然鸟群的实验数据中推断个体之间的有效相互作用。与之前的研究相比，我们向前迈出了重要一步，因为我们获得了相互作用对距离的完整函数依赖关系，并发现它在几个个体的范围内呈指数衰减。尽管ME的实验输入是长程关联函数，但它给出了短程相互作用，这一事实表明该方法能够区分编码在这种关联中的相关信息，并挑选出最少数量的有效参数。最后，我们展示了该方法如何用于捕捉相互作用的各向异性程度。
