社会互动主导了驱使自然群体走向临界状态的速度控制
Social interactions dominate speed control in driving natural flocks toward criticality
摘要：
鸟群表现出显著的协调性和集体反应。这不仅仅是因为平均而言，成千上万的个体以相同的速度朝同一方向飞行，而且即使是平均速度的波动也在长距离上相关。特别是对椋鸟群的定量测量表明，这些波动是无标度的，有效的相关长度与群的线性大小成正比。在这里，我们构建模型的联合分布的速度在羊群中，再现观察到的个人和他们的邻居之间的局部相关性，以及个体之间的飞行速度的方差，但在其他方面有尽可能少的结构。这些最小结构或最大熵模型为整个群体的相关性传播提供了定量的、无参数的预测，这些预测与数据非常吻合。这些模型在数学上等价于磁体有序化的统计物理模型，并且由于参数（完全由数据确定）处于临界状态，因此可以正确预测无标度相关性。从生物学的角度来说，临界性允许群体在有限的速度波动下实现长距离的最大相关性。
英文摘要：
Flocks of birds exhibit a remarkable degree of coordination and collective response. It is not just that thousands of individuals fly, on average, in the same direction and at the same speed, but that even the fluctuations around the mean velocity are correlated over long distances. Quantitative measurements on flocks of starlings, in particular, show that these fluctuations are scale-free, with effective correlation lengths proportional to the linear size of the flock. Here we construct models for the joint distribution of velocities in the flock that reproduce the observed local correlations between individuals and their neighbors, as well as the variance of flight speeds across individuals, but otherwise have as little structure as possible. These minimally structured, or maximum entropy models provide quantitative, parameter-free predictions for the spread of correlations throughout the flock, and these are in excellent agreement with the data. These models are mathematically equivalent to statistical physics models for ordering in magnets, and the correct prediction of scale-free correlations arises because the parameters - completely determined by the data - are in the critical regime. In biological terms, criticality allows the flock to achieve maximal correlation across long distances with limited speed fluctuations.
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