论文标题
部分可观测时空混沌系统的无模型预测
A spectrum of complexity uncovers Dunbar's number and other leaps in social structure
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Social dynamics are shaped by each person's actions, as well as by collective trends that emerge when individuals are brought together. These latter kind of influences escape anyone's control. They are, instead, dominated by aggregate societal properties such as size, polarization, cohesion, or hierarchy. Such features add nuance and complexity to social structure, and might be present, or not, for societies of different sizes. How do societies become more complex? Are there specific scales at which they are reorganized into emergent entities? In this paper we introduce the {\em social complexity spectrum}, a methodological tool, inspired by theoretical considerations about dynamics on complex networks, that addresses these questions empirically. We use as a probe a sociolinguistic process that has unfolded over decades within the north-western Spanish region of Galicia, across populations of varied sizes. We estimate how societal complexity increases monotonously with population size; and how specific scales stand out, at which complexity would build up faster. These scales are noted as dips in our spectra, similarly to missing wavelengths in light spectroscopy. Also, `red-' and `blue-shifts' take place as the general population shifted from more rural to more urban settings. These shifts help us sharpen our observations. Besides specific results around social complexity build-up, our work introduces a powerful tool to be applied in further study cases.
