论文标题
盒子缩放作为有限大小相关的代理
Box-scaling as a proxy of finite-size correlations
论文作者
论文摘要
相关性随系统大小的函数的缩放提供了重要的提示，以了解各种系统上的关键现象。它在生物系统中的研究提供了两个挑战：通常它们的规模不是无限的，并且在大多数情况下，尺寸不能随意变化。在这里，我们讨论了如何通过计算各种尺寸的降低视场（即“盒子尺寸”）的相关性来在固定且相对较小的实验系统中近似有限尺寸的缩放。神经元网络的数值模拟用于验证这种近似值以及铁磁2D ISING模型。数值结果支持启发式方法的有效性，这对于表征生物系统中关键现象的相关方面应该很有用。
The scaling of correlations as a function of system size provides important hints to understand critical phenomena on a variety of systems. Its study in biological systems offers two challenges: usually they are not of infinite size, and in the majority of cases sizes can not be varied at will. Here we discuss how finite-size scaling can be approximated in an experimental system of fixed and relatively small size by computing correlations inside of a reduced field of view of various sizes (i.e., "box-scaling"). Numerical simulations of a neuronal network are used to verify such approximation, as well as the ferromagnetic 2D Ising model. The numerical results support the validity of the heuristic approach, which should be useful to characterize relevant aspects of critical phenomena in biological systems.
