Box-scaling as a proxy of finite-size correlations

TL;DR

This paper proposes a method called box-scaling to approximate finite-size correlations in small biological systems by analyzing correlations within variable-sized subregions, validated through simulations of neuronal networks and the 2D Ising model.

Contribution

It introduces a novel heuristic approach to study finite-size correlations in fixed-size biological systems, bridging a gap in critical phenomena analysis.

Findings

Numerical simulations support the validity of box-scaling as an approximation.

The method is applicable to biological systems where size variation is limited.

Results align with established models like the 2D Ising model.

Abstract

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.