Box scaling as a proxy of finite size correlations

• Autores: Martin, Daniel Alejandro; Ribeiro, Tiago L.; Cannas, Sergio A.; Grigera, Tomás Sebastián; Plenz, Dietmar; Chialvo, Dante R.
• Año de publicación: 2021
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Física; Computational biology and bioinformatics; Mathematics and computing; Neuroscience; Physics; Statistical physics, thermodynamics and nonlinear dynamics
• Institución: Universidad Nacional de La Plata

The scaling of correlations as a function of size provides important hints to understand critical phenomena on a variety of systems. Its study in biological structures offers two challenges: usually they are not of infinite size, and, in the majority of cases, dimensions 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 extent, by computing correlations inside of a reduced field of view of various widths (we will refer to this procedure as "box-scaling"). A relation among the size of the field of view, and measured correlation length, is derived at, and away from, the critical regime. Numerical simulations of a neuronal network, as well as the ferromagnetic 2D Ising model, are used to verify such approximations. Numerical results support the validity of the heuristic approach, which should be useful to characterize relevant aspects of critical phenomena in biological systems.
Facultad de Ciencias Exactas
Instituto de Física de Líquidos y Sistemas Biológicos