Abstract

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.

Details

Title
Box scaling as a proxy of finite size correlations
Author
Martin, Daniel A 1 ; Ribeiro, Tiago L 2 ; Cannas, Sergio A 3 ; Grigera, Tomas S 4 ; Plenz Dietmar 2 ; Chialvo, Dante R 5 

 Universidad Nacional de Gral. San Martín, Instituto de Ciencias Físicas (ICIFI-CONICET), Center for Complex Systems and Brain Sciences (CEMSC3), Escuela de Ciencia y Tecnología, San Martín, Argentina; Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires, Argentina (GRID:grid.423606.5) (ISNI:0000 0001 1945 2152) 
 Section on Critical Brain Dynamics, National Institute of Mental Health, National Institutes of Health, Bethesda, USA (GRID:grid.416868.5) (ISNI:0000 0004 0464 0574) 
 Universidad Nacional de Córdoba, Instituto de Física Enrique Gaviola (IFEG-CONICET), Facultad de Matemática Astronomía Física y Computación, Córdoba, Argentina (GRID:grid.10692.3c) (ISNI:0000 0001 0115 2557); Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires, Argentina (GRID:grid.423606.5) (ISNI:0000 0001 1945 2152) 
 Universidad Nacional de La Plata, Instituto de Física de Líquidos y Sistemas Biológicos (IFLySiB-CONICET), La Plata, Argentina (GRID:grid.9499.d) (ISNI:0000 0001 2097 3940); Universidad Nacional de La Plata, Departamento de Física, Facultad de Ciencias Exactas, La Plata, Argentina (GRID:grid.9499.d) (ISNI:0000 0001 2097 3940); Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires, Argentina (GRID:grid.423606.5) (ISNI:0000 0001 1945 2152) 
 Universidad Nacional de Gral. San Martín, Instituto de Ciencias Físicas (ICIFI-CONICET), Center for Complex Systems and Brain Sciences (CEMSC3), Escuela de Ciencia y Tecnología, San Martín, Argentina (GRID:grid.416868.5); Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires, Argentina (GRID:grid.423606.5) (ISNI:0000 0001 1945 2152) 
Publication year
2021
Publication date
2021
Publisher
Nature Publishing Group
e-ISSN
20452322
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2558266546
Copyright
© The Author(s) 2021. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.