Year: 2014
Type: article
Abstract: The joint probability distribution of states of many degrees of freedom in biological systems, such as firing patterns in neural networks or antibody sequence compositions, often follows Zipf's law, where a power law is observed on a rank-frequency plot. This behavior has been shown to imply that these systems reside near a unique critical point where the extensive parts of the entropy and energy are exactly equal. Here, we show analytically, and via numerical simulations, that Zipf-like probability distributions arise naturally if there is a fluctuating unobserved variable (or variables) that affects the system, such as a common input stimulus that causes individual neurons to fire at time-varying rates. In statistics and machine learning, these are called latent-variable or mixture models. We show that Zipf's law arises generically for large systems, without fine-tuning parameters to a point. Our work gives insight into the ubiquity of Zipf's law in a wide range of systems.
Source: Physical Review Letters
Authors: David J. Schwab, Ilya Nemenman, Pankaj Mehta
Institutions: Princeton University, Emory University, Boston University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2066610273