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Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…

Disordered Systems and Neural Networks · Physics 2015-06-25 Albert-Laszlo Barabasi , Reka Albert

Dynamical universality plays a fundamental role in understanding the scaling properties of critical dynamics, including absorbing phase transitions and physical aging. Although individual universality classes have been extensively studied,…

Statistical Mechanics · Physics 2025-03-10 Rong Li , Qirui Ding , Weicheng Cui

We show that an equilibriumlike additivity property can remarkably lead to power-law distributions observed frequently in a wide class of out-of-equilibrium systems. The additivity property can determine the full scaling form of the…

Statistical Mechanics · Physics 2015-12-17 Arghya Das , Sayani Chatterjee , Punyabrata Pradhan , P. K. Mohanty

Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…

Statistical Mechanics · Physics 2026-02-23 Edson D. Leonel , Diego F. M. Oliveira

Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…

Physics and Society · Physics 2022-06-07 Jinkui Zhao

In nature or societies, the power-law is present ubiquitously, and then it is important to investigate the mathematical characteristics of power-laws in the recent era of big data. In this paper we prove the superposition of non-identical…

Statistics Theory · Mathematics 2018-04-18 Masaru Shintani , Ken Umeno

We study universal traits which emerge both in real-world complex datasets, as well as in artificially generated ones. Our approach is to analogize data to a physical system and employ tools from statistical physics and Random Matrix Theory…

Machine Learning · Computer Science 2024-04-08 Noam Levi , Yaron Oz

Models of how things spread often assume that transmission mechanisms are fixed over time. However, social contagions--the spread of ideas, beliefs, innovations--can lose or gain in momentum as they spread: ideas can get reinforced, beliefs…

In this paper we study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction…

Disordered Systems and Neural Networks · Physics 2015-06-04 D. P. Almond , C. J. Budd , M. A. Freitag , G. W. Hunt , N. J. McCullen , N. D. Smith

Recently, a novel model to describe ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ``+'' or ``-'', ``up'' or ``down'', ``yes'' or ``no''), still differing in…

Statistical Mechanics · Physics 2024-09-25 M. Krasnytska

This Thesis explores how tools from Statistical Physics and Information Theory can help us describe and understand complex systems. In the first part, we study the interplay between internal interactions, environmental changes, and…

Statistical Mechanics · Physics 2023-03-01 Giorgio Nicoletti

We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real-world networks. We first provide a rigorous definition of power-law distributions, equivalent to the definition of regularly varying…

Physics and Society · Physics 2019-10-23 Ivan Voitalov , Pim van der Hoorn , Remco van der Hofstad , Dmitri Krioukov

Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in…

Machine Learning · Computer Science 2022-11-01 Alexander Maloney , Daniel A. Roberts , James Sully

Unveiling universal non-equilibrium scaling laws has been a central theme in modern statistical physics, with recent attention increasingly directed toward non-equilibrium phases that exhibit rich dynamical phenomena. A striking example…

Statistical Mechanics · Physics 2025-12-15 Shuoguang Liu , Peter B. Littlewood , Ryo Hanai

We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with…

Statistical Mechanics · Physics 2025-03-12 Nicolas Nessi

We study the emergence of a power law distribution in the systems which can be characterized by a hierarchically organized supplying network. It is shown that conservation laws on the branches of the network can, at some approximation,…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 V. Gafiychuk , I. Lubashevsky , A. Stosyk

We have investigated scaling properties of the Aubry-Andr\'e model and related one-dimensional quasiperiodic Hamiltonians near their localisation transitions. We find numerically that the scaling of characteristic energies near the ground…

Disordered Systems and Neural Networks · Physics 2018-10-09 Attila Szabó , Ulrich Schneider

The study of complex networks has pursued an understanding of macroscopic behavior by focusing on power-laws in microscopic observables. Here, we uncover two universal fundamental physical principles that are at the basis of complex…

Physics and Society · Physics 2015-09-16 Tom Lorimer , Florian Gomez , Ruedi Stoop

Power-law scaling in coarse-grained data suggests critical dynamics, but the true source of this scaling often remains unclear. Here, we analyze neural activity recorded during spatial navigation, reproducing power-law scaling under a…

Neurons and Cognition · Quantitative Biology 2025-08-01 John J. Briguglio , Jaesung Lee , Albert K. Lee , Vincent Hakim , Sandro Romani

How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…

Social and Information Networks · Computer Science 2026-03-24 Upasana Dutta , Alexander Ray , Aaron Clauset