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The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…

Physics and Society · Physics 2025-08-28 Yanguang Chen

In this work, we develop a general method for estimating the Shannon entropy of a bidimensional sequence based on the extrapolation of block entropies. We apply this method to analyse the spatial configurations of cities of different…

Physics and Society · Physics 2024-09-04 E. Brigatti , V. M. Netto , F. N. M. de Sousa Filho , C. Cacholas

Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…

Statistical Mechanics · Physics 2025-06-16 Fabian Coupette , Tanja Schilling

Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…

Statistical Mechanics · Physics 2008-01-13 Richard A. Neher , Klaus Mecke , Herbert Wagner

We study the scaling of (i) numbers of workers and aggregate incomes by occupational categories against city size, and (ii) total incomes against numbers of workers in different occupations, across the functional metropolitan areas of…

Physics and Society · Physics 2019-10-17 Somwrita Sarkar , Elsa Arcaute , Erez Hatna , Tooran Alizadeh , Glen Searle , Michael Batty

Understanding urban form is crucial for sustainable urban planning and enhancing quality of life. This study presents a data-driven framework to systematically identify and compare urban typologies across geographically and culturally…

Computers and Society · Computer Science 2025-05-07 Arthur Carmès , Léo Catteau , Andrew Sonta , Arash Tavakoli

Percolation has long served as a model for diverse phenomena and systems. The percolation transition, that is, the formation of a giant cluster on a macroscopic scale, is known as one of the most robust continuous transitions. Recently,…

Statistical Mechanics · Physics 2016-12-08 Deokjae Lee , Young Sul Cho , Byungnam Kahng

The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…

Machine Learning · Statistics 2016-10-20 Xiurui Geng , Hairong Tang

We investigate urban street networks as a whole within the frameworks of information physics and statistical physics. Urban street networks are envisaged as evolving social systems subject to a Boltzmann-mesoscopic entropy conservation. For…

Physics and Society · Physics 2019-07-18 Jerome Benoit , Saif Eddin Jabari

Migration is central in various societal problems related to socioeconomic development. While much of the existing research has focused on international migration, migration patterns within a single country remain relatively unexplored. In…

Physics and Society · Physics 2025-07-16 Thomas Robiglio , Martina Contisciani , Márton Karsai , Tiago P. Peixoto

Cities are often compared through scaling laws, usually expressed as power-law relations between population size and aggregate urban quantities related to infrastructure, socioeconomic activity, or environmental impacts. These laws are…

Physics and Society · Physics 2026-05-19 Ulysse Marquis , Marc Barthelemy

We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which…

Statistical Mechanics · Physics 2020-05-07 Claudio Castellano , Romualdo Pastor-Satorras

Understanding how size influences the internal characteristics of a system is a crucial concern across various fields. Concepts like scale invariance, universalities, and fractals are fundamental to this inquiry and find application in…

Physics and Society · Physics 2024-04-04 Fabiano L. Ribeiro , Vinicius M. Netto

Cities are typical dynamic complex systems that connect people and facilitate interactions. Revealing universal collective patterns behind spatio-temporal interactions between residents is crucial for various urban studies, of which we are…

Physics and Society · Physics 2024-06-11 Chenxin Liu , Yu Yang , Bingsheng Chen , Tianyu Cui , Fan Shang , Jingfang Fan , Ruiqi Li

The emergence of interconnected urban networks is a crucial feature of globalisation processes. Understanding the drivers behind the growth of such networks - in particular urban firm networks -, is essential for the economic resilience of…

Physics and Society · Physics 2020-09-14 Juste Raimbault , Natalia Zdanowska , Elsa Arcaute

The structure of interconnected systems and its impact on the system dynamics is a much-studied cross-disciplinary topic. Although various critical phenomena have been found in different models, the study on the connections between…

Statistical Mechanics · Physics 2020-08-03 Ming Li , Linyuan Lü , Youjin Deng , Mao-Bin Hu , Hao Wang , Matúš Medo , H. Eugene Stanley

We present a novel analytical framework to examine socio-spatial segregation across multiple spatial scales, explicitly leveraging information theory and percolation theory. This framework emphasizes the interplay between regional…

Physics and Society · Physics 2025-05-22 Mateo Neira , Valentina Marin , Elsa Arcaute

Robust and efficient design of networks on a realistic geographical space is one of the important issues for the realization of dependable communication systems. In this paper, based on a percolation theory and a geometric graph property,…

Data Analysis, Statistics and Probability · Physics 2011-11-04 Yukio Hayashi

Floods affected more than 2 billion people worldwide from 1998 to 2017 and their occurrence is expected to increase due to climate warming, population growth and rapid urbanization. Recent approaches for understanding the resilience of…

Physics and Society · Physics 2022-02-03 Simone Loreti , Enrico Ser-Giacomi , Andreas Zischg , Margreth Keiler , Marc Barthelemy

Collective phenomena emerge from the interaction of natural or artificial units with a complex organization. The interplay between structural patterns and dynamics might induce functional clusters that, in general, are different from…

Physics and Society · Physics 2017-04-25 Manlio De Domenico