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The presented model provides an explanation to several empirically observed phenomena in spatial economics. By representing the system as a complex network of fixed-size land areas connected by trade between harbored activities, city size…

Statistical Mechanics · Physics 2007-05-23 Claes Andersson , Alexander Hellervik , Kristian Lindgren

Usually, the study of city population distribution has been reduced to power laws. In such analysis, a common practice is to consider cities with more than one hundred thousand inhabitants. Here, we argue that the distribution of cities for…

Statistical Mechanics · Physics 2009-11-07 L. C. Malacarne , R. S. Mendes , E. K. Lenzi

The share of the world population living in cities with more than one million people rose from 11% in 1975 to 24% in 2025 (our estimates). Will this trend towards greater concentration in large cities continue or level off? We introduce two…

Physics and Society · Physics 2026-03-31 Andrea Musso , Diego Rybski , Dirk Helbing , Frank Neffke

We introduce a model in which city populations grow at rates proportional to the area of their "sphere of influence", where the influence of a city depends on its population (to power \alpha) and distance from city (to power -\beta) and…

Physics and Society · Physics 2012-09-25 David Aldous , Bowen Huang

Clustering algorithms aim to organize data into groups or clusters based on the inherent patterns and similarities within the data. They play an important role in today's life, such as in marketing and e-commerce, healthcare, data…

Machine Learning · Computer Science 2024-01-17 Hui Yin , Amir Aryani , Stephen Petrie , Aishwarya Nambissan , Aland Astudillo , Shengyuan Cao

Population displacement is a housing-related involuntary residential dislocation. It has become increasingly widespread in many cities, particularly in neighbourhoods undergoing rapid economic and demographic change, and measuring it is…

Computational Geometry · Computer Science 2026-04-15 Rita Rodríguez Vázquez , Manuel Cuerno

We propose a metapopulation version of the Schelling model where two kinds of agents relocate themselves, with unconstrained destination, if their local fitness is lower than a tolerance threshold. We show that, for small values of the…

Physics and Society · Physics 2015-05-05 Floriana Gargiulo , Yerali Gandica , Timoteo Carletti

Barriers in cities, such as administrative boundaries, natural obstacles, railways or major roads are thought to induce segregation. However, the empirical knowledge about this phenomenon is limited. Here, we present a network science…

Physics and Society · Physics 2025-08-13 Gergő Pintér , Balázs Lengyel

The patterns of particulate matter with diameters that are generally 2.5 micrometers and smaller (PM2.5) are heterogeneous in China nationwide but can be homogeneous region-wide. To reduce the adverse effects from PM2.5, policymakers need…

Applications · Statistics 2023-11-07 Tingyin Wang , Xueqin Wang , Xiaobo Guo , Heping Zhang

Scaling laws are powerful summaries of the variations of urban attributes with city size. However, the validity of their universal meaning for cities is hampered by the observation that different scaling regimes can be encountered for the…

Physics and Society · Physics 2016-06-15 Clementine Cottineau , Erez Hatna , Elsa Arcaute , Michael Batty

We show here that population growth, resolved at the county level, is spatially heterogeneous both among and within the U.S. metropolitan statistical areas. Our analysis of data for over 3,100 U.S. counties reveals that annual population…

Physics and Society · Physics 2022-10-11 Sandro M. Reia , P. Suresh C. Rao , Marc Barthelemy , Satish V. Ukkusuri

Urban space is highly heterogeneous, with population and human activities concentrating in localized centers. However, the global organization of such intra-urban centers remains poorly understood due to the lack of consistent, comparable…

Physics and Society · Physics 2026-01-21 Shuai Pang , Junlong Zhang , Yu Liu , Lei Dong

The behaviour and functioning of a variety of complex physical and biological systems depend on the spatial organisation of their constituent units, and on the presence and formation of clusters of functionally similar or related…

Physics and Society · Physics 2023-08-16 Silvia Rognone , Vincenzo Nicosia

Social media outlets such as Twitter constitute valuable data sources for understanding human activities in the virtual world from a geographic perspective. This paper examines spatial distribution of tweets and densities within cities. The…

Physics and Society · Physics 2020-09-04 Bin Jiang , Ding Ma , Junjun Yin , Mats Sandberg

Self-organisation in territories leads to the emergence of patterns in urban systems that shape the interactions between cities, resulting in a hierarchical organisation. Governance follows as well a hierarchical structure, breaking the…

Physics and Society · Physics 2023-02-13 Valentina Marin , Carlos Molinero , Elsa Arcaute

Given an underlying graph, we consider the following \emph{dynamics}: Initially, each node locally chooses a value in $\{-1,1\}$, uniformly at random and independently of other nodes. Then, in each consecutive round, every node updates its…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-07-26 Luca Becchetti , Andrea Clementi , Emanuele Natale , Francesco Pasquale , Luca Trevisan

Scatterplots are used for a variety of visual analytics tasks, including cluster identification, and the visual encodings used on a scatterplot play a deciding role on the level of visual separation of clusters. For visualization designers,…

Human-Computer Interaction · Computer Science 2020-09-22 Ghulam Jilani Quadri , Paul Rosen

Motivated by empirical evidence on the interplay between geography, population density and societal interaction, we propose a generative process for the evolution of social structure in cities. Our analytical and simulation results predict…

Physics and Society · Physics 2013-06-12 Wei Pan , Gourab Ghoshal , Coco Krumme , Manuel Cebrian , Alex Pentland

Individual participants in human society collectively exhibit aggregation behavior. In this study, we present a simple microscopic model of labor force migration based on the active Brownian particles framework. In particular, agent-based…

Adaptation and Self-Organizing Systems · Physics 2024-10-29 Hirotaka Goto

We present a graph-theoretical approach to data clustering, which combines the creation of a graph from the data with Markov Stability, a multiscale community detection framework. We show how the multiscale capabilities of the method allow…

Information Retrieval · Computer Science 2020-01-14 Zijing Liu , Mauricio Barahona