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We present continuum models that describe the evolution of the position of a random walker on a growing network using four different growth algorithms. Three of these involve a random element, including one in which the motility rate of the…

Adaptation and Self-Organizing Systems · Physics 2019-06-26 Robert Ross , Walter Fontana

We investigate the emergence of self-organised trails between two specific target areas in collective motion of social organisms by means of an agent-based model. We present numerical evidences that an increase in the efficiency of…

Adaptation and Self-Organizing Systems · Physics 2018-02-27 E. Brigatti , A. Hernández

Uncovering the mechanism behind the scaling law in human trajectories is of fundamental significance in understanding many spatio-temporal phenomena. In combination of the exploration and the preferential returns, we propose a simple…

Physics and Society · Physics 2013-05-24 Xiao-Pu Han , Xiang-Wen Wang , Xiao-Yong Yan , Bing-Hong Wang

This paper deals with the early results of a new model of pedestrian flow, conceived within a measure-theoretical framework. The modeling approach consists in a discrete-time Eulerian macroscopic representation of the system via a family of…

Mathematical Physics · Physics 2011-03-29 Benedetto Piccoli , Andrea Tosin

It is suggested that the motion of pedestrians can be described as if they would be subject to `social forces'. These `forces' are not directly exerted by the pedestrians' personal environment, but they are a measure for the internal…

Statistical Mechanics · Physics 2009-10-31 Dirk Helbing , Peter Molnar

Pedestrian behavior prediction is one of the major challenges for intelligent driving systems in urban environments. Pedestrians often exhibit a wide range of behaviors and adequate interpretations of those depend on various sources of…

Computer Vision and Pattern Recognition · Computer Science 2020-12-02 Amir Rasouli , Tiffany Yau , Mohsen Rohani , Jun Luo

Urban systems are composed by complex couplings of several components, and more particularly between the built environment and transportation networks. Their interaction is involved in the emergence of the urban form. We propose in this…

Physics and Society · Physics 2018-12-03 Juste Raimbault

Understanding the complex behavior of pedestrians walking in crowds is a challenge for both science and technology. In particular, obtaining reliable models for crowd dynamics, capable of exhibiting qualitatively and quantitatively the…

Physics and Society · Physics 2018-04-12 Alessandro Corbetta , Luca Bruno , Adrian Muntean , Federico Toschi

The knowledge of city exploration trails of people is in short supply because of the complexity in defining meaningful trails representative of individual behaviours and in the access to actionable data. Existing datasets have only recorded…

Social and Information Networks · Computer Science 2020-01-01 Diego Monti , Enrico Palumbo , Giuseppe Rizzo , Raphaël Troncy , Thibault Ehrhart , Maurizio Morisio

Human crowd motion is mainly driven by self-organized processes based on local interactions among pedestrians. While most studies of crowd behavior consider only interactions among isolated individuals, it turns out that up to 70% of people…

Physics and Society · Physics 2015-05-18 Mehdi Moussaid , Niriaska Perozo , Simon Garnier , Dirk Helbing , Guy Theraulaz

Predicting where people can walk in a scene is important for many tasks, including autonomous driving systems and human behavior analysis. Yet learning a computational model for this purpose is challenging due to semantic ambiguity and a…

Computer Vision and Pattern Recognition · Computer Science 2020-08-21 Jin Sun , Hadar Averbuch-Elor , Qianqian Wang , Noah Snavely

The distribution of information is essential for living system's ability to coordinate and adapt. Random walkers are often used to model this distribution process and, in doing so, one effectively assumes that information maintains its…

Statistical Mechanics · Physics 2010-03-12 Ludvig Lizana , Martin Rosvall , Kim Sneppen

Usually, routing models in pedestrian dynamics assume that agents have fulfilled and global knowledge about the building's structure. However, they neglect the fact that pedestrians possess no or only parts of information about their…

Artificial Intelligence · Computer Science 2016-02-08 Erik Andresen , David Haensel , Mohcine Chraibi , Armin Seyfried

Recent advances in human mobility research have revealed consistent pairwise characteristics in movement behavior, yet existing mobility models often overlook the spatial and topological structure of mobility networks. By analyzing millions…

Physics and Society · Physics 2025-05-22 Lu Zhong , Lei Dong , Qi Wang , Chaoming Song , Jianxi Gao

Pedestrian crowds can very realistically be simulated with a social force model which describes the different influences affecting individual pedestrian motion by a few simple force terms. The model is able to reproduce the emergence of…

Statistical Mechanics · Physics 2007-05-23 Dirk Helbing , Peter Molnar

Modeling how human moves in the space is useful for policy-making in transportation, public safety, and public health. Human movements can be viewed as a dynamic process that human transits between states (\eg, locations) over time. In the…

Artificial Intelligence · Computer Science 2021-03-24 Hua Wei , Dongkuan Xu , Junjie Liang , Zhenhui Li

The strategic behaviour of pedestrians is largely determined by how they perceive and react to neighbouring people. This issue is addressed in this paper by a model which combines, in a time and space-dependent way, discrete and continuous…

Physics and Society · Physics 2016-06-23 Annachiara Colombi , Marco Scianna , Andrea Tosin

In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, co-evolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted…

Populations and Evolution · Quantitative Biology 2025-12-10 G. Briozzo , G. J. Sibona , F. Peruani

Uncovering the mechanism leading to the scaling law in human trajectories is of fundamental importance in understanding many spatiotemporal phenomena. We propose a hierarchical geographical model to mimic the real traffic system, upon which…

Data Analysis, Statistics and Probability · Physics 2015-05-13 Xiaopu Han , Qiang Hao , Binghong Wang , Tao Zhou

Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…

Dynamical Systems · Mathematics 2016-01-20 M. Mert Ankaralı , Shahin Sefati , Manu S. Madhav , Andrew Long , Amy J. Bastian , Noah J. Cowan