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We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [Tadi\'c, Physica A {\bf 293},…
The statistical properties of human mobility have been studied in the framework of complex systems physics. Taking advantage from the new datasets made available by the information and communication technologies, the distributions of…
Models of social mobility inspired by the Newton's law of gravity have been used for several decades to describe migrations of people, goods, and information. Despite an eminent reference and widespread use, these models lack the background…
Zipf's law is a hallmark of several complex systems with a modular structure, such as books composed by words or genomes composed by genes. In these component systems, Zipf's law describes the empirical power law distribution of component…
In this paper, a model (called the elliptic model) is proposed to estimate the number of social ties between two locations using population data in a similar manner to how transportation research deals with trips. To overcome the asymmetry…
Understanding human mobility is essential for applications ranging from urban planning to public health. Traditional mobility models such as flow networks and colocation matrices capture only pairwise interactions between discrete…
In the era of mobile computing, understanding human mobility patterns is crucial in order to better design protocols and applications. Many studies focus on different aspects of human mobility such as people's points of interests, routes,…
Free recall of random lists of words is a standard paradigm used to probe human memory. We proposed an associative search process that can be reduced to a deterministic walk on random graphs defined by the structure of memory…
Zipf's law, which states that the probability of an observation is inversely proportional to its rank, has been observed in many domains. While there are models that explain Zipf's law in each of them, those explanations are typically…
Random walk in random environment (RWRE) is a fundamental model of statistical mechanics, describing the movement of a particle in a highly disordered and inhomogeneous medium as a random walk with random jump probabilities. It has been…
In this paper, we propose and analyze a novel one-dimensional inhomogeneous random walk model that combines spatial decay of transition probabilities with a temporal renewal structure for each excursion. In this model, the probability of…
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…
This article introduces a model for interacting vertex-reinforced random walks, each taking values on a complete sub-graph of a locally finite undirected graph. The transition probability for a walk to a given vertex depends on the…
We derive a perturbation expansion for general self-interacting random walks, where steps are made on the basis of the history of the path. Examples of models where this expansion applies are reinforced random walk, excited random walk, the…
The science of cities seeks to understand and explain regularities observed in the world's major urban systems. Modelling the population evolution of cities is at the core of this science and of all urban studies. Quantitatively, the most…
Understanding human mobility is essential for many fields, including transportation planning. Currently, surveys are the primary source for such analysis. However, in the recent past, many researchers have focused on Call Detail Records…
Fundamental laws of human mobility have been extensively studied, yet we are still lacking a comprehensive understanding of the mobility patterns of sharing conveyances. Since travellers would highly probably no longer possess their own…
Inverse power-law interaction forms, such as the inverse-square law, recur across a wide range of physical, social, and spatial systems. While traditionally derived from specific microscopic mechanisms, the ubiquity of these laws suggests a…
Understanding the movement behaviours of individuals and the way they react to the external world is a key component of any problem that involves the modelling of human dynamics at a physical level. In particular, it is crucial to capture…
Human mobility is influenced by environmental change and natural disasters. Researchers have used trip distance distribution, radius of gyration of movements, and individuals' visited locations to understand and capture human mobility…