Related papers: Rural-urban migration in d-dimensional lattices
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…
Lattice structures have great potential for several application fields ranging from medical and tissue engineering to aeronautical one. Their development is further speeded up by the continuing advances in additive manufacturing…
We study branching random walks in random environment on the $d$-dimensional square lattice, $d \geq 1$. In this model, the environment has finite range dependence, and the population size cannot decrease. We prove limit theorems (laws of…
Why are online community sizes so extremely unequal? Most answers to this question have pointed to general mathematical processes drawn from physics like cumulative advantage. These explanations provide little insight into specific social…
Modeling human behavior in urban environments is fundamental for social science, behavioral studies, and urban planning. Prior work often rely on rigid, hand-crafted rules, limiting their ability to simulate nuanced intentions, plans, and…
Mathematical models are vital interpretive and predictive tools used to assist in the understanding of cell migration. There are typically two approaches to modelling cell migration: either micro-scale, discrete or macro-scale, continuum.…
In several network problems the optimum behavior of the agents (i.e., the nodes of the network) is not known before deployment. Furthermore, the agents might be required to adapt, i.e. change their behavior based on the environment…
Exploring the possible consequences of spatial reciprocity on the evolution of cooperation is an intensively studied research avenue. Related works assumed a certain interaction graph of competing players and studied how particular…
There are different functional regions in cities such as tourist attractions, shopping centers, workplaces and residential places. The human mobility patterns for different functional regions are different, e.g., people usually go to work…
Human settlements on Earth are scattered in a multitude of shapes, sizes and spatial arrangements. These patterns are often not random but a result of complex geographical, cultural, economic and historical processes that have profound…
The aim of this paper is to study the derivation of appropriate meso- and macroscopic models for interactions as appearing in social processes. There are two main characteristics the models take into account, namely a network structure of…
This study assessed the effects of migration on the dynamics of a species population. It was considered that the species in its natural state and without the presence of migration exhibited Allee effect. This work also considered migration…
The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…
We consider a class of continuous-time stochastic growth models on $d$-dimensional lattice with non-negative real numbers as possible values per site. The class contains examples such as binary contact path process and potlatch process. We…
We describe a new model to simulate the dynamic interactions between market price and the decisions of two different kind of traders. They possess spatial mobility allowing to group together to form coalitions. Each coalition follows a…
In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…
Social acceptability is an important consideration for HCI designers who develop technologies for social contexts. However, the current theoretical foundations of social acceptability research do not account for the complex interactions…
Because of the mass gap, lattice QCD simulations exhibit stochastic locality: distant regions of the lattice fluctuate independently. There is a long history of exploiting this to increase statistics by obtaining multiple…
The one-dimensional long-range voter model, where an agent takes the opinion of another at distance $r$ with probability $\propto r^{-\alpha}$, is studied analytically. The model displays rich and diverse features as $\alpha$ is changed.…
Understanding quantitative relationships between urban elements is crucial for a wide range of applications. The observation at the macroscopic level demonstrates that the aggregated urban quantities (e.g., gross domestic product) scale…