Related papers: Spatial correlations in vote statistics: a diffusi…
Exploiting the coherent medium approximation, random walk among sites distributed randomly in space is investigated when the jump rate depends on the distance between two adjacent sites. In one dimension, it is shown that when the jump rate…
In applications like environment monitoring and pollution control, physical quantities are modeled by spatio-temporal fields. It is of interest to learn the statistical distribution of such fields as a function of space, time or both. In…
We present an analysis of the dynamics of discussions in Twitter (before it became X) among supporters of various candidates in the 2022 French presidential election, and followers of different types of media. Our study demonstrates that we…
We study a one dimensional generalization of the exponential trap model using both numerical simulations and analytical approximations. We obtain the asymptotic shape of the average diffusion front in the sub-diffusive phase. Our central…
The urban-rural divide is increasing in modern societies calling for geographical extensions of social influence modelling. Improved understanding of innovation diffusion across locations and through social connections can provide us with…
We model an electorate voting on the funding of a public good in a two-party system in an evolutionary game theory framework. Voters adopt one of four strategies: Consensus-makers, Gridlockers, Party 1 Zealots, and Party 2 Zealots, which…
The dynamic spatial redistribution of individuals is a key driving force of various spatiotemporal phenomena on geographical scales. It can synchronise populations of interacting species, stabilise them, and diversify gene pools [1-3].…
Many democratic countries use district-based elections where there is a "seat" for each district in the governing body. In each district, the party whose candidate gets the maximum number of votes wins the corresponding seat. The result of…
The spatial panel regression model has shown great success in modelling econometric and other types of data that are observed both spatially and temporally with associated predictor variables. However, model checking via testing for spatial…
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.…
The Hotelling-Downs model considers parties changing policy to maximise their vote-share. Where policy position lies on a left-right axis, it describes a tendency for political parties to move towards centrist platforms. This is in contrast…
We consider a heterogeneous diffusion equation and its corresponding generalization to the Cattaneo-Vernotte equation. It is derived by a combination of the continuity equation and the constitutive relation in various stochastic…
Quantifying the spatial organization of human settlements is fundamental to understanding the complexity of urban systems. However, the quantitative patterns of the distribution of villages, towns, and cities that lie between random and…
Non-linear voter models assume that the opinion of an agent depends on the opinions of its neighbors in a non-linear manner. This allows for voting rules different from majority voting. While the linear voter model is known to reach…
The stochastic models investigated in this paper describe the evolution of a set of $F_N$ identical balls scattered into $N$ urns connected by an underlying symmetrical graph with constant degree $h_N$. After some random amount of time {\em…
We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…
We propose a novel method for numerical modeling of spatially inhomogeneous moment dynamics of populations with nonlocal dispersal and competition in continuous space. It is based on analytically solvable decompositions of the time…
We analyze the evolution of political organizations using a model in which agents change their opinions via two competing mechanisms. Two agents may interact and reach consensus, and additionally, individual agents may spontaneously change…
Human dynamics and sociophysics suggest statistical models that may explain and provide us with better insight into social phenomena. Here we propose a generative model based on a stochastic differential equation that allows us to analyse…
Diffusion of innovation can be interpreted as a social spreading phenomena governed by the impact of media and social interactions. Although these mechanisms have been identified by quantitative theories, their role and relative importance…