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We study an individual-based model in which two spatially-distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in…

This paper studies a strategic model of marketing and product diffusion in social networks. We consider two firms offering substitutable products which can improve their market share by seeding the key individuals in the market. Consumers…

We consider the diffusion of new products in social networks, where consumers who adopt the product can later "recover" and stop influencing others to adopt the product. We show that the diffusion is not described by the SIR model, but…

Diffusion on a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We…

Collective adaptation, whether in innovation adoption, pro-environmental or organizational change, emerges from the interplay between individual decisions and social influence. Agent-based modeling provides a useful tool for studying such…

This paper investigates the interplay between information diffusion in social networks and its impact on financial markets with an Agent-Based Model (ABM). Agents receive and exchange information about an observable stochastic component of…

This paper investigates causal influences between agents linked by a social graph and interacting over time. In particular, the work examines the dynamics of social learning models and distributed decision-making protocols, and derives…

Opinion diffusion is a crucial phenomenon in social networks, often underlying the way in which a collective of agents develops a consensus on relevant decisions. The voter model is a well-known theoretical model to study opinion spreading…

Learning the distribution of a continuous or categorical response variable $\boldsymbol y$ given its covariates $\boldsymbol x$ is a fundamental problem in statistics and machine learning. Deep neural network-based supervised learning…

In recent years, numerous mathematical models of opinion formation have been developed, incorporating diverse interaction mechanisms such as imitation and majority rule. However, limited attention has been given to models grounded in…

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models,…

Recent studies suggest that human emotions diffuse in not only real-world communities but also online social media. More and more mechanisms beyond emotion contagion are revealed, including emotion correlations which indicate their…

Heterogeneous media diffusion is often described using position-dependent diffusion coefficients and estimated indirectly through mean squared displacement in experiments. This approach may overlook other mechanisms and their interaction…

A Langevin equation is suggested to describe a system driven by correlated Gaussian white noise as well as with positive and negative damping demarcated by a critical velocity. The equation can be transformed into the Fokker-Planck equation…

The spreading of news, memes and other pieces of information occurring via online social platforms has a strong and growing impact on our modern societies, with enormous consequences, that may be beneficial but also catastrophic. In this…

In this paper we obtain uniform propagation estimates for systems of interacting diffusions. We adopt a general model, satisfying various conditions which ensure that the decay resulting from the internal dynamics term dominates the…

The paper proposes a way to add marketing into the standard threshold model of social networks. Within this framework, the paper studies logical properties of the influence relation between sets of agents in social networks. Two different…

This study uses agent-based modeling to examine the impact of various recommendation algorithms on the propagation of misinformation on online social networks. We simulate a synthetic environment consisting of heterogeneous agents,…

Empirical data of supermarket sales show stylised facts that are similar to stock markets, with a broad (truncated) Levy distribution of weekly sales differences in the baseline sales [R.D. Groot, Physica A 353 (2005) 501]. To investigate…

Cross-diffusion systems are formally derived from multispecies kinetic models in the diffusion limit. The first limit in the multispecies BGK model of Gross and Krook leads to a variant of the non-isothermal Maxwell-Stefan equations. The…