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We present certain mathematical aspects of an information method which was formulated in an attempt to investigate diffusion phenomena. We imagine a regular dynamical hamiltonian systems under the random perturbation of thermal (molecular)…
The understanding and prediction of information diffusion processes on networks is a major challenge in network theory with many implications in social sciences. Many theoretical advances occurred due to stochastic spreading models.…
This short note contains a few comments and corrections about some recent models for the spread of rumors in a population. We consider a system of ordinary differential equations which describes the evolution of Ignorant-Spreaders-Stiflers…
A new mechanism, the forget-remember mechanism, is proposed for studying the spreading process in 2-state model. Such mechanism exhibits behaviors of message spreading influenced by some kinds of functions about time and history caring…
The spread of ideas in online social networks is a crucial phenomenon to understand nowadays the proliferation of fake news and their impact in democracies. This makes necessary to use models that mimic the circulation of rumors. The law of…
In the last years, the study of rumor spreading on social networks produced a lot of interest among the scientific community, expecially due to the role of social networks in the last political events. The goal of this work is to reproduce…
False rumors are known to have detrimental effects on society. To prevent the spread of false rumors, social media platforms such as Twitter must detect them early. In this work, we develop a novel probabilistic mixture model that…
We consider a collective behavior model in which individuals try to imitate each others' velocity and have a preferred speed. We show that a phase change phenomenon takes place as diffusion decreases, bringing the system from a "disordered"…
We study four discrete time stochastic systems on $\bbN$ modeling processes of rumour spreading. The involved individuals can either have an active or a passive role, speaking up or asking for the rumour. The appetite in spreading or…
Biological systems can share and collectively process information to yield emergent effects, despite inherent noise in communication. While man-made systems often employ intricate structural solutions to overcome noise, the structure of…
In this paper, we study PUSH-PULL style rumor spreading algorithms in the mobile telephone model, a variant of the classical telephone model in which each node can participate in at most one connection per round; i.e., you can no longer…
Dynamic networks exhibit temporal patterns that vary across different time scales, all of which can potentially affect processes that take place on the network. However, most data-driven approaches used to model time-varying networks…
Recent work on modeling influence propagation focus on progressive models, i.e., once a node is influenced (active) the node stays in that state and cannot become inactive. However, this assumption is unrealistic in many settings where…
Research on social contagion dynamics has not yet including a theoretical analysis of the ubiquitous local trend imitation (LTI) characteristic. We propose a social contagion model with a tent-like adoption probability distribution to…
Fluctuations in biochemical networks, e.g., in a living cell, have a complex origin that precludes a description of such systems in terms of bipartite or multipartite processes, as is usually done in the framework of stochastic and/or…
Motivated by applications to COVID dynamics, we describe a branching process in random environments model $\{Z_n\}$ whose characteristics change when crossing upper and lower thresholds. This introduces a cyclical path behavior involving…
Studying information propagation dynamics in social media can elucidate user behaviors and patterns. However, previous research often focuses on single platforms and fails to differentiate between the nuanced roles of source users and other…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
We study a tractable opinion dynamics model that generates long-run disagreements and persistent opinion fluctuations. Our model involves an inhomogeneous stochastic gossip process of continuous opinion dynamics in a society consisting of…
We develop a simple and generic method to analyze randomized rumor spreading processes in fully connected networks. In contrast to all previous works, which heavily exploit the precise definition of the process under investigation, we only…