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This paper models information diffusion in a network of Large Language Models (LLMs) that is designed to answer queries from distributed datasets, where the LLMs can hallucinate the answer. We introduce a two-time-scale dynamical model for…
We consider singularly perturbed convection-diffusion equations on one-dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling condition at inner vertices are…
The influence model is a discrete-time stochastic model that succinctly captures the interactions of a network of Markov chains. The model produces a reduced-order representation of the stochastic network, and can be used to describe and…
Many of the biological, social and man-made networks around us are inherently dynamic, with their links switching on and off over time. The evolution of these networks is often non-Markovian, and the dynamics of their links correlated.…
Current social networks are of extremely large-scale generating tremendous information flows at every moment. How information diffuse over social networks has attracted much attention from both industry and academics. Most of the existing…
Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its…
A Markovian model of the evolution of intermittent connections of various classes in a communication network is established and investigated. Any connection evolves in a way which depends only on its class and the state of the network, in…
Information diffusion on social networks has been described as a collective outcome of threshold behaviors in the framework of threshold models. However, since the existing models do not take into account individuals' optimization problem,…
While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…
The problem of finding the optimal set of source nodes in a diffusion network that maximizes the spread of information, influence, and diseases in a limited amount of time depends dramatically on the underlying temporal dynamics of the…
A fundamental question related to innovation diffusion is how the social network structure influences the process. Empirical evidence regarding real-world influence networks is very limited. On the other hand, agent-based modeling…
Social influence plays a significant role in shaping individual sentiments and actions, particularly in a world of ubiquitous digital interconnection. The rapid development of generative AI has engendered well-founded concerns regarding the…
Understanding the behaviors of information propagation is essential for the effective exploitation of social influence in social networks. However, few existing influence models are tractable and efficient for describing the information…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
Spreading phenomena essentially underlie the dynamics of various natural and technological networked systems, yet how spatiotemporal propagation patterns emerge from such networks remains largely unknown. Here we propose a novel approach…
Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…
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…
Diffusion-based text-to-image models have shown immense potential for various image-related tasks. However, despite their prominence and popularity, customizing these models using unauthorized data also brings serious privacy and…
Distributed diffusion is a powerful algorithm for multi-task state estimation which enables networked agents to interact with neighbors to process input data and diffuse information across the network. Compared to a centralized approach,…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…