Related papers: Diffusion approximation of a network model of meme…
We build models for the distribution of social states in Twitter communities. States can be defined by the participation vs silence of individuals in conversations that surround key words, and we approximate the joint distribution of these…
Online social networks represent a main source of communication and information exchange in today's life. They facilitate exquisitely news sharing, knowledge elicitation, and forming groups of same interests. Researchers in the last two…
Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…
We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…
In recent years, diffusion models trained on equilibrium molecular distributions have proven effective for sampling biomolecules. Beyond direct sampling, the score of such a model can also be used to derive the forces that act on molecular…
We study epidemic processes using a metapopulation approach on the line featuring random transport rates between arbitrarily distant sites. An average transport network is found using a recently developed variant of the effective medium…
Models of disease spreading are critical for predicting infection growth in a population and evaluating public health policies. However, standard models typically represent the dynamics of disease transmission between individuals using…
This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…
A pivotal idea in network science, marketing research and innovation diffusion theories is that a small group of nodes -- called influencers -- have the largest impact on social contagion and epidemic processes in networks. Despite the…
This paper proposes a dynamic epidemic model for successive opinion diffusion in social networks, extending the SHIMR model. It incorporates dynamic decision-making influenced by social distances and captures accumulative opinion diffusion…
Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…
Epidemic spreading processes in the real world can interact with each other in a cooperative, competitive, or asymmetric way, requiring a description based on coevolution dynamics. Rich phenomena such as discontinuous outbreak transitions…
Diffusion of particles in velocity space undergoing turbulent field was extensively studied in the problem of warm beam relaxation. Under low field intensities the diffusion is described by the Fokker-Planck equation with the diffusion…
We propose consensus propagation, an asynchronous distributed protocol for averaging numbers across a network. We establish convergence, characterize the convergence rate for regular graphs, and demonstrate that the protocol exhibits better…
Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative…
Searching for influential spreaders in complex networks is an issue of great significance for applications across various domains, ranging from the epidemic control, innovation diffusion, viral marketing, social movement to idea…
A sleeping beauty in diffusion indicates that the information, can be ideas or innovations, will experience a hibernation before a sudden spike of popularity and it is widely found in citation history of scientific publications. However, in…
Collective phenomena emerge from the interaction of natural or artificial units with a complex organization. The interplay between structural patterns and dynamics might induce functional clusters that, in general, are different from…
Cultural trends and popularity cycles can be observed all around us, yet our theories of social influence and identity expression do not explain what perpetuates these complex, often unpredictable social dynamics. We propose a theory of…
We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…